GCSE Maths · Higher · Chapter 8: Algebraic manipulation · Lesson 4

Changing the subject of a formula

Grades 5–8About 50 minutesNo calculator41 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
Solve $\frac{x}{6} - 4 = 1$ .
[1 mark]
Answer
A2
Last lesson
Factorise $x^{2} - 2 x - 24$ .
[1 mark]
Answer
A3
From chapter 5
Boys to girls is $3 : 5$ . There are 21 boys. How many girls?
[1 mark]
Answer
A4
From chapter 8
Expand $(x + 6)^{2}$ .
[1 mark]
Answer

Grades 5–6

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

Example 1

Make $x$ the subject of $y = 4 x - 9$ .

Hint

x

was multiplied by 4, then 9 was taken away. Undo them in reverse order.

Example 2

Make $r$ the subject of $A = 3 r^{2} - 4$ .

Hint Get

r^{2}

on its own first. The last step undoes the square with a square root.

Example 3

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

Hint Multiply both sides by

(x - 3)

, collect the

x

terms on one side, then factorise.

Grades 5–7

C3
Make $x$ the subject of $a x + 7 = b x$ .
[3 marks]
Answer
C4
$A = \frac{1}{2} (a + b) h$ . Work out $h$ when $A = 56$ , $a = 5$ and $b = 9$ .
[2 marks]
Answer
C5
Make $u$ the subject of $v^{2} = u^{2} + 2 a s$ .
[2 marks]
Answer
C6
Make $x$ the subject of $y = \frac{5}{x + 2}$ .
[2 marks]
Answer

Grades 6–8

D1
Max makes $x$ the subject of $y = 2 x + 10$ . He writes $x = \frac{y}{2} - 10$ .
Explain why Max is wrong, and write the correct formula.
[2 marks]

Grade 8 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 undo a chain of operations in reverse order.
I can undo a square with a square root.
I can collect the subject when it appears twice.

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