Using Algebra in Word Problems
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Using Algebra in Word Problems — Free MYP3 Mathematics Practice Questions

1QuestionCreating Algebraic Expressions from Word ProblemsConcept Practice
2 marks~3 minCriterion A
A rectangle has side lengths of (x+3)(x + 3) cm and (2x−1)(2x - 1) cm. The perimeter of a rectangle is given by

P=2(l+w)P = 2(l + w)

where ll is the length and ww is the width.
a
Write an expression for the perimeter PP in terms of xx. [1]
b
Calculate the perimeter when x=4x = 4. [1]
Question diagram

Solutions

2QuestionChecking Solutions for Word-Based ExpressionsAssessment Practice
4 marks~6 minCriterion D
A student models the total cost of a school bake sale using the equation C=2.50n+15C = 2.50n + 15, where nn is the number of cupcakes sold and 1515 dollars covers fixed costs such as table rental.
a
Calculate the total cost when n=10n = 10. [1]
b
Explain one assumption made by this model. [1]
c
A classmate says the model must be wrong because 40 dollars for 10 cupcakes is too expensive. Analyse whether this objection identifies a mathematical error or a real-world limitation, and justify your conclusion. [2]
Question diagram

Solutions

3QuestionChecking Solutions for Word-Based ExpressionsConcept Practice
4 marks~6 minCriterion C
A student solves the word problem "a number plus three times the number equals 20" and writes:

x+3x=20x + 3x = 20

The student claims the solution is x=5x = 5.
a
Apply the substitution x=5x = 5 into the equation x+3x=20x + 3x = 20 and calculate the value of the left-hand side. [2]
b
Justify whether x=5x = 5 is a correct solution to the equation. [2]

Solutions

4QuestionCreating Algebraic Expressions from Word ProblemsAssessment Practice
5 marks~8 minCriterion B
A tiling pattern is made of square tiles arranged in rows. The first row has 1 tile, the second row has 3 tiles, the third row has 5 tiles, and the fourth row has 7 tiles.
a
Describe the pattern in the sequence 1,3,5,7,…1, 3, 5, 7, \ldots and write an algebraic expression for the number of tiles in row nn. [2]
b
Calculate the number of tiles in the 20th row. [1]
c
A designer claims that row 50 will have more than 100 tiles. Justify whether this claim is correct. [2]

Solutions

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