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Solving One and Two Step Equations - Worksheets, Questions and Revision

28 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

Download PDFJump to mark scheme (page 7)Solving One and Two Step Equations revision guide

This topic is chapter 7 of KS3 Maths: Algebra Practice Book 1.

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KS3 · Algebra

2.10 Solving One and Two Step Equations

AQA KS3.M-A10 · Calculators not allowed · about 85 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Solve the equation (1/4)k = 10. Give your answer as an integer.
(2)
2
Solve the equation (2/5)b + 2 = 7. Give your answer as a fraction or mixed number where appropriate.
(3)
3
Solve the equation 3/4 x - 1 = 5. Give your answer as a fraction or integer.
(2)
4
Solve the equation 6 + 1.5x = 12. Show your working and give your answer as a decimal.
(3)
5
Solve the two-step equation and check by substitution: 2(3 + n) = 14.
(2)
6
Solve the equation 8 + x = 11 and check your answer by substitution.
(2)
7
Solve the two-step equation. Show your working.
(a)3x + 4 = 19(3)
8
Solve the equation 5k + 9 = -1. Show each step.
(3)
9
Solve each equation. Show each step.
(a)4p - 6 = 10(2)
(b)7 = 2m + 1(2)
10
Solve the equation -2x - 8 = -14. Show your working.
(3)
11
Solve the equation -2t - 5 = 4. Show the steps and give your answer as a fraction or decimal.
(3)
12
Solve the equation (1/3) x = 3. Give your answer as an integer.
(2)
13
Solve x + 9 = 14.
(1)
14
Solve the equation -4t - 7 = 5. Show the steps and give your answer as an integer.
(2)
15
Solve (1/2)x = 6. Give your answer as an integer.
(1)
16
Solve (1/5)k = 4. Give your answer as an integer.
(1)
17
Kwame thinks of a number, doubles it, then adds 9. The result is 31. Form an equation using x for Kwame's number and solve it to find x.
(3)
18
A plumber charges a call-out fee of £20 plus £15 per hour worked. The total charge for a job was £95. Form an equation for the number of hours, h, worked and solve it.
(3)
19
Three times a number is subtracted from 40, giving a result of 7. Form an equation for the number, n, and solve it.
(3)
20
Erin has 5 bags of marbles, each containing the same number of marbles, plus 3 loose marbles. She has 48 marbles in total. Form an equation and solve it to find how many marbles are in each bag.
(3)
21
Solve y - 6 = 2.
(1)
22
Solve the equation 2(x - 3) = 8, giving your answer as an integer. Then check your solution by substitution.
(3)
23
Solve 3a = 21.
(1)
24
Solve b/5 = 4.
(1)
25
Solve the equation 6 + x = 13 and check your answer by substitution.
(2)
26
Solve the equation 4x + 5 = 25. Show the steps.
(2)
27
Solve the equation 7k - 4 = 24. Show each step.
(2)
28
Solve each equation. Show each step.
9 = 3m + 3
(2)
Mark scheme · 2.10 Solving One and Two Step Equations

Question 1

  • M1 multiply both sides by 4 to clear denominator: k = 40
  • A1 k = 40 cao
  • Answer: 40

Question 2

  • M1 subtract 2 from both sides to give (2/5)b = 5
  • M1 multiply both sides by 5/2 to give b = 5 x 5/2 = 25/2
  • A1 b = 25/2 or 12 1/2 cao
  • Answer: 25/2

Question 3

  • M1 add 1 to both sides to give 3/4 x = 6
  • A1 x = 6 x 4/3 = 8 cao
  • Answer: 8

Question 4

  • M1 subtract 6 from both sides to get 1.5x = 6
  • M1 divide both sides by 1.5 to give x = 4
  • A1 x = 4 cao
  • Answer: 4

Question 5

  • M1 expand or divide by 2 first: 2(3+n)=14 gives 3+n=7
  • A1 n = 4 cao
  • Answer: 4

Question 6

  • M1 isolation of the variable, e.g. x = 11 - 8
  • A1 x = 3 cao
  • Answer: 3

Question 7

  • (a) M1 subtract 4 from both sides to give 3x = 15
  • (a) M1 divide both sides by 3 to give x = 5
  • (a) A1 x = 5 cao
  • (a) Answer: 5

Question 8

  • M1 subtract 9 from both sides or show 5k = -10
  • M1 divide both sides by 5 to give k = -2
  • A1 k = -2 cao
  • Answer: -2

Question 9

  • (a) M1 add 6 to both sides to get 4p = 16
  • (a) A1 p = 4 cao
  • (a) Answer: 4
  • (b) M1 subtract 1 to give 2m = 6
  • (b) A1 m = 3 cao
  • (b) Answer: 3

Question 10

  • M1 add 8 to both sides giving -2x = -6
  • M1 divide both sides by -2 to give x = 3
  • A1 x = 3 cao
  • Answer: 3

Question 11

  • M1 add 5 to both sides to give -2t = 9
  • M1 divide both sides by -2 to give t = -9/2
  • A1 t = -9/2 or t = -4.5 cao
  • Answer: -9/2

Question 12

  • M1 multiply both sides by 3 to give x = 9
  • A1 x = 9 cao
  • Answer: 9

Question 13

  • B1 x = 5 cao
  • Answer: x = 5

Question 14

  • M1 correct first step, e.g. -4t = 12
  • A1 t = -3 cao
  • Answer: t = -3

Question 15

  • B1 x = 12 cao
  • Answer: x = 12

Question 16

  • B1 k = 20 cao
  • Answer: k = 20

Question 17

  • M1 forms 2x + 9 = 31
  • M1 correct rearrangement, e.g. 2x = 22
  • A1 x = 11 cao
  • Answer: x = 11

Question 18

  • M1 forms 15h + 20 = 95
  • M1 correct rearrangement, e.g. 15h = 75
  • A1 h = 5 cao
  • Answer: h = 5

Question 19

  • M1 forms 40 - 3n = 7
  • M1 correct rearrangement, e.g. 3n = 33
  • A1 n = 11 cao
  • Answer: n = 11

Question 20

  • M1 forms 5x + 3 = 48
  • M1 correct rearrangement, e.g. 5x = 45
  • A1 x = 9 cao
  • Answer: x = 9

Question 21

  • B1 y = 8 cao
  • Answer: y = 8

Question 22

  • M1 expands the bracket, 2x - 6 = 8
  • M1 correct rearrangement, e.g. 2x = 14
  • A1 x = 7 cao, with check shown
  • Answer: x = 7

Question 23

  • B1 a = 7 cao
  • Answer: a = 7

Question 24

  • B1 b = 20 cao
  • Answer: b = 20

Question 25

  • M1 correct rearrangement, x = 13 - 6
  • A1 x = 7 cao
  • Answer: x = 7

Question 26

  • M1 correct first step, e.g. 4x = 20
  • A1 x = 5 cao
  • Answer: x = 5

Question 27

  • M1 correct first step, e.g. 7k = 28
  • A1 k = 4 cao
  • Answer: k = 4

Question 28

  • M1 correct first step, e.g. 3m = 6
  • A1 m = 2 cao
  • Answer: m = 2

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Question 1

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Question 2

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Question 3

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Question 4

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Question 5

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Question 7

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Question 8

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Question 9

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Question 10

3 marks

Question 11

3 marks

Question 12

2 marks

Question 13

1 mark

Question 14

2 marks

Question 15

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Question 16

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Question 17

3 marks

Question 18

3 marks

Question 19

3 marks

Question 20

3 marks

Question 21

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Question 22

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Question 23

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Question 24

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Question 25

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Question 26

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Question 27

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