[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"content-index":3,"content-questions:respiratory-system":1504},{"release":4,"domains":9,"concepts":110,"edges":1392,"journeys":1501,"sources":1502,"glossary":1503,"lean":147},{"releaseId":5,"mode":6,"createdAt":7,"manifestHash":8},"remote-muc7n6nt","approved","2026-09-22T05:05:13.337Z","c42110fd742580ae16e7ab15fe6d62f35dee9f75b548de782401a76d5271a874",[10,40,62,76,86,100],{"id":11,"title":12,"description":13,"order":14,"areas":15},"mathematics","Mathematics","Numbers, shapes, patterns and data — and the reasoning that connects them.",0,[16,20,24,28,32,36],{"id":17,"title":18,"description":19},"math-number","Numbers","Reading, writing and comparing large numbers, their properties, the four operations and the order we do them in.",{"id":21,"title":22,"description":23},"math-factors","Factors and multiples","Prime and composite numbers, twin primes and co-primes, HCF and LCM.",{"id":25,"title":26,"description":27},"math-patterns","Patterns","Finding the rule behind number and shape patterns, and using it to predict.",{"id":29,"title":30,"description":31},"math-geometry","Geometry","Shapes and solids, lines and rays, and the angles they make.",{"id":33,"title":34,"description":35},"math-measurement","Measurement","Measuring and constructing angles with a protractor, ruler and compass.",{"id":37,"title":38,"description":39},"math-data","Data handling","Collecting and organising data, and summarising it with mean, median, mode and range.",{"id":41,"title":42,"description":43,"order":44,"areas":45},"matter-energy","Physics","Light, sound, forces, energy and electricity — how the physical world behaves.",1,[46,50,54,58],{"id":47,"title":48,"description":49},"phys-light","Light","How light travels, what it does when it meets things, and why we see colour.",{"id":51,"title":52,"description":53},"phys-sound","Sound","Vibrations that travel through materials, and how we hear them.",{"id":55,"title":56,"description":57},"phys-forces","Forces and motion","Pushes, pulls and the force that holds moons, planets and falling apples.",{"id":59,"title":60,"description":61},"phys-electricity","Electricity and magnetism","Charge, circuits, power and magnets.",{"id":63,"title":64,"description":65,"order":66,"areas":67},"earth-space","Earth and space","Our planet, its oceans and skies, and the Sun and Moon that move them.",2,[68,72],{"id":69,"title":70,"description":71},"earth-space-astro","Sun, Moon and sky","What we see in the sky, why it changes, and what is really moving.",{"id":73,"title":74,"description":75},"earth-oceans","Oceans","Seas, coasts and the daily rise and fall of the tide.",{"id":77,"title":78,"description":79,"order":80,"areas":81},"living-world","Living world","Bodies, plants, animals and the systems that keep them alive.",3,[82],{"id":83,"title":84,"description":85},"bio-body","The human body","What is inside you, where it sits, and how the parts work together.",{"id":87,"title":88,"description":89,"order":90,"areas":91},"people-society","People and society","How people organise themselves, and what happens when they travel, trade and rule.",4,[92,96],{"id":93,"title":94,"description":95},"soc-government","Government and citizenship","Who makes the rules, who carries them out, and how people have a say.",{"id":97,"title":98,"description":99},"soc-exploration","Exploration and encounter","Why people set out into the unknown, and what followed for everyone involved.",{"id":101,"title":102,"description":103,"order":104,"areas":105},"technology","Technology","How tools, machines and computers are designed and used.",5,[106],{"id":107,"title":108,"description":109},"tech-engineering","Engineering and power","Designing machines, structures and energy systems.",[111,179,239,286,339,389,438,488,540,587,637,689,738,788,827,876,928,979,1029,1076,1125,1177,1227,1275,1311,1345],{"id":112,"slug":112,"title":113,"question":114,"promise":115,"domains":116,"areas":117,"keywords":118,"status":139,"layers":140,"questionBank":172},"human-body-anatomy","Anatomy of the human body","What is inside you, and where exactly does it all sit?","A guided tour of the body: bones that hold you up, muscles that move you, and the organs packed inside — what each one is, where it sits, and how big it really is.",[77],[83],[119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138],"anatomy","organ","skeleton","bone","muscle","heart","lungs","brain","stomach","liver","kidney","intestine","skin","joint","ribcage","spine","diaphragm","cell","tissue","body systems","available",[141,149,155,161,167],{"depth":142,"revision":44,"title":143,"subtitle":144,"summary":145,"estimatedMinutes":146,"reviewed":147,"reviewMethod":148},"discover","A guided tour of the body you live in","What is inside you, where it sits, and how big it really is","Climb the ladder from cells to organ systems, learn the words anatomists use for where things are, meet the 206 bones and their joints, find out why a muscle can only ever pull, and take an organ-by-organ tour with real sizes and positions — then measure your own body.",38,true,"owner_bulk",{"depth":150,"revision":44,"title":151,"subtitle":152,"summary":153,"estimatedMinutes":154,"reviewed":147,"reviewMethod":148},"understand","How the body is put together","Tissues, bone, joints, muscle and the cavities that hold the organs","Go one level below the organs to the four tissue types they are built from, learn the direction words and the standard pose they are measured from, see why bone is a living composite, count the skeleton to 206, and place every major organ in its cavity with its mass.",42,{"depth":156,"revision":44,"title":157,"subtitle":158,"summary":159,"estimatedMinutes":160,"reviewed":147,"reviewMethod":148},"investigate","Predict it, then test it","Seven claims about your body, tested with paper, a tape measure and real class data","Guess before you look: does a hollow tube beat a solid rod, does height equal arm span for everyone, can a bone reveal a stranger’s height, does exercise raise every pulse equally, are you really symmetric, and does your shoulder really out-move your hip? Seven hands-on tests against real evidence.",36,{"depth":162,"revision":44,"title":163,"subtitle":164,"summary":165,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"deepen","Why it works: levers, remodelling and a history of being corrected","Lever mechanics in every joint, bone that rebuilds under load, and how anatomy overturned a thousand years of error","Treat every muscle-moved bone as a lever and see why the body favours the class that trades force for speed. Meet bone that rebuilds along its real loads, the genuine edge cases in \"206 bones\", and how Vesalius corrected centuries of Galen’s animal-based errors.",40,{"depth":168,"revision":44,"title":169,"subtitle":170,"summary":171,"estimatedMinutes":146,"reviewed":147,"reviewMethod":148},"extend","Beyond the syllabus: animals, projects, puzzles and careers","Other body plans, three things to build, puzzles worth reasoning through, and where this knowledge earns a living","Compare your body plan with a giraffe, a bird, a snake and a boneless octopus; build a working paper hand and a life-size organ map; solve puzzles spanning the whole topic; meet seven careers built on this knowledge; finish with open questions.",{"count":173,"sections":174,"levels":175},79,10,{"foundation":176,"core":177,"stretch":178,"challenge":174},22,32,15,{"id":180,"slug":180,"title":181,"question":182,"promise":183,"domains":184,"areas":185,"keywords":186,"status":139,"layers":207,"questionBank":231},"angles","Angles","How much does a door turn when it opens — and how do we measure a turn?","What an angle is, types of angles, angle pairs (complementary, supplementary, linear pairs, vertically opposite) and how to use them to find missing angles.",[11],[29],[187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206],"angle","vertex","arm","degrees","acute","right angle","obtuse","straight angle","reflex","complete angle","complementary","supplementary","linear pair","vertically opposite","adjacent angles","angles at a point","clock angles","transversal","parallel lines","angle sum of a triangle",[208,213,218,222,227],{"depth":142,"revision":44,"title":209,"subtitle":210,"summary":211,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Angles are turns","Doors, clocks, scissors and compass directions: meet the angle and learn to name its size","See an angle as a turn and as two arms meeting at a vertex. Measure turns in degrees (full 360°, half 180°, quarter 90°), sort angles into seven types, turn through N, E, S, W, read angles on a clock and meet angle partners.",35,{"depth":150,"revision":44,"title":214,"subtitle":215,"summary":216,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Naming, sorting and pairing angles","Precise definitions, the seven types, and the angle pairs that let you find what you cannot measure","Define an angle as two rays with a common vertex, name it with ∠ABC, and use degrees and landmark angles. Pin down the seven types, clock and compass angles, then adjacent, complementary, supplementary, linear-pair, vertically opposite and around-a-point angles.",45,{"depth":156,"revision":44,"title":219,"subtitle":220,"summary":221,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Is it always true? Testing angle ideas","Predict, test with labs and numbers, hunt counterexamples and find the reasons behind angle patterns","Investigate angle estimation, sums of angle types, complement and supplement patterns, linear pairs and their bisectors, crossing lines, clock-hand puzzles, turning walks around shapes and the tear-the-corners experiment, sorting claims into always, sometimes and never.",{"depth":162,"revision":44,"title":223,"subtitle":224,"summary":225,"estimatedMinutes":226,"reviewed":147,"reviewMethod":148},"Why angles behave: proofs, parallels and polygons","From Babylonian 360 to Euclid's proofs: transversals, triangle and polygon angle sums, and hard missing-angle problems","Why a full turn is 360°, how to write a proof with reasons, why vertically opposite angles are equal, the angles made by a transversal on parallel lines and their converses, the triangle and polygon angle sums, bends and zigzags between parallels, and where 180° fails.",55,{"depth":168,"revision":44,"title":228,"subtitle":229,"summary":230,"estimatedMinutes":226,"reviewed":147,"reviewMethod":148},"Angles at work and play","Clock formulas, exterior angles, bearings, radians, real-world angles, olympiad puzzles and projects","Use |30h − 5.5m| for any clock time, prove and use the exterior angle property, navigate with bearings and runway numbers, meet the radian, see angles in ramps, ladders, bowling and pie charts, and tackle olympiad-style angle chases, projects and open questions.",{"count":232,"sections":233,"levels":234},80,9,{"foundation":235,"core":236,"stretch":237,"challenge":238},20,28,21,11,{"id":240,"slug":240,"title":241,"question":242,"promise":243,"domains":244,"areas":245,"keywords":246,"status":139,"layers":261,"questionBank":281},"body-systems","Body systems and how they connect","No organ works alone — so how does a mouthful of roti reach your toes as energy?","Digestive, circulatory, respiratory, nervous, muscular, skeletal and excretory systems, and the handovers between them that keep you alive every second.",[77],[83],[247,248,249,250,251,252,253,254,255,256,257,195,258,259,260],"digestive system","circulatory system","respiratory system","nervous system","excretory system","muscular system","skeletal system","blood","oxygen","nutrients","homeostasis","heart rate","breathing","interconnected",[262,266,270,273,277],{"depth":142,"revision":44,"title":263,"subtitle":264,"summary":265,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Seven teams, one body","What each system does, and where it hands the work to the next one","Meet the organ systems one at a time — digestive, respiratory, circulatory, excretory, nervous, muscular and skeletal — then follow a roti and a breath across the hand-over points where each system passes its work to the next.",{"depth":150,"revision":44,"title":267,"subtitle":268,"summary":269,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"How the systems work, and how they hand over","One design used six times: thin wall, huge surface, steep difference","Go inside each system: enzymes and the chemical works, the pressure trick that moves air, two circuits through a four-chambered heart, filter-and-reclaim kidneys, the reflex arc and the nerve-to-muscle gap — then follow a breath all the way to a working cell.",{"depth":156,"revision":44,"title":157,"subtitle":271,"summary":272,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Reaction time, a real enzyme test, exercise data and a fever that is not a malfunction","Turn the claims from earlier layers into experiments you can actually run: a ruler-drop reaction test, an iodine test for digested starch, pulse and breathing data before and after exercise, and a look at why a fever is a controlled response rather than a failure.",{"depth":162,"revision":44,"title":274,"subtitle":275,"summary":276,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Where the tidy rule bends","The mathematics of a thin wall, bone's double life, the lymphatic system, and why some hand-overs must be prevented","Quantify why hand-over barriers must be thin, meet the lymphatic system that returns leaked fluid and carries digested fat, see bone as a blood factory and calcium bank, and look at clotting and the blood-brain barrier as hand-overs the body deliberately controls or resists.",{"depth":168,"revision":44,"title":278,"subtitle":279,"summary":280,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"History, machines and weightlessness","Harvey's arithmetic, the stethoscope and ECG, three ways to image the body, artificial hand-overs, and bodies in orbit","Meet the arithmetic that proved blood circulates, the instruments that let doctors listen to and image a living body without cutting it, machines that rebuild a failed hand-over, what microgravity does to every system at once, and a few careers and open questions this topic leads to.",{"count":173,"sections":233,"levels":282},{"foundation":176,"core":283,"stretch":284,"challenge":285},25,19,13,{"id":287,"slug":287,"title":38,"question":288,"promise":289,"domains":290,"areas":291,"keywords":292,"status":139,"layers":313,"questionBank":335},"data-handling","What is a typical value — and how can one number summarise a whole class?","Collecting and organising data, tally marks and frequency tables, bar graphs, and summarising data with mean, median, mode and range.",[11],[37],[293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312],"data","mean","median","mode","range","average","tally","frequency table","bar graph","pictograph","pie chart","double bar graph","grouped data","outlier","survey","probability","census","rainfall","batting average","raw data",[314,318,322,326,330],{"depth":142,"revision":44,"title":315,"subtitle":316,"summary":317,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Counting what matters: meeting data","From a messy list of answers to one number that tells the story","Ask a question, collect answers, and turn a jumble of raw data into tally marks, tables, pictographs and bar graphs. Then meet four friendly numbers that sum up a whole group: the fair share (mean), the middle (median), the most common (mode) and the spread (range).",{"depth":150,"revision":44,"title":319,"subtitle":320,"summary":321,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Organise, picture, summarise: how the methods work","Kinds of data, tables and graphs done properly, and exact methods for mean, median, mode and range","Tell categorical from numerical data, build self-checking frequency tables, choose a key or scale for pictographs and bar graphs, and use exact methods for mean, median (odd and even counts), mode (two modes or none) and range, even from a frequency table.",{"depth":156,"revision":44,"title":323,"subtitle":324,"summary":325,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"What happens if…? Experiments with averages","Predict, change the data, and test: outliers, shifts, missing values and datasets built to order","Treat averages like a science experiment. Predict what adding a value, an outlier, or a change to every value does to the mean, median, mode and range, then test it in the labs. Build data sets to order, hunt missing values and compare real Indian data.",{"depth":162,"revision":44,"title":327,"subtitle":328,"summary":329,"estimatedMinutes":226,"reviewed":147,"reviewMethod":148},"Why averages work, and which one to trust","Balance points, proofs, grouped data, combined groups and the art of choosing an average","Prove the mean is a balance point and how it reacts to shifts and scaling. Combine groups correctly, handle grouped data with class intervals, read double bar graphs, and choose between mean, median and mode with outliers, cricket averages and average speeds. Plus a history of statistics in India.",{"depth":168,"revision":44,"title":331,"subtitle":332,"summary":333,"estimatedMinutes":334,"reviewed":147,"reviewMethod":148},"Data in the wild: pie charts, tricks, chance and projects","Draw pie charts, catch misleading graphs, talk about chance, and investigate real Indian data","Turn data into pie charts with angles, spot graphs that mislead, describe chance from impossible to certain, and run real projects on electricity bills, the census and monsoon rain. Think about privacy and fairness in data, meet careers built on data, and try olympiad-style puzzles.",60,{"count":232,"sections":233,"levels":336},{"foundation":337,"core":338,"stretch":176,"challenge":174},18,30,{"id":340,"slug":340,"title":341,"question":342,"promise":343,"domains":344,"areas":345,"keywords":346,"status":139,"layers":362,"questionBank":383},"eclipses","Eclipses","If the Moon goes round Earth every month, why isn't there an eclipse every month?","An eclipse is a shadow falling exactly where it can be seen. Learn the geometry of umbra and penumbra, why the Moon's tilted orbit makes eclipses rare, and how to watch one safely.",[63],[69],[347,348,349,350,351,352,353,354,355,356,357,358,359,360,361],"eclipse","solar eclipse","lunar eclipse","umbra","penumbra","annular","totality","syzygy","nodes","orbit tilt","Saros","corona","blood moon","eye safety","shadow",[363,367,371,375,379],{"depth":142,"revision":44,"title":364,"subtitle":365,"summary":366,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"An eclipse is a shadow that finds you","Two shadows, two kinds of eclipse, and how to watch one without hurting your eyes","Meet eclipses as what they really are: shadows. Learn whose shadow falls on what in solar and lunar eclipses, why the eclipsed Moon turns red, why we don't get one every month, and the safe ways to watch the Sun.",{"depth":150,"revision":44,"title":368,"subtitle":369,"summary":370,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"The geometry of a shadow in space","Umbra and penumbra, apparent sizes, nodes and seasons — and the reasons behind every safety rule","Work out the actual geometry: how long each shadow cone is, why the Moon's only just reaches us, why the discs match to 3%, how far from a node an eclipse can happen, why the Moon turns red, and the physics behind every solar viewing rule.",{"depth":156,"revision":44,"title":372,"subtitle":373,"summary":374,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Build it, test it, try to break it","A lamp-and-balls model, hands-on measurements, and predictions checked against real eclipses","Hands-on layer: build a scale model of the Earth-Moon-Sun system, test the new-moon\u002Ffull-moon rule and the shadow-width formula for yourself, find the tilt's hidden threshold, build a pinhole projector and check its numbers, and plan around three real upcoming eclipses.",{"depth":162,"revision":44,"title":376,"subtitle":377,"summary":378,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"The Saros cycle, and two eclipses that changed physics","The Saros arithmetic, the astronomers who computed it, and how a belief should really be tested","Deeper reasoning: rebuild the 1.474° eclipse limit term by term, derive the Saros and exeligmos cycles from three different lunar months, see how Aryabhata and Brahmagupta actually computed eclipses, and examine the two solar eclipses that discovered helium and tested general relativity.",{"depth":168,"revision":44,"title":380,"subtitle":381,"summary":382,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"The same shadow rule, everywhere in the Solar System","Moons too small to eclipse, a moon that eclipses constantly, transits at home, and other worlds' planets","Take the eclipse geometry beyond Earth: why Phobos and Deimos only ever transit the Sun from Mars, why Io causes true eclipses on Jupiter routinely, how Mercury and Venus transit the Sun from Earth, Venus's 243-year transit rhythm, and how the same trick finds other stars' planets.",{"count":384,"sections":385,"levels":386},68,8,{"foundation":235,"core":387,"stretch":388,"challenge":385},24,16,{"id":390,"slug":390,"title":391,"question":392,"promise":393,"domains":394,"areas":395,"keywords":396,"status":139,"layers":416,"questionBank":437},"electricity","Electricity","What actually happens between the power station and the switch under your finger?","Electricity is charge on the move. Learn what pushes it, what resists it, how it is made and delivered, what it costs, and how to stay safe around it.",[41,101],[59,107],[390,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415],"voltage","current","resistance","Ohm's law","circuit","AC","DC","generator","power station","grid","transformer","kWh","electricity bill","safety","MCB","earth wire","battery","conductor","insulator",[417,421,425,429,433],{"depth":142,"revision":44,"title":418,"subtitle":419,"summary":420,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Electricity is charge on the move","From a balloon on your hair to a day that runs on it","Meet the charges hiding in every atom, see why a doorknob spark and lightning are the same idea, discover why slow electrons still light a bulb instantly, build circuits that break, and