Solve the equation 6 + x = 13 and check your answer by substitution.
(2)
6
Solve the equation 4x + 5 = 25. Show the steps.
(2)
7
Solve the two-step equation. Show your working. 2x + 9 = 17
(2)
8
Solve the equation 7k - 4 = 24. Show each step.
(2)
9
Solve each equation. Show each step. 9 = 3m + 3
(2)
10
Solve the equation -3x - 5 = 10. Show your working.
(2)
11
Solve the equation -4t - 7 = 5. Show the steps and give your answer as an integer.
(2)
12
Solve (1/2)x = 6. Give your answer as an integer.
(1)
13
Solve (1/5)k = 4. Give your answer as an integer.
(1)
14
Solve the equation (3/5)b + 1 = 7. Give your answer as an integer.
(2)
15
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)
16
A plumber charges a call-out fee of 20 pounds plus 15 pounds per hour worked. The total charge for a job was 95 pounds. Form an equation for the number of hours, h, worked and solve it.
(3)
17
Three times a number is subtracted from 40, giving a result of 7. Form an equation for the number, n, and solve it.
(3)
18
A rectangle has width x cm. Its length is 4 cm more than its width. The perimeter of the rectangle is 36 cm. Form an equation in x and solve it to find the width.
(3)
19
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)
20
Solve the equation 2(x - 3) = 8, giving your answer as an integer. Then check your solution by substitution.
(3)
Mark scheme · KS3.M-A10D Solving One and Two Step Equations: Fluency and Exam Drill
Question 1
B1 x = 5 cao
Answer: x = 5
Question 2
B1 y = 8 cao
Answer: y = 8
Question 3
B1 a = 7 cao
Answer: a = 7
Question 4
B1 b = 20 cao
Answer: b = 20
Question 5
M1 correct rearrangement, x = 13 - 6
A1 x = 7 cao
Answer: x = 7
Question 6
M1 correct first step, e.g. 4x = 20
A1 x = 5 cao
Answer: x = 5
Question 7
M1 correct first step, e.g. 2x = 8
A1 x = 4 cao
Answer: x = 4
Question 8
M1 correct first step, e.g. 7k = 28
A1 k = 4 cao
Answer: k = 4
Question 9
M1 correct first step, e.g. 3m = 6
A1 m = 2 cao
Answer: m = 2
Question 10
M1 correct first step, e.g. -3x = 15
A1 x = -5 cao
Answer: x = -5
Question 11
M1 correct first step, e.g. -4t = 12
A1 t = -3 cao
Answer: t = -3
Question 12
B1 x = 12 cao
Answer: x = 12
Question 13
B1 k = 20 cao
Answer: k = 20
Question 14
M1 correct first step, e.g. (3/5)b = 6
A1 b = 10 cao
Answer: b = 10
Question 15
M1 forms 2x + 9 = 31
M1 correct rearrangement, e.g. 2x = 22
A1 x = 11 cao
Answer: x = 11
Question 16
M1 forms 15h + 20 = 95
M1 correct rearrangement, e.g. 15h = 75
A1 h = 5 cao
Answer: h = 5
Question 17
M1 forms 40 - 3n = 7
M1 correct rearrangement, e.g. 3n = 33
A1 n = 11 cao
Answer: n = 11
Question 18
M1 forms 4x + 8 = 36 or equivalent from 2(x + x + 4)