Substitution into Expressions and Formulae
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Substitution into Expressions and Formulae — Free MYP3 Mathematics Practice Questions

1QuestionUsing Substitution in Real-World FormulaeConcept Practice
2 marks~3 minCriterion A
A rectangle has a length of 8 cm and a width of 5 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.

Calculate the perimeter of the rectangle. [2]
Question diagram

Solutions

2QuestionEvaluating Algebraic Formulas with Given ValuesAssessment Practice
8 marks~12 minCriterion D
A civil engineer uses the formula V=lwhV = lwh to calculate the volume of concrete needed for a rectangular foundation slab, where ll is length, ww is width, and hh is height. The design dimensions are l=12.0l = 12.0 m, w=8.0w = 8.0 m, and h=0.50h = 0.50 m. Each dimension has a tolerance of ±5%\pm 5\%. Concrete costs 120 dollars per cubic metre.
a
Calculate the design volume of concrete needed. [2]
b
Calculate the minimum and maximum possible volumes of concrete, taking into account the ±5%\pm 5\% tolerance on each dimension. Show your working. [3]
c
Analyse how the volume uncertainty affects the cost of the concrete and explain one limitation of modelling the foundation slab as a rectangular prism. [3]
Question diagram

Solutions

3QuestionEvaluating Algebraic Formulas with Given ValuesConcept Practice
2 marks~3 minCriterion B
A square has side length ss cm and perimeter PP cm.

ss (cm)1234
PP (cm)481216
a
Write a formula for PP in terms of ss. [1]
b
Calculate the perimeter when s=5s = 5 cm and when s=10s = 10 cm. [1]

Solutions

4QuestionSubstituting Values into Simple ExpressionsAssessment Practice
2 marks~3 minCriterion C
A fruit seller charges 3 dollars per kilogram of apples plus a fixed delivery fee of 2 dollars. Let cc represent the total cost in dollars and kk represent the number of kilograms of apples.
a
Write an expression for cc in terms of kk. [1]
b
Describe what the term 3k3k and the constant 22 each represent in your expression. [1]

Solutions

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