Literal Equations and Rearranging Formulae

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Literal Equations and Rearranging Formulae — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionRearranging with Fractions and BracketsAssessment Practice

2 marks~3 minCriterion A

A surveyor models a triangular plot of land. The three sides measure

a = 5

b = 7

m, and

c = 6

m, where angle

\theta

is opposite side

c

. The cosine rule states:

c^2 = a^2 + b^2 - 2ab\cos\theta

Rearrange the cosine rule to make

\cos\theta

the subject. [1]

Calculate

\theta

and hence justify whether the triangular plot contains any obtuse angle. [1]

Solutions

2QuestionCommon Mistakes in RearrangingAssessment Practice

2 marks~3 minCriterion C

A landscape architect is designing a triangular garden bed. The area must be exactly

30\ \text{m}^2

and the base measures

6\ \text{m}

.

To find the required height

h

, a student rearranges

A = \frac{1}{2}bh

and writes:

h = \frac{1}{2} \times 30 \times 6

Identify the error in the student's rearrangement. [1]

Deduce the correct value of

h

. [1]

Solutions

3QuestionApplications in Geometry and Physics FormulasAssessment Practice

4 marks~6 minCriterion D

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

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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