Number Patterns and Sequences
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Number Patterns and Sequences — Free MYP2 Mathematics Practice Questions

1QuestionCreating Patterns Using RulesConcept Practice
2 marks~3 minCriterion B
A gardener plants trees in rows. The first row has 3 trees, and each row after that has 2 more trees than the row before it.
a
State a rule for the number of trees in row nn. [1]
b
Calculate the number of trees in the 5th row. [1]
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2QuestionDescribing Patterns Using Words and SymbolsAssessment Practice
6 marks~9 minCriterion C
A student predicts the number of tiles in a growing garden path using the rule n2n^2, where nn is the step number, giving 1, 4, 9, 16, … The builder's actual sequence is 1, 4, 8, 13, …
a
Calculate the student's predicted number of tiles at step 5, and the builder's actual number at step 5. [2]
b
Explain why the rule n2n^2 becomes less accurate as the step number increases. In your answer, refer to the differences between the predicted and actual values. [2]
c
Compare the rule n2n^2 with the rule Tn=n2+3n−22T_n = \dfrac{n^2 + 3n - 2}{2}, and state which better fits the builder's sequence. Show a check for one value of nn. [2]
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Solutions

3QuestionFinding the Next Term in a SequenceConcept Practice
2 marks~3 minCriterion A
A sequence of shapes follows a repeating pattern:

square, triangle, square, triangle, square, triangle, …
a
Identify the repeating unit of this pattern. [1]
b
State the 7th shape in the sequence. [1]
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Solutions

4QuestionCreating Patterns Using RulesAssessment Practice
8 marks~12 minCriterion D
A gardening club plants seeds and records how long each takes to sprout.

Depth (cm)1234
Days until sprouting121086


The club writes a rule: days=14−2×depth\text{days} = 14 - 2 \times \text{depth}
a
Calculate the predicted sprouting time for a seed planted at a depth of 2.5 cm. [2]
b
The ruler has a possible measurement error of ±0.5\pm 0.5 cm. Calculate the range of possible sprouting times for a depth of 2.5 cm. [2]
c
The club wants to use the same rule for depths greater than 5 cm. Compare the rule's prediction at 7 cm with what might actually happen, and explain one reason why the rule may no longer be reliable at that depth. [4]
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Solutions

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