Writing and Interpreting Algebraic Expressions
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Writing and Interpreting Algebraic Expressions — Free MYP3 Mathematics Practice Questions

1QuestionConstructing Expressions with BracketsConcept Practice
4 marks~6 minCriterion A
A rectangular garden has a length of (x+5)(x + 5) metres and a width of (x−2)(x - 2) metres. The owner plans to enclose the entire garden with fencing.
a
Write an expression, including brackets, for the total length of fencing required. [2]
b
Calculate the simplified form of your expression from part (a). [1]
c
The owner uses your expression to order fencing for a value of x=4x = 4. Interpret one reason why the actual fencing needed may differ from this calculated value. [1]
Question diagram

Solutions

2QuestionCreating Expressions from Situational ProblemsAssessment Practice
5 marks~8 minCriterion D
A student is designing a rectangular garden. The length is 3 m more than twice the width. To stay within the fencing budget, the perimeter must not exceed 30 m. The student writes the inequality 2(w+(2w+3))≤302(w + (2w + 3)) \leq 30.
a
Explain what the expression 2(w+(2w+3))2(w + (2w + 3)) represents in this context. [1]
b
Calculate the perimeter when w=4w = 4 m, and determine whether this width satisfies the budget constraint. [2]
c
Analyse one limitation of using this algebraic model for real-world garden planning. [2]
Question diagram

Solutions

3QuestionCreating Expressions from Situational ProblemsAssessment Practice
5 marks~8 minCriterion C
A school drama club sells tickets for a show at 8 dollars each and spends 50 dollars on advertising. A student writes the profit expression P=8x−50P = 8x - 50, where xx is the number of tickets sold.
a
Write the value of PP when no tickets are sold. Explain what this value means in context. [2]
b
Calculate the profit when 120 tickets are sold. [2]
c
The student claims that selling 80 tickets will produce twice the profit of selling 40 tickets. Analyse whether this claim is correct. [1]

Solutions

4QuestionConstructing Expressions with BracketsAssessment Practice
5 marks~8 minCriterion B
When a bracket of the form (x+n)2(x + n)^2 is expanded, a pattern emerges in the terms produced.
a
Expand each expression and complete the table below. [2]

Expression: (x+1)2(x+1)^2, (x+2)2(x+2)^2, (x+3)2(x+3)^2, (x+4)2(x+4)^2

Constant term: ___ , ___ , ___ , ___

Coefficient of xx: ___ , ___ , ___ , ___
b
Describe the relationship between nn and each of the two values you recorded in part (a). [1]
c
A student claims that (x+7)2=x2+14x+49(x + 7)^2 = x^2 + 14x + 49. Using your answer from part (b), explain whether the student is correct. [2]

Solutions

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