Revision Library

revisionlibrary.co.uk

KS3 · Algebra

KS3.M-A10 Solving One and Two Step Equations

AQA KS3.M-A10 · Calculators not allowed · about 50 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Solve the equations. Write your answer for each part.

(a)x + 5 = 12(1)

(b)y - 3 = 4(1)

(d)b/4 = 3(1)

Solve the equation 8 + x = 11 and check your answer by substitution.

(2)

Solve the equation 3x + 7 = 22. Show the steps.

(2)

Solve the two-step equation. Show your working.

(a)3x + 4 = 19(3)

Solve the equation 5k + 9 = -1. Show each step.

(3)

Solve each equation. Show each step.

(a)4p - 6 = 10(2)

(b)7 = 2m + 1(2)

Solve the equation -2x - 8 = -14. Show your working.

(3)

Solve the equation -2t - 5 = 4. Show the steps and give your answer as a fraction or decimal.

(3)

Solve the equation (1/3) x = 3. Give your answer as an integer.

(2)

Solve the equation (1/4)k = 10. Give your answer as an integer.

(2)

Solve the equation (2/5)b + 2 = 7. Give your answer as a fraction or mixed number where appropriate.

(3)

Solve the equation 3/4 x - 1 = 5. Give your answer as a fraction or integer.

(2)

Solve the equation 5 - 2y = 11. Show your steps.

(2)

Solve the equation 6 + 1.5x = 12. Show your working and give your answer as a decimal.

(3)

Solve the two-step equation and check by substitution: 2(3 + n) = 14.

(2)

Mark scheme · KS3.M-A10 Solving One and Two Step Equations

Question 1

(a) B1 x = 7 cao
(a) Answer: 7
(b) B1 y = 7 cao
(b) Answer: 7
(c) B1 a = 5 cao
(c) Answer: 5
(d) B1 b = 12 cao
(d) Answer: 12

Question 2

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

Question 3

M1 subtract 7 from both sides or show 3x = 15
A1 x = 5 cao
Answer: 5

Question 4

(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 5

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 6

(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 7

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 8

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 9

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

Question 10

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

Question 11

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 12

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

Question 13

M1 subtract 5 from both sides to give -2y = 6
A1 y = -3 cao
Answer: -3

Question 14

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 15

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

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