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Building and Solving Equations from Word Problems — Free MYP3 Mathematics Practice Questions
1QuestionChecking Solutions in the Context of the ProblemConcept Practice
2 marks~3 minCriterion A
A rectangle has side lengths of cm and cm. Its perimeter is 46 cm.
a
Calculate the value of . [1]
b
Justify whether your value of gives valid side lengths for this rectangle. [1]
Solutions
2QuestionChecking Solutions in the Context of the ProblemAssessment Practice
4 marks~6 minCriterion D
A school bake sale has a fixed booth fee of 30 dollars and a cost of 2 dollars per cupcake. The total cost (in dollars) for making cupcakes is . Each cupcake sells for 5 dollars.
a
Write an equation for the value of that gives a profit of exactly 100 dollars. [1]
b
Calculate the value of . [1]
c
Analyse whether your answer to part (b) is reasonable for this situation. Support your reasoning with calculations. [2]
Solutions
3QuestionSolving Problems Involving Age and TimeConcept Practice
2 marks~3 minCriterion B
Tom is 10 years old, Anna is 6 years old, and Sam is 4 years old.
a
Complete the table of ages.
Today — Tom: 10, Anna: 6, Sam: 4
In 2 years — Tom: ___, Anna: ___, Sam: ___
In 5 years — Tom: ___, Anna: ___, Sam: ___ [1]
Today — Tom: 10, Anna: 6, Sam: 4
In 2 years — Tom: ___, Anna: ___, Sam: ___
In 5 years — Tom: ___, Anna: ___, Sam: ___ [1]
b
Using your completed table, explain whether the age difference between Tom and Anna changes over time, and state the general rule about age differences. [1]
Solutions
4QuestionTranslating Word Problems into EquationsAssessment Practice
6 marks~9 minCriterion C
A basketball court charges 5 dollars for the first hour and 8 dollars for each additional hour. A student models the total cost for hours with the equation , which incorrectly includes a flat booking fee of 20 dollars.
a
Calculate the number of hours given by the student's model when the total cost is 110 dollars. [1]
b
Write the correct piecewise function for the actual total cost of hours, where . [2]
c
Explain why the student's single linear equation does not accurately represent the actual pricing structure, using values from both models to support your answer. [3]
Solutions
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