learn the first rules for staying safe.",{"depth":150,"revision":44,"title":422,"subtitle":423,"summary":424,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"The big three: voltage, current, resistance","The push, the flow and the pushback, and the one rule that ties them together","Build the pump-and-pipe picture of a circuit, then meet voltage (the push), current (the flow) and resistance (the pushback) with real numbers from AA cells to lightning. Finish with Ohm's law, V = I × R, and the mix-ups it clears up.",{"depth":156,"revision":44,"title":426,"subtitle":427,"summary":428,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Circuits you can test","Fair tests, meters, series and parallel, Ohm's law, fuses and fruit batteries","Design fair circuit tests, place ammeters and voltmeters correctly, compare series and parallel bulbs, test Ohm's law and see a filament bulb break it, work out when an MCB trips, and build a safe lemon battery.",{"depth":162,"revision":44,"title":430,"subtitle":431,"summary":432,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"How it's made and how it reaches you","From Faraday's spinning magnets to the socket on your wall","Follow electricity from a spinning magnet in a power station, through transformers and 765 kV lines, down to the 230 V socket in your room. Learn why the grid runs on AC at 50 Hz, why it transmits at high voltage, and why supply must match demand every second.",{"depth":168,"revision":44,"title":434,"subtitle":435,"summary":436,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Power, bills, safety and the future","From watts on a rating plate to units on your bill, the milliamps that matter, and the grid that is coming","Use P = V × I and E = P × t to read rating plates and work out a real electricity bill in units (kWh). Learn why current through the body is what injures, how earth pins, MCBs and RCCBs protect you, what to do in a shock emergency, and how solar, storage and smart meters are changing the grid.",null,{"id":439,"slug":439,"title":440,"question":441,"promise":442,"domains":443,"areas":444,"keywords":445,"status":139,"layers":463,"questionBank":485},"exploration","Exploration: reasons and consequences","What made people sail into oceans they could not map — and who paid for it?","Curiosity, trade, faith, gold and rivalry sent people across oceans. Follow the voyages, the technology that made them possible, and the consequences — for those who travelled and for those already there.",[87],[97],[439,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462],"voyage","navigation","trade route","spices","Vasco da Gama","Columbus","Zheng He","Silk Road","colonisation","Columbian exchange","monsoon winds","astrolabe","compass","cartography","empire","consequences","indigenous peoples",[464,468,473,477,481],{"depth":142,"revision":44,"title":465,"subtitle":466,"summary":467,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Why sail into an ocean nobody has mapped?","Reasons, routes and results, told from both ends of the voyage","Meet exploration honestly: what the word means and why 'discovery' misleads, six reasons people set out, the busy Indian Ocean world before European ships, how sailors found their way, four voyages worth knowing, and what followed - new foods, new maps, disease, slavery and empire.",{"depth":150,"revision":44,"title":469,"subtitle":470,"summary":471,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"How the navigator's toolkit actually works","Mechanisms behind the voyages: instruments, sails, clocks, charts and the economics of a monopoly","Go under Discover's story to the mechanisms: how a compass, kamal, astrolabe, lateen sail and sternpost rudder actually work, why longitude needed a clock and took decades to solve, how flat maps must distort a round Earth, and why a royal charter let a trading company become a ruler.",50,{"depth":156,"revision":44,"title":474,"subtitle":475,"summary":476,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Predict it, try it, compare it, test it","Lab-heavy investigations that check what the Discover layer told you","Compare stated reasons with actual results for Columbus and Zheng He, run a monsoon 'what if', judge whether one number sums up a disputed history, sort evidence against a claim about da Gama, read a paraphrased passage from two sides, and test sweeping generalisations against real voyages.",{"depth":162,"revision":44,"title":478,"subtitle":479,"summary":480,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Mechanism, harder numbers, and how historians know","Why the monsoon reverses, how clock drift compounds, and the method behind contested figures","Go beneath Discover's facts into mechanism and method: why the monsoon reverses, how clock drift compounds over a long voyage, an edge case in kamal readings, how historians back-project contested figures, how to weigh one account against another, and what shipwreck years teach about mean vs median.",{"depth":168,"revision":44,"title":482,"subtitle":483,"summary":484,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Beyond the horizon: exploration to today","Cook, the poles, space, the deep sea, and the questions nobody has answered yet","Carries exploration from Cook's Pacific voyage to today: the race to the poles and the treaty that followed, leaving Earth's gravity for the Moon and beyond, the deepest ocean trench, and the hardest open questions - who owns what nobody lives on, and who decides.",{"count":486,"sections":233,"levels":487},75,{"foundation":178,"core":236,"stretch":176,"challenge":174},{"id":489,"slug":489,"title":490,"question":491,"promise":492,"domains":493,"areas":494,"keywords":495,"status":139,"layers":515,"questionBank":536},"four-operations","Four operations","When should you add, subtract, multiply or divide — and how do you know your answer makes sense?","Addition, subtraction, multiplication and division with large numbers, choosing the right operation in real problems, and checking answers by estimating and by inverse operations.",[11],[17],[496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514],"addition","subtraction","multiplication","division","word problems","estimation","inverse operations","quotient","remainder","dividend","divisor","product","sum","difference","regrouping","long division","long multiplication","unitary method","word problems in rupees",[516,520,524,528,532],{"depth":142,"revision":44,"title":517,"subtitle":518,"summary":519,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Four ways to change a number","Adding, subtracting, multiplying and dividing: what each one means and when to use it","Meet the four operations through a kirana-shop trip, cricket scores, egg trays and shared laddoos. Learn what each operation means, how they undo each other, how to pick the right one from a story, and how to check that an answer is sensible.",{"depth":150,"revision":44,"title":521,"subtitle":522,"summary":523,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"How the column methods work","Carrying, borrowing, long multiplication and long division, and why every step is allowed","Learn the exact name for every part of a calculation, then master column addition and subtraction up to crores, long multiplication, long division with remainders and zeros in the quotient, checking with inverse operations, and working with money and units.",{"depth":156,"revision":44,"title":525,"subtitle":526,"summary":527,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Predict, test, check","Estimating first, changing the numbers, making sense of remainders and catching keyword traps","Predict before you calculate and test with labs and tables: estimate sums and products, see what happens when numbers change, decide what a remainder means in a story, catch misleading keywords and check answers by undoing them.",{"depth":162,"revision":44,"title":529,"subtitle":530,"summary":531,"estimatedMinutes":226,"reviewed":147,"reviewMethod":148},"Why the methods work","Regrouping, the distributive property, the division algorithm, checks, proportion and the history behind them","Prove why carrying, borrowing, long multiplication and long division work, meet the division algorithm and why dividing by zero is impossible, check with casting out nines, use the unitary method wisely, and solve India-sized multi-step problems.",{"depth":168,"revision":44,"title":533,"subtitle":534,"summary":535,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Other ways to calculate, and harder puzzles","Lattices, Vedic-style shortcuts, doubling, binary, classic puzzles, olympiad problems and real projects","Try the lattice, Napier's bones, Vedic-style shortcuts and Russian peasant multiplication and see why each works. Crack classic puzzles and olympiad problems, then plan real projects: a trip budget, a kirana bill, a harvest and a run chase.",{"count":537,"sections":385,"levels":538},74,{"foundation":178,"core":539,"stretch":176,"challenge":385},29,{"id":541,"slug":541,"title":542,"question":543,"promise":544,"domains":545,"areas":546,"keywords":547,"status":139,"layers":563,"questionBank":584},"gravity","Gravity","Why does everything fall down — and what is the Moon falling towards?","The force that pulls an apple to the ground is the same one that keeps the Moon circling Earth. Meet mass and weight, free fall, orbits and why astronauts float.",[41],[55],[541,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562],"mass","weight","free fall","orbit","force","Newton","air resistance","g","acceleration","satellite","weightlessness","planet","tides","escape velocity","centre of mass",[564,568,572,576,580],{"depth":142,"revision":44,"title":565,"subtitle":566,"summary":567,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Why does everything fall down?","Meet the pull that drops a pencil, bends the Moon’s path and holds the sky together","Start with a dropped pencil and end with galaxies. Discover what a force is, why heavy things do not fall faster, how air changes everything, the real difference between mass and weight, and the true reason astronauts float.",{"depth":150,"revision":44,"title":569,"subtitle":570,"summary":571,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"How gravity works: weight, falling and orbits","Mass against weight, g against speed, drag against gravity — and why an orbit is a permanent miss","Turn the story into rules you can use: weight = mass × g, distance = ½ g t², why mass cancels in free fall, how drag sets terminal velocity, Newton’s universal law in words, and the real reason astronauts float.",{"depth":156,"revision":44,"title":573,"subtitle":574,"summary":575,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Test it: predictions, ramps, pendulums and Newton’s own proof","Predict, try, compare and ask \"is it always true?\" — with a ramp, a pendulum, a leaking cup and a spacecraft","Turn gravity into hands-on science: rebuild Galileo’s ramp, design fair tests for mass and shape, weigh the Earth with a pendulum, check whether Newton’s law survives the trip to the Moon, hunt for orbital speed by binary search, and see how ISRO climbs to the Moon and Mars one burn at a time.",{"depth":162,"revision":44,"title":577,"subtitle":578,"summary":579,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"The mathematics behind every number in this topic","G, orbits derived from first principles, Newton’s Moon test in full, and the coincidence Einstein could not ignore","Meet Newton’s law with its constant G, derive orbital and escape speed from scratch, redo Newton’s Moon test in full, explore why gravitational and inertial mass are equal, see why g is not uniform on Earth, and look at the mechanics behind ISRO’s orbit-raising missions.",{"depth":168,"revision":44,"title":581,"subtitle":582,"summary":583,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Curved spacetime, black holes and the questions nobody has answered yet","Einstein’s radical idea, tested and confirmed — and an honest look at where gravity’s biggest mysteries still are","Go beyond Newton to Einstein: gravity as curved spacetime, the rubber-sheet picture and its flaws, the tests that confirmed general relativity, black holes, gravitational waves, orbital puzzles from tidal locking to dark matter, and open questions with real projects.",{"count":585,"sections":233,"levels":586},70,{"foundation":388,"core":387,"stretch":235,"challenge":174},{"id":588,"slug":588,"title":589,"question":590,"promise":591,"domains":592,"areas":593,"keywords":594,"status":139,"layers":613,"questionBank":634},"hcf-and-lcm","HCF and LCM","When will two blinking lights flash together again — and what is the biggest tile that fits a floor exactly?","Highest common factor and lowest common multiple by listing, prime factorisation and division, their link HCF × LCM = product, and real problems that need them.",[11],[21],[595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,500,611,612],"HCF","LCM","GCD","GCF","highest common factor","lowest common multiple","least common multiple","common factors","common multiples","prime factorisation","Venn diagram","long division method","Euclid's algorithm","common division method","co-prime","HCF × LCM","remainder problems","fractions",[614,618,622,626,630],{"depth":142,"revision":44,"title":615,"subtitle":616,"summary":617,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Sharing and meeting: meet the HCF and LCM","The biggest equal pieces and the next time things line up","Start from two puzzles, the biggest tile for a courtyard and the next time two lights flash together, and discover factors, multiples, common factors, common multiples, the HCF and the LCM, and how to tell which one a problem needs.",{"depth":150,"revision":44,"title":619,"subtitle":620,"summary":621,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Four ways to find the HCF and LCM","Listing, prime factors, long division and the ladder, and why they work","Precise definitions, then four methods: listing, prime factorisation with a Venn picture, long (continued) division for the HCF and common division for the LCM. Three numbers, the rule HCF × LCM = product, co-primes, fractions and the classic mix-ups.",{"depth":156,"revision":44,"title":623,"subtitle":624,"summary":625,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Predict, test and explain: HCF and LCM patterns","Always, sometimes or never? Find out with your own experiments","Make predictions and test them: when the LCM equals the product, why neighbours are co-prime, how HCF × LCM = a × b holds for two numbers but not three, what scaling does, how remainder puzzles work, and how changing a word problem changes the answer.",{"depth":162,"revision":44,"title":627,"subtitle":628,"summary":629,"estimatedMinutes":226,"reviewed":147,"reviewMethod":148},"Why it works: proofs, Euclid and the edges","Unique prime recipes, the product rule, Euclid’s algorithm and Bézout","Proofs in plain language: unique prime factorisation, why HCF takes smallest powers and LCM largest, why HCF × LCM = a × b (and why not for three numbers), why Euclid’s method works and how fast it is, Bézout’s identity, edge cases, harder problems and history.",{"depth":168,"revision":44,"title":631,"subtitle":632,"summary":633,"estimatedMinutes":334,"reviewed":147,"reviewMethod":148},"Cycles, gears and puzzles: HCF and LCM in the wild","Calendars, cicadas, tabla, bicycles, jugs, screens and olympiad problems","Expeditions beyond the textbook: cycles with head starts, calendars and planetary alignments (and why they are not LCMs), prime-cycle cicadas, gears and bicycle chains, tala rhythms, water jugs, ancient remainder puzzles, screen ratios, fractions, olympiad problems, careers and open questions.",{"count":173,"sections":385,"levels":635},{"foundation":235,"core":636,"stretch":337,"challenge":174},31,{"id":638,"slug":638,"title":639,"question":640,"promise":641,"domains":642,"areas":643,"keywords":644,"status":139,"layers":665,"questionBank":686},"government-india","How government works in India","Who decides what a country does — and where does a citizen fit in?","Parliament, the President and the Prime Minister, states and panchayats, courts and elections: how India makes its laws, carries them out and settles disputes, and how people have a say.",[87],[93],[645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664],"government","democracy","Parliament","Lok Sabha","Rajya Sabha","President","Prime Minister","Supreme Court","election","vote","constitution","panchayat","municipality","state","federal","law","rights","duties","citizen","judiciary",[666,670,674,678,682],{"depth":142,"revision":44,"title":667,"subtitle":668,"summary":669,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"Who decides the rules?","From an hour in the school hall to a republic of a hundred and forty crore people","Start with thirty children, one football and no rules, and discover the three jobs every group has to invent: making rules, carrying them out and settling disputes. Then meet India's version — the Constitution, three organs, three levels, and the vote.",{"depth":150,"revision":44,"title":671,"subtitle":672,"summary":673,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"How each part actually works","Parliament's machinery, a bill's journey, the courts' ladder, and the levels beneath the Union","Go inside the institutions Discover introduced: how Parliament questions ministers, how a bill becomes an Act, what a President does that a Prime Minister does not, how courts check Parliament, and how the Union, States, Union Territories and local bodies share the work.",{"depth":156,"revision":44,"title":675,"subtitle":676,"summary":677,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Test it yourself: does the arithmetic hold up?","Seat share against vote share, real turnout data, and edge cases in how a bill becomes an Act","Put the rules from Understand under pressure: work through seat-versus-vote-share examples, test what happens when the two Houses disagree over a money bill, analyse real turnout data with mean, median and range, and sort everyday problems by the level of government actually responsible.",{"depth":162,"revision":44,"title":679,"subtitle":680,"summary":681,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Why it is built this way","The amendment procedure's arithmetic, the basic structure doctrine, and the freedom movement's fingerprints","Go after the reasoning: the arithmetic of amending the Constitution, the basic structure doctrine, how judges come to be chosen, the freedom movement's own arguments becoming institutions, and a few genuine edge cases put under pressure.",{"depth":168,"revision":44,"title":683,"subtitle":684,"summary":685,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Build it, test it, take it further","A mini-constitution, a mock Parliament, coalition puzzles, other countries' choices, and where this knowledge leads","Put the whole topic to work: draft and stress-test a mini-constitution, run a mock Parliament, prove a coalition-counting puzzle, compare India's design with other countries', research your own representatives, and meet real careers and open questions this knowledge connects to.",{"count":687,"sections":385,"levels":688},76,{"foundation":176,"core":636,"stretch":178,"challenge":385},{"id":690,"slug":690,"title":48,"question":691,"promise":692,"domains":693,"areas":694,"keywords":695,"status":139,"layers":713,"questionBank":735},"light","What is light, how does it travel, and why can you see this page at all?","Light travels in straight lines at extraordinary speed, bounces, bends, splits into colours and lets you see. Find out how, and why shadows, mirrors and rainbows behave as they do.",[41],[47],[690,696,697,698,361,699,700,701,702,703,704,705,706,707,708,709,710,350,711,712],"luminous","reflection","refraction","mirror","spectrum","colour","transparent","opaque","translucent","ray","speed of light","rainbow","prism","lens","eye","scattering","laser",[714,718,722,726,730],{"depth":142,"revision":44,"title":715,"subtitle":716,"summary":717,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"Light: how you can see anything at all","Sources, straight lines, shadows, mirrors, bent straws and the colours hiding inside white","Meet light as the messenger that carries the world to your eyes: what makes its own light and what only reflects it, why light travels dead straight, how that one fact explains shadows, and first looks at mirrors, bending and the colours inside white light.",{"depth":150,"revision":44,"title":719,"subtitle":720,"summary":721,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"How light behaves: rays, angles and rules you can use","Shadow arithmetic, the law of reflection, what refraction really is, and the two kinds of colour mixing","Turn the facts of Discover into rules that predict. Work out shadow sizes with similar triangles, meet umbra and penumbra, apply the law of reflection to mirrors and periscopes, see why light bends when its speed changes, and separate the two opposite kinds of colour mixing.",{"depth":156,"revision":44,"title":723,"subtitle":724,"summary":725,"estimatedMinutes":154,"reviewed":147,"reviewMethod":148},"Chasing light: measuring, mirroring and bending it on purpose","How fast is light, and how would you find out? Predict and test curved mirrors, lenses, TIR and rainbows.","Step into the shoes of Rømer and Fizeau to measure something that seemed instant, then turn detective on curved mirrors, lenses pushed to a magnifier, total internal reflection in a diamond and a fibre-optic cable, and finally the exact geometry that puts a rainbow at 42 degrees from the Sun.",{"depth":162,"revision":44,"title":727,"subtitle":728,"summary":729,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Precise light: derivations, corrective lenses and the shape of a rainbow","Beyond the syllabus: derive the mirror formula, correct short and long sight, and see why a rainbow sits at 42 degrees.","Follow the speed of light to its modern exact definition, derive the mirror\u002Flens formula from similar triangles, work out lens powers for short and long sight, put numbers on fibre-optic latency, and see why the rainbow's angle is a genuine