Inequalities and Number Lines - Worksheets, Questions and Revision

18 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

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KS3 · Algebra

KS3.M-A18 Inequalities and Number Lines

AQA KS3.M-A18 · Calculators not allowed · about 60 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Write down the inequality shown on the number line. A filled dot at 3 and an arrow to the right.
Figure (to be drawn): Number line with a filled dot at 3 and arrow to the right indicating values greater than or equal to 3.
(2)
2
Write down the inequality shown on the number line. An open circle at -1 and arrow to the left.
Figure (to be drawn): Number line with an open circle at -1 and arrow to the left indicating values less than -1.
(2)
3
On the number line, a filled dot at 0 and arrow to the right. Write the inequality and give three example values that satisfy it.
Figure (to be drawn): Number line with filled dot at 0 and arrow right indicating values ≥ 0.
(2)
4
Draw on a number line the inequality x > 2. Use an open circle at the boundary and an arrow to show direction.
(2)
5
Write the inequality represented by the shaded section between -2 and 4, including both endpoints.
Figure (to be drawn): Number line with filled dots at -2 and 4 and the section between shaded.
(2)
6
Write the inequality shown: shading from 1 (open circle) to the right but not including 5 (open circle).
Figure (to be drawn): Number line with open circle at 1 and open circle at 5, shading between them and to the right of 1 up to but not including 5.
(2)
7
Solve the inequality 3x + 2 < 11. Show your working and give the final answer in inequality form.
(3)
8
Solve the inequality 5 - 2x ≥ 1. Give your answer in inequality form.
(3)
9
Solve and represent on a number line: 2x - 7 > 1. Give the final answer and a short description of the number line representation.
(3)
10
Solve the inequality and give the answer in simplest form: -3x ≤ 12.
(2)
11
Solve 4(x - 3) > 8. Show your steps and give the solution as an inequality.
(2)
12
Solve the inequality 2x + 5 ≤ 2x + 9. State any special conclusion.
(2)
13
Solve the inequality 3(x + 2) < 3x + 6 and state what this tells you about the solution set.
(2)
14
Solve the compound inequality and give the solution in inequality form: 1 ≤ 2x + 1 < 7.
(2)
15
A shop only allows customers aged at least 16 but under 65 for a day pass. Represent this rule as an inequality and give two ages that are not allowed.
(2)
16
Solve the inequality 7 - 2x > 1 and write the solution in inequality form.
(2)
17
Find all integer values of x that satisfy -2 ≤ x < 4. List them.
(2)
18
Stretch: Solve the inequality and give the answer in inequality form: 2(3x - 1) ≤ 5x + 7. Show working.
(3)
Mark scheme · KS3.M-A18 Inequalities and Number Lines

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