Robinson Tuition
Year 9 · Key Stage 3 · free KS3 maths worksheet

Substitution and simultaneous equations

14 original questions, 47 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1

F = 5v + 20

  1. Work out the value of F when v = 6.
  2. Work out the value of v when F = 95.
4 marks
Show answer
a) 50 b) 15
2

The area of a trapezium is given by the formula

A = 12(a + b)h

  1. Work out A when a = 5, b = 9 and h = 4
  2. Work out h when A = 42, a = 5 and b = 9
3 marks
Show answer
a) 28 b) 6
3

v = u + at

  1. Work out the value of v when u = 7, a = 9.8 and t = 5.
  2. Work out the value of t when v = 87, u = 12 and a = 5.
4 marks
Show answer
a) 56 b) 15
4

Make x the subject of the formula

y = 2x + 9

2 marks
Show answer
x = y - 92
5

Make k the subject of the formula

m = k5 - 2

2 marks
Show answer
k = 5(m + 2)
6
  1. Make r the subject of  C = 2πr
  2. Make b the subject of  P = 2(a + b)
  3. Make x the subject of  y = x + 43
3 marks
Show answer
a) r = C/(2π) b) b = P/2 - a c) x = 3y - 4
7

Solve the simultaneous equations

x + y = 11

x - y = 3

3 marks
Show answer
x = 7, y = 4
8

Solve the simultaneous equations

2x + 3y = 12

2x + y = 8

3 marks
Show answer
x = 3, y = 2
9

At the school tuck shop:

2 cookies and 1 drink cost £2.30
1 cookie and 1 drink cost £1.60

Work out the cost of one cookie and the cost of one drink.

3 marks
Show answer
cookie 70p, drink 90p
10

Solve the simultaneous equations

3x + 2y = 16
x + y = 6

3 marks
Show answer
x = 4, y = 2
11

Assume a ≠ b.

Make x the subject of

ax = bx + c

3 marks
Show answer
x = ca-b

Extension questions: beyond the core Year 9 objectives, for pupils who want a stretch.

12
  1. Make t the subject of  3t + a = bt − 5
  2. Make x the subject of  y = 2x + 1x − 3
5 marks
Show answer
a) t = (a + 5)/(b - 3) or t = (-5 - a)/(3 - b) b) x = (3y + 1)/(y - 2)
13

Solve the simultaneous equations

3x + 2y = 24

2x + 5y = 27

4 marks
Show answer
x = 6, y = 3

Extension questions: beyond the core Year 9 objectives, for pupils who want a stretch.

14

A theme park sells adult tickets and child tickets.

3 adult tickets and 2 child tickets cost £40
2 adult tickets and 5 child tickets cost £45

Mr Okafor buys 2 adult tickets and 3 child tickets. He pays with a £50 note.

Work out how much change he should get.

5 marks
Show answer
£15

Your score

Answer the questions above and your score appears here.

Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

All Year 9 topics