Literal Equations and Rearranging Formulae

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

1QuestionCommon Mistakes in RearrangingAssessment Practice

2 marks~3 minCriterion C

A household toaster is rated at

P = 920\ \text{W}

and has a heating element with resistance

R = 28.8\ \Omega

.

A student rearranges

P = I^2 R

incorrectly, writing

I = \dfrac{1}{2}\sqrt{\dfrac{P}{R}}

, and uses this to select a wire for the toaster circuit.

Explain why this algebraic error leads to an unsafe choice of wire. [2]

Solutions

2QuestionRearranging 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

3QuestionCommon Mistakes in RearrangingAssessment Practice

4 marks~6 minCriterion D

A civil engineer uses the formula

d = \frac{v^2}{2\mu g}

to model the braking distance

d

(in metres) of a car on a wet road, where

v

is the initial speed (in m/s),

\mu

is the coefficient of friction, and

g = 9.8 \text{ m/s}^2

Show that rearranging the formula for

\mu

gives

\mu = \frac{v^2}{2dg}.

[1]

Calculate

\mu

when

d = 50

m and

v = 20

m/s. Round your answer to two decimal places. [1]

A road safety standard requires

\mu \geq 0.45

on wet roads. Using your result from part (b), advise the engineer whether this road should remain open to traffic in wet conditions, and explain one limitation of using this model to support that decision. [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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