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 3: Challenge

2026-11-09

Tutor Prep Guide · S2 Maths

Space diagonals, the converse and reverse problems needing several steps.

Direct answers　The hardest paper: question 1 is a space diagonal, questions 3 and 8 combine the hypotenuse with the perimeter, 5 and 9 use the converse, and 10 targets the common error of halving the hypotenuse. 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)

FoundationA cuboid measures 3 cm by 4 cm by 12 cm. Find its space diagonal.
FoundationPoints P(-2, 3) and Q(4, 11) lie on a plane. Find the length of PQ.
FoundationThe legs of a right-angled triangle are 9 cm and 40 cm. Find its perimeter.
IntermediateA 15 m ladder leans on a wall with its foot 9 m from the wall. Find the height reached.
IntermediateIs a triangle with sides 1.5 m, 2 m and 2.5 m right-angled?
IntermediateA square has diagonal 10√2 cm. Find the length of its side.
ChallengeA triangle has sides 10 cm, 24 cm and 26 cm. Find its area.
ChallengeA right-angled triangle has hypotenuse 25 cm and perimeter 60 cm. Find its area.
ChallengeIs a triangle with sides 7 cm, 9 cm and 12 cm right-angled?
Error redoRedo item: an isosceles right-angled triangle has hypotenuse 8 cm. A student wrote the leg as 4 cm. What is correct?

03　Answers and one-line notes

#	Answer	One-line note
1	13 cm	9 + 16 + 144 = 169, so the space diagonal is 13 cm.
2	10 units	The differences are 6 and 8; 36 + 64 = 100, so PQ = 10 units.
3	90 cm	The hypotenuse is √1681 = 41, so the perimeter is 9 + 40 + 41 = 90 cm.
4	12 m	225 − 81 = 144, so the top reaches 12 m.
5	Yes	2.25 + 4 = 6.25, which equals 2.5², so it is right-angled.
6	10 cm	Twice the square of the side is 200, so the side squared is 100 and the side is 10 cm.
7	120 cm²	100 + 576 = 676, so the right angle is between 10 and 24; area = 10 × 24 ÷ 2 = 120 cm².
8	150 cm²	The legs are 15 cm and 20 cm, so the area is 15 × 20 ÷ 2 = 150 cm².
9	No	49 + 81 = 130, which is less than 144, so it is not right-angled.
10	5.66 cm	Each leg is 8 ÷ √2 = 5.66 cm; halving the hypotenuse is wrong.

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.