Visual and Spatial Patterns
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Visual and Spatial Patterns — Free MYP3 Mathematics Practice Questions

1QuestionIdentifying Pattern Rules in DiagramsConcept Practice
2 marks~3 minCriterion B
The diagrams show the first three terms of a dot pattern sequence.

Pattern 1: 11 dot
Pattern 2: 44 dots in a 2×22 \times 2 square
Pattern 3: 99 dots in a 3×33 \times 3 square
a
Describe how the number of dots changes from one pattern to the next. [1]
b
Write an algebraic expression for the number of dots in Pattern nn. [1]
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Solutions

2QuestionIdentifying Pattern Rules in DiagramsAssessment Practice
5 marks~8 minCriterion C
A student claims that the total number of dots in a square grid with side length nn is given by the formula n2+2nn^2 + 2n.

The actual dot counts are:
n=1n = 1: 1 dot, n=2n = 2: 4 dots, n=3n = 3: 9 dots, n=4n = 4: 16 dots
a
Calculate the value of n2+2nn^2 + 2n for each of n=1,2,3,4n = 1, 2, 3, 4. [2]
b
Compare your results from part (a) with the actual values above. [1]
c
The student's claim is incorrect. Identify the correct formula for the total number of dots and justify why it fits the actual values. [2]
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Solutions

3QuestionFractal Patterns and RepetitionConcept Practice
2 marks~3 minCriterion A
The diagram shows a Sierpinski triangle after 2 iterations. At iteration 0, there is 1 shaded triangle. At each iteration, every shaded triangle is divided into 4 smaller congruent triangles and the central triangle is removed, leaving 3 shaded triangles in its place.

Calculate the total number of shaded triangles after 2 iterations. [2]
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Solutions

4QuestionIdentifying Pattern Rules in DiagramsAssessment Practice
6 marks~9 minCriterion D
A construction company designs square patios using a pattern of square tiles. For a patio with side length nn tiles (where n≥2n \geq 2), the number of tiles required is:

T=n2+(n−1)2T = n^2 + (n-1)^2

The diagram below shows the first three patio sizes (side lengths 2, 3, and 4 tiles).
a
Calculate the number of tiles needed for a patio with a side length of 5 tiles. [2]
b
The company orders 5% extra tiles to cover manufacturing waste. Explain how this affects the total number of tiles ordered for the side-length-5 patio, and why the formula T=n2+(n−1)2T = n^2 + (n-1)^2 would give an inaccurate estimate for a rectangular patio. [2]
c
A customer requests a patio measuring 5 tiles by 6 tiles. The company uses the formula with n=5n = 5 to estimate the tile order. Analyse whether this estimate is sufficient, and justify one change the company should make to their method. [2]
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Solutions

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