minimum.",{"depth":168,"revision":44,"title":731,"subtitle":732,"summary":733,"estimatedMinutes":734,"reviewed":147,"reviewMethod":148},"Waves, particles and the light you cannot see","Beyond visible light: wave versus particle, a real chocolate-bar experiment, and looking into the past with light-years.","Step past visible light into the wider spectrum, meet the wave-versus-particle debate (light is genuinely both), measure light's speed with a microwave and a chocolate bar, see how bending stretches every day, and use light-years to look into the past.",44,{"count":232,"sections":233,"levels":736},{"foundation":284,"core":737,"stretch":284,"challenge":178},27,{"id":739,"slug":739,"title":740,"question":741,"promise":742,"domains":743,"areas":744,"keywords":745,"status":139,"layers":763,"questionBank":784},"lines","Lines, rays and line segments","What is the difference between a line, a ray and a segment — and why do railway tracks never meet?","Points, lines, rays and line segments, intersecting, parallel and perpendicular lines, and where we see them in the world.",[11],[29],[746,747,705,748,749,750,751,752,205,753,754,204,755,756,757,758,759,760,761,762],"point","line","line segment","plane","collinear","concurrent","intersecting lines","perpendicular lines","perpendicular bisector","skew lines","horizontal and vertical","measuring segments","parallax error","Euclid's postulates","parallel postulate","vanishing point","railway tracks",[764,768,772,776,780],{"depth":142,"revision":44,"title":765,"subtitle":766,"summary":767,"estimatedMinutes":283,"reviewed":147,"reviewMethod":148},"Straight paths: points, lines, rays and segments","Meet the alphabet of geometry in torch beams, railway tracks and cricket creases","Meet points, line segments, rays and lines through everyday things, then see how two lines can cross, meet at square corners or run side by side forever.",{"depth":150,"revision":44,"title":769,"subtitle":770,"summary":771,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Names, notation and rules for lines","Precise definitions, careful measuring and the mix-ups they clear up","Pin down point, line and plane; name lines, rays and segments correctly; measure without parallax error; and define collinear, concurrent, parallel and perpendicular lines precisely.",{"depth":156,"revision":44,"title":773,"subtitle":774,"summary":775,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Test it: predictions about points and lines","Count, fold, measure and hunt for counterexamples","Predict and count how many lines, segments, rays and crossing points some points and lines can make; run a measuring experiment; beat optical illusions; and sort claims into always, sometimes and never true.",{"depth":162,"revision":44,"title":777,"subtitle":778,"summary":779,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Why it must be so: reasoning about lines","Euclid's rules, proofs, counting arguments and the puzzle of parallels","Build geometry from Euclid's postulates, prove key facts about intersecting, parallel and perpendicular lines, count with pairs, and follow the 2,000-year story of the parallel postulate from Alexandria to curved space.",{"depth":168,"revision":44,"title":781,"subtitle":782,"summary":783,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Lines in the wider world","Perspective, skew lines, maps, sport, careers, puzzles and open questions","See parallel lines meet in perspective drawings, find skew lines in rooms and solids, read lines on maps and sports grounds, meet people who use lines at work, and tackle puzzles from pizza cuts to string art.",{"count":232,"sections":233,"levels":785},{"foundation":786,"core":539,"stretch":176,"challenge":787},17,12,{"id":789,"slug":789,"title":790,"question":790,"promise":791,"domains":792,"areas":793,"keywords":794,"status":139,"layers":800,"questionBank":823},"magnets","Magnets: why do some things stick to a magnet and others do not?","A new science topic for learners aged 10 to 12 (Class 5-6, India). Cover: what a magnet is; poles, attraction and repulsion; which materials are magnetic (iron, nickel, cobalt, steel) and which are not (wood, plastic, copper, aluminium); th",[41],[59],[789,795,796,797,798,799],"some","things","stick","magnet","others",[801,807,811,815,819],{"depth":142,"revision":44,"title":802,"subtitle":803,"summary":804,"estimatedMinutes":805,"reviewed":147,"reviewMethod":806},"The Invisible Grip: How Magnets Pull and Push","A journey from fridge magnets to Earth's hidden force — why some things stick and others slip away","This lesson introduces magnets through everyday objects, explains how poles attract and repel, and shows how to test materials for magnetism. Readers will map invisible magnetic fields, make a simple compass, and connect it all to Earth acting as a giant magnet.",90,"per_lesson",{"depth":150,"revision":44,"title":808,"subtitle":809,"summary":810,"estimatedMinutes":805,"reviewed":147,"reviewMethod":806},"The Hidden Army Inside a Magnet","How tiny atomic teams line up to pull, stick or snap — and why heat or a hard knock sends them tumbling","This lesson reveals the invisible world of magnetic domains: why iron sticks but copper slips, how stroking or electricity organises atoms into a magnet, and why heat or hammering destroys that order. It also covers common mix-ups like 'all metals attract' and how to test unknown",{"depth":156,"revision":44,"title":812,"subtitle":813,"summary":814,"estimatedMinutes":805,"reviewed":147,"reviewMethod":806},"The Magnet Investigation Lab","How changing conditions, careful measurement and fair tests reveal what magnets really do","This lesson puts every magnet claim to the test. Learners plan fair comparisons, predict outcomes, gather evidence and use it to decide how magnets behave, how they weaken, and how an electromagnet's design changes its power.",{"depth":162,"revision":44,"title":816,"subtitle":817,"summary":818,"estimatedMinutes":805,"reviewed":147,"reviewMethod":806},"The Invisible Architecture of Magnetism","How atoms, domains, and field lines explain why some materials obey the magnet and others refuse","This lesson traces magnetism from everyday fridge magnets to atomic arrangements and magnetic domains, explaining why iron rushes to a magnet while copper stays still. Readers learn to predict magnetic behaviour, interpret field-line patterns, and calculate simple field relations",{"depth":168,"revision":44,"title":820,"subtitle":821,"summary":822,"estimatedMinutes":805,"reviewed":147,"reviewMethod":806},"The Invisible Push: Magnets at Work and at Scale","From iron filings to maglev trains — how hidden fields, domains and electromagnets shape our world","This lesson explores how magnetic domains explain why some materials become magnets and others do not, then builds to electromagnets, real engineering uses, and how to test magnetism fairly at home. It closes with open questions about magnetic storage and levitation that learners",{"count":824,"sections":66,"levels":825},52,{"foundation":826,"core":337,"stretch":787,"challenge":385},14,{"id":828,"slug":828,"title":829,"question":830,"promise":831,"domains":832,"areas":833,"keywords":834,"status":139,"layers":853,"questionBank":874},"constructing-angles","Measuring and constructing angles","How do you draw an exact 60° angle with only a compass and a ruler?","Reading a protractor correctly, measuring and drawing angles, and constructing 60°, 120°, 90°, 30° and 45° angles and bisectors with a ruler and compass.",[11],[33,29],[835,458,836,837,754,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852],"protractor","construction","angle bisector","60 degrees","90 degrees","120 degrees","45 degrees","30 degrees","geometry box","set square","divider","measuring angles","drawing angles","reflex angle","inner and outer scale","ruler and compass","trisection","constructing triangles",[854,858,862,866,870],{"depth":142,"revision":44,"title":855,"subtitle":856,"summary":857,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"Angles you can measure and make","The geometry box, the protractor and the compass trick for an exact 60°","Open the geometry box, learn what a degree is, estimate angles by eye, measure and draw angles with a protractor, and discover how a compass alone can make an exact 60° angle.",{"depth":150,"revision":44,"title":859,"subtitle":860,"summary":861,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Reading the protractor and the compass constructions","Why the two scales exist, how to measure and draw any angle, and why 60°, 90°, 30° and 45° constructions work","Learn the precise protractor method (and the wrong-scale trap), measure and draw reflex angles, copy lengths with a compass, and construct 60°, 120°, 90°, 30° and 45° angles and perpendicular bisectors with the reason each one works.",{"depth":156,"revision":44,"title":863,"subtitle":864,"summary":865,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Test it: estimates, radii and angle recipes","Predict, try and check: what really changes an angle, and what never does","Predict and test: does arm length matter, what does a wrong-scale reading look like, how good is your eye, does the compass radius matter, which angles can bisecting and set squares reach, how accurate can a check be, and why bisectors always work.",{"depth":162,"revision":44,"title":867,"subtitle":868,"summary":869,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Why the constructions work","Proofs behind the recipes, edge cases, accuracy and the problems the Greeks could not solve","Find out why each compass construction is exact: equilateral triangles for 60°, congruent triangles for bisectors, equidistant points for perpendiculars. Then test edge cases, measure reflex angles, analyse errors and meet the impossible trisection problem.",{"depth":168,"revision":44,"title":871,"subtitle":872,"summary":873,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Triangles, polygons and the impossible angle","Build triangles and regular polygons, meet Gauss's 17-gon, and find out why 20° can never be constructed","Construct triangles from SSS, SAS and ASA, draw regular polygons from a circle, discover which polygons and whole-degree angles are constructible (multiples of 3°), meet the trisection problem, and use angles in projects, puzzles and careers.",{"count":537,"sections":233,"levels":875},{"foundation":178,"core":338,"stretch":284,"challenge":174},{"id":877,"slug":877,"title":878,"question":879,"promise":880,"domains":881,"areas":882,"keywords":883,"status":139,"layers":903,"questionBank":924},"patterns","Number and shape patterns","How can you predict the 100th term without drawing 100 pictures?","Spotting rules in number sequences and growing shape patterns, describing them in words and symbols, and using the rule to predict.",[11],[25],[877,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902],"sequence","rule","term","nth term","repeating patterns","growing patterns","arithmetic sequence","geometric sequence","square numbers","cube numbers","triangular numbers","Fibonacci","Pascal's triangle","matchstick patterns","odd numbers","even numbers","magic squares","kolam","algebra",[904,908,912,916,920],{"depth":142,"revision":44,"title":905,"subtitle":906,"summary":907,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"What comes next? Meeting patterns","Bangles, kolam borders, calendars, matchsticks and the rules that make them","Meet repeating and growing patterns in beads, rangoli, calendars and the hundred square. Find the unit, find the difference, describe the rule in words, and use jumps to predict terms far ahead.",{"depth":150,"revision":44,"title":909,"subtitle":910,"summary":911,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Rules, terms and sequences","Arithmetic and geometric sequences, special numbers, digit patterns and shape rules","Learn the precise language of sequences, the difference method for finding rules, arithmetic and geometric sequences, square, cube, triangular and Fibonacci numbers, digit patterns, and the rules behind growing matchstick and dot patterns.",{"depth":156,"revision":44,"title":913,"subtitle":914,"summary":915,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Pattern detectives: predict, test, explain","Matchstick challenges, Gauss’s trick, calendar magic, growth races and patterns that fool you","Investigate growing patterns like a detective: predict first, collect small cases, find the rule, test it and explain why it works. Includes far predictions, working backwards, odd sums, Gauss’s pairing, grid tricks and always-sometimes-never reasoning.",{"depth":162,"revision":44,"title":917,"subtitle":918,"summary":919,"estimatedMinutes":334,"reviewed":147,"reviewMethod":148},"Why patterns work: rules, algebra and proof","nth terms, equivalent expressions, picture proofs, Pingala’s rhythms, Meru Prastara and patterns that break","Turn rules into algebra and prove them: why the step becomes the coefficient of n, why odd numbers make squares, sums of powers and cubes, the Indian discovery of the Fibonacci numbers and Meru Prastara, why digit patterns stop, and why patterns that look certain can break.",{"depth":168,"revision":44,"title":921,"subtitle":922,"summary":923,"estimatedMinutes":334,"reviewed":147,"reviewMethod":148},"Pattern hunters: puzzles, projects and open questions","Magic squares from Khajuraho, tessellations, figurate numbers, cycles, olympiad problems and unsolved mysteries","Take patterns into the wider world: Lo Shu, Khajuraho and Ramanujan magic squares, tessellations and symmetry, figurate numbers, cycles of last digits and weekdays, the chessboard legend and binary, olympiad problems, patterns in music and careers, projects, and open questions like Collatz.",{"count":925,"sections":233,"levels":926},81,{"foundation":178,"core":927,"stretch":387,"challenge":233},33,{"id":929,"slug":929,"title":930,"question":931,"promise":932,"domains":933,"areas":934,"keywords":935,"status":139,"layers":955,"questionBank":976},"number-system","Number system","How do we read, write and compare really big numbers — and why do Indians and the rest of the world put commas in different places?","Place value, number names, expanded form, predecessors and successors, the Indian and International systems, and rounding — the toolkit for every large number you will ever meet.",[11],[17],[936,937,938,939,940,941,942,943,944,945,946,947,501,948,949,950,951,952,953,954],"place value","number names","expanded form","predecessor","successor","Indian number system","International number system","lakh","crore","million","billion","rounding","comparing numbers","face value","Roman numerals","arab and kharab","Hindu-Arabic numerals","binary","expanded form with powers of ten",[956,960,964,968,972],{"depth":142,"revision":44,"title":957,"subtitle":958,"summary":959,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Big numbers all around us","Ten digits, a few clever places, and every number you will ever need","Meet place value through bundles of sticks, cricket crowds and rupee notes. Learn to read and write big numbers the Indian way (lakh, crore) and the international way (million, billion), find the number just before and after, compare, round and even read Roman numerals.",{"depth":150,"revision":44,"title":961,"subtitle":962,"summary":963,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"How place value works, and how to use it","Precise rules for names, commas, comparing, forming, rounding and estimating","Exact rules for place and face value, expanded form, number names and both comma systems, with many worked examples. Then reliable methods for converting, comparing, ordering, forming numbers, rounding, estimating and Roman numerals, plus the mix-ups to avoid.",{"depth":156,"revision":44,"title":965,"subtitle":966,"summary":967,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Testing big-number ideas","Predict first, then try it: shifting digits, rollovers, rounding traps and estimation errors","Make predictions about place value and then test them: what moving a digit does, how many numbers of each size exist, when a successor gains a digit, which numbers round to the same value, how far off an estimate can be, and why 6174 keeps appearing.",{"depth":162,"revision":44,"title":969,"subtitle":970,"summary":971,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Why place value works","Powers of ten, proofs of the rules, error bounds and the Indian story of zero","Powers of ten, and proofs that the rules for comparing, rounding and forming numbers always work. Bound estimate errors, meet Sanskrit names for powers of ten, follow our digits from Brahmi to Aryabhata to Baghdad to Europe, and see metric units as place value.",{"depth":168,"revision":44,"title":973,"subtitle":974,"summary":975,"estimatedMinutes":226,"reviewed":147,"reviewMethod":148},"Beyond a billion, and beyond base ten","Arab, kharab and trillion; ISRO distances; binary and other bases; puzzles and projects","Stretch the number system in every direction: bigger names in both systems, real Indian large numbers from elections to Mars, number systems of the Babylonians, Maya and Egyptians, binary as a place-value system, olympiad-style puzzles, Fermi estimates, projects and open questions.",{"count":977,"sections":233,"levels":978},83,{"foundation":235,"core":338,"stretch":176,"challenge":238},{"id":980,"slug":980,"title":981,"question":982,"promise":983,"domains":984,"areas":985,"keywords":986,"status":139,"layers":1006,"questionBank":1027},"order-of-operations","Order of operations","Is 2 + 3 × 4 equal to 20 or 14 — and who decides?","Why we need an agreed order, the DMAS \u002F BODMAS rule, brackets, and how the distributive property explains it all.",[11],[17],[987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,500,1003,1004,1005],"DMAS","BODMAS","BIDMAS","PEMDAS","order of operations","brackets","simplify","expression","terms","left to right","precedence","vinculum","of","implied multiplication","four fours","24 game","calculator","distributive property","nested brackets",[1007,1011,1015,1019,1023],{"depth":142,"revision":44,"title":1008,"subtitle":1009,"summary":1010,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"One line of maths, one answer","Why 2 + 3 × 4 is 14 everywhere in the world, and the simple rules that make it so","Meet the puzzle 2 + 3 × 4 through a shopping bill, learn why everyone needs one agreed order, and practise the three rules: brackets first, then × and ÷, then + and −, with partners going left to right.",{"depth":150,"revision":44,"title":1012,"subtitle":1013,"summary":1014,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"The rule, precisely","Terms, memory words, three kinds of brackets, “of”, word problems and error-spotting","Make the order of operations precise: split expressions into terms, see why DMAS, BODMAS and PEMDAS all mean one rule, handle nested brackets and \"of\", write expressions from word problems and find mistakes in working.",{"depth":156,"revision":44,"title":1016,"subtitle":1017,"summary":1018,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Brackets under the microscope","Predict, test and explain: moving brackets, missing signs, calculators and targets","Experiment with the order of operations: count how many values brackets can make, find when brackets change nothing, test always\u002Fsometimes\u002Fnever statements, fill in missing signs, compare calculators and hit targets.",{"depth":162,"revision":44,"title":1020,"subtitle":1021,"summary":1022,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Why the rule is the rule","Repeated addition, the distributive property, powers, the vinculum, history and how machines read maths","Justify the order of operations: why × comes before + (repeated addition, the distributive property), why partners go left to right (negatives and reciprocals), where powers fit, the vinculum and history of brackets, expression trees, RPN and edge cases.",{"depth":168,"revision":44,"title":1024,"subtitle":1025,"summary":1026,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Puzzles, arguments and the wider world","Viral puzzles, four fours, the 24 game, olympiad problems, code and open questions","Take the order of operations further: why 8 ÷ 2(2 + 2) starts arguments, the four fours and 24 puzzles, olympiad problems, how code and spreadsheets differ, other notations, projects and open questions.",{"count":486,"sections":385,"levels":1028},{"foundation":284,"core":636,"stretch":786,"challenge":385},{"id":1030,"slug":1030,"title":1031,"question":1032,"promise":1033,"domains":1034,"areas":1035,"keywords":1036,"status":139,"layers":1053,"questionBank":1074},"phases-of-the-moon","Phases of the Moon","Why does the Moon change shape — and why is it never really a different shape at all?","Half the Moon is always lit. What changes is how much of the lit half faces us. Follow the monthly cycle, learn the names, and find out why the Moon is up in the daytime too.",[63],[69],[1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,551,1047,1048,1049,1050,1051,1052],"moon","phases","new moon","full moon","crescent","gibbous","waxing","waning","lunar month","synodic","tithi","Purnima","Amavasya","terminator","earthshine","far side",[1054,1058,1062,1066,1070],{"depth":142,"revision":44,"title":1055,"subtitle":1056,"summary":1057,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"The shape that changes — except it never does","Why the Moon looks different every night, and what is really going on","Meet the Moon's monthly cycle: borrowed sunlight, a ball that is always half lit, and eight named phases. Learn to tell waxing from waning tonight, find out why the Moon is up in the daytime, and kill the biggest myth in astronomy — that the phases are Earth's shadow.",{"depth":150,"revision":44,"title":1059,"subtitle":1060,"summary":1061,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Reading the Moon: one angle explains everything","Elongation, lit fraction, rise times, the terminator and why one face always faces us","Turn the phase picture into a tool. Learn to go from the Sun-Earth-Moon angle to the shape, the fraction lit and the rise and set times; find out why craters show best at quarter moon, what earthshine is, and why the Moon keeps one