IGCSE Math RevisionQuestion 1
Write down every integer \(n\) that satisfies \(-4 \lt n \le 1\).
Show the worked answer
- \(-4\) is not included (\(\lt\)); \(1\) is included (\(\le\)).
Answer: \(-3, -2, -1, 0, 1\)
Cambridge IGCSE Maths (0580) · Topic 2: Algebra and graphs · 2.6
Cambridge IGCSE Maths 0580 Inequalities Questions
Inequalities questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
- 9 questions
- 5 Core
- 4 Extended
- 7 non-calculator
- Free, no sign-in
What the syllabus asks
- 2.6 Inequalities Core Extended
Represent and interpret inequalities, including on a number line.
Extended also: Construct, solve and interpret linear inequalities; Represent linear inequalities in two variables on a graph and list the inequalities that define a region.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
Inequalities questions: Core
For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).
Question 2
On a number line, an open circle is drawn at \(-1\) and a filled circle at \(4\), with a line joining them.
Write down the inequality in \(x\) that this shows.
Show the worked answer
- An open circle means the value is not included (\(\lt\)); a filled circle means it is included (\(\le\)).
Answer: \(-1 \lt x \le 4\)
Question 3
Describe how you would show \(x \ge 1.5\) on a number line.
Show the answer and mark scheme
- B1 a filled (solid) circle at 1.5
- B1 the line (arrow) going to the right
Answer: a filled circle at \(1.5\) with the line going to the right
Question 4
\(x\) is greater than \(-3\) and at most \(5\).
(a) Write this as a single inequality.
(b) How many integers satisfy it?
Show the answer and mark scheme
- B1 (a) \(-3 \lt x \le 5\)
- B1 (b) 8
Answer: (a) \(-3 \lt x \le 5\) (b) \(8\)
Question 5
A number line has a filled circle at \(-4\) and an open circle at \(1\), joined by a line.
(a) Write down the inequality shown.
(b) Write down the smallest and the largest integers that satisfy it.
Show the answer and mark scheme
- B1 (a) \(-4 \le x \lt 1\)
- B1 (b) smallest −4
- B1 (b) largest 0
Answer: (a) \(-4 \le x \lt 1\) (b) \(-4\) and \(0\)
Inequalities questions: Extended
Extended content, for Papers 2 and 4. Core students can skip these.
Question 6
Solve \(5x - 3 \gt 2x + 9\).
Show the worked answer
- Subtract \(2x\): \(3x - 3 \gt 9\).
- \(3x \gt 12\), so \(x \gt 4\).
Answer: \(x \gt 4\)
Question 7
(a) Solve \(-4 \le 2x + 6 \lt 10\).
(b) List the integer values of \(x\) that satisfy the inequality.
Show the worked answer
- (a) Subtract \(6\): \(-10 \le 2x \lt 4\). Divide by \(2\): \(-5 \le x \lt 2\).
- (b) \(-5, -4, -3, -2, -1, 0, 1\)
Answer: (a) \(-5 \le x \lt 2\) (b) \(-5, -4, -3, -2, -1, 0, 1\)
Question 8
Solve \(7 - 3x \ge 19\).
Show the worked answer
- Subtract \(7\): \(-3x \ge 12\).
- Divide by \(-3\) and reverse the sign: \(x \le -4\).
Answer: \(x \le -4\)
Question 9
The region \(R\) is defined by \(y \ge 1\), \(x + y \le 6\) and \(y \le 2x\).
Find the point in \(R\) with integer coordinates for which \(x + 2y\) is greatest.
Show the worked answer
- List the integer points: for \(y = 4\), only \(x = 2\) works (\(2x \ge 4\) and \(x \le 2\)); \(y = 5\) is impossible (\(x \ge 2.5\) but \(x \le 1\)).
- Check the best candidates: \((2, 4)\) gives \(10\), \((3, 3)\) gives \(9\), \((4, 2)\) gives \(8\), \((5, 1)\) gives \(7\).
Answer: \((2, 4)\)
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Keep going
- Algebra and graphs practice for 0580: more questions, each one marked, tagged Core or Extended
- My mistakes, then a Skill Builder on the skills you missed
- Common mistakes in 0580: what the Cambridge examiner reports say
- Algebra and graphs revision notes and the 0580 formula sheet
- Cambridge IGCSE Maths 0580 past papers, when you are ready for a full paper
Questions students ask
Which Cambridge 0580 papers can test inequalities?
Inequalities is on both tiers (syllabus 2.6), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.
Are these Cambridge past-paper questions?
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
Where can I practise more inequalities questions?
In the 0580 practice for topic 2 (Algebra and graphs), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.