Algebraic Patterns and Expressions
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Algebraic Patterns and Expressions — Free MYP3 Mathematics Practice Questions

1QuestionEvaluating Expressions Derived from PatternsConcept Practice
2 marks~3 minCriterion A
A square has a side length of (2n+1)(2n + 1) cm.

Calculate the perimeter of the square when n=3n = 3. [2]
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Solutions

2QuestionCreating Expressions from PatternsAssessment Practice
2 marks~3 minCriterion D
At a party with nn attendees, each person shakes hands with every other person exactly once. The total number of handshakes is given by

n(n−1)2\frac{n(n-1)}{2}

For a party of 1000 attendees, explain one reason why this formula may not reflect the actual number of handshakes that take place. [2]
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Solutions

3QuestionCreating Expressions from PatternsConcept Practice
2 marks~3 minCriterion B
The diagrams show a sequence of square grids.

Grid 11×11 \times 1containing 11 unit square.
Grid 22×22 \times 2containing 44 unit squares.
Grid 33×33 \times 3containing 99 unit squares.
a
State the number of unit squares in the 4th grid. [1]
b
Write an expression for the total number of unit squares in the nnth grid. [1]
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Solutions

4QuestionUsing Letters to Represent NumbersAssessment Practice
4 marks~6 minCriterion C
A school fair charges a base entry fee of 5 dollars. Game tokens cost 2.50 dollars each. Tickets bought in advance receive a 10% discount on the total cost.

A student models the total ticket cost as

C=5+2nC = 5 + 2n

where nn is the number of game tokens purchased.
a
Identify one difference between the student's model and the actual pricing. [1]
b
Explain how this difference affects the cost calculated by the model compared to the actual cost. [1]
c
Write an improved equation for CC that correctly reflects the actual token price and the advance-purchase discount. Justify why your equation is a more accurate model. [2]
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Solutions

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