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Number and shape patterns · question bank

Number and shape patterns: question bank

Practise every skill in this topic: repeating patterns and remainders, continuing sequences, finding rules with differences and ratios, arithmetic and geometric sequences, square, cube, triangular and Fibonacci numbers, digit patterns, matchstick and dot patterns, nth-term rules, and puzzles from Gauss’s trick to patterns that break. Questions go from foundation to challenge, and every one has a full worked solution. Keep a pencil handy: drawing the first few cases often cracks a problem.

Foundation 15Core 33Stretch 24Challenge 9

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All 81 questions

Showing 15 of 81 matching questions.

Q1

FoundationRepeating patterns

What is the repeating unit of this pattern? sun, moon, star, sun, moon, star, sun, moon, star

Q2

FoundationRepeating patterns

A necklace repeats the beads red, blue, blue, red, blue, blue, …. What colour is the 17th bead?

Q3

CoreRepeating patterns

A kolam border repeats four motifs: loop, dot, loop, line. How many loops are there in the first 30 motifs?

Q4

CoreRepeating patterns

Bangles are stacked in the pattern 2 red, then 3 gold, again and again. What colour is the 23rd bangle?

Q5

StretchRepeating patterns

The word INDIA is written again and again with no spaces: INDIAINDIAINDIA… What is the 2,026th letter?

Q6

StretchRepeating patterns

A traffic signal shows green for 45 seconds, amber for 5 seconds, red for 40 seconds, and then repeats. It turns green at 0 seconds. What colour is it at 200 seconds?

Q7

FoundationWhat comes next?

What is the next term? 12, 17, 22, 27, …

Q8

FoundationWhat comes next?

What is the next term? 90, 81, 72, …

Q9

FoundationWhat comes next?

What is the next term? 1, 2, 4, 8, …

Q10

FoundationWhat comes next?

What is the next term? 1, 4, 9, 16, 25, …

Q11

CoreWhat comes next?

What is the next term? 1, 3, 6, 10, 15, …

Q12

CoreWhat comes next?

What is the next term? 2, 5, 4, 7, 6, 9, …

Q13

CoreWhat comes next?

What is the next term? 3, 5, 8, 13, 21, …

Q14

StretchWhat comes next?

What is the next term? 2, 6, 12, 20, 30, …

Q15

FoundationFinding the rule

Which rule makes the sequence 5, 10, 15, 20, 25, …?

Stuck? The lessons explain every idea these questions use.