How many items are in this paper?

Ten: three basic, three intermediate, three challenge and one redo item.

How long should it take?

About 25 minutes; finish under timing before checking the answers.

Are the answers reliable?

Every value is computed and checked by program, each with a one-line explanation.

Are these past public examination questions?

No. All items are original and are not past papers or official marking schemes.

Which level is it for?

S2, for revising the Pythagoras theorem and school tests.

S2 Maths Pythagoras Theorem Paper 1: Basics

2026-11-09

Tutor Prep Guide · S2 Maths

Find the hypotenuse from two legs, and a missing leg from the hypotenuse.

Direct answers　Ten items on applying a² + b² = c² directly: questions 1-3, 6 and 8 find the hypotenuse, 4-5 find a missing leg, 7 involves a surd, 9 uses the converse, and 10 is a redo item. Allow 25 minutes.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: S2 Maths: Pythagoras Theorem
Level	S2

02　Questions (10 items)

FoundationThe legs of a right-angled triangle are 3 cm and 4 cm. Find the hypotenuse.
FoundationThe legs of a right-angled triangle are 6 cm and 8 cm. Find the hypotenuse.
FoundationThe legs of a right-angled triangle are 5 m and 12 m. Find the hypotenuse.
IntermediateA right-angled triangle has hypotenuse 13 cm and one leg 5 cm. Find the other leg.
IntermediateA right-angled triangle has hypotenuse 25 cm and one leg 7 cm. Find the other leg.
IntermediateThe legs of a right-angled triangle are 8 cm and 15 cm. Find the hypotenuse.
ChallengeAn isosceles right-angled triangle has legs of 6 cm each. Find the hypotenuse, correct to 2 d.p.
ChallengeThe legs of a right-angled triangle are 9 cm and 12 cm. Find the hypotenuse.
ChallengeIs a triangle with sides 7 cm, 24 cm and 25 cm right-angled?
Error redoRedo item: a student wrote the hypotenuse as 3 + 4 = 7 cm. What is the correct value?

03　Answers and one-line notes

#	Answer	One-line note
1	5 cm	3² + 4² = 25, so the hypotenuse is √25 = 5 cm.
2	10 cm	36 + 64 = 100, so the hypotenuse is 10 cm.
3	13 m	25 + 144 = 169, so the hypotenuse is 13 m.
4	12 cm	169 − 25 = 144, so the other leg is 12 cm.
5	24 cm	625 − 49 = 576, so the other leg is 24 cm.
6	17 cm	64 + 225 = 289, so the hypotenuse is 17 cm.
7	8.49 cm	36 + 36 = 72, and √72 = 8.49 cm.
8	15 cm	81 + 144 = 225, so the hypotenuse is 15 cm.
9	Yes	49 + 576 = 625, which equals 25², so it is right-angled.
10	5 cm	The hypotenuse is not the sum of the legs; add the squares, then take the root.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.