Formulas in Real-World Contexts

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Formulas in Real-World Contexts — Free MYP3 Mathematics Practice Questions

1QuestionApplying the Speed Distance Time FormulaConcept Practice

2 marks~3 minCriterion A

A car travels at a constant speed of

75

km/h for

3

hours.

\text{Distance} = \text{Speed} \times \text{Time}

Calculate the total distance travelled by the car. [2]

Solutions

2QuestionUsing Volume and Surface Area FormulasAssessment Practice

3 marks~5 minCriterion B

The table below shows the volume

V

(in cm³) of a cube with side length

s

(in cm).

$s$ (cm)	1	2	3	4
$V$ (cm³)	1	8	27	64

These points are plotted on a graph with a smooth curve connecting them.

Apply the formula

V = s^3

to calculate the volume of a cube with side length

s = 5

cm. [1]

Explain why the graph of

V = s^3

is a curve and not a straight line. [1]

The increases in volume between consecutive values of

s

in the table are 7, 19, and 37. Analyse what these increasing differences tell you about the rate at which volume grows as side length increases. [1]

Solutions

3QuestionUsing the Formula for Area of ShapesAssessment Practice

5 marks~8 minCriterion C

A gardener designs an L-shaped flower bed made from two rectangles. The left rectangle measures

3 \text{ m} \times 5 \text{ m}

and the right rectangle measures

4 \text{ m} \times 2 \text{ m}

. Their top edges are aligned.

Describe how dividing the L-shape into two rectangles allows you to find the total area. [1]

Calculate the area of each rectangle and the total area of the flower bed. [2]

A second flower bed is a single rectangle measuring

7 \text{ m} \times 5 \text{ m}

. The gardener says the L-shaped bed uses less than half the area of the rectangular bed. Justify whether the gardener is correct. [2]

Solutions

4QuestionApplying the Speed Distance Time FormulaAssessment Practice

6 marks~9 minCriterion D

A delivery company uses the formula

\text{Time} = \frac{\text{Distance}}{\text{Speed}}

to schedule drivers in a city. Driver A travels 120 km, Driver B travels 90 km, and Driver C travels 60 km. All three drive at an average speed of 60 km/h through city routes with traffic lights, speed bumps, and variable traffic.

Calculate the theoretical time, in hours, for each driver. [2]

Explain why the constant-speed assumption is unrealistic for city driving. Give two specific examples from the scenario. [2]

A manager notices that Driver A consistently arrives 30 minutes later than the formula predicts. Calculate Driver A's actual average speed, then analyse what this tells you about the reliability of the formula for scheduling. [2]

Solutions

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