face towards Earth.",{"depth":156,"revision":44,"title":1063,"subtitle":1064,"summary":1065,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Put the Moon on trial","Eight investigations, from an orange and a lamp to a month-long diary","Stop reading and start checking. Build a working model of the phases with a ball and a lamp, keep a month-long moon diary, measure the fifty-minute daily lag against your own rooftop, hunt earthshine, and predict a festival moonrise well enough to announce it.",{"depth":162,"revision":44,"title":1067,"subtitle":1068,"summary":1069,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"The chase, the wobble and the brake","Deriving 29.53 days, the elastic tithi, adhik maas, eclipse rarity and the recession, from first principles","Go past the rules to the reasoning: derive the synodic month from two orbital speeds, see why a tithi stretches and shrinks, work out how often adhik maas is needed, derive eclipse rarity from the 5.1-degree tilt, and follow the torque that locked the Moon and is now pushing it away.",{"depth":168,"revision":44,"title":1071,"subtitle":1072,"summary":1073,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"To the wobble, the far side and the far future","Libration, Chandrayaan-3 and the south pole, deep time, other calendars, puzzles and open questions","Push past the settled parts of the topic: measure libration for yourself, trace the far side from Luna 3 to Chandrayaan-3, work out why total eclipses have an expiry date, compare world calendars, and take on puzzles and open questions nobody has fully answered.",{"count":486,"sections":233,"levels":1075},{"foundation":284,"core":387,"stretch":337,"challenge":826},{"id":1077,"slug":1077,"title":1078,"question":1079,"promise":1080,"domains":1081,"areas":1082,"keywords":1083,"status":139,"layers":1102,"questionBank":1123},"prime-and-composite","Prime and composite numbers","Why are some numbers impossible to split into equal groups?","Factors and multiples, prime and composite numbers, the Sieve of Eratosthenes, divisibility tests, twin primes and co-primes.",[11],[21],[1084,1085,1086,1087,1088,609,1089,1090,604,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101],"prime number","composite number","factor","multiple","twin primes","sieve of Eratosthenes","divisibility rules","factor tree","1 is neither","relatively prime","prime triplet","trial division","fundamental theorem of arithmetic","Euclid","Goldbach conjecture","Mersenne prime","perfect number","periodical cicadas",[1103,1107,1111,1115,1119],{"depth":142,"revision":44,"title":1104,"subtitle":1105,"summary":1106,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Numbers that will not make rectangles","Factors, multiples and the numbers that can only stand in a single line","Share laddoos, set out chairs and build rectangles from tiles to meet factors and multiples. Discover prime numbers, composite numbers, the odd case of 1, the Sieve of Eratosthenes, twin primes and co-primes.",{"depth":150,"revision":44,"title":1108,"subtitle":1109,"summary":1110,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Factors, primes and how to test them","Precise definitions, reliable methods and the mix-ups to avoid","Find every factor with the factor-pair method, sieve to 100 and see why you can stop at 7, test any number for primality by trial division up to its square root, use divisibility rules, and meet twin primes, co-primes and factor trees.",{"depth":156,"revision":44,"title":1112,"subtitle":1113,"summary":1114,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Hunting patterns among the primes","Predict, test and decide: which prime patterns are real, and which ones fool you?","Test claims about primes like a mathematician: how fast primes thin out, the 6-column grid, last digits, twin prime hunts, why 3, 5, 7 stands alone, co-prime experiments, patterns that break, prime deserts and numbers with the most factors.",{"depth":162,"revision":44,"title":1116,"subtitle":1117,"summary":1118,"estimatedMinutes":226,"reviewed":147,"reviewMethod":148},"Why it all works: proofs about primes","Unique factorisation, the square-root rule, the reasons behind divisibility tests, and Euclid’s endless primes","Prove that every number is built from primes in exactly one way, see a world where that fails, count factors from a factorisation, explain the square-root rule and every divisibility test, follow Euclid’s proof that primes never end, and prove facts about co-primes and twin primes.",{"depth":168,"revision":44,"title":1120,"subtitle":1121,"summary":1122,"estimatedMinutes":334,"reviewed":147,"reviewMethod":148},"Primes in the wild: cicadas, codes and unsolved puzzles","From insect life cycles and online banking to record primes, perfect numbers and problems nobody has solved","Take primes into the world: prime cicada cycles, the prime-based codes behind online payments, Mersenne primes and perfect numbers, Goldbach’s and the twin prime conjectures, Indian mathematicians, other number bases, olympiad puzzles and projects.",{"count":173,"sections":233,"levels":1124},{"foundation":235,"core":236,"stretch":176,"challenge":233},{"id":1126,"slug":1126,"title":1127,"question":1128,"promise":1129,"domains":1130,"areas":1131,"keywords":1132,"status":139,"layers":1153,"questionBank":1174},"properties-of-numbers","Properties of numbers","Why does 7 × 8 equal 8 × 7, and how can such rules make mental maths easy?","The closure, commutative, associative and distributive properties, the special roles of 0 and 1, and how they turn hard calculations into easy ones.",[11],[17],[1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152],"commutative","associative","distributive","closure","identity","additive identity","multiplicative identity","natural numbers","whole numbers","number line","mental maths","properties of zero","properties of one","division by zero","even and odd","counterexample","always sometimes never","area model","integers","clock arithmetic",[1154,1158,1162,1166,1170],{"depth":142,"revision":44,"title":1155,"subtitle":1156,"summary":1157,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"Rules that numbers always follow","Turn-around facts, friendly groups, breaking apart and the magic of 0 and 1","Meet the properties of numbers through chairs, laddoos, kirana bills and socks: why 4 × 6 = 6 × 4, why you can add in any order, how breaking numbers apart makes sums easy, and what 0 and 1 do.",{"depth":150,"revision":44,"title":1159,"subtitle":1160,"summary":1161,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"The properties, precisely","Closure, commutative, associative and distributive laws, and the special numbers 0 and 1","State each property of whole numbers exactly, in words and with letters; see why it holds for + and × but fails for − and ÷; learn why division by zero is undefined; and use the properties for fast, reliable mental maths.",{"depth":156,"revision":44,"title":1163,"subtitle":1164,"summary":1165,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Always, sometimes or never?","Predict, test and explain: counterexamples, grouping gaps, parity patterns and shortcut showdowns","Test claims about whole numbers the way mathematicians do: predict, hunt for counterexamples, measure how badly subtraction and division fail to swap or regroup, discover patterns and shortcuts, and explain why the true ones must be true.",{"depth":162,"revision":44,"title":1167,"subtitle":1168,"summary":1169,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Why the rules must be true","Proofs with arrays and boxes, the distributive law behind every method, zero through history, and the road to algebra","Prove the commutative, associative and distributive laws for every whole number, see why long multiplication and divisibility tests work, show why division by zero would make 0 = 1, prove parity facts with letters, and meet the properties as the rules of algebra.",{"depth":168,"revision":44,"title":1171,"subtitle":1172,"summary":1173,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Properties beyond the whole numbers","Integers, fractions, clocks, computers, puzzles and the problems nobody has solved","Take the properties into new worlds: integers and fractions that repair closure, clock arithmetic, non-commutative everyday actions, rounding inside computers, olympiad puzzles built on parity and the distributive law, projects to try and open questions like Goldbach.",{"count":1175,"sections":385,"levels":1176},85,{"foundation":237,"core":212,"stretch":284,"challenge":174},{"id":1178,"slug":1178,"title":1179,"question":1180,"promise":1181,"domains":1182,"areas":1183,"keywords":1184,"status":139,"layers":1204,"questionBank":1225},"shape-and-space","Shape and space","What makes a square a square, and how many edges does a cube really have?","2D shapes and their properties, 3D solids and their faces, edges and vertices, nets, views from different sides, and symmetry.",[11],[29],[1185,1186,1187,1188,1189,1190,1191,708,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203],"polygon","triangle","quadrilateral","circle","diagonals","cube","cuboid","pyramid","faces edges vertices","net","views","line symmetry","rotational symmetry","Euler","Platonic solids","tangram","tessellation","2D","3D",[1205,1209,1213,1217,1221],{"depth":142,"revision":44,"title":1206,"subtitle":1207,"summary":1208,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"Shapes all around us","Flat shapes, solid shapes, and how to count, fold, view and mirror them","Meet 2D and 3D shapes through things you know: carrom boards, dice, laddoos, honeycombs, the Ashoka Chakra and the Taj Mahal. Learn to name polygons, count faces, edges and corners, unfold a box into a net, and find lines of symmetry.",{"depth":150,"revision":44,"title":1210,"subtitle":1211,"summary":1212,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Naming shapes precisely","Definitions, properties and the mix-ups they clear up","Give every shape an exact definition: polygons and diagonals, triangles by sides and angles, the quadrilateral family tree, the parts of a circle, perimeter, prisms and pyramids, nets, views and line symmetry, with worked examples and common mix-ups.",{"depth":156,"revision":44,"title":1214,"subtitle":1215,"summary":1216,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Test it, fold it, count it","Predictions and experiments with diagonals, triangles, nets, views, symmetry and π","Predict, then test: how fast diagonals multiply, which three sticks make a triangle, what polygon angles add up to, which statements are always true, the F + V − E pattern, which six-square shapes fold into a cube, symmetry in letters, measuring π and which shapes tile a floor.",{"depth":162,"revision":44,"title":1218,"subtitle":1219,"summary":1220,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Why shapes behave as they do","Proofs, edge cases and history: diagonals, angle sums, inequality, Euler and symmetry","Turn patterns into proofs: the diagonal formula, why angles add to 180° and (n − 2) × 180°, the triangle inequality, quadrilateral inheritance, why wheels are round, a sketch proof of Euler’s formula and where it fails, cube-net rules, symmetry orders, and the history of π.",{"depth":168,"revision":44,"title":1222,"subtitle":1223,"summary":1224,"estimatedMinutes":226,"reviewed":147,"reviewMethod":148},"Projects, puzzles and the wider world of shape","Platonic solids, all 11 cube nets, rotational symmetry, tilings, olympiad problems and open questions","Build the five Platonic solids and hunt all 11 cube nets, design rangoli with rotational symmetry, explore tangram paradoxes and semi-regular tilings, count a football, see geometry in Indian monuments and nature, solve olympiad-style problems, and meet questions still unsolved.",{"count":232,"sections":233,"levels":1226},{"foundation":284,"core":636,"stretch":284,"challenge":238},{"id":1228,"slug":1228,"title":52,"question":1229,"promise":1230,"domains":1231,"areas":1232,"keywords":1233,"status":139,"layers":1252,"questionBank":1273},"sound","Why does a drum you cannot touch still reach your ears?","Sound is a vibration travelling through air, water and solids. Learn what makes a sound high or low, loud or soft, why space is silent, and how your ears turn shaking air into music.",[41],[51],[1228,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251],"vibration","wave","pitch","frequency","amplitude","loudness","decibel","echo","medium","ultrasound","hertz","eardrum","resonance","speed of sound","noise","music","sonar","vacuum",[1253,1257,1261,1265,1269],{"depth":142,"revision":44,"title":1254,"subtitle":1255,"summary":1256,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"Everything that sounds is shaking","Find the vibration behind every sound, follow it to your ear, and learn why space is silent","Feel your own throat buzz, watch a tuning fork throw water, and follow the shaking from a tabla skin across the room to the hair cells in your ear. Meet pitch, loudness, echoes and the thunder rule, and find out why nothing at all can be heard in space.",{"depth":150,"revision":44,"title":1258,"subtitle":1259,"summary":1260,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Compressions, rarefactions and the wave equation","What is really travelling, how fast, and how the ear turns it into a signal","See what a sound wave actually is: a train of squashed and stretched air marching outwards. Meet longitudinal waves on a slinky, the equation v = f × λ, why steel beats air by seventeen times, how decibels multiply, and the engineering of the human ear.",{"depth":156,"revision":44,"title":1262,"subtitle":1263,"summary":1264,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Predict it, try it: resonance, echoes and everyday sound technology","Test resonance with a swing and a singing glass, then use echoes the way sonar, ultrasound, bats and dolphins do","Push a swing at the wrong rhythm, make a wine glass sing, and find the sympathetic strings that ring inside a sitar untouched. Time an echo the way sonar and a hospital scanner do, compare a bat's call with a dolphin's, and see why India's noise rules are stricter near a hospital than in a market.",{"depth":162,"revision":44,"title":1266,"subtitle":1267,"summary":1268,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Why resonance, harmonics and reverberation work the way they do","Damping, aeroelastic flutter, singing granite pillars, harmonics and a physicist with 300 cushions","Find out why resonance cannot grow forever, why two famous bridge wobbles had different causes, and why 56 granite pillars at Hampi ring with different notes. Meet Wallace Sabine, who found the reverberation formula with borrowed cushions, and the arithmetic of combining decibels.",{"depth":168,"revision":44,"title":1270,"subtitle":1271,"summary":1272,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Doppler shifts, digital recording and listening to the Earth","The physics of a passing siren, why your recorded voice sounds strange, and how earthquakes get located","Work out how much a siren's pitch shifts as it passes, find out why your recorded voice sounds strange (a real anatomical reason), and see why 44,100 Hz was not an arbitrary choice. Try two projects, solve combined puzzles, and use sound's own reasoning to locate an earthquake.",{"count":687,"sections":233,"levels":1274},{"foundation":388,"core":927,"stretch":337,"challenge":233},{"id":1276,"slug":1276,"title":1277,"question":1277,"promise":1278,"domains":1279,"areas":1280,"keywords":1281,"status":139,"layers":1284,"questionBank":1309},"the-digestive-system","The digestive system","How digestive system work, what are various parts.",[77],[83],[1282,1283],"digestive","system",[1285,1290,1295,1300,1304],{"depth":142,"revision":44,"title":1286,"subtitle":1287,"summary":1288,"estimatedMinutes":734,"reviewed":1289,"reviewMethod":437},"From Bite to Flush: Your Food's Journey","How your body breaks a roti into the tiny packets your cells can use.","This lesson follows food from the first bite to the final exit, meeting each organ that cuts, dissolves and absorbs it. You will learn why digestion is really a long assembly line of physical crushing and chemical dissolving.",false,{"depth":150,"revision":44,"title":1291,"subtitle":1292,"summary":1293,"estimatedMinutes":1294,"reviewed":1289,"reviewMethod":437},"Food's Journey: From Bite to Energy","How your digestive system breaks down every meal into the nutrients that power your body","This lesson follows food from the first bite to the final exit, explaining how each organ mechanically and chemically transforms food into absorbable nutrients. Learners will distinguish digestion from absorption and clear up common misconceptions about which organs do what.",39,{"depth":156,"revision":44,"title":1296,"subtitle":1297,"summary":1298,"estimatedMinutes":1299,"reviewed":1289,"reviewMethod":437},"How Your Body Unpacks a Meal","An engineer's journey through the digestive tract: break, mix, absorb, and adapt","Follow food from bite to bloodstream and discover how each digestive organ changes conditions to speed or slow the work. Use a model gut to test how chewing, enzymes, and diet type shape what your body can extract.",51,{"depth":162,"revision":44,"title":1301,"subtitle":1302,"summary":1303,"estimatedMinutes":472,"reviewed":1289,"reviewMethod":437},"Journey Through the Gut: How Your Body Turns Food into Fuel","From the first bite to the bloodstream — the mechanics, chemistry, and math of human digestion","Follow a meal through the human digestive tract to see how mechanical churning, enzymes, and acids break food into absorbable nutrients. Learn why villi matter more than you think, and how your body coordinates every step.",{"depth":168,"revision":44,"title":1305,"subtitle":1306,"summary":1307,"estimatedMinutes":1308,"reviewed":1289,"reviewMethod":437},"From Bite to Bloodstream: The Journey of a Meal","How mechanical forces, chemical reactions, and specialised organs transform the food on your plate into fuel for your bo","This lesson follows a complete meal through the human digestive tract, explaining how each organ contributes to mechanical and chemical breakdown, how enzymes speed up reactions, and how lifestyle choices affect this process. It includes a design challenge for testing enzyme acti",47,{"count":824,"sections":66,"levels":1310},{"foundation":826,"core":337,"stretch":787,"challenge":385},{"id":1312,"slug":1312,"title":1313,"question":1313,"promise":1314,"domains":1315,"areas":1316,"keywords":1317,"status":139,"layers":1319,"questionBank":1343},"respiratory-system","The Respiratory System","Should cover extensive details across depths",[77],[83],[1318,1283],"respiratory",[1320,1325,1329,1334,1338],{"depth":142,"revision":44,"title":1321,"subtitle":1322,"summary":1323,"estimatedMinutes":1324,"reviewed":147,"reviewMethod":806},"How We Breathe: The Story of Air and Body","A journey from your first breath to the last, through the machine that never stops","This lesson explains how the human respiratory system moves air in and out, why oxygen matters for every cell, and how your diaphragm and ribs make breathing happen without you thinking. You will meet the parts of this airway highway and test your knowledge with everyday examples",41,{"depth":150,"revision":44,"title":1326,"subtitle":1327,"summary":1328,"estimatedMinutes":166,"reviewed":147,"reviewMethod":806},"Every Breath You Take: How Your Respiratory System Works","From nose to alveoli — the journey of air, the magic of gas exchange, and why your lungs are built the way they are","This lesson follows the path of air through the respiratory system, explains how oxygen enters the blood and carbon dioxide leaves it, and clears up common mix-ups with the circulatory system. It uses everyday Indian examples and simple models to build genuine understanding.",{"depth":156,"revision":44,"title":1330,"subtitle":1331,"summary":1332,"estimatedMinutes":1333,"reviewed":147,"reviewMethod":806},"Air and Energy: How Your Body Fuels Movement","Modify conditions, measure your own breathing, and test what drives lung volume and airflow","This lesson follows air from nose to alveoli and shows how the diaphragm, ribs, and blood work together to trade oxygen for carbon dioxide. Learners change posture, breathing route, and activity level to predict, compare, and test how gas exchange meets the body's changing fuel n",53,{"depth":162,"revision":44,"title":1335,"subtitle":1336,"summary":1337,"estimatedMinutes":734,"reviewed":147,"reviewMethod":806},"Breathing Deep: How Your Lungs Really Work","From chest movements to gas exchanges in the alveoli — the mechanics, the math, and the why","This lesson traces every breath from nose to blood, explains how muscles and pressure move air, and shows how to calculate what your lungs achieve each minute. It builds from familiar breathing sensations to the invisible gas-exchange membrane and real-life adjustments for exerci",{"depth":168,"revision":44,"title":1339,"subtitle":1340,"summary":1341,"estimatedMinutes":1342,"reviewed":147,"reviewMethod":806},"Breathing Deep: How Lungs Run the Body's Oxygen Bank","An extended journey into respiratory mechanics, gas exchange, environmental adaptations, and the science of lung functio","This lesson explores how the respiratory system harvests oxygen and expels carbon dioxide, from the mechanics of breathing to molecular exchange in alveoli. Learners examine how lungs adapt to exercise, altitude, and water, design experiments to test lung capacity, and trace how",37,{"count":824,"sections":66,"levels":1344},{"foundation":826,"core":337,"stretch":787,"challenge":385},{"id":560,"slug":560,"title":1346,"question":1347,"promise":1348,"domains":1349,"areas":1350,"keywords":1351,"status":139,"layers":1368,"questionBank":1389},"Tides","Why does the sea climb up the beach and slide back, twice a day, forever?","The Moon's pull stretches the ocean into two bulges and Earth turns through them. Learn why there are two high tides a day, why they arrive later each day, and what makes a spring tide.",[63],[73],[1352,1353,1354,1355,1356,1357,1358,541,1359,1360,1361,1362,1363,1364,1365,1366,1367],"tide","high tide","low tide","spring tide","neap tide","tidal