Add 3: $4x\le16$. Divide by 4: $x\le4$. Answer: $x\le4$

Solve $-3<2x+1\le9$ and list the integer solutions.

Subtract 1 throughout: $-4<2x\le8$. Divide by 2: $-2<x\le4$. Integers: $-1,0,1,2,3,4$. Answer: $-2<x\le4$; −1, 0, 1, 2, 3, 4

Solve $x^2-5x+4\le0$.

Factorise: $(x-1)(x-4)\le0$. Critical values 1 and 4; the curve is below the axis between them. $1\le x\le4$. Answer: $1\le x\le4$

Edexcel IGCSE 4MA1 Inequalities: Exam Questions & Answers

Q: Which Edexcel IGCSE Maths papers test inequalities?

Either Higher tier paper, 1H or 2H, can test inequalities: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Q: Where can I practise more inequalities questions?

In the IGCSE student hub: Unit 2 (Algebra Basics) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

Edexcel IGCSE 4MA1 Inequalities: Exam Questions and Answers

Inequalities questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 3 worked examples first, then cover each solution and redo it yourself.

3 worked examples

Higher tier · calculator allowed

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1 of 5

Question 1 of 5
Question 2 of 5
Question 3 of 5
Question 4 of 5
Question 5 of 5

Start with one question on linear inequalities. Stuck? Take a hint. No sign-in needed.

Solve

3 - 4 x < 23

Choose your answer · keys 1–4

x > - 5

x < - 5

x > - \frac{13}{2}

x > 5

What this topic covers

Linear Inequalities 1: Solving one- and two-step linear inequalities.
Linear Inequalities 2: Inequalities with variables on both sides.
Quadratic Inequalities (algebra & graphs): Solving quadratic inequalities graphically and algebraically.

Inequalities worked examples

Worked example 1: Solving an inequality

Solve $4 x - 3 \leq 13$ .

Solution

Add 3: $4 x \leq 16$ .
Divide by 4: $x \leq 4$ .

3 steps

Tip: Only reverse the sign when multiplying or dividing by a negative.

Worked example 2: Double inequality

Solve $- 3 < 2 x + 1 \leq 9$ and list the integer solutions.

Solution

Subtract 1 throughout: $- 4 < 2 x \leq 8$ .
Divide by 2: $- 2 < x \leq 4$ .
Integers: $- 1, 0, 1, 2, 3, 4$ .

4 steps

Tip: −2 is not included because the inequality is strict.

Worked example 3: Quadratic inequality

Solve $x^{2} - 5 x + 4 \leq 0$ .

Solution

Factorise: $(x - 1) (x - 4) \leq 0$ .
Critical values 1 and 4; the curve is below the axis between them.
$1 \leq x \leq 4$ .

4 steps

Tip: Sketch the parabola to decide which part you need.

Where students lose marks on inequalities

Examiner's noteQuadratic inequalities: the final answer

Where marks are lost: Most factorise correctly but cannot write the final inequality (or write two separate conditions that contradict).

Examiners flagged this in 2 exam series (November 2024, June 2025). Summarised in our own words from Pearson Edexcel examiner reports. Read the full note →

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Questions students ask

Which Edexcel IGCSE Maths papers test inequalities?

Either Higher tier paper, 1H or 2H, can test inequalities: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more inequalities questions?

In the IGCSE student hub: Unit 2 (Algebra Basics) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

Practise inequalities with your progress saved

Save your answers and track your progressA free account remembers the questions you have done and brings you back to this page.

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Edexcel IGCSE 4MA1 Inequalities: Exam Questions and Answers

Try it first

What this topic covers

Inequalities worked examples

Worked example 1: Solving an inequality

Solution

Worked example 2: Double inequality

Solution

Worked example 3: Quadratic inequality

Solution

Where students lose marks on inequalities

Revise inequalities for the exam

Questions students ask

Practise inequalities with your progress saved

More Unit 2 topics: Algebra Basics