Using and Manipulating Formulae
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Using and Manipulating Formulae — Free MYP2 Mathematics Practice Questions

1QuestionCreating Formulae from Contextual SituationsConcept Practice
2 marks~3 minCriterion A
The diagram shows a rectangle with side lengths x+3x + 3 and xx.
a
Write an expression for the perimeter of the rectangle in terms of xx. [1]
b
Calculate the perimeter when x=4x = 4. [1]
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2QuestionSolving Problems Involving Real-Life FormulaeAssessment Practice
5 marks~8 minCriterion D
A car's fuel use (in litres) is modelled by the formula

F=d×0.08F = d \times 0.08

where dd is the distance driven in kilometres. The fuel tank holds 60 litres.
a
Calculate the fuel needed for a 350 km highway trip. [1]
b
Explain why the model may underestimate fuel use during stop-and-go city driving. Identify one assumption the model makes and describe how city driving breaks that assumption. [2]
c
A driver completes a 350 km trip: half on the highway and half in the city. Compare the fuel predicted by the original model with the fuel predicted by the improved model F=(dcity×0.12)+(dhighway×0.08)F = (d_{\text{city}} \times 0.12) + (d_{\text{highway}} \times 0.08), and state which gives the higher estimate. [2]
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3QuestionSolving Problems Involving Real-Life FormulaeAssessment Practice
6 marks~9 minCriterion B
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
The length and width of a rectangle sum to 10 cm. Calculate the perimeter when l=3l = 3 cm and when l=7l = 7 cm. [2]
b
Describe what you notice about the perimeters in part (a). State a general rule linking the perimeter to any fixed sum SS of length and width. [2]
c
A second rectangle has l+w=15l + w = 15 cm. Using your rule, compare the perimeter of this rectangle with that of a rectangle where l+w=10l + w = 10 cm. Explain which is larger and by how much. [2]
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4QuestionUsing Standard Formulae Area Volume SpeedAssessment Practice
6 marks~9 minCriterion C
A rectangular prism has a length of 12 cm, a width of 8 cm, and a height of 10 cm. A cylindrical hole (a circular tunnel) with a radius of 3 cm is drilled vertically through the prism from top to bottom.

Use V=l×w×hV = l \times w \times h and V=πr2hV = \pi r^2 h, where π≈3.14\pi \approx 3.14.
a
State the volume of the rectangular prism. [1]
b
Calculate the volume of the cylindrical hole. [2]
c
A student says the remaining solid has a volume of about 700 cm³. Calculate the correct remaining volume, rounded to the nearest cm³, and explain whether the student is right or wrong. [3]
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