Free IB MYP Practice Questions | RevisionPrep

Literal Equations and Rearranging Formulae — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionRearranging to Make a Variable the SubjectConcept Practice

2 marks~3 minCriterion A

A landscape architect is designing a triangular garden bed. The area formula for a triangle is

A = \frac{1}{2}bh

where

b

is the base length and

h

is the perpendicular height.

The garden bed has a base of

b = 8

m and must cover an area of

A = 24

^2

.

Rearrange the formula to make

h

the subject, then calculate the height of the garden bed. [2]

Solutions

2QuestionApplications in Geometry and Physics FormulasAssessment Practice

4 marks~6 minCriterion C

A photographer uses a thin lens with a focal length of

f = 50

mm. The lens formula

\frac{1}{f} = \frac{1}{u} + \frac{1}{v}

relates object distance

u

and image distance

v

Show that

v = \dfrac{uf}{u - f}

. [1]

An object is placed at

u = 200

mm from the lens. Calculate the image distance

v

. [1]

A sharp image requires

v

to fall within 2 mm of the calculated value. Assess whether the thin-lens model is reliable enough to guarantee this precision for a professional camera lens, justifying your answer with two distinct physical limitations of the model. [2]

Solutions

3QuestionApplications in Geometry and Physics FormulasAssessment Practice

6 marks~9 minCriterion D

A civil engineer is designing a crash barrier for a highway. The barrier must stop a test vehicle of mass 1500 kg traveling at 20 m/s within a stopping distance such that the average force on the vehicle does not exceed 50 kN. The work-energy principle states that the work done by the stopping force equals the change in kinetic energy: $F \cdot d = \frac{1}{2}mv^2$ , where $F$ is the average force, $d$ is the stopping distance, $m$ is the mass, and $v$ is the speed.

Rearrange the formula

F \cdot d = \frac{1}{2}mv^2

to express

d

in terms of

F

m

, and

v

Using the given values, calculate the minimum stopping distance required so that the average force does not exceed 50 kN.

Suppose the actual mass of the test vehicle could be up to 5% higher than stated (i.e., 1575 kg). Evaluate how this measurement error affects the calculated stopping distance. Specifically, calculate the new stopping distance if the mass is 1575 kg and comment on the impact on the safety margin.

The work-energy model assumes constant deceleration (i.e., constant force throughout the stopping process). Discuss one real-world limitation of this assumption and explain how it could affect the actual safety of the barrier. In your response, evaluate whether the model is still useful for engineering design despite this limitation.

Solutions

4QuestionApplications in Geometry and Physics FormulasAssessment Practice

4 marks~6 minCriterion B

A construction team is checking whether a triangular brace is truly right-angled before installing it. They measure the three sides as 2.5 m, 6 m, and 6.5 m.

Before applying this to the brace, investigate the relationship between side lengths in right triangles using the four Pythagorean triples below.

Triangle 1:

(3, 4, 5)

— Triangle 2:

(5, 12, 13)

— Triangle 3:

(6, 8, 10)

— Triangle 4:

(7, 24, 25)

For each triangle, calculate the sum of the squares of the two shorter sides and the square of the longest side. [1]

Deduce a general equation relating the three side lengths of any right triangle. [1]

Using your equation from (b), advise the construction team whether the brace with sides 2.5 m, 6 m, and 6.5 m should be approved for installation, justifying your answer with full working. [2]

Solutions

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