Inequalities - Worksheets, Questions and Revision

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

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GCSE · Algebra

4.5 Inequalities

EDEXCEL 1MA1 · Calculator allowed · about 75 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Write down what each inequality symbol means.
(a)>(1)
(b)≤(1)
(Total for Question 1 is 2 marks)
2
The diagram shows two number lines, A and B.
A -5 -4 -3 -2 -1 0 1 2 3 4 5 B -5 -4 -3 -2 -1 0 1 2 3 4 5
(a)Write down the inequality shown by number line A.(1)
(b)Write down the inequality shown by number line B.(1)
(Total for Question 2 is 2 marks)
3
n is an integer such that -3 < n ≤ 2. List all the possible values of n.
(Total for Question 3 is 2 marks)
4
Solve the inequalities.
(a)x + 6 < 10(1)
(b)5x ≥ 20(1)
(Total for Question 4 is 2 marks)
5
Solve the inequality 2x + 5 < 17.
(Total for Question 5 is 2 marks)
6
Solve the inequality 3x - 4 ≥ 11.
(Total for Question 6 is 2 marks)
7
n is an integer such that -2 ≤ n < 5.
(a)List all the possible values of n.(2)
(b)Write down the smallest possible value of n.(1)
(Total for Question 7 is 3 marks)
8
Solve the inequality 5x + 2 ≤ 3x + 10.
(Total for Question 8 is 3 marks)
9
Solve the inequality 4(x - 1) > 2x + 6.
(Total for Question 9 is 3 marks)
10
(a) Solve the inequality x - 3 > -5. (b) Show the solution set on the number line below.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
(a)Solve x - 3 > -5.(1)
(b)Show the solution set on the number line.(2)
(Total for Question 10 is 3 marks)
11
Anjali has p pounds. She has more than 15 pounds but no more than 40 pounds. Write down an inequality, in terms of p, to show this information.
(Total for Question 11 is 2 marks)
12
Tom thinks of a number, x. He multiplies it by 3, then subtracts 7. The result is greater than 14.
(a)Write an inequality, in terms of x, to show this information.(1)
(b)Solve your inequality to find the possible values of x.(2)
(Total for Question 12 is 3 marks)
13
Which of the following is the solution to 2x + 1 ≥ x - 4?
  • A) x ≥ -5
  • B) x ≤ -5
  • C) x ≥ -3
  • D) x ≤ 5
(Total for Question 13 is 1 mark)
14
Priya is designing a rectangular garden. It has length x metres and width 6 metres. The perimeter of the garden must be at least 30 metres. Form an inequality in x and solve it to find the possible values of x.
Diagram NOT accurately drawn
x metres 6 metres
(Total for Question 14 is 3 marks)
15
Solve the inequality 7 - 2x > 1.
(Total for Question 15 is 2 marks)
16
Solve the inequality 3 - 5x ≤ 18.
(Total for Question 16 is 2 marks)
17
Solve the inequality -3 < 2x + 1 ≤ 9. Show the solution set on the number line below.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
(Total for Question 17 is 4 marks)
18
Solve the inequality 3(x - 2) ≥ 5(x + 4), giving your answer in the form x ≤ k, where k is an integer.
(Total for Question 18 is 3 marks)
19
Jamal measures the length of a plank of wood, l cm, as 8 cm, correct to the nearest centimetre. Write down the error interval for l.
(Total for Question 19 is 2 marks)
20
On the grid, shade the region R that satisfies all three of these inequalities: x ≥ 1, y > 2, x + y ≤ 6. Label your region R.
0 1 2 3 4 5 6 1 2 3 4 5 6 x y
(Total for Question 20 is 3 marks)
21
n is an integer. Show that n = 3 is the only value of n that satisfies both 3n - 1 < 11 and 2n + 3 ≥ 9.
(Total for Question 21 is 4 marks)
Mark scheme · 4.5 Inequalities

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21