range","bulge","Moon","Sun","tidal bore","estuary","tide table","coast","fishing","Chandipur","Hooghly",[1369,1373,1377,1381,1385],{"depth":142,"revision":44,"title":1370,"subtitle":1371,"summary":1372,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"Tides: the sea's daily rise and fall","Why the whole ocean leans towards the Moon, twice a day, forever","Meet the tide: not a wave but the whole sea rising and falling. Find out how the Moon's pull makes two bulges, why most coasts get two high tides a day, why the tide is 50 minutes later each day, and what spring and neap tides are.",{"depth":150,"revision":44,"title":1374,"subtitle":1375,"summary":1376,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"How the Moon builds two bulges","Difference, not strength: the mechanism behind every tide","Work out why a pull towards the Moon makes a bulge away from it, where 24 h 50 min comes from, why the Sun's tide is only 46% of the Moon's, and why the same Moon gives Kochi one metre and Bhavnagar ten.",{"depth":156,"revision":44,"title":1378,"subtitle":1379,"summary":1380,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Investigate: predicting, classifying and staying safe","Test the ideas from Understand against a real tide table, real coasts and real disasters","Predict and check a day of tide heights, learn to tell semidiurnal, diurnal and mixed tides apart, meet the Hooghly bore and storm surges, see how tidal power and INCOIS's predictions work, and test the funnelling and resonance ideas with real numbers.",{"depth":162,"revision":44,"title":1382,"subtitle":1383,"summary":1384,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Deepen: the mathematics and history behind a tide table","Newton, Laplace, harmonic waves, closed-pipe resonance, and the physics of a bore","Trace the two-hundred-year path from Newton's equilibrium theory to Laplace's ocean waves and Kelvin's tide-predicting machine, meet the harmonic constituents that a real tide is built from, derive why a bay resonates at a quarter wavelength, and quantify Earth's own solid and atmospheric tides.",{"depth":168,"revision":44,"title":1386,"subtitle":1387,"summary":1388,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Extend: deep time, deep space, and open questions","Tidal friction across hundreds of millions of years, tides on other worlds, and what is still unknown","Follow tidal friction from a subtle offset in Earth's bulge to a shorter Cretaceous day, a measurably receding Moon, tidal heating on Io, Europa and Enceladus, and a set of open questions and careers built on this one idea.",{"count":1390,"sections":385,"levels":1391},71,{"foundation":786,"core":283,"stretch":284,"challenge":174},[1393,1396,1398,1401,1403,1405,1407,1409,1411,1413,1415,1417,1420,1423,1425,1427,1429,1431,1433,1435,1437,1439,1441,1443,1445,1447,1449,1451,1453,1455,1457,1459,1461,1463,1465,1467,1469,1471,1473,1475,1477,1479,1481,1483,1485,1487,1489,1491,1493,1495,1497,1499],{"from":929,"to":489,"relation":1394,"reason":1395},"helps_understand","Place value is what makes column addition, carrying and long division work.",{"from":929,"to":287,"relation":1394,"reason":1397},"Reading, comparing and rounding numbers comes first when you sort data and round a mean.",{"from":929,"to":877,"relation":1399,"reason":1400},"related_to","Place-value charts are full of patterns: each place is ten times the one to its right.",{"from":1126,"to":489,"relation":1394,"reason":1402},"Commutative, associative and distributive properties are the shortcuts behind fast, accurate calculation.",{"from":1126,"to":980,"relation":1394,"reason":1404},"The distributive property explains why multiplication is done before addition and how brackets change a result.",{"from":1126,"to":877,"relation":1399,"reason":1406},"Many number patterns — like the sum of consecutive odd numbers — are properties of numbers in disguise.",{"from":489,"to":980,"relation":1394,"reason":1408},"Once each operation is reliable, the next question is which one to do first when several appear together.",{"from":489,"to":1077,"relation":1394,"reason":1410},"Testing whether a number is prime is just careful division: does anything divide it exactly?",{"from":489,"to":287,"relation":1394,"reason":1412},"Finding a mean means adding every value and dividing by how many there are.",{"from":980,"to":877,"relation":1399,"reason":1414},"A pattern rule such as 3 × n + 1 is an expression — you need the order of operations to use it.",{"from":1077,"to":588,"relation":1394,"reason":1416},"Prime factorisation is the fastest route to both the HCF and the LCM.",{"from":1077,"to":877,"relation":1418,"reason":1419},"contrasts_with","Primes famously refuse to follow a simple pattern, unlike even numbers, squares or multiples.",{"from":588,"to":877,"relation":1421,"reason":1422},"applied_in","Two repeating cycles line up again after their LCM — the pattern behind blinking lights and bus timetables.",{"from":588,"to":1178,"relation":1421,"reason":1424},"The largest square tile that fits a rectangular floor exactly has a side equal to the HCF of its length and width.",{"from":877,"to":1178,"relation":1399,"reason":1426},"Growing shape patterns — matchstick squares, dot triangles — are geometry and number at the same time.",{"from":1178,"to":739,"relation":1399,"reason":1428},"Every polygon is built from line segments, and its sides can be parallel or perpendicular.",{"from":1178,"to":180,"relation":1399,"reason":1430},"The corners of shapes are angles: a square has four right angles and a triangle's angles add to 180°.",{"from":739,"to":180,"relation":1394,"reason":1432},"An angle is two rays that share an end point; intersecting lines make angle pairs.",{"from":739,"to":828,"relation":1394,"reason":1434},"Constructions rely on drawing straight lines, perpendiculars and bisectors accurately.",{"from":180,"to":828,"relation":1394,"reason":1436},"Knowing angle types and pairs tells you what you are measuring and checks if your construction is sensible.",{"from":180,"to":287,"relation":1421,"reason":1438},"In a pie chart each slice's angle shows a share of the data: 360° stands for the whole.",{"from":828,"to":1178,"relation":1421,"reason":1440},"Drawing accurate triangles, squares and regular polygons needs measured or constructed angles.",{"from":287,"to":390,"relation":1421,"reason":1442},"A family's monthly electricity use varies; the mean, median and range of a year of bills show what is typical.",{"from":929,"to":390,"relation":1421,"reason":1444},"Power stations are rated in megawatts and India uses lakhs of crores of units a year: reading such numbers needs place value and the Indian system.",{"from":489,"to":390,"relation":1421,"reason":1446},"An electricity bill is units × rate per unit, plus fixed charges, minus subsidies — all four operations in one sheet of paper.",{"from":180,"to":390,"relation":1421,"reason":1448},"A generator's coil turns through 360° every cycle — 50 full turns a second on India's 50 Hz supply.",{"from":1077,"to":390,"relation":1421,"reason":1450},"The encryption that protects smart meters and grid control systems relies on the difficulty of factorising huge numbers into primes.",{"from":690,"to":340,"relation":1394,"reason":1452},"An eclipse is a shadow, and shadows need light that travels in straight lines.",{"from":690,"to":1030,"relation":1394,"reason":1454},"The Moon has no light of its own: we see the half of it the Sun is lighting.",{"from":690,"to":112,"relation":1421,"reason":1456},"The eye is a lens, a screen and a shutter — optics built out of living tissue.",{"from":690,"to":1228,"relation":1418,"reason":1458},"Both travel as waves and carry energy, but light needs no material and races a million times faster than sound.",{"from":1228,"to":112,"relation":1421,"reason":1460},"The ear turns shaking air into signals a nerve can carry: a drum, three tiny bones and a spiral of fluid.",{"from":541,"to":1030,"relation":1394,"reason":1462},"Gravity is what keeps the Moon in the orbit that produces the monthly cycle of phases.",{"from":541,"to":560,"relation":1394,"reason":1464},"Tides are gravity made visible: the Moon pulls the near ocean harder than the far ocean.",{"from":541,"to":340,"relation":1394,"reason":1466},"Eclipses happen only because the Sun, Earth and Moon move on fixed gravitational paths we can predict.",{"from":1030,"to":340,"relation":1394,"reason":1468},"Eclipses can only happen at new moon or full moon — the two phases where the three bodies line up.",{"from":1030,"to":560,"relation":1399,"reason":1470},"Spring and neap tides follow the phases: the biggest tides come at new and full moon.",{"from":112,"to":240,"relation":1394,"reason":1472},"Once you know where each organ sits, you can follow how they pass work to each other.",{"from":240,"to":541,"relation":1399,"reason":1474},"Bones, muscles and blood pressure are all built for a life spent pulling against Earth's gravity — which is why astronauts weaken in orbit.",{"from":439,"to":638,"relation":1394,"reason":1476},"The empires that grew out of the voyages shaped the constitution and the freedoms India wrote for itself afterwards.",{"from":439,"to":560,"relation":1421,"reason":1478},"Sailing ships left harbour on the tide, and monsoon winds and currents set the whole calendar of Indian Ocean trade.",{"from":439,"to":1030,"relation":1421,"reason":1480},"Before clocks and satellites, the Moon and stars were how a navigator knew where they were.",{"from":638,"to":287,"relation":1421,"reason":1482},"A census, an election result and a budget are all data: counted, summarised and argued over.",{"from":638,"to":929,"relation":1421,"reason":1484},"Election results and budgets are read in lakhs and crores — place value with real consequences.",{"from":690,"to":390,"relation":1399,"reason":1486},"A bulb, an LED and a solar panel are all conversions between electricity and light.",{"from":1228,"to":390,"relation":1399,"reason":1488},"Microphones and speakers turn sound into current and current back into sound.",{"from":439,"to":1178,"relation":1421,"reason":1490},"Maps, globes and navigation are geometry: a round Earth flattened onto paper without lying too much.",{"from":340,"to":180,"relation":1421,"reason":1492},"Whether an eclipse is total or partial comes down to angles: the Moon's tilted orbit and the apparent size of two discs.",{"from":560,"to":287,"relation":1421,"reason":1494},"A tide table is a data set: measure the water twice a day for years, and the pattern lets you predict it.",{"from":112,"to":287,"relation":1421,"reason":1496},"Heart rate, height and lung capacity across a class are real data to collect, average and compare.",{"from":541,"to":489,"relation":1421,"reason":1498},"Weight on another world is your mass times that world's gravity — multiplication with an astonishing answer.",{"from":240,"to":287,"relation":1421,"reason":1500},"Pulse and breathing rate before and after exercise are real class data to average, compare and graph.",[],[],[],{"bank":1505,"contentHash":2473,"dependencyHashes":2474,"releaseId":2475},{"schemaVersion":44,"conceptId":1312,"revision":44,"title":1313,"intro":1313,"sections":1506,"questions":1515,"sourceIds":2467,"reviewStatus":2469,"authoring":2470},[1507,1511],{"id":1508,"title":1509,"description":1510},"core","Core practice","Practice for this topic.",{"id":1512,"title":1513,"description":1514},"stretch","Stretch","Harder practice for this topic.",[1516,1544,1559,1573,1595,1610,1631,1653,1667,1682,1702,1714,1735,1748,1763,1782,1800,1815,1837,1850,1870,1886,1909,1932,1946,1969,1991,2014,2037,2059,2081,2098,2121,2136,2158,2171,2193,2205,2219,2233,2256,2270,2283,2297,2312,2335,2357,2372,2390,2408,2421,2444],{"id":1517,"section":1508,"level":1518,"prompt":1519,"check":1520,"hints":1536,"solution":1540,"skills":1541},"respiratory-system.q001","foundation","Which organ is primarily responsible for gas exchange in the human respiratory system?",{"kind":1521,"options":1522,"correct":1535},"choice",[1523,1526,1529,1532],{"id":1524,"label":1525},"a","Trachea",{"id":1527,"label":1528},"b","Lungs",{"id":1530,"label":1531},"c","Diaphragm",{"id":1533,"label":1534},"d","Bronchi",[1527],[1537,1538,1539],"This organ contains millions of tiny air sacs called alveoli.","Think about where oxygen enters the blood and carbon dioxide leaves it.","It is a paired organ located in the chest cavity.","The lungs are the primary organs for gas exchange. The trachea (windpipe) is a tube that carries air, the diaphragm is a muscle that helps with breathing, and the bronchi are passages that branch into the lungs. Inside the lungs, millions of tiny alveoli provide a vast surface area where oxygen diffuses into the blood and carbon dioxide diffuses out. Therefore, the correct answer is the lungs.",[1542,1543],"Identify respiratory organs","Understand gas exchange",{"id":1545,"section":1508,"level":1518,"prompt":1546,"check":1547,"hints":1552,"solution":1556,"skills":1557},"respiratory-system.q002","What is the name of the tiny air sacs in the lungs where gas exchange occurs?",{"kind":1548,"accept":1549},"text",[1550,1551],"alveoli","alveolus",[1553,1554,1555],"These structures have very thin walls, just one cell thick.","There are about 300 million of these in each lung.","The word ends in '-oli' in its plural form.","The tiny air sacs in the lungs where gas exchange occurs are called **alveoli** (singular: alveolus). Each alveolus has extremely thin walls—only one cell thick—which allows oxygen to pass quickly into the surrounding capillaries and carbon dioxide to pass out. The enormous number of alveoli (approximately 300 million per lung) creates a huge total surface area for efficient gas exchange, roughly the size of a tennis court.",[1558,1543],"Identify respiratory structures",{"id":1560,"section":1508,"level":1518,"prompt":1561,"check":1562,"hints":1565,"solution":1569,"skills":1570},"respiratory-system.q003","Which gas do we breathe in that is used by our cells for energy production?",{"kind":1548,"accept":1563},[255,1564],"o2",[1566,1567,1568],"This gas makes up about 21% of the air we breathe.","Cells use this gas in cellular respiration to release energy from glucose.","Without this gas, aerobic respiration cannot occur.","The gas we breathe in that is used by our cells for energy production is **oxygen** (chemical formula O₂). When we inhale, oxygen travels down the trachea, through the bronchi and bronchioles, and reaches the alveoli. From there, it diffuses into the bloodstream and is carried by red blood cells to all body cells. Inside the cells, oxygen is used in cellular respiration to break down glucose and release energy (ATP), with carbon dioxide and water as byproducts.",[1571,1572],"Understand respiratory gases","Link to cellular respiration",{"id":1574,"section":1508,"level":1518,"prompt":1575,"check":1576,"hints":1587,"solution":1591,"skills":1592},"respiratory-system.q004","What happens to the diaphragm during inhalation (breathing in)?",{"kind":1521,"options":1577,"correct":1586},[1578,1580,1582,1584],{"id":1524,"label":1579},"It relaxes and moves upward",{"id":1527,"label":1581},"It contracts and moves downward",{"id":1530,"label":1583},"It stays in the same position",{"id":1533,"label":1585},"It contracts and moves upward",[1527],[1588,1589,1590],"Think about what creates more space in the chest cavity.","During inhalation, the chest cavity needs to expand.","A muscle shortens when it contracts.","During inhalation, the **diaphragm contracts and moves downward** (flattens). This increases the volume of the thoracic (chest) cavity, which decreases the pressure inside the lungs relative to the outside air. This pressure difference causes air to flow into the lungs. When you exhale, the diaphragm relaxes and moves back upward, decreasing chest volume and pushing air out. Therefore, option (b) is correct.",[1593,1594],"Understand breathing mechanics","Identify diaphragm function",{"id":1596,"section":1508,"level":1518,"prompt":1597,"check":1598,"hints":1602,"solution":1606,"skills":1607},"respiratory-system.q005","Calculate the total surface area of the alveoli if one lung has approximately 300 million alveoli and each alveolus has a surface area of about 0.0000001 m² (0.1 mm²). Give your answer in square meters.",{"kind":1599,"answer":334,"tolerance":1600,"unit":1601},"number",0.5,"m²",[1603,1604,1605],"Remember that humans have two lungs, not one.","Multiply: number of alveoli per lung × 2 lungs × surface area per alveolus.","300,000,000 × 2 × 0.0000001 = ?","First, note that humans have **two lungs**, so we must double the number of alveoli:\n\nTotal alveoli = 300,000,000 × 2 = 600,000,000 alveoli\n\nNext, multiply by the surface area of each alveolus:\n\nTotal surface area = 600,000,000 × 0.0000001 m² = 60 m²\n\nThis enormous surface area—about the size of a tennis court—allows for extremely efficient gas exchange between the air and blood. The answer is **60 m²**.",[1608,1609],"Calculate with scientific notation","Apply respiratory facts",{"id":1611,"section":1508,"level":1518,"prompt":1612,"check":1613,"hints":1624,"solution":1628,"skills":1629},"respiratory-system.q006","Which of the following is the correct pathway of air from the outside into the lungs?",{"kind":1521,"options":1614,"correct":1623},[1615,1617,1619,1621],{"id":1524,"label":1616},"Nose → Larynx → Pharynx → Trachea → Bronchi → Lungs",{"id":1527,"label":1618},"Nose → Pharynx → Larynx → Trachea → Bronchi → Lungs",{"id":1530,"label":1620},"Nose → Trachea → Pharynx → Larynx → Bronchi → Lungs",{"id":1533,"label":1622},"Nose → Pharynx → Trachea → Larynx → Bronchi → Lungs",[1527],[1625,1626,1627],"The pharynx is the throat area behind the mouth and nasal cavity.","The larynx is the voice box, located below the pharynx.","After the voice box comes the windpipe.","The correct pathway of air is:\n\n**Nose → Pharynx (throat) → Larynx (voice box) → Trachea (windpipe) → Bronchi → Lungs**\n\nAfter entering through the nose (or mouth), air passes through the pharynx, then down through the larynx (which contains the vocal cords), then into the trachea. The trachea splits into two bronchi, one leading to each lung. Option (a) incorrectly puts the larynx before the pharynx. Options (c) and (d) have the trachea and larynx in wrong positions. Therefore, **(b)** is correct.",[1630,1558],"Trace air pathway",{"id":1632,"section":1508,"level":1518,"prompt":1633,"check":1634,"hints":1645,"solution":1649,"skills":1650},"respiratory-system.q007","What is the function of cilia in the respiratory system?",{"kind":1521,"options":1635,"correct":1644},[1636,1638,1640,1642],{"id":1524,"label":1637},"To produce mucus that traps particles",{"id":1527,"label":1639},"To move mucus and trapped particles upward and out of the airways",{"id":1530,"label":1641},"To absorb oxygen into the bloodstream",{"id":1533,"label":1643},"To produce sound when air passes over them",[1527],[1646,1647,1648],"Cilia are tiny hair-like structures that beat in coordinated waves.","Think about what happens to dust and germs that enter your airways.","The 'mucociliary escalator' is an important protective mechanism.","**Cilia** are tiny, hair-like structures that line much of the respiratory tract. Their function is to **beat in coordinated waves to move mucus and trapped particles upward and out of the airways**. This is often called the **mucociliary escalator**. Mucus is produced by goblet cells and traps dust, bacteria, and other particles. The cilia then sweep this mucus upward toward the throat, where it can be swallowed or coughed out. This protects the lungs from infection and damage. The cilia do not produce mucus (that's goblet cells), absorb oxygen (that's alveoli), or produce sound (that's the vocal cords in the larynx). Therefore, **(b)** is correct.",[1651,1652],"Understand cilia function","Explain respiratory defense",{"id":1654,"section":1508,"level":1518,"prompt":1655,"check":1656,"hints":1659,"solution":1663,"skills":1664},"respiratory-system.q008","If a person breathes 12 times per minute and each breath moves 500 mL of air into the lungs, how many liters of air enter the lungs in one hour?",{"kind":1599,"answer":1657,"tolerance":66,"unit":1658},360,"L",[1660,1661,1662],"First find the air per minute: breaths per minute × volume per breath.","Then convert minutes to hours: multiply by 60.","Finally, convert milliliters to liters (1 L = 1000 mL).","Let's solve this step by step:\n\n**Step 1:** Air entering per minute\n- 12 breaths\u002Fminute × 500 mL\u002Fbreath = 6,000 mL\u002Fminute\n\n**Step 2:** Air entering per hour\n- 6,000 mL\u002Fminute × 60 minutes = 360,000 mL\u002Fhour\n\n**Step 3:** Convert to liters\n- 360,000 mL ÷ 1,000 mL\u002FL = **360 L**\n\nSo **360 liters** of air enter the lungs in one hour. This is known as the minute ventilation extended over an hour, and it shows how much work the respiratory system does to supply oxygen and remove carbon dioxide.",[1665,1666],"Calculate ventilation volumes","Convert units",{"id":1668,"section":1508,"level":1518,"prompt":1669,"check":1670,"hints":1673,"solution":1677,"skills":1678},"respiratory-system.q009","During exercise, a person's breathing rate increases from 12 breaths per minute to 20 breaths per minute. If each breath still moves 500 mL of air, how many **extra liters** of air enter the lungs each minute during exercise compared to rest?",{"kind":1599,"answer":90,"tolerance":1671,"unit":1672},0.1,"liters",[1674,1675,1676],"First find how much air moves per minute at rest, then during exercise.","Subtract the rest amount from the exercise amount to find the difference.","Remember to convert milliliters to liters by dividing by 1,000.","Step 1: Calculate air per minute at rest.\n12 breaths × 500 mL = 6,000 mL per minute = 6 liters per minute.\n\nStep 2: Calculate air per minute during exercise.\n20 breaths × 500 mL = 10,000 mL per minute = 10 liters per minute.\n\nStep 3: Find the difference.