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Visual and Spatial Patterns — Free MYP1 Mathematics Practice Questions
1QuestionIdentifying Pattern Rules in DiagramsConcept Practice
2 marks~3 minCriterion B
The diagram shows squares made from matchsticks in a row.
1 square uses 4 matchsticks. 2 squares share a side and use 7 matchsticks. 3 squares share sides and use 10 matchsticks.
1 square uses 4 matchsticks. 2 squares share a side and use 7 matchsticks. 3 squares share sides and use 10 matchsticks.
a
Identify the number of extra matchsticks needed each time one more square is added. [1]
b
Calculate the number of matchsticks needed for 4 squares in a row. [1]
Solutions
2QuestionFractal Patterns and RepetitionConcept Practice
2 marks~3 minCriterion B
A fractal tree grows by splitting. At Stage 1 there is 1 branch. At Stage 2 there are 2 branches. At Stage 3 there are 4 branches.
a
Identify the number of branches at Stage 4. [1]
b
Describe the rule that connects the number of branches at one stage to the next. [1]
Solutions
3QuestionFractal Patterns and RepetitionConcept Practice
2 marks~3 minCriterion A
The diagram shows a Sierpinski triangle at stage 1. A large triangle with area is split into 4 equal smaller triangles by joining the midpoints of its sides. The middle triangle is then removed.
a
State the number of small triangles that remain. [1]
b
Calculate the remaining area as a fraction of the original triangle's area. Give your answer in its simplest form. [1]
Solutions
4QuestionIdentifying Pattern Rules in DiagramsConcept Practice
5 marks~8 minCriterion C
Each step in a dot pattern is shown below.
Step 1: 1 dot — Step 2: 5 dots — Step 3: 9 dots — Step 4: 13 dots
A student says the rule for the number of dots in Step is .
Step 1: 1 dot — Step 2: 5 dots — Step 3: 9 dots — Step 4: 13 dots
A student says the rule for the number of dots in Step is .
a
List the number of dots that the rule gives for Steps 1, 2, 3, and 4. [2]
b
Describe in one sentence how the number of dots changes from one step to the next. [1]
c
State whether the student's rule is correct or incorrect, and give one reason using your results from part (a). [2]
Solutions
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