Cambridge IGCSE · Mathematics (0580)

Inequalities: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Inequalities.

10 questions24 marksFree, no account

Question 1

1 mark

How many integers satisfy the inequality \( -1 \le x < 4 \)?

Question 2

1 mark

Solve the inequality \(2(3 - x) < 12\).

Question 3

1 mark

Find the set of all integers, \(x\), that satisfy both of the following inequalities:
\(\frac{2x + 1}{3} \le 3\) and \(5 - x < 3\).

Question 4

1 mark

Which inequality is represented by the diagram on the number line?
(Note: The diagram shows a closed circle at \(4\) and a solid line extending to the left.)

Question 5

1 mark

Solve the inequality \( 7 - 2(x + 1) \le 15 \).

Question 6

2 marks

Draw a number line to represent the inequality \(x < 5\).

Write your answer out first, then check it against the worked solution.

Question 7

4 marks

Solve the inequality \( 7 - 3x < 19 \).

Write your answer out first, then check it against the worked solution.

Question 8

5 marks

Find the largest integer value of \(k\) that satisfies the simultaneous linear inequalities:
\(4k - 7 < 13\) and \(5 - 2k \le 1\)

Write your answer out first, then check it against the worked solution.

Question 9

4 marks

(a) Solve the inequality \( 5x + 3 \le 18 \).

(b) Represent the solution set for \( x \) from part (a) on a number line.

(c) List all the positive integers that satisfy the inequality.

Write your answer out first, then check it against the worked solution.

Question 10

4 marks

A car rental company charges a daily fee of $30 plus $0.25 for every kilometer driven.
Let \( k \) be the number of kilometers driven in one day.

(a) Write an expression, in terms of \( k \), for the total daily cost in dollars.

(b) A customer wants the total daily cost to be at most $80.
Form an inequality in \( k \) to represent this condition.

(c) Solve your inequality to find the maximum number of kilometers the customer can drive.

Write your answer out first, then check it against the worked solution.

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