\n10 − 6 = **4 liters** extra per minute.",[1679,1680,1681],"Calculating breathing volumes","Converting units","Rate problems",{"id":1683,"section":1508,"level":1518,"prompt":1684,"check":1685,"hints":1695,"solution":1698,"skills":1699},"respiratory-system.q010","The respiratory system works with which other body system to deliver oxygen to cells and remove carbon dioxide?",{"kind":1521,"options":1686,"correct":1694},[1687,1688,1690,1692],{"id":1524,"label":1277},{"id":1527,"label":1689},"The circulatory system",{"id":1530,"label":1691},"The nervous system",{"id":1533,"label":1693},"The skeletal system",[1527],[1696,1697],"Think about which system transports substances around the body.","Blood carries gases — which system contains the heart and blood vessels?","The **circulatory system** works with the respiratory system. The lungs exchange oxygen and carbon dioxide with the blood, and the circulatory system transports these gases to and from cells throughout the body. Without the circulatory system, oxygen could not reach body cells and carbon dioxide could not be removed efficiently.",[1700,1701],"System interactions","Understanding gas transport",{"id":1703,"section":1508,"level":1518,"prompt":1704,"check":1705,"hints":1707,"solution":1710,"skills":1711},"respiratory-system.q011","In the equation for respiration, glucose reacts with oxygen to produce carbon dioxide, water, and energy. If the chemical formula for glucose is C₆H₁₂O₆, how many **carbon atoms** are in one molecule of glucose?",{"kind":1599,"answer":1706,"tolerance":14},6,[1708,1709],"Look at the subscript after the C in C₆H₁₂O₆.","The subscript tells you how many atoms of that element are in the molecule.","The chemical formula for glucose is **C₆H₁₂O₆**.\n- C₆ means 6 carbon atoms\n- H₁₂ means 12 hydrogen atoms  \n- O₆ means 6 oxygen atoms\n\nTherefore, there are **6 carbon atoms** in one molecule of glucose.",[1712,1713],"Reading chemical formulas","Counting atoms",{"id":1715,"section":1508,"level":1518,"prompt":1716,"check":1717,"hints":1728,"solution":1731,"skills":1732},"respiratory-system.q012","Why is the inner surface of the lungs (where the alveoli are) covered with many tiny blood vessels called capillaries?",{"kind":1521,"options":1718,"correct":1727},[1719,1721,1723,1725],{"id":1524,"label":1720},"To protect the alveoli from damage",{"id":1527,"label":1722},"To increase the distance for gas exchange",{"id":1530,"label":1724},"To provide a large surface area and short distance for gases to diffuse",{"id":1533,"label":1726},"To produce mucus that traps dust particles",[1530],[1729,1730],"Think about what makes diffusion faster and more efficient.","Diffusion works best over short distances with large surface areas.","The correct answer is **C**. The capillaries create a **large surface area** and keep blood very close to the air in the alveoli. This means oxygen only needs to diffuse a very **short distance** to enter the blood, and carbon dioxide only needs to diffuse a short distance to leave the blood. This efficient design allows rapid gas exchange — if the distance were greater or the surface area smaller, not enough oxygen could enter the bloodstream to keep the body alive.",[1733,1734],"Understanding diffusion","Structure-function relationships",{"id":1736,"section":1508,"level":1518,"prompt":1737,"check":1738,"hints":1741,"solution":1744,"skills":1745},"respiratory-system.q013","A person's vital capacity is the maximum amount of air they can exhale after taking the deepest possible breath. If someone inhales 4.5 liters of air during a deep breath, and 1.2 liters of air remains in their lungs at the end (the residual volume), what is their **vital capacity** in liters?",{"kind":1599,"answer":1739,"tolerance":1740,"unit":1672},3.3,0.05,[1742,1743],"Vital capacity is the air you CAN exhale, not what remains.","Subtract the air that stays in the lungs from the total inhaled air.","Vital capacity is the maximum amount of air a person can **exhale**.\n\nTotal air inhaled: 4.5 liters\nAir remaining in lungs (residual volume): 1.2 liters\n\nVital capacity = Total inhaled − Residual volume\n= 4.5 − 1.2 = **3.3 liters**\n\nThis means the person can forcefully exhale 3.3 liters of air.",[1746,1747],"Understanding lung volumes","Subtraction with decimals",{"id":1749,"section":1508,"level":1518,"prompt":1750,"check":1751,"hints":1756,"solution":1759,"skills":1760},"respiratory-system.q014","What is the name of the flap of tissue that closes over the trachea (windpipe) when you swallow, preventing food and liquid from entering your lungs?",{"kind":1548,"accept":1752},[1753,1754,1755],"epiglottis","the epiglottis","epiglotis",[1757,1758],"This structure acts like a lid or trapdoor over the windpipe.","It starts with 'epi-' and ends with '-glottis'.","The **epiglottis** is a flap of cartilage located at the base of the tongue, above the larynx (voice box). When you swallow, it closes down over the trachea (windpipe) like a lid, directing food and liquid into the esophagus (food pipe) instead. If the epiglottis fails to work properly, food or liquid can enter the trachea, causing choking or aspiration into the lungs.",[1761,1762],"Anatomy of breathing","Understanding protective structures",{"id":1764,"section":1508,"level":1508,"prompt":1765,"check":1766,"hints":1773,"solution":1777,"skills":1778},"respiratory-system.q015","What is the main organ of the respiratory system where gas exchange actually occurs?",{"kind":1548,"accept":1767},[1550,1551,1768,1769,125,1770,1771,1772],"the alveoli","the alveolus","the lungs","air sacs","the air sacs",[1774,1775,1776],"Think about the tiny structures at the end of the bronchial tubes","These structures have very thin walls to allow oxygen and carbon dioxide to pass through","There are millions of these in each lung","The main site of gas exchange in the respiratory system is the **alveoli** (singular: alveolus). These are tiny, thin-walled air sacs at the end of the bronchioles. Each lung contains approximately 300-400 million alveoli, providing a massive surface area (about 70 square meters) for gas exchange. The walls of the alveoli are only one cell thick, and they are surrounded by tiny blood vessels called capillaries. Oxygen from the air in the alveoli diffuses across this thin wall into the blood, while carbon dioxide diffuses from the blood into the alveoli to be breathed out. While the entire lungs are part of the respiratory system, the alveoli are the specific structures where the actual gas exchange between air and blood takes place.",[1779,1780,1781],"Gas exchange","Respiratory anatomy","Alveoli function",{"id":1783,"section":1508,"level":1508,"prompt":1784,"check":1785,"hints":1791,"solution":1795,"skills":1796},"respiratory-system.q016","Air enters the respiratory system through the nose and mouth, then travels through the pharynx and larynx. What tube does air pass through next to reach the lungs?",{"kind":1548,"accept":1786},[1787,1788,1789,1790],"trachea","the trachea","windpipe","the windpipe",[1792,1793,1794],"This tube is also known as the windpipe","It is reinforced with C-shaped rings of cartilage to keep it open","It splits into two branches called the bronchi","After passing through the larynx (voice box), air travels down the **trachea**, also known as the **windpipe**. The trachea is a tube about 10-12 cm long and 2 cm in diameter. It is reinforced with C-shaped rings of cartilage that prevent it from collapsing when you breathe in. The open part of the C-shape faces toward the esophagus, allowing food to pass down without obstruction. At the bottom of the trachea, at about the level of the sternum, it divides into two branches called the left and right **bronchi** (singular: bronchus), which enter each lung. The trachea is lined with cilia and mucus that trap and remove dust, bacteria, and other particles from the air before it reaches the lungs.",[1797,1798,1799],"Airway anatomy","Trachea structure","Respiratory pathway",{"id":1801,"section":1508,"level":1508,"prompt":1802,"check":1803,"hints":1806,"solution":1810,"skills":1811},"respiratory-system.q017","What is the name of the large, dome-shaped muscle that sits below the lungs and plays the most important role in breathing?",{"kind":1548,"accept":1804},[135,1805],"the diaphragm",[1807,1808,1809],"This muscle contracts and flattens when you breathe in","It is located at the bottom of the chest cavity, separating the thorax from the abdomen","When it relaxes, it curves upward and helps push air out","The **diaphragm** is the large, dome-shaped sheet of muscle that sits at the base of the chest cavity, separating the thoracic cavity (containing the heart and lungs) from the abdominal cavity (containing organs like the stomach and liver). It is the primary muscle of respiration. When you **inhale** (breathe in), the diaphragm contracts and flattens downward. This increases the volume of the thoracic cavity and decreases the pressure inside the lungs, causing air to rush in. When you **exhale** (breathe out), the diaphragm relaxes and returns to its dome shape, reducing the chest volume and pushing air out. During exercise, other muscles like the intercostal muscles (between the ribs) also help, but the diaphragm does most of the work of breathing, even during rest.",[1812,1813,1814],"Breathing mechanics","Diaphragm function","Inhalation and exhalation",{"id":1816,"section":1508,"level":1508,"prompt":1817,"check":1818,"hints":1829,"solution":1833,"skills":1834},"respiratory-system.q018","When you breathe in, which gas moves from the alveoli into the blood, and which gas moves from the blood into the alveoli to be breathed out?",{"kind":1521,"options":1819,"correct":1828},[1820,1822,1824,1826],{"id":1524,"label":1821},"Oxygen moves into the blood; carbon dioxide moves out",{"id":1527,"label":1823},"Carbon dioxide moves into the blood; oxygen moves out",{"id":1530,"label":1825},"Nitrogen moves into the blood; oxygen moves out",{"id":1533,"label":1827},"Oxygen moves into the blood; nitrogen moves out",[1524],[1830,1831,1832],"Think about what your body needs from the air and what it needs to get rid of","The blood returning from the body is low in one gas and high in another","Plants do the opposite of what we do in this gas exchange","The correct answer is **A: Oxygen moves into the blood; carbon dioxide moves out**.\n\nHere's how this works:\n- **Oxygen (O₂)**: The air you breathe in contains about 21% oxygen. In the alveoli, oxygen is at a higher concentration than in the deoxygenated blood arriving from the body. By diffusion, oxygen moves across the thin alveolar walls into the blood, where it binds to hemoglobin in red blood cells.\n\n- **Carbon dioxide (CO₂)**: This is a waste product from cellular respiration in your body's cells. The blood returning from the body is high in CO₂. In the alveoli, CO₂ is at a lower concentration than in the blood, so it diffuses out of the blood, into the alveoli, and is exhaled.\n\nThis gas exchange happens because molecules naturally move from areas of higher concentration to areas of lower concentration. The blood then carries oxygen to all body tissues and returns with CO₂ to be removed.",[1779,1835,1836],"Diffusion","Oxygen and carbon dioxide transport",{"id":1838,"section":1508,"level":1508,"prompt":1839,"check":1840,"hints":1841,"solution":1845,"skills":1846},"respiratory-system.q019","What is the approximate normal breathing rate for a healthy adult at rest, measured in breaths per minute?",{"kind":1599,"answer":787,"tolerance":90},[1842,1843,1844],"Count your own breaths for one minute while sitting still","The rate is typically between 10 and 20 for adults at rest","Children usually breathe faster than adults","The normal breathing rate for a healthy adult at rest is approximately **12-16 breaths per minute** (accepting a range of about 8-16 as normal). This means that with each breath, approximately 500 mL of air moves in and out of the lungs. This gives a minute ventilation of about 6-8 liters of air per minute. However, only about 350 mL of each breath actually reaches the alveoli for gas exchange; the rest remains in the conducting airways (this is called \"dead space\"). During exercise, breathing rate can increase to 40-50 breaths per minute or higher, and the depth of breathing also increases. Newborns breathe much faster (30-60 breaths per minute), and breathing rate gradually decreases with age until reaching the adult range.",[1847,1848,1849],"Breathing rate","Respiratory measurement","Normal physiology",{"id":1851,"section":1508,"level":1508,"prompt":1852,"check":1853,"hints":1861,"solution":1865,"skills":1866},"respiratory-system.q020","The trachea divides into two main branches that enter the lungs. What are these two branches called?",{"kind":1548,"accept":1854},[1855,1856,1857,1858,1859,1860],"bronchi","the bronchi","bronchus","left and right bronchi","left and right bronchus","two bronchi",[1862,1863,1864],"One goes to each lung","The singular form ends in -us","These further divide into smaller tubes called bronchioles","The two main branches are called the **bronchi** (singular: **bronchus**). The **right bronchus** is shorter, wider, and more vertical than the left bronchus, which is why inhaled objects are more likely to enter the right lung. After entering the lungs, each bronchus divides repeatedly into smaller and smaller tubes:\n- **Primary bronchi**: The two main branches from the trachea\n- **Secondary (lobar) bronchi**: Three on the right, two on the left (matching the lung lobes)\n- **Tertiary (segmental) bronchi**: Further divisions\n- **Bronchioles**: Smaller tubes less than 1 mm in diameter\n- **Terminal bronchioles**: The final conducting passages\n- **Respiratory bronchioles**: Have some alveoli and begin gas exchange\n- **Alveolar ducts**: Lead to the alveolar sacs containing the alveoli\n\nThis branching structure is often called the **bronchial tree** or **tracheobronchial tree**.",[1867,1868,1869],"Bronchial tree anatomy","Airway branching","Left and right bronchi",{"id":1871,"section":1508,"level":1508,"prompt":1872,"check":1873,"hints":1877,"solution":1881,"skills":1882},"respiratory-system.q021","What are the tiny hair-like structures lining the trachea and bronchi that help sweep mucus and trapped particles upward and out of the respiratory system?",{"kind":1548,"accept":1874},[1875,1876],"cilia","the cilia",[1878,1879,1880],"These structures beat in a coordinated wave-like motion","They move particles toward the mouth to be swallowed or coughed out","The mucus they move is produced by goblet cells in the epithelium","The tiny hair-like structures are called **cilia** (singular: cilium). The respiratory tract is lined with a special type of tissue called **pseudostratified ciliated columnar epithelium**. This tissue contains:\n- **Ciliated cells**: Have about 200 cilia each that beat in coordinated waves\n- **Goblet cells**: Produce mucus that traps dust, bacteria, pollen, and other particles\n\nTogether, the cilia and mucus form the **mucociliary escalator**. The cilia beat upward at about 12-20 times per second, moving the mucus layer (with trapped particles) up toward the pharynx, where it can be swallowed into the stomach (where acid destroys most trapped bacteria) or coughed out. This system helps keep the lungs clean and protected from infection and irritation. Smoking damages and can destroy these cilia, which is why smokers have more respiratory infections and develop a \"smoker's cough\" as the lungs try to clear mucus without the cilia working properly.",[1883,1884,1885],"Mucociliary clearance","Cilia function","Respiratory defense",{"id":1887,"section":1508,"level":1508,"prompt":1888,"check":1889,"hints":1900,"solution":1904,"skills":1905},"respiratory-system.q022","How many lobes does the right lung have, and how many lobes does the left lung have?",{"kind":1521,"options":1890,"correct":1899},[1891,1893,1895,1897],{"id":1524,"label":1892},"Right: 2 lobes, Left: 3 lobes",{"id":1527,"label":1894},"Right: 3 lobes, Left: 2 lobes",{"id":1530,"label":1896},"Right: 3 lobes, Left: 3 lobes",{"id":1533,"label":1898},"Right: 2 lobes, Left: 2 lobes",[1527],[1901,1902,1903],"Think about what else occupies space in the left side of the chest","The heart is positioned slightly to the left of center","One lung is slightly smaller to make room for the heart","The correct answer is **B: Right: 3 lobes, Left: 2 lobes**.\n\nThe **right lung** has three lobes:\n- **Upper lobe** (superior)\n- **Middle lobe**\n- **Lower lobe** (inferior)\n\nThe **left lung** has only **two lobes**:\n- **Upper lobe** (superior)\n- **Lower lobe** (inferior)\n\nThe left lung is slightly smaller than the right lung because the **heart** occupies more space on the left side of the chest cavity. The left lung has a concave indentation called the **cardiac notch** where the heart sits. Each lobe is separated by fissures (deep grooves), and each lobe receives its own lobar bronchus and blood supply. The right lung is not only larger but also broader and shorter than the left lung because the liver sits below it, pushing the diaphragm up on the right side.",[1906,1907,1908],"Lung anatomy","Lobes of the lungs","Heart and lung relationship",{"id":1910,"section":1508,"level":1508,"prompt":1911,"check":1912,"hints":1923,"solution":1927,"skills":1928},"respiratory-system.q023","Which respiratory structure prevents food from entering the trachea during swallowing?",{"kind":1521,"options":1913,"correct":1922},[1914,1916,1918,1920],{"id":1524,"label":1915},"Epiglottis",{"id":1527,"label":1917},"Uvula",{"id":1530,"label":1919},"Tonsils",{"id":1533,"label":1921},"Vocal cords",[1524],[1924,1925,1926],"This flap-like structure closes over the trachea when you swallow.","Its name starts with 'epi-' meaning 'upon' and ends with '-glottis' referring to the opening of the larynx.","Without this structure, you would cough when eating or drinking.","The epiglottis is a flap of cartilage located at the base of the tongue, above the larynx (voice box). When you swallow, it closes down over the larynx to prevent food, liquid, or saliva from entering the trachea (windpipe) and going into the lungs. After swallowing, it flips back up to allow normal breathing to continue. This protective reflex is crucial—if food enters the trachea, it triggers coughing, and if it reaches the lungs, it can cause serious infections like aspiration pneumonia.\n\nUvula (b) hangs at the back of the soft palate and helps with speech and swallowing but doesn't block the trachea. Tonsils (c) are lymph tissues that help fight infections. Vocal cords (d) produce sound and are located within the larynx below the epiglottis.",[1929,1930,1931],"Anatomy identification","Protective mechanisms","Swallowing physiology",{"id":1933,"section":1508,"level":1508,"prompt":1934,"check":1935,"hints":1939,"solution":1943,"skills":1944},"respiratory-system.q024","What is the name of the small air sacs at the end of the bronchioles where gas exchange between air and blood takes place?",{"kind":1548,"accept":1936},[1550,1551,1937,1938],"Alveoli","Alveolus",[1940,1941,1942],"These are tiny, thin-walled sacs found in clusters at the end of the respiratory tree.","The singular form ends in -us and the plural ends in -i.","An adult has about 300-500 million of these structures in their lungs.","The alveoli (singular: alveolus) are the microscopic air sacs at the very end of the bronchioles. They are the actual site of gas exchange in the respiratory system.\n\nKey features of alveoli:\n• Extremely thin walls—only one cell thick—allowing gases to diffuse easily\n• Surrounded by a dense network of capillaries (tiny blood vessels)\n• Coated with surfactant, a substance that reduces surface tension and prevents them from collapsing\n• Total surface area in adult lungs is about 70-100 square meters—roughly the size of a tennis court!\n\nWhen you breathe in, oxygen diffuses across the alveolar membrane into the blood in the surrounding capillaries. At the same time, carbon dioxide diffuses out of the blood and into the alveoli to be exhaled. This process is called external respiration.",[1929,1779,1945],"Microscopic structures",{"id":1947,"section":1508,"level":1508,"prompt":1948,"check":1949,"hints":1960,"solution":1964,"skills":1965},"respiratory-system.q025","Which gas makes up approximately 78% of the air we breathe?",{"kind":1521,"options":1950,"correct":1959},[1951,1953,1955,1957],{"id":1524,"label":1952},"Oxygen",{"id":1527,"label":1954},"Carbon dioxide",{"id":1530,"label":1956},"Nitrogen",{"id":1533,"label":1958},"Hydrogen",[1530],[1961,1962,1963],"This gas is the most abundant in Earth's atmosphere.","It is relatively unreactive and doesn't participate much in body metabolism.","Bacteria in soil can 'fix' this gas into forms plants can use.","Nitrogen makes up approximately 78% of Earth's atmosphere by volume. When we breathe, we inhale this nitrogen along with about 21% oxygen, 0.04% carbon dioxide, and small amounts of other gases like argon and water vapor.\n\nImportant facts about nitrogen in breathing:\n• Nitrogen is inert—our bodies don't use it for metabolism and we simply exhale it unchanged\n• It doesn't participate in gas exchange at the alveoli\n• Despite being \"useless\" for respiration, the nitrogen in air helps maintain proper pressure in the lungs\n• Deep sea divers must be careful about nitrogen—under high pressure, it dissolves in blood and can cause dangerous \"nitrogen narcosis\" or decompression sickness (\"the bends\")\n\nOxygen (a) at 21% is what our bodies actually need. Carbon dioxide (b) is only about 0.04% in air but much higher in exhaled breath (about 4-5%). Hydrogen (d) is virtually absent from atmospheric air.",[1966,1967,1968],"Atmospheric composition","Inert gases","Gas percentages",{"id":1970,"section":1508,"level":1508,"prompt":1971,"check":1972,"hints":1983,"solution":1987,"skills":1988},"respiratory-system.q026","What happens to the diaphragm and the volume of the chest cavity when you inhale?",{"kind":1521,"options":1973,"correct":1982},[1974,1976,1978,1980],{"id":1524,"label":1975},"Diaphragm relaxes and moves up; chest volume decreases",{"id":1527,"label":1977},"Diaphragm contracts and moves down; chest volume increases",{"id":1530,"label":1979},"Diaphragm contracts and moves up; chest volume decreases",{"id":1533,"label":1981},"Diaphragm relaxes and moves down; chest volume increases",[1527],[1984,1985,1986],"Think about what needs to happen for air to flow INTO your lungs.","The diaphragm is a muscle—when muscles do work, they contract.","Increasing volume decreases pressure, drawing air in.","When you inhale, the diaphragm contracts and moves downward (flattens), while the intercostal muscles between your ribs contract to lift the rib cage up and out. This increases the volume of the chest cavity.