Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed
Pythagoras' Theorem — exam questions
10 original Incandio exam-style questions on Pythagoras' Theorem, 28 marks, about 36 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 Pythagoras' Theorem — 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
6 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
- Work out (1–5 marks)
- a calculated result, with the working that produced it
- 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
- Explain why (1–2 marks)
- one short justification — mathematics almost never asks for extended explanation
- Find (1–5 marks)
- a value or expression obtained by a method the learner chooses
- Give a reason for your answer (1–3 marks)
- the geometric or statistical reason NAMED precisely — the mark scheme demands the terminology Misread as: describing what you did instead of naming the property that justifies it
Assessed on Paper 1 and Paper 2.
Where these sit in the specification
Pearson Edexcel International GCSE Mathematics A (4MA1) — statement 4.8. 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
A right-angled triangle has sides of 5 cm, 12 cm and 13 cm. Write down which side is the hypotenuse.
............................ cm
(Total for Question 1 = 1 mark)
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(3)Work out
A right-angled triangle has two shorter sides of 8 cm and 15 cm. Work out the length of the hypotenuse.
length of the hypotenuse = ............................ cm
(Total for Question 2 = 3 marks)
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(3)Work out
A ladder 4.2 m long leans against a vertical wall with its foot 1.3 m from the base of the wall. Work out how far up the wall the ladder reaches. Give your answer to 2 decimal places.
............................ m
(Total for Question 3 = 3 marks)
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(3)Show that
A triangle has sides of 9 cm, 40 cm and 41 cm. Show that this triangle is right-angled.
(Total for Question 4 = 3 marks)
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(1)Explain why
A student calculates the third side of a right-angled triangle with a hypotenuse of 10 cm and one shorter side of 6 cm, and gets 11.7 cm. Explain why this answer must be wrong without doing the calculation.
(Total for Question 5 = 1 mark)
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(4)Work out
A rectangular field measures 87 m by 64 m. Work out how much shorter it is to walk diagonally across the field than to walk along two sides. Give your answer to the nearest metre.
............................ m
(Total for Question 6 = 4 marks)
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(3)Find
An isosceles triangle has two equal sides of 26 cm and a base of 20 cm. Find its perpendicular height.
perpendicular height = ............................ cm
(Total for Question 7 = 3 marks)
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(4)Work out
A cuboid measures 6 cm by 8 cm by 24 cm. Work out the length of the longest straight rod that will fit inside it.
............................ cm
(Total for Question 8 = 4 marks)
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(3)Give a reason for your answer
A triangle has sides of 7 cm, 24 cm and 26 cm. Decide whether it is right-angled, and give a reason for your answer.
(Total for Question 9 = 3 marks)
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(3)Work out
Point A has coordinates (−3, 5) and point B has coordinates (9, −2). Work out the length of AB. Give your answer to 3 significant figures.
length of AB = ............................
(Total for Question 10 = 3 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 Pythagoras' Theorem 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
- Pythagoras' Theorem — a² + b² = c² — finding missing sides in right-angled triangles, and spotting the hidden right triangles inside other shapes.
- All of Incandio Mathematics · Incandio Exam Practice