Circle the letter next to the correct solution to the equation.
A) x = 6
B) x = 7
C) x = 54
D) x = 72
(Total for Question 2 is 1 mark)
3
Solve each equation.
(a)x + 14 = 20(1)
(b)x - 7 = 5(1)
(Total for Question 3 is 2 marks)
4
Solve each equation.
(a)x + 3.6 = 9.2(2)
(b)x - 4.8 = 2.5(2)
(Total for Question 4 is 4 marks)
5
Solve each equation.
(a)x - 10 = -3(2)
(b)15 - x = 22(2)
(Total for Question 5 is 4 marks)
6
Solve each equation.
(a)6x = 45(2)
(b)-5x = 35(2)
(Total for Question 6 is 4 marks)
7
The table below shows three equations. Work out the missing solution in each row.
(a)24 / x = 6(1)
(b)x / 5 = -3(1)
(c)45 / x = -9(1)
(Total for Question 7 is 3 marks)
8
Match each equation to its solution. Each solution on the right is used exactly once: -9, 4, 16, 20
(a)x + 5 = 9(1)
-9
4
16
20
(b)x - 5 = -14(1)
-9
4
16
20
(c)4x = 64(1)
-9
4
16
20
(d)x / 4 = 5(1)
-9
4
16
20
(Total for Question 8 is 4 marks)
9
A school coach trip normally costs £45 per student. After a group discount is applied, each student pays £38.
Form an equation for the discount, d, in pounds, and solve it to find d.
(Total for Question 9 is 2 marks)
10
In a 400 m relay race, Aaliyah runs a distance of L metres before passing the baton to her teammate, who then runs the remaining 250 m to finish the race.
Form an equation in terms of L and solve it to find how far Aaliyah ran.
(Total for Question 10 is 2 marks)
11
Tickets for the school fair cost £3 each.
A parent buys n tickets and spends £24 in total.
Form an equation in terms of n and solve it to find how many tickets the parent bought.
(Total for Question 11 is 2 marks)
12
Chloe is solving the equation x - 7 = 15. Her working is shown below, but her final answer is wrong.
x - 7 = 15 x = 15 - 7 x = 8
(a)Explain the mistake Chloe has made.(1)
(b)Work out the correct value of x.(1)
(Total for Question 12 is 2 marks)
13
Show that x = -4 is the solution to the equation
x + 9 = 5
(Total for Question 13 is 2 marks)
14
Solve
12x = 3
(Total for Question 14 is 2 marks)
15
Solve
6x = -0.9
(Total for Question 15 is 2 marks)
16
Solve
x / (-8) = -3.5
(Total for Question 16 is 2 marks)
17
Solve
17 - x = -6
(Total for Question 17 is 2 marks)
18
Show that x = -3.5 is the solution to the equation
2x = -7
(Total for Question 18 is 2 marks)
19
A small company's total loss for the year, L pounds, is shared equally between 5 investors.
Each investor's share of the loss is recorded as -£620 on their year-end statement.
Form an equation for L and solve it to find the company's total loss for the year.
(Total for Question 19 is 3 marks)
20
Solve
-6x = -0.3
(Total for Question 20 is 2 marks)
Mark scheme · 2.9B Solving One Step Equations (Part 2)
Question 1
(a) B1 x = 7 cao
(a) Answer: x = 7
(b) B1 x = 15 cao
(b) Answer: x = 15
(c) B1 x = 6 cao
(c) Answer: x = 6
Question 2
B1 B circled, cao
Answer: B) x = 7
Question 3
(a) B1 x = 6 cao
(a) Answer: x = 6
(b) B1 x = 12 cao
(b) Answer: x = 12
Question 4
(a) M1 3.6 subtracted from both sides oe
(a) A1 x = 5.6 cao
(a) Answer: x = 5.6
(b) M1 4.8 added to both sides oe
(b) A1 x = 7.3 cao
(b) Answer: x = 7.3
Question 5
(a) M1 10 added to both sides oe
(a) A1 x = 7 cao
(a) Answer: x = 7
(b) M1 15 subtracted from both sides oe, -x = 7 seen
(b) A1 x = -7 cao
(b) Answer: x = -7
Question 6
(a) M1 both sides divided by 6 oe
(a) A1 x = 7.5 oe cao
(a) Answer: x = 7.5
(b) M1 both sides divided by -5 oe
(b) A1 x = -7 cao
(b) Answer: x = -7
Question 7
(a) B1 x = 4 cao
(a) Answer: x = 4
(b) B1 x = -15 cao
(b) Answer: x = -15
(c) B1 x = -5 cao
(c) Answer: x = -5
Question 8
(a) B1 matched to 4 cao
(a) Answer: 4
(b) B1 matched to -9 cao
(b) Answer: -9
(c) B1 matched to 16 cao
(c) Answer: 16
(d) B1 matched to 20 cao
(d) Answer: 20
Question 9
M1 correct equation formed, 45 - d = 38 oe
A1 d = 7 (or £7) cao
Answer: d = £7
Question 10
M1 correct equation formed, L + 250 = 400 oe
A1 L = 150 (m) cao
Answer: L = 150 m
Question 11
M1 correct equation formed, 3n = 24 oe
A1 n = 8 cao
Answer: n = 8
Question 12
(a) C1 correct explanation given, e.g. she subtracted 7 from 15 instead of adding 7 to both sides oe
(a) Answer: She should have added 7 to both sides, not subtracted it.
(b) B1 x = 22 cao
(b) Answer: x = 22
Question 13
M1 -4 substituted into x + 9, -4 + 9 = 5 seen
A1 5 = 5 stated, so x = -4 is a correct solution, cso
Answer: -4 + 9 = 5, which equals the right-hand side, so x = -4 is correct.
Question 14
M1 both sides divided by 12 oe
A1 x = 0.25 oe cao
Answer: x = 0.25
Question 15
M1 both sides divided by 6 oe
A1 x = -0.15 oe cao
Answer: x = -0.15
Question 16
M1 both sides multiplied by -8 oe
A1 x = 28 cao
Answer: x = 28
Question 17
M1 17 subtracted from both sides oe, -x = -23 seen
A1 x = 23 cao
Answer: x = 23
Question 18
M1 -3.5 substituted into 2x, 2 x -3.5 = -7 seen
A1 -7 = -7 stated, so x = -3.5 is a correct solution, cso
Answer: 2 x -3.5 = -7, which equals the right-hand side, so x = -3.5 is correct.
Question 19
M1 correct equation formed, L / 5 = -620 oe
A1 L = -3100 cao
C1 correct interpretation stated, the company's total loss for the year was 3100 pounds (or -3100 pounds)