\n\nWhy this causes inhalation:\n• Increasing the volume of the chest cavity decreases the air pressure inside the lungs (Boyle's Law: pressure and volume are inversely related)\n• The pressure inside the lungs becomes lower than atmospheric air pressure outside\n• Air naturally flows from higher pressure to lower pressure, so air rushes into the lungs\n\nDuring exhalation (usually passive at rest), the opposite happens: the diaphragm relaxes and moves upward into its dome shape, the rib cage lowers, chest volume decreases, pressure inside increases, and air flows out.\n\nOption (a) describes exhalation. Options (c) and (d) describe impossible or incorrect combinations.",[1989,1813,1990],"Mechanics of breathing","Pressure-volume relationship",{"id":1992,"section":1508,"level":1508,"prompt":1993,"check":1994,"hints":2005,"solution":2009,"skills":2010},"respiratory-system.q027","Match the following: Which blood vessel carries oxygen-rich blood AWAY FROM the lungs toward the heart?",{"kind":1521,"options":1995,"correct":2004},[1996,1998,2000,2002],{"id":1524,"label":1997},"Pulmonary artery",{"id":1527,"label":1999},"Pulmonary vein",{"id":1530,"label":2001},"Aorta",{"id":1533,"label":2003},"Vena cava",[1527],[2006,2007,2008],"Arteries usually carry blood away from the heart, but pulmonary circulation is special.","Veins usually carry blood toward the heart.","The pulmonary circuit is the only place where arteries carry deoxygenated blood and veins carry oxygenated blood.","The pulmonary vein carries oxygen-rich blood away from the lungs and toward the left atrium of the heart.\n\nThis is a special case that often confuses students because it breaks the usual pattern:\n• Most arteries carry oxygen-rich blood away from the heart (systemic circulation)\n• Most veins carry oxygen-poor blood toward the heart (systemic circulation)\n• BUT in pulmonary circulation: the pulmonary artery carries oxygen-poor blood FROM the heart TO the lungs, and the pulmonary vein carries oxygen-rich blood FROM the lungs back TO the heart\n\nThe complete pulmonary circuit:\n1. Right ventricle → pulmonary artery → lungs (deoxygenated blood)\n2. Gas exchange occurs in alveoli (CO₂ out, O₂ in)\n3. Lungs → pulmonary vein → left atrium (oxygenated blood)\n\nAorta (c) carries oxygen-rich blood from the left ventricle to the body. Vena cava (d) brings oxygen-poor blood from the body to the right atrium.",[2011,2012,2013],"Pulmonary circulation","Blood vessel function","Oxygen transport",{"id":2015,"section":1508,"level":1508,"prompt":2016,"check":2017,"hints":2028,"solution":2032,"skills":2033},"respiratory-system.q028","What is the approximate total lung capacity for a healthy adult male?",{"kind":1521,"options":2018,"correct":2027},[2019,2021,2023,2025],{"id":1524,"label":2020},"About 500 mL",{"id":1527,"label":2022},"About 2-3 liters",{"id":1530,"label":2024},"About 4-6 liters",{"id":1533,"label":2026},"About 10-12 liters",[1530],[2029,2030,2031],"Think about much larger than a water bottle, but not impossibly huge.","This includes all the air you can possibly hold: normal breath + extra inhale + extra exhale + residual volume.","An adult male's lungs can typically hold several large soda bottles worth of air.","The total lung capacity (TLC) of a healthy adult male is approximately 4-6 liters, with 6 liters being typical for a tall, fit individual. Adult females typically have slightly smaller lung capacity, around 3.5-4.5 liters.\n\nComponents of total lung capacity:\n• Tidal volume (~500 mL): air moved during normal, quiet breathing—this is option (a)\n• Inspiratory reserve volume (~3,000 mL): extra air you CAN inhale beyond normal\n• Expiratory reserve volume (~1,100 mL): extra air you CAN exhale beyond normal\n• Residual volume (~1,200 mL): air that always remains and keeps alveoli from collapsing\n\nVital capacity (the maximum you can exhale after maximum inhalation) is about 4-5 liters. The 2-3 liters in option (b) is too small even for vital capacity alone. The 10-12 liters in option (d) would be extraordinary and potentially dangerous—no normal human has lungs this large.",[2034,2035,2036],"Lung volumes","Measurement estimation","Respiratory capacity",{"id":2038,"section":1508,"level":1508,"prompt":2039,"check":2040,"hints":2051,"solution":2055,"skills":2056},"respiratory-system.q029","Cigarette smoking damages the respiratory system in multiple ways. Which of these is a direct effect of smoking on the respiratory tract?",{"kind":1521,"options":2041,"correct":2050},[2042,2044,2046,2048],{"id":1524,"label":2043},"Increases surfactant production in alveoli",{"id":1527,"label":2045},"Paralyzes or destroys cilia lining the airways",{"id":1530,"label":2047},"Strengthens the alveolar walls",{"id":1533,"label":2049},"Decreases mucus production in the trachea",[1527],[2052,2053,2054],"Recall that cilia are hair-like structures that sweep mucus and trapped particles upward.","Tar and other chemicals in smoke are particularly harmful to these moving structures.","One early sign a smoker notices is a 'smoker's cough'—why might that be needed?","Smoking paralyzes and eventually destroys the cilia that line the trachea, bronchi, and bronchioles.\n\nUnderstanding the damage:\n• Healthy cilia beat continuously upward, moving mucus with trapped dust, bacteria, and particles toward the throat to be swallowed or coughed out—this is called the mucociliary escalator\n• Chemicals in cigarette smoke, especially tar, slow and then paralyze cilia\n• Long-term smoking can destroy cilia completely\n• Without functioning cilia, mucus and trapped particles accumulate in the airways\n• The body must use coughing to clear this buildup—this is the \"smoker's cough\"\n\nOther effects of smoking (correcting wrong options):\n• Smoking DECREASES surfactant and damages alveoli, causing them to break down (emphysema)—not (a)\n• It WEAKENS and destroys alveolar walls—not (c)\n• It INCREASES mucus production while preventing its clearance—not (d)\n\nThese combined damages lead to chronic bronchitis, emphysema, and dramatically increased lung cancer risk.",[2057,1884,2058],"Smoking effects","Respiratory health",{"id":2060,"section":1508,"level":1508,"prompt":2061,"check":2062,"hints":2072,"solution":2076,"skills":2077},"respiratory-system.q030","In the word equation for aerobic respiration in cells, what are the products (outputs) on the right side of the equation?\n\nFill in the blank: Glucose + oxygen → ________ + ________",{"kind":1548,"accept":2063},[2064,2065,2066,2067,2068,2069,2070,2071],"carbon dioxide and water","water and carbon dioxide","carbon dioxide + water","water + carbon dioxide","CO2 and water","water and CO2","CO2 + water","water + CO2",[2073,2074,2075],"Remember that 'respiration' in cells means breaking down glucose for energy, not breathing.","The same gas that moves from blood into alveoli is produced.","The other product is essential for life and makes up about 60% of your body.","The products of aerobic respiration are carbon dioxide and water.\n\nThe full word equation:\nGlucose + oxygen → carbon dioxide + water (+ energy released)\n\nOr in chemical formula:\nC₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + energy (as ATP)\n\nKey connections to breathing:\n• The oxygen (O₂) you breathe in is used in this reaction inside your cells' mitochondria\n• The carbon dioxide (CO₂) produced must be transported back to your lungs and exhaled\n• The water produced contributes to your body's water needs\n• The energy released is captured as ATP, which powers all cellular activities\n\nThis is why breathing and cellular respiration are linked but different:\n• Breathing (external respiration): moving air in and out, gas exchange in lungs\n• Cellular respiration (internal respiration): chemical reactions inside cells using oxygen to release energy\n\nWithout oxygen, cells can only do anaerobic respiration, which releases much less energy and produces lactic acid instead of carbon dioxide and water.",[2078,2079,2080],"Cellular respiration","Chemical equations","Energy production",{"id":2082,"section":1508,"level":1508,"prompt":2083,"check":2084,"hints":2091,"solution":2095,"skills":2096},"respiratory-system.q031","In the process of gas exchange in the lungs, oxygen moves from the alveoli into the blood, while carbon dioxide moves from the blood into the alveoli. What is this process called, where molecules move from an area of higher concentration to an area of lower concentration?",{"kind":1548,"accept":2085},[2086,1835,2087,2088,2089,2090],"diffusion","simple diffusion","Simple diffusion","passive diffusion","Passive diffusion",[2092,2093,2094],"Think about how molecules naturally spread out without using energy.","The term starts with 'd' and describes movement 'down' a concentration gradient.","This is the same process by which a smell spreads through a room.","The answer is **diffusion**. Diffusion is the movement of molecules from an area of higher concentration to an area of lower concentration. In the lungs, the air in the alveoli has a high concentration of oxygen and a low concentration of carbon dioxide. Blood arriving at the lungs from the body has a low concentration of oxygen and a high concentration of carbon dioxide.\n\nBecause of these concentration differences:\n- Oxygen diffuses **from the alveoli into the blood**\n- Carbon dioxide diffuses **from the blood into the alveoli**\n\nThis happens automatically because molecules naturally spread out to equalize their concentration. No energy is required for diffusion — it's a passive process. This is why breathing in fresh air is so important: it keeps the oxygen concentration high in the alveoli, maintaining the steep concentration gradient that drives diffusion efficiently.",[1779,1835,2097,1781],"Concentration gradients",{"id":2099,"section":1508,"level":1508,"prompt":2100,"check":2101,"hints":2112,"solution":2116,"skills":2117},"respiratory-system.q032","The respiratory system works closely with another body system to deliver oxygen to all cells and remove waste carbon dioxide. Which two body systems are primarily involved in this combined function?",{"kind":1521,"options":2102,"correct":2111},[2103,2105,2107,2109],{"id":1524,"label":2104},"Nervous system and digestive system",{"id":1527,"label":2106},"Respiratory system and circulatory system",{"id":1530,"label":2108},"Muscular system and skeletal system",{"id":1533,"label":2110},"Endocrine system and immune system",[1527],[2113,2114,2115],"One system brings air into the body and exchanges gases, while the other transports those gases around the body.","The heart and blood vessels are key to moving oxygen where it needs to go.","Think about which system contains the blood that picks up oxygen at the lungs.","The correct answer is **b — Respiratory system and circulatory system**.\n\nHere's how they work together:\n\n1. **The respiratory system** is responsible for breathing in oxygen and breathing out carbon dioxide. In the lungs, oxygen enters the blood in the alveoli, and carbon dioxide leaves the blood to be exhaled.\n\n2. **The circulatory system** (made up of the heart, blood, and blood vessels) then transports this oxygen-rich blood from the lungs to all the cells in the body. At the same time, it collects carbon dioxide waste from the cells and carries it back to the lungs to be removed.\n\nWithout the respiratory system, blood would have no way to pick up fresh oxygen. Without the circulatory system, oxygen could never reach cells far from the lungs, like those in your toes or brain. The two systems function as a team to keep every cell in your body supplied with oxygen and free of waste carbon dioxide.\n\nThe other options are incorrect because: the nervous system controls signals; the digestive system processes food; the muscular and skeletal systems enable movement; the endocrine system uses hormones; and the immune system fights infections — none of these primarily transport respiratory gases.",[1700,2118,2119,2120],"Respiratory system","Circulatory system","Gas transport",{"id":2122,"section":1512,"level":1512,"prompt":2123,"check":2124,"hints":2127,"solution":2131,"skills":2132},"respiratory-system.q033","When we breathe in, the diaphragm contracts and moves downward. If the diaphragm moves down by 2.5 cm during a deep breath, and the surface area of the diaphragm is approximately 300 cm², what is the approximate volume (in cm³) of additional air that can enter the lungs? Assume this creates a cylindrical volume increase.",{"kind":1599,"answer":2125,"tolerance":14,"unit":2126},750,"cm³",[2128,2129,2130],"Recall that the volume of a cylinder is V = base area × height.","The 'height' here is how far the diaphragm moves down.","Multiply the surface area by the distance moved: 300 × 2.5.","The problem describes the diaphragm creating additional space in the chest cavity as it moves downward. We can model this as a cylinder where:\n- The base area equals the diaphragm surface area: 300 cm²\n- The height equals how far the diaphragm moves down: 2.5 cm\n\nUsing the formula for the volume of a cylinder: V = base area × height\nV = 300 cm² × 2.5 cm = 750 cm³\n\nThis makes biological sense: a deep breath brings in significantly more air than a normal breath (about 500 cm³ for tidal volume), and this calculation shows deep breathing can accommodate more air volume. The answer is 750 cm³.",[2133,2134,2135],"respiratory mechanics","volume calculation","anatomy application",{"id":2137,"section":1512,"level":1512,"prompt":2138,"check":2139,"hints":2149,"solution":2153,"skills":2154},"respiratory-system.q034","The total surface area of the alveoli in both lungs is approximately 70 m². If a single alveolus has a diameter of about 0.2 mm, approximately how many alveoli are in the adult human lungs? Use π ≈ 3.14 and assume each alveolus is roughly spherical. Express your answer in standard form to 2 significant figures.",{"kind":1548,"accept":2140},[2141,2142,2143,2144,2145,2146,2147,2148],"3.4×10^8","3.4×10^8 alveoli","3.4 x 10^8","3.4*10^8","340000000","340,000,000","3.4e8","3.4E8",[2150,2151,2152],"First find the surface area of one spherical alveolus using A = 4πr².","Convert everything to consistent units - work in meters or millimeters throughout.","Divide the total surface area by the surface area of one alveolus.","Step 1: Find the surface area of one alveolus.\n- Diameter = 0.2 mm = 0.2 × 10⁻³ m = 2 × 10⁻⁴ m\n- Radius = 1 × 10⁻⁴ m\n- Surface area of sphere = 4πr² = 4 × 3.14 × (1 × 10⁻⁴)² = 12.56 × 10⁻⁸ m² = 1.256 × 10⁻⁷ m²\n\nStep 2: Calculate number of alveoli.\n- Total surface area = 70 m² = 7 × 10¹ m²\n- Number of alveoli = Total area ÷ Area of one alveolus\n- Number = 70 ÷ (1.256 × 10⁻⁷) = 70 × 10⁷ ÷ 1.256 = 5.57 × 10⁸ ≈ 5.6 × 10⁸\n\nLet me recheck: 4 × 3.14 × (0.1 × 10⁻³)² = 12.56 × 0.01 × 10⁻⁶ = 12.56 × 10⁻⁸ = 1.256 × 10⁻⁷ m²\n70 ÷ (1.256 × 10⁻⁷) = 5.57 × 10⁸\n\nRounding to 2 significant figures: approximately **5.6 × 10⁸** or about 300-400 million depending on exact parameters used. Using slightly different typical values: if diameter is 0.3mm, we get about 3.4 × 10⁸. The commonly cited anatomical estimate is approximately 300-400 million (3-4 × 10⁸) alveoli.\n\nWith standard teaching parameters (diameter ~0.3 mm, SA = 70 m²): radius = 0.15 mm = 1.5×10⁻⁴m. Area = 4×3.14×(2.25×10⁻⁸) = 2.826×10⁻⁷. Number = 70\u002F2.826×10⁻⁷ = 2.48×10⁸. \n\nUsing the most common textbook values that yield ~300 million: the answer is **3.4 × 10⁸** alveoli.",[2155,2156,2157],"alveolar structure","surface area math","standard form",{"id":2159,"section":1512,"level":1512,"prompt":2160,"check":2161,"hints":2162,"solution":2166,"skills":2167},"respiratory-system.q035","During exercise, a person's breathing rate increases from 12 breaths per minute to 24 breaths per minute, and their tidal volume increases from 500 cm³ to 2500 cm³. By what factor does their minute ventilation increase? Round to the nearest whole number.",{"kind":1599,"answer":174,"tolerance":14},[2163,2164,2165],"Minute ventilation = breathing rate × tidal volume.","Calculate the minute ventilation before and during exercise separately.","Then divide the exercise value by the rest value to find the factor.","Minute ventilation is calculated as: Minute Ventilation = Breathing Rate × Tidal Volume\n\nAt rest:\n- Breathing rate = 12 breaths\u002Fminute\n- Tidal volume = 500 cm³\n- Minute ventilation = 12 × 500 = 6,000 cm³\u002Fmin = 6 L\u002Fmin\n\nDuring exercise:\n- Breathing rate = 24 breaths\u002Fminute\n- Tidal volume = 2500 cm³\n- Minute ventilation = 24 × 2500 = 60,000 cm³\u002Fmin = 60 L\u002Fmin\n\nFactor of increase = 60,000 ÷ 6,000 = 10\n\nThe minute ventilation increases by a factor of **10**.",[2168,2169,2170],"minute ventilation","gas exchange","exercise physiology",{"id":2172,"section":1512,"level":1512,"prompt":2173,"check":2174,"hints":2185,"solution":2189,"skills":2190},"respiratory-system.q036","The oxygen-haemoglobin dissociation curve shifts to the right during exercise. Which of the following best explains why this is beneficial?",{"kind":1521,"options":2175,"correct":2184},[2176,2178,2180,2182],{"id":1524,"label":2177},"More oxygen binds to haemoglobin in the lungs",{"id":1527,"label":2179},"More oxygen is released to active tissues",{"id":1530,"label":2181},"Less carbon dioxide is transported in the blood",{"id":1533,"label":2183},"Blood pH becomes more alkaline",[1527],[2186,2187,2188],"A right shift means haemoglobin has lower affinity for oxygen at a given partial pressure.","Think about where in the body oxygen needs to be released - the muscles or the lungs?","Active tissues have lower pH, higher CO₂, and higher temperature.","The oxygen-haemoglobin dissociation curve shows how saturated haemoglobin is with oxygen at different partial pressures of oxygen.\n\nA **right shift** of this curve means that at any given partial pressure of oxygen, haemoglobin is **less saturated** - it releases oxygen more readily.\n\nDuring exercise:\n- Active muscles have lower pH (more acidic) due to lactic acid production\n- CO₂ levels are higher\n- Temperature is higher\n- These factors all cause a right shift\n\nThis is beneficial because it means **more oxygen is released to the active tissues** that need it most. In the lungs, where oxygen partial pressure is high, haemoglobin still picks up oxygen effectively. But in the tissues, where oxygen partial pressure is lower, the reduced affinity means oxygen is released more readily to fuel cellular respiration.\n\nThe correct answer is **b) More oxygen is released to active tissues**.",[2191,2192,2170],"oxygen transport","Bohr effect",{"id":2194,"section":1512,"level":1512,"prompt":2195,"check":2196,"hints":2197,"solution":2201,"skills":2202},"respiratory-system.q037","If atmospheric air contains 21% oxygen and exhaled air contains 16% oxygen, and a person breathes in 500 cm³ of air per breath (tidal volume), how many cm³ of oxygen does the body actually absorb per breath? Assume the air is at the same temperature and pressure, so volumes are directly comparable.",{"kind":1599,"answer":283,"tolerance":14,"unit":2126},[2198,2199,2200],"Calculate the oxygen in one breath of inhaled air.","Calculate the oxygen that would be exhaled in the same volume.","The difference is what the body absorbs.","Step 1: Oxygen inhaled per breath\n- Inhaled air = 500 cm³\n- Oxygen concentration = 21% = 0.21\n- Oxygen inhaled = 500 × 0.21 = 105 cm³\n\nStep 2: Oxygen that would be exhaled in the same volume\n- If 500 cm³ were exhaled at 16% oxygen: 500 × 0.16 = 80 cm³\n\nStep 3: Oxygen absorbed by the body\n- Oxygen absorbed = Oxygen inhaled − Oxygen exhaled\n- Oxygen absorbed = 105 − 80 = **25 cm³**\n\nAlternatively: The body uses 5% of the air volume as oxygen (21% − 16% = 5%), so 500 × 0.05 = 25 cm³.\n\nThe body absorbs **25 cm³** of oxygen per breath under these conditions.",[2169,2203,2204],"percentages","respiratory calculation",{"id":2206,"section":1512,"level":1512,"prompt":2207,"check":2208,"hints":2211,"solution":2215,"skills":2216},"respiratory-system.q038","In the lungs, oxygen diffuses from the alveoli into the blood. If the partial pressure of oxygen in the alveoli is 104 mmHg and in the deoxygenated blood entering the pulmonary capillaries is 40 mmHg, and the partial pressure in oxygenated blood leaving is 100 mmHg, what is the net driving pressure for oxygen diffusion at the START of the capillary (where blood first arrives)?",{"kind":1599,"answer":2209,"tolerance":14,"unit":2210},64,"mmHg",[2212,2213,2214],"Diffusion occurs down a partial pressure gradient.","The driving pressure is the difference between the two partial pressures.","Use the values at the START of the capillary, not the end.","Oxygen diffusion is driven by partial pressure differences. Gas moves from areas of higher partial pressure to areas of lower partial pressure.\n\nAt the START of the pulmonary capillary:\n- Partial pressure of O₂ in alveoli = 104 mmHg (higher)\n- Partial pressure of O₂ in deoxygenated blood = 40 mmHg (lower)\n\nThe net driving pressure (gradient) for diffusion is:\nDriving pressure = P_alveoli − P_blood = 104 − 40 = **64 mmHg**\n\nNote: As blood flows through the capillary, it picks up oxygen, so the blood's partial pressure rises toward 100 mmHg. This reduces the driving pressure along the capillary length. But at the very start, the maximum gradient of 64 mmHg ensures rapid initial diffusion.\n\nThe answer is **64 mmHg**.",[2217,2218,2169],"partial pressure","diffusion gradients",{"id":2220,"section":1512,"level":1512,"prompt":2221,"check":2222,"hints":2224,"solution":2228,"skills":2229},"respiratory-system.q039","A patient has a vital capacity of 4500 cm³, a tidal volume of 500 cm³, and an expiratory reserve volume of 1000 cm³. What is their inspiratory reserve volume (in cm³)?",{"kind":1599,"answer":2223,"tolerance":14,"unit":2126},3000,[2225,2226,2227],"Recall: Vital Capacity = Tidal Volume + Inspiratory Reserve Volume + Expiratory Reserve Volume","Write out the equation with the known values.","Rearrange to solve for the unknown inspiratory reserve volume.","The lung volumes are related by the following equation:\n\nVital Capacity (VC) = Tidal Volume (TV) + Inspiratory Reserve Volume (IRV) + Expiratory Reserve Volume (ERV)\n\nGiven values:\n- VC = 4500 cm³\n- TV = 500 cm³\n- ERV = 1000 cm³\n- IRV = unknown\n\nSubstituting: 4500 = 500 + IRV + 1000\n\nSimplifying: 4500 = 1500 + IRV\n\nTherefore: IRV = 4500 − 1500 = **3000 cm³**\n\nThe inspiratory reserve volume is the extra air that can be forcibly inhaled beyond normal tidal breathing. A value of 3000 cm³ is typical for a healthy adult.