Simplifying and Rearranging Expressions
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Simplifying and Rearranging Expressions — Free MYP3 Mathematics Practice Questions

1QuestionCombining Like TermsConcept Practice
2 marks~3 minCriterion A
A rectangle has side lengths (2x+3)(2x + 3) cm and (x+1)(x + 1) cm.

Calculate the perimeter of the rectangle, giving your answer as a simplified expression. [2]
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Solutions

2QuestionCombining Like TermsAssessment Practice
2 marks~3 minCriterion D
A student tracks weekly spending on snacks and drinks. Chips cost 2 dollars each, candy costs 1 dollar each, juice costs 3 dollars each, and water costs 1 dollar each. Let cc represent the total number of snack items (chips and candy) purchased, and dd represent the total number of drink items (juice and water) purchased. The student writes the total cost as 2c+1c+3d+1d2c + 1c + 3d + 1d.
a
Calculate the simplified expression for the total cost by combining like terms. [1]
b
Explain one limitation of using this simplified expression to model the student's actual spending. [1]
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Solutions

3QuestionUsing the Distributive PropertyConcept Practice
2 marks~3 minCriterion B
The diagram shows three rectangles, each divided into two smaller rectangles.

Rectangle 1: width =3= 3 cm, heights xx cm and 22 cm.
Rectangle 2: width =4= 4 cm, heights xx cm and 33 cm.
Rectangle 3: width =5= 5 cm, heights xx cm and 11 cm.
a
Calculate the total area of Rectangle 1 in two different ways and show that both expressions are equal. [1]
b
State the general rule shown by this pattern in the form a(b+c)=…a(b + c) = \ldots [1]
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Solutions

4QuestionUsing the Distributive PropertyAssessment Practice
6 marks~9 minCriterion C
A student buys 5 identical items, each priced at xx dollars, using a coupon that gives a fixed discount of dd dollars off each item. The student writes 5(x−d)5(x - d) for the total cost.
a
Apply the distributive property to expand 5(x−d)5(x - d) and explain what each term in your result represents. [2]
b
The store instead offers a percentage discount of pp% off each item. Write an expression for the total cost of 5 items after this discount is applied. [2]
c
Compare the two models and explain whether 5(x−d)5(x - d) could still be useful when the discount is actually pp%. [2]
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Solutions

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