KS3 Maths · Year 7 · Chapter 15: Equations and formulae · Lesson 4

Rearranging formulae

Year 7About 70 minutesNo calculator51 marks

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Date

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Quick questions to start.

A1
Needed today
$y = 4 x - 7$ . Work out $x$ when $y = 25$ .
[1 mark]
Answer
A2
Last lesson
Solve $2 t^{2} - 3 = 69$ .
[1 mark]
Answer
A3
From chapter 14
A circle has radius $5$ cm. Write down its circumference in terms of $π$ .
[1 mark]
Answer
A4
From chapter 10
Expand $3 (2 a - 5)$ .
[1 mark]
Answer

Example, then your turn

Year 7

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

Example 1

Make $x$ the subject of $y = 3 x - 7$ .

Hint Undo the steps in reverse order: first add

7

to both sides, then divide by

3

B1
Make $x$ the subject of $y = 5 x + 2$ .
[2 marks]
Answer

Example 2

Here is a formula: $c = 5 p + 2 q$ . Make $p$ the subject.

Hint Treat

2 q

like a number: take it from both sides.

B2
Here is a formula: $m = 4 a - 5 b$ . Make $a$ the subject.
[2 marks]
Answer

Example 3

Here is a formula: $P = \frac{a + b}{2}$ . Make $a$ the subject.

Hint The right-hand side is divided by

2

, so multiply both sides by

2

first.

B3
Here is a formula: $M = \frac{x - y}{3}$ . Make $x$ the subject.
[2 marks]
Answer

Example 4

Here is a formula: $A = 3 r^{2}$ . Make $r$ the subject.

Hint Get

r^{2}

on its own first. Taking the square root is the last step.

B4
Here is a formula: $T = 2 m^{2} + 9$ . Make $m$ the subject.
[3 marks]
Answer

Example 5

Here is a formula: $v = u + 6 t$ . Make $t$ the subject. Then work out $t$ when $v = 50$ and $u = 8$ .

Hint Rearrange first, then put the numbers into your new formula.

B5
Here is a formula: $P = 2 l + 2 w$ . Make $w$ the subject. Then work out $w$ when $P = 46$ and $l = 15$ .
[3 marks]
Answer

Practice

Year 7

C1
Make $x$ the subject of $y = 15 - 3 x$ .
[2 marks]
Answer
C2
The area of a trapezium is $A = \frac{( a + b ) h}{2}$ . Make $h$ the subject.
[2 marks]
Answer

C3
Make $n$ the subject of $S = 3 n^{2} - 12$ .
[3 marks]
Answer
C4
A distance of $m$ miles is about $k$ kilometres, where $k = \frac{8 m}{5}$ . Make $m$ the subject.
[2 marks]
Answer
C5
Make $y$ the subject of $3 x + 2 y = 18$ .
[2 marks]
Answer
C6
Make $x$ the subject of $y = 4 (x - 3)$ .
[2 marks]
Answer

Exam-style questions

GCSE Foundation

D1
Ben makes $u$ the subject of $v = u + 9 t$ . He writes: $u = v + 9 t$ .
Ben is wrong. Explain the mistake and write the correct formula.
[2 marks]

D2
The diagram shows an isosceles triangle. Its perimeter is $p$ cm.
Not drawn accurately
(a)
Write down a formula for $p$ in terms of $x$ .
[1 mark]
Answer
(b)
Make $x$ the subject of your formula.
[2 marks]
Answer
(c)
The perimeter is $34$ cm. Work out the value of $x$ .
[1 mark]
Answer
Total for D2: 4 marks
D3
Here are four formulae.
$A$ : $y = 2 (x + 3)$ $B$ : $x = \frac{y - 6}{2}$ $C$ : $x = \frac{y}{2} - 3$ $D$ : $x = \frac{y - 3}{2}$
Three of them say the same thing. Which one is different? Show how you decide.
[3 marks]
Answer
D4
The area of a semicircle with radius $r$ is $A = \frac{1}{2} π r^{2}$ .
(a)
Make $r$ the subject of the formula.
[2 marks]
Answer
(b)
A semicircle has area $50 π$ cm². Work out its diameter.
[2 marks]
Answer
Total for D4: 4 marks
D5
A stone is dropped from a cliff. After $t$ seconds it has fallen $d$ metres, where $d = 5 t^{2}$ .
(a)
Work out how far the stone falls in the first $3$ seconds.
[1 mark]
Answer
(b)
Make $t$ the subject of $d = 5 t^{2}$ .
[2 marks]
Answer
(c)
The stone falls $80$ m before it hits the sea. Use your answer to part (b) to work out how long it takes.
[2 marks]
Answer
(d)
$t^{2} = 16$ has two solutions. Explain why only one of them answers part (c).
[1 mark]
Total for D5: 6 marks

Extension

Stretch

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

E1
Make $x$ the subject of $p x + 5 = 2 x + q$ .
[3 marks]
Hint 1 · What to try
$x$ appears on both sides. Get both $x$ terms on the same side, as you do when solving an equation.
Hint 2 · The first line
$p x - 2 x = q - 5$
Hint 3 · The full method
$p x - 2 x$ is $x (p - 2)$ , so divide both sides by $p - 2$ : $x = \frac{q - 5}{p - 2}$ .
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can change the subject of a formula by undoing the steps in reverse order.
I can rearrange a formula with a fraction or a square in it.
I can rearrange a formula and then use it to work out a value.
I can check a new formula by putting numbers into both.

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