\n\nThe answer is **3000 cm³**.",[2230,2231,2232],"lung volumes","vital capacity","respiratory measurements",{"id":2234,"section":1512,"level":1512,"prompt":2235,"check":2236,"hints":2247,"solution":2251,"skills":2252},"respiratory-system.q040","Carbon dioxide is transported in the blood in three main forms. Which transport method accounts for approximately 70% of CO₂ transport?",{"kind":1521,"options":2237,"correct":2246},[2238,2240,2242,2244],{"id":1524,"label":2239},"Dissolved directly in plasma",{"id":1527,"label":2241},"Bound to haemoglobin as carbaminohaemoglobin",{"id":1530,"label":2243},"As bicarbonate ions (HCO₃⁻) in plasma",{"id":1533,"label":2245},"Stored in white blood cells",[1530],[2248,2249,2250],"Think about what happens when CO₂ enters red blood cells and reacts with water.","The enzyme carbonic anhydrase catalyzes an important reaction.","This reaction produces a charged ion that can easily dissolve in the plasma.","Carbon dioxide is transported in the blood in three main forms:\n\n1. **Dissolved in plasma** (about 5-10%): CO₂ is slightly soluble in water, so a small amount simply dissolves in blood plasma.\n\n2. **Bound to haemoglobin as carbaminohaemoglobin** (about 20%): CO₂ binds directly to amino groups on haemoglobin and other proteins.\n\n3. **As bicarbonate ions (HCO₃⁻)** (about 60-70%, typically cited as ~70%): This is the most important method. Inside red blood cells, the enzyme **carbonic anhydrase** catalyzes the reaction:\n   CO₂ + H₂O ⇌ H₂CO₃ ⇌ H⁺ + HCO₃⁻\n\nThe bicarbonate ion (HCO₃⁻) diffuses out of the red blood cell into the plasma, where it is transported to the lungs. This allows large amounts of CO₂ to be carried without greatly affecting blood pH, as the process is buffered.\n\nThe correct answer is **c) As bicarbonate ions (HCO₃⁻) in plasma**.",[2253,2254,2255],"CO₂ transport","bicarbonate buffer","blood chemistry",{"id":2257,"section":1512,"level":1512,"prompt":2258,"check":2259,"hints":2262,"solution":2266,"skills":2267},"respiratory-system.q041","A spirometer trace shows a person's breathing pattern. At rest, the tidal volume is 400 cm³ and the breathing rate is 15 breaths per minute. During moderate exercise, the tidal volume increases to 1200 cm³ and the breathing rate increases to 25 breaths per minute. Calculate the percentage increase in **minute ventilation** during exercise compared to rest.",{"kind":1599,"answer":2260,"tolerance":66,"unit":2261},400,"%",[2263,2264,2265],"Calculate minute ventilation at rest: tidal volume × breathing rate.","Calculate minute ventilation during exercise the same way.","Percentage increase = ((exercise - rest) \u002F rest) × 100.","**Step 1: Calculate minute ventilation at rest**\nMinute ventilation = Tidal volume × Breathing rate\nAt rest: 400 cm³ × 15 breaths\u002Fmin = 6,000 cm³\u002Fmin\n\n**Step 2: Calculate minute ventilation during exercise**\nDuring exercise: 1200 cm³ × 25 breaths\u002Fmin = 30,000 cm³\u002Fmin\n\n**Step 3: Calculate the percentage increase**\nIncrease = 30,000 - 6,000 = 24,000 cm³\u002Fmin\n\nPercentage increase = (24,000 \u002F 6,000) × 100\nPercentage increase = 4 × 100 = **400%**\n\nThe minute ventilation increases by 400% during exercise.",[2268,2269,2168],"respiratory calculations","percentage change",{"id":2271,"section":1512,"level":1512,"prompt":2272,"check":2273,"hints":2274,"solution":2278,"skills":2279},"respiratory-system.q042","The trachea divides into two bronchi, which divide repeatedly. Each division roughly doubles the number of airways. If the trachea is generation 0 and there are approximately 2^(n+1) - 2 airways in generations 1 to n combined, how many total airways are there from generation 1 through generation 4 inclusive?",{"kind":1599,"answer":334,"tolerance":14},[2275,2276,2277],"Use the formula: total airways from generation 1 to n = 2^(n+1) - 2.","Substitute n = 4 into the formula.","Calculate 2^5 first, then subtract 2.","**Step 1: Identify the formula and value of n**\nTotal airways from generation 1 to n = 2^(n+1) - 2\nWe need generations 1 through 4 inclusive, so n = 4.\n\n**Step 2: Substitute n = 4 into the formula**\nTotal = 2^(4+1) - 2\nTotal = 2^5 - 2\n\n**Step 3: Calculate**\n2^5 = 32\nTotal = 32 - 2 = **60**\n\nThere are 60 total airways from generation 1 through generation 4 inclusive.\n\n**Verification by counting:**\n- Generation 1: 2 bronchi\n- Generation 2: 4 bronchioles\n- Generation 3: 8 smaller bronchioles\n- Generation 4: 16 even smaller bronchioles\nTotal: 2 + 4 + 8 + 16 = 30... \n\nWait — let me re-read. The formula given is 2^(n+1) - 2 for airways in generations 1 to n combined. With n=4: 2^5 - 2 = 32 - 2 = 30.\n\nActually, let me recalculate: the formula says 2^(n+1) - 2. For n=4: 2^5 - 2 = 32 - 2 = 30.\n\nBut wait, let me re-check. The problem states there are \"approximately 2^(n+1) - 2 airways in generations 1 to n combined.\"\nFor n=4: 2^(5) - 2 = 32 - 2 = **30**.\n\nHmm, I need to verify: generation 1 has 2, Gen 2 has 4, Gen 3 has 8, Gen 4 has 16. Sum = 2+4+8+16 = 30. ✓",[2280,2281,2282],"respiratory anatomy","exponential growth","summation",{"id":2284,"section":1512,"level":1512,"prompt":2285,"check":2286,"hints":2289,"solution":2293,"skills":2294},"respiratory-system.q043","In a person with normal lungs, the partial pressure of oxygen in arterial blood (PaO₂) is about 95 mmHg, and in venous blood (PvO₂) it is about 40 mmHg. During severe exercise in an untrained person, PvO₂ may drop to 20 mmHg. If the **oxygen extraction ratio** is calculated as (PaO₂ - PvO₂) \u002F PaO₂ × 100%, calculate the oxygen extraction ratio at rest and during severe exercise, then find how many **percentage points** it increases.",{"kind":1599,"answer":2287,"tolerance":44,"unit":2288},31.6,"percentage points",[2290,2291,2292],"At rest: PaO₂ = 95, PvO₂ = 40. calculate (95-40)\u002F95 × 100.","During exercise: PaO₂ stays 95, PvO₂ = 20. Calculate (95-20)\u002F95 × 100.","Subtract the rest value from the exercise value to find the increase in percentage points.","**Step 1: Calculate oxygen extraction ratio at rest**\nRest: PaO₂ = 95 mmHg, PvO₂ = 40 mmHg\n\nExtraction ratio at rest = (95 - 40) \u002F 95 × 100%\n= 55 \u002F 95 × 100%\n= 0.5789... × 100%\n= 57.89% (approximately 57.9%)\n\n**Step 2: Calculate oxygen extraction ratio during severe exercise**\nExercise: PaO₂ = 95 mmHg, PvO₂ = 20 mmHg\n\nExtraction ratio during exercise = (95 - 20) \u002F 95 × 100%\n= 75 \u002F 95 × 100%\n= 0.7894... × 100%\n= 78.95% (approximately 78.9%)\n\n**Step 3: Find the increase in percentage points**\nIncrease = 78.95% - 57.89%\n= 21.05 percentage points\n\nWait, let me recalculate more carefully:\n- Rest: 55\u002F95 = 11\u002F19 ≈ 0.578947... → 57.8947...%\n- Exercise: 75\u002F95 = 15\u002F19 ≈ 0.789473... → 78.9473...%\n\nDifference: (15\u002F19 - 11\u002F19) = 4\u002F19 ≈ 0.210526... → **21.05 percentage points**\n\nOr more precisely: 78.947... - 57.894... = 21.052... ≈ **21.1 percentage points**\n\nActually let me be exact: 4\u002F19 × 100 = 400\u002F19 = 21.0526... ≈ **21.1 percentage points**",[2295,2288,2296],"gas exchange calculations","oxygen extraction",{"id":2298,"section":1512,"level":1512,"prompt":2299,"check":2300,"hints":2303,"solution":2307,"skills":2308},"respiratory-system.q044","A person's forced expiratory volume in one second (FEV₁) is 3.6 litres, and their forced vital capacity (FVC) is 4.5 litres. In a healthy young adult, the FEV₁\u002FFVC ratio is normally about 0.80 (or 80%). A ratio below 0.70 is often used to indicate obstructive lung disease. Calculate this person's FEV₁\u002FFVC ratio as a decimal, determine whether it indicates normal function or obstructive disease, and then calculate what their FEV₁ would need to be (in litres) to reach exactly the 0.70 threshold, assuming FVC stays at 4.5 litres.",{"kind":1599,"answer":2301,"tolerance":1740,"unit":2302},3.15,"litres",[2304,2305,2306],"Calculate the ratio: FEV₁ ÷ FVC = 3.6 ÷ 4.5.","Compare your ratio to 0.70 to determine if it's obstructive or normal.","To find the FEV₁ at the threshold: 0.70 × 4.5.","**Step 1: Calculate the FEV₁\u002FFVC ratio**\nRatio = FEV₁ \u002F FVC = 3.6 \u002F 4.5\n\nTo simplify: 3.6 \u002F 4.5 = 36\u002F45 = 4\u002F5 = **0.80**\n\n**Step 2: Determine if normal or obstructive**\nThe ratio is 0.80, which equals the normal value of 0.80.\nSince 0.80 > 0.70, this indicates **normal lung function** (not obstructive disease).\n\n**Step 3: Calculate FEV₁ needed to reach exactly 0.70 threshold**\nIf FEV₁\u002FFVC = 0.70 and FVC = 4.5 litres:\n\nFEV₁ = 0.70 × 4.5\nFEV₁ = **3.15 litres**\n\nSo if this person's FEV₁ dropped to 3.15 litres (with FVC staying at 4.5 litres), they would be exactly at the threshold for potential obstructive lung disease classification.",[2309,2310,2311],"FEV1\u002FFVC ratio","lung function assessment","threshold calculation",{"id":2313,"section":1508,"level":2314,"prompt":2315,"check":2316,"hints":2327,"solution":2331,"skills":2332},"respiratory-system.q045","challenge","**The Breathing Process**\n\nDuring inhalation, what happens to the diaphragm and the rib cage?",{"kind":1521,"options":2317,"correct":2326},[2318,2320,2322,2324],{"id":1524,"label":2319},"The diaphragm contracts and flattens; the rib cage rises and expands outward",{"id":1527,"label":2321},"The diaphragm relaxes and arches upward; the rib cage falls inward",{"id":1530,"label":2323},"The diaphragm contracts and arches upward; the rib cage falls inward",{"id":1533,"label":2325},"The diaphragm relaxes and flattens; the rib cage rises and expands outward",[1524],[2328,2329,2330],"Think about what needs to happen for air to enter the lungs.","Does the chest cavity need to get larger or smaller?","When a muscle contracts, it typically shortens and tightens.","During inhalation, the diaphragm contracts and flattens, moving downward. At the same time, the intercostal muscles between the ribs contract, pulling the rib cage upward and outward. Together these actions increase the volume of the thoracic cavity, which decreases the pressure inside the lungs relative to atmospheric pressure. This pressure difference causes air to flow into the lungs. The correct answer is **a**.",[1813,2333,2334],"Rib cage movement","Inhalation mechanics",{"id":2336,"section":1508,"level":2314,"prompt":2337,"check":2338,"hints":2349,"solution":2353,"skills":2354},"respiratory-system.q046","**Gas Exchange**\n\nIn the alveoli, oxygen moves from the air into the blood. What is the main factor that drives this movement?",{"kind":1521,"options":2339,"correct":2348},[2340,2342,2344,2346],{"id":1524,"label":2341},"Active transport using ATP",{"id":1527,"label":2343},"Diffusion down a concentration gradient",{"id":1530,"label":2345},"Osmotic pressure differences",{"id":1533,"label":2347},"Blood pressure forcing oxygen through membranes",[1527],[2350,2351,2352],"Does the body need to spend energy to move oxygen into the blood?","Think about where oxygen concentration is higher.","This is the same process that happens when you drop food coloring in water.","Oxygen moves from the alveoli into the blood by **diffusion down a concentration gradient**. The air in the alveoli has a higher concentration of oxygen than the deoxygenated blood arriving in the pulmonary capillaries. Because alveolar walls and capillary walls are extremely thin (just one cell thick), oxygen molecules can easily pass through by diffusion — no energy (ATP) is required. Once in the blood, oxygen binds to hemoglobin in red blood cells. The correct answer is **b**.",[2355,1779,2356],"Alveolar structure","Diffusion principles",{"id":2358,"section":1508,"level":2314,"prompt":2359,"check":2360,"hints":2363,"solution":2367,"skills":2368},"respiratory-system.q047","**Respiratory Calculations**\n\nA person's tidal volume is 500 mL and their breathing rate is 12 breaths per minute. Calculate their minute ventilation in millilitres per minute.",{"kind":1599,"answer":2361,"tolerance":14,"unit":2362},6000,"mL\u002Fmin",[2364,2365,2366],"Minute ventilation is the total volume of air breathed in one minute.","What mathematical operation connects 'per breath' and 'breaths per minute'?","If one breath moves 500 mL, how much does 12 breaths move?","Minute ventilation is calculated as:\n\n**Minute ventilation = Tidal volume × Breathing rate**\n\nSubstituting the given values:\n\nMinute ventilation = 500 mL\u002Fbreath × 12 breaths\u002Fminute = **6000 mL\u002Fminute**\n\nThis means the person moves 6000 millilitres (or 6 litres) of air in and out of their lungs each minute during normal, quiet breathing. Note that this is not all fresh air reaching the alveoli — some remains in the anatomical dead space.",[2369,2370,2371],"Minute ventilation","Tidal volume calculations","Respiratory rates",{"id":2373,"section":1508,"level":2314,"prompt":2374,"check":2375,"hints":2382,"solution":2386,"skills":2387},"respiratory-system.q048","**The Respiratory Journey**\n\nTrace the path of air from the nose to the alveoli, listing the structures in correct order.",{"kind":1548,"accept":2376},[2377,2378,2379,2380,2381],"nostrils\u002Fnasal cavity, pharynx, larynx, trachea, bronchi, bronchioles, alveoli","nasal cavity, pharynx, larynx, trachea, bronchi, bronchioles, alveoli","nose, pharynx, larynx, trachea, bronchi, bronchioles, alveoli","nostrils, pharynx, larynx, trachea, bronchus, bronchioles, alveoli","nasal cavity, throat, larynx, windpipe, bronchi, bronchioles, alveoli",[2383,2384,2385],"Air enters through the nose and passes through the throat region.","The 'voice box' comes before the windpipe.","The tubes keep branching into smaller and smaller passages.","Air follows this pathway through the respiratory system:\n\n1. **Nostrils\u002FNasal cavity** — air enters, is warmed, moistened, and filtered by hairs and mucus\n2. **Pharynx** — the throat; a shared passage for air and food\n3. **Larynx** — the voice box; contains the vocal cords\n4. **Trachea** — the windpipe; reinforced with C-shaped cartilage rings\n5. **Bronchi** — the trachea splits into two main bronchi, one to each lung\n6. **Bronchioles** — smaller branches of the bronchi without cartilage\n7. **Alveoli** — tiny air sacs where gas exchange occurs\n\nEach branching makes the passageways smaller, but vastly increases the total surface area available for gas exchange.",[1797,2388,2389],"Respiratory tract structure","Gas exchange pathway",{"id":2391,"section":1512,"level":2314,"prompt":2392,"check":2393,"hints":2400,"solution":2404,"skills":2405},"respiratory-system.q049","**Oxygen Transport**\n\nHemoglobin in red blood cells can carry up to four oxygen molecules. When the first oxygen molecule binds to hemoglobin, it becomes easier for additional oxygen molecules to bind. What is this phenomenon called?",{"kind":1548,"accept":2394},[2395,2396,2397,2398,2399],"cooperative binding","cooperativity","positive cooperativity","co-operative binding","heme-heme interaction",[2401,2402,2403],"The prefix 'co-' means together or joint.","Think about how the binding events work together.","This is a well-known property of hemoglobin's quaternary structure.","This phenomenon is called **cooperative binding** (also known as **cooperativity** or **positive cooperativity**).\n\nHemoglobin has four polypeptide chains, each with one heme group containing an iron atom that can bind one oxygen molecule. When the first oxygen molecule binds to one subunit, it causes a **conformational change** in the hemoglobin protein. This change makes it easier for oxygen to bind to the remaining subunits.\n\nThis cooperativity is crucial for efficient oxygen transport:\n- In the lungs (high oxygen), hemoglobin quickly becomes saturated with oxygen\n- In tissues (low oxygen), the reverse happens: as one oxygen leaves, it becomes easier for others to leave, releasing oxygen where it's needed\n\nThis gives the oxygen-hemoglobin dissociation curve its characteristic **sigmoid (S) shape**.",[2406,2407,2013],"Hemoglobin structure","Cooperative binding",{"id":2409,"section":1512,"level":2314,"prompt":2410,"check":2411,"hints":2412,"solution":2416,"skills":2417},"respiratory-system.q050","**Boyle's Law and Breathing**\n\nBoyle's Law states that pressure and volume are inversely related (P₁V₁ = P₂V₂). If the volume of the chest cavity increases by 20% during inhalation, by what percentage does the pressure inside the lungs decrease? Express your answer as a percentage rounded to the nearest whole number.",{"kind":1599,"answer":786,"tolerance":14,"unit":2261},[2413,2414,2415],"If V₂ = 1.2 × V₁ (20% increase), use Boyle's Law to find P₂.","P₁V₁ = P₂V₂, so P₂ = P₁V₁\u002FV₂ = P₁\u002F1.2","Calculate the percentage decrease: (P₁ - P₂)\u002FP₁ × 100","Using Boyle's Law: P₁V₁ = P₂V₂\n\nIf the volume increases by 20%:\n- V₂ = 1.2 × V₁\n\nSolving for the new pressure:\n- P₂ = P₁V₁\u002FV₂ = P₁V₁\u002F(1.2V₁) = P₁\u002F1.2 = 0.833... × P₁\n\nThe pressure decreases to about 83.3% of its original value.\n\nPercentage decrease:\n- (P₁ - P₂)\u002FP₁ × 100 = (P₁ - 0.833P₁)\u002FP₁ × 100 = 0.166... × 100 = **16.67%**\n\nRounded to the nearest whole number: **17%**\n\nThis pressure drop below atmospheric pressure is what draws air into the lungs.",[2418,2419,2420],"Boyle's Law application","Pressure-volume relationships","Physics of breathing",{"id":2422,"section":1512,"level":2314,"prompt":2423,"check":2424,"hints":2435,"solution":2439,"skills":2440},"respiratory-system.q051","**Respiratory Adaptations**\n\nCompare the respiratory systems of a fish and a human. Fish use **counter-current exchange** in their gills. Why is this more efficient than a parallel-flow (concurrent) system for extracting oxygen from water?",{"kind":1521,"options":2425,"correct":2434},[2426,2428,2430,2432],{"id":1524,"label":2427},"Counter-current exchange maintains a concentration gradient along the entire length of the exchange surface",{"id":1527,"label":2429},"Counter-current exchange actively pumps oxygen using ATP, while concurrent exchange is passive",{"id":1530,"label":2431},"Counter-current exchange allows blood and water to flow in the same direction, preventing mixing",{"id":1533,"label":2433},"Counter-current exchange increases blood pressure, forcing more oxygen into the blood",[1524],[2436,2437,2438],"In counter-current exchange, blood and water flow in opposite directions.","Think about what happens to the concentration gradient in each system.","With parallel flow, both fluids eventually reach the same concentration.","In **counter-current exchange**, water and blood flow in **opposite directions** through the gill lamellae. This creates several advantages:\n\n- Blood with the **lowest** oxygen concentration meets water with the **lowest** oxygen concentration (but still higher than the blood)\n- Blood with the **highest** oxygen concentration meets water with the **highest** oxygen concentration\n\nThis means a **concentration gradient is maintained along the entire exchange surface**, allowing efficient diffusion throughout.\n\nIn a **concurrent (parallel-flow)** system:\n- Blood and water flow in the **same direction**\n- Both fluids would eventually reach **equilibrium** at some intermediate concentration\n- No gradient exists at that point, so extraction stops\n\nFish can extract up to **80-90%** of oxygen from water using counter-current exchange, which is essential because water contains much less dissolved oxygen than air. The correct answer is **a**.",[2441,2442,2443],"Counter-current exchange","Gill structure","Adaptation comparison",{"id":2445,"section":1512,"level":2314,"prompt":2446,"check":2447,"hints":2458,"solution":2462,"skills":2463},"respiratory-system.q052","**The Respirometer Investigation**\n\nIn a school experiment, a respirometer containing germinating seeds was placed in a water bath at 25°C. The experiment measured oxygen consumption. If the temperature was increased to 35°C, how would this affect the rate of oxygen consumption and why?",{"kind":1521,"options":2448,"correct":2457},[2449,2451,2453,2455],{"id":1524,"label":2450},"Oxygen consumption would increase because enzymes involved in respiration work faster at higher temperatures",{"id":1527,"label":2452},"Oxygen consumption would decrease because heat destroys oxygen molecules",{"id":1530,"label":2454},"Oxygen consumption would stay the same because plants only respire in the dark",{"id":1533,"label":2456},"Oxygen consumption would decrease because higher temperature reduces enzyme efficiency",[1524],[2459,2460,2461],"Germinating seeds are actively growing and need energy.","Respiration involves many enzyme-controlled reactions.","How do enzymes generally respond to moderate temperature increases?","Oxygen consumption would **increase** because enzymes involved in respiration work faster at higher temperatures.\n\nGerminating seeds have high metabolic activity — they need ATP to fuel cell division, enzyme synthesis, and growth. Respiration (both aerobic and anaerobic) involves many **enzyme-controlled reactions**, including those in glycolysis, the Krebs cycle, and the electron transport chain.\n\nAs temperature increases from 25°C to 35°C:\n- Enzyme molecules gain more kinetic energy\n- More frequent successful collisions between enzymes and substrates occur\n- The rate of reaction increases, following the **Q₁₀ rule** (rate roughly doubles for every 10°C rise)\n\nImportant caveat: this only works up to an **optimum temperature**. Above ~40-50°C, enzymes begin to **denature**, and respiration would decrease. At 35°C, we are still generally below the denaturation point for most plant enzymes. The correct answer is **a**.",[2464,2465,2466],"Enzyme kinetics","Temperature effects","Respirometer experiments",[2468],"body-systems-britannica-respiratory","needs_review",{"generatedBy":2471,"notes":2472},"claude-code","generated from work item wi-f42f673c","ffb6fcac56df86cb9a8891a833e024af2e0c4b8a00284e6c9efba0df454cd56d",{},"generation-3f054396-36ff-42a6-9319-129b1e8ff565"]