GCSE Maths · Higher · Chapter 24: Algebraic fractions and functions · Lesson 2

Rearranging when the subject appears twice

Grades 6–9About 50 minutesCalculator allowed38 marks

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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
Make $x$ the subject of $y = 3 x + 1$ .
[1 mark]
Answer
A2
From chapter 22
A triangle has sides 8 cm and 12 cm with $9 0^{\circ}$ between them. Find its area using $\frac{1}{2} ab sin C$ .
[1 mark]
Answer
A3
From chapter 1
Estimate $\frac{58.3 \times 4.1}{0.18}$ by rounding each number to 1 s.f.
[1 mark]
Answer
A4
Last lesson
Simplify $\frac{x ^{2} - 25}{x + 5}$ .
[1 mark]
Answer

Grades 6–8

Your teacher works through each example with you. Then try the one beside it.

Example 1

Make $x$ the subject of $p x + 7 = 3 x + q$ .

Hint Get every

x

term on one side and everything else on the other. Then take

x

out as a factor.

Example 2

Make $x$ the subject of $y = \frac{3 x + 2}{x - 5}$ .

Hint Multiply both sides by

(x - 5)

first, then expand the bracket.

Grades 6–8

C3
Make $x$ the subject of $k (x - 2) = 3 (x + k)$ .
[3 marks]
Answer
C4
Make $y$ the subject of $\frac{2}{x} + \frac{3}{y} = 1$ .
[3 marks]
Answer
C5
A solid has volume $V = π r^{2} h + 2 π r^{2}$ . Make $r$ the subject. Take $r$ to be positive.
[3 marks]
Answer

Grades 7–9

D1
Sam makes $y$ the subject of $3 y + a = b y - 5$ . He writes $y = \frac{a + 5}{b + 3}$ .
Explain the mistake Sam has made, and write down the correct answer.
[2 marks]

D2
A jug holds 200 ml of a drink that is 20% fruit juice. Ella adds $x$ ml of pure fruit juice. The percentage of fruit juice in the jug is now $c$ , where $c = \frac{100 ( 40 + x )}{200 + x}$ .
(a)
Make $x$ the subject of the formula. You must show your working.
[3 marks]
Answer
(b)
Work out how much pure fruit juice Ella must add to make a drink that is 36% fruit juice.
[2 marks]
Answer $\dots\dots$ ml
(c)
Use your formula from part (a) to explain why the drink can never be 100% fruit juice.
[1 mark]
Total for D2: 6 marks
D3
Show that making $p$ the subject of $q = \frac{2 p - 3}{5 - p}$ gives $p = \frac{5 q + 3}{q + 2}$ .
[3 marks]

Grade 9 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can collect every term with the subject on one side and factorise it out.
I can rearrange a formula with fractions, brackets, squares or roots in it.
I can use a rearranged formula and say when it has no value.

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