Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed
Surds — exam questions
10 original Incandio exam-style questions on surds, 24 marks, about 29 minutes of writing. Each one carries the command word, the tariff and the specification statement it assesses, exactly as a paper presents them. This is an original Incandio practice question, written to reflect the structure and demands of the qualification. It is not an official Pearson Edexcel past-paper question.
This is the practice set for Surds — the module that teaches it. Read the module first if the idea is new; come here when you want to find out whether you can turn it into marks. Completely free, no account needed to read.
What these questions ask of you
7 command words run through this set, and on Pearson Edexcel International GCSE Mathematics A each one means something precise. Answering the wrong command is the commonest way a candidate who understands the module still loses the mark.
- Write down (1–2 marks)
- a value that needs no working — read off, recalled or stated
- Simplify (1–3 marks)
- an equivalent expression in its simplest form
- Explain why (1–2 marks)
- one short justification — mathematics almost never asks for extended explanation
- Work out (1–5 marks)
- a calculated result, with the working that produced it
- Expand (1–3 marks)
- the brackets removed and like terms collected
- Show that (2–5 marks)
- every step of a derivation to a value that is already printed in the question Misread as: stating the printed answer again instead of deriving it
- Find (1–5 marks)
- a value or expression obtained by a method the learner chooses
Assessed on Paper 1 and Paper 2.
Where these sit in the specification
Pearson Edexcel International GCSE Mathematics A (4MA1) — statement 1.4. Incandio is aligned to this specification; it is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording.
The 10 questions
Answer them on paper, then open the module's exam practice to have them marked. The mark scheme, the accepted and rejected answers and the annotated model answer are in Incandio and are not printed here — an answer beside its question is not practice.
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(1)Write down
Write down the value of (√7)².
(Total for Question 1 = 1 mark)
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(2)Simplify
Simplify √72.
(Total for Question 2 = 2 marks)
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(2)Simplify
Simplify √8 + √18.
(Total for Question 3 = 2 marks)
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(1)Explain why
A student writes √9 + √16 = √25. Explain why the student is wrong.
(Total for Question 4 = 1 mark)
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(2)Work out
Work out √5 × √20.
(Total for Question 5 = 2 marks)
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(3)Expand
Expand and simplify (3 + √5)(2 − √5).
(Total for Question 6 = 3 marks)
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(3)Show that
Show that √48 ÷ √3 is equal to 4.
(Total for Question 7 = 3 marks)
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(3)Work out
Work out 6 ÷ √3, giving your answer in the form a√b where a and b are integers.
(Total for Question 8 = 3 marks)
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(3)Simplify
Simplify (2√5)³.
(Total for Question 9 = 3 marks)
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(4)Find
A square has an area of 32 cm². Find the perimeter of the square in the form a√b cm, where a and b are integers.
(Total for Question 10 = 4 marks)
Have them marked, then defend the answer
Practice tells you the mark; teaching it back tells you whether you understand it. On Incandio a topic counts as mastered only once you have taught it and defended it.
- Mark these questions — 10 questions, marked on Incandio against the authored scheme, with the mistake you actually made named.
- Teach it — explain surds to Ember, an AI pupil who does not have it yet and asks the awkward question.
- Defend it — argue it against Euclid over three rounds, marked against descriptors you can read first.
Completely free. No subscriptions, no paywalls, no account needed to start.
Back to the module
- Surds — Exact answers with square roots: simplifying √48, expanding surd brackets, and rationalising denominators. Higher Tier.
- All of Incandio Mathematics · Incandio Exam Practice