Simplifying and Rearranging Expressions
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Simplifying and Rearranging Expressions — Free MYP1 Mathematics Practice Questions

1QuestionCombining Like TermsConcept Practice
2 marks~3 minCriterion A
A rectangle has side lengths of (2x+3)(2x + 3) cm and (x+5)(x + 5) cm. Its perimeter is 40 cm.

Using P=2(length+width)P = 2(\text{length} + \text{width}), calculate the value of xx. [2]
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Solutions

2QuestionUsing the Distributive PropertyAssessment Practice
5 marks~8 minCriterion C
A garden has two sections side by side, both with a width of 3 m. One section is 4 m long and the other is xx m long.
a
Identify the expression that shows the total area of the garden as a single multiplication. [1]
b
Calculate the total area of the garden when x=5x = 5, using both expressions below. Show your working.

3(4+x)and3×4+3×x3(4 + x) \qquad \text{and} \qquad 3 \times 4 + 3 \times x [2]
c
Describe one way in which the expression 3(4+x)3(4 + x) and the expression 3×4+3×x3 \times 4 + 3 \times x are the same and one way in which they are different. [2]

Solutions

3QuestionCombining Like TermsConcept Practice
2 marks~3 minCriterion B
The diagram shows a row of squares growing one square at a time.

Shape 1 has 1 square. Shape 2 has 2 squares. Shape 3 has 3 squares.
a
Identify how many squares Shape 4 has. [1]
b
Describe, in one sentence, how the number of squares changes each time the shape number goes up by one. [1]
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Solutions

4QuestionUsing the Distributive PropertyAssessment Practice
6 marks~9 minCriterion D
A rectangular garden bed has a length of (x+3)(x + 3) metres and a width of (x+2)(x + 2) metres, where xx is a whole number.
a
Name the expression for the area of the garden bed. [1]
b
Calculate the area when x=4x = 4. Show your working. [2]
c
A friend says: "This formula will always give the exact area of any real garden."

Describe one reason why this might not be true, and give an example of a garden feature that would cause a problem. [3]
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Solutions

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