IGCSE Math Revision Questions by topic Revision notes Past papers Student hub

Edexcel IGCSE Maths (4MA1) · Unit 1: Number

Edexcel IGCSE 4MA1 Surds: Exam Questions and Answers

Surds questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the worked example first, then try the 8 exam-style questions yourself and check your working against the mark scheme.

1 worked example
8 questions with mark schemes
Higher tier · calculator allowed
Free, no sign-in

Practise surds in Unit 1 →Surds revision notes

What this topic covers

Surds 1: Simplifying, Expanding & Rationalising: Simplifying surds, expanding brackets with surds and rationalising denominators.

Surds worked examples

Worked example 1: Adding surds

Simplify $\sqrt{75} + \sqrt{12}$ .

Solution

$\sqrt{75} = \sqrt{25 \times 3} = 5 \sqrt{3}$ .
$\sqrt{12} = \sqrt{4 \times 3} = 2 \sqrt{3}$ .
Add like surds: $7 \sqrt{3}$ .

4 steps

Tip: Look for the largest square factor.

Surds exam-style questions

Try each question before you open the answer (one has its full worked solution open). The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.

Question 1 · easy · 1 mark

Write $\sqrt{75}$ in the form $k \sqrt{3}$ , where $k$ is an integer.

Show the answer and mark scheme

B1 5√3 cao

Answer: $5 \sqrt{3}$

Question 2 · easy · 2 marks

Simplify fully $\sqrt{48} + \sqrt{27}$ .

Show the answer and mark scheme

M1 writes √48 = 4√3 or √27 = 3√3
A1 7√3 cao

Answer: $7 \sqrt{3}$

Question 3 · easy · 2 marks

Expand and simplify $(3 + \sqrt{5}) (3 - \sqrt{5})$ .

Show the answer and mark scheme

M1 at least 3 of the 4 terms 9, −3√5, +3√5, −5 correct
A1 4 cao

Answer: 4

Question 4 · medium · 2 marks

Rationalise the denominator and simplify fully $\frac{12}{\sqrt{6}}$ .

Show the answer and mark scheme

M1 multiplies numerator and denominator by √6, e.g. 12√6/6
A1 2√6 cao

Answer: $2 \sqrt{6}$

Question 5 · medium · 2 marks

Expand $(2 + \sqrt{7})^{2}$ . Give your answer in the form $a + b \sqrt{7}$ , where $a$ and $b$ are integers.

Full worked solution Free, no sign-in

M1 4 terms with at least 3 correct: 4 + 2√7 + 2√7 + 7
A1 11 + 4√7 cao

Answer: $11 + 4 \sqrt{7}$

Every question here has a full worked solution. See them all →

Question 6 · hard · 3 marks

Show that $(\sqrt{18} + \sqrt{8})^{2} = 50$ . Show each stage of your working clearly.

Show the answer and mark scheme

M1 √18 = 3√2 or √8 = 2√2
M1 (5√2)² or full expansion 18 + 2√144 + 8
A1 = 50 with complete correct working (cso)

Answer: 50 (shown)

Question 7 · hard · 3 marks

Rationalise the denominator of $\frac{1}{3 - \sqrt{2}}$ . Give your answer in its simplest form.

Show the answer and mark scheme

M1 multiplies numerator and denominator by (3 + √2)
M1 denominator 9 − 2 = 7
A1 (3 + √2)/7 oe

Answer: $\frac{3 + \sqrt{2}}{7}$

Question 8 · very hard · 3 marks

Express $\frac{5 + \sqrt{3}}{2 - \sqrt{3}}$ in the form $a + b \sqrt{3}$ , where $a$ and $b$ are integers.

Show the answer and mark scheme

M1 multiplies numerator and denominator by (2 + √3)
M1 numerator expanded 10 + 5√3 + 2√3 + 3 (3 of 4 terms correct) and denominator 4 − 3 = 1
A1 13 + 7√3 cao

Answer: $13 + 7 \sqrt{3}$

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.

Revise surds for the exam

Unit 1 practice: Number in the student hub (more questions with mark schemes)
IGCSE Maths revision notes for this topic and the IGCSE Maths formula sheet
Edexcel IGCSE Maths 4MA1 past papers to practise under exam conditions
IGCSE Maths 4MA1 examiner report summary: where students lose marks

Questions students ask

Which Edexcel IGCSE Maths papers test surds?

Either Higher tier paper, 1H or 2H, can test surds: 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 surds questions?

In the IGCSE student hub: Unit 1 (Number) 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 surds 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.

Join free

Already have an account? Sign in

Edexcel IGCSE 4MA1 Surds: Exam Questions and Answers

Try it first

What this topic covers

Surds worked examples

Worked example 1: Adding surds

Solution

Surds exam-style questions

Question 1 · easy · 1 mark

Question 2 · easy · 2 marks

Question 3 · easy · 2 marks

Question 4 · medium · 2 marks

Question 5 · medium · 2 marks

Full worked solution Free, no sign-in

Question 6 · hard · 3 marks

Question 7 · hard · 3 marks

Question 8 · very hard · 3 marks

Revise surds for the exam

Questions students ask

Practise surds with your progress saved

More Unit 1 topics: Number