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 2: Intermediate

2026-11-09

Tutor Prep Guide · S2 Maths

Diagonals, ladders, coordinate distances and isosceles triangles.

Direct answers　This paper places the theorem in rectangles, ladders, coordinate geometry and isosceles triangles. Questions 7-9 test the converse and the fact that the hypotenuse is the longest side. Question 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)

FoundationA rectangular poster is 12 cm by 16 cm. Find the length of its diagonal.
FoundationA right-angled triangle has hypotenuse 41 cm and one leg 9 cm. Find the other leg.
FoundationA ladder leans on a wall, 1.8 m from its foot and 2.4 m up the wall. Find its length.
IntermediateThe legs of a right-angled triangle are 20 cm and 21 cm. Find the hypotenuse.
IntermediateA right-angled triangle has hypotenuse 26 cm and one leg 10 cm. Find the other leg.
IntermediatePoints A(0, 0) and B(9, 12) lie on a plane. Find the length of AB.
ChallengeIs a triangle with sides 8 cm, 15 cm and 17 cm right-angled?
ChallengeAn isosceles triangle has base 16 cm and height 6 cm. Find the equal sides.
ChallengeCan a right-angled triangle have hypotenuse 8 m and one leg 15 m?
Error redoRedo item: a student added 13² + 5² to get 194. What is the correct method?

03　Answers and one-line notes

#	Answer	One-line note
1	20 cm	144 + 256 = 400, so the diagonal is 20 cm.
2	40 cm	1681 − 81 = 1600, so the other leg is 40 cm.
3	3 m	5.76 + 3.24 = 9, so the ladder is 3 m long.
4	29 cm	400 + 441 = 841, so the hypotenuse is 29 cm.
5	24 cm	676 − 100 = 576, so the other leg is 24 cm.
6	15 units	The differences are 9 and 12; 81 + 144 = 225, so AB = 15 units.
7	Yes	64 + 225 = 289, which equals 17², so it is right-angled.
8	10 cm	Half the base is 8; 64 + 36 = 100, so each equal side is 10 cm.
9	No	The hypotenuse is the longest side, so 8 m cannot be the hypotenuse when a leg is 15 m.
10	Subtract instead: 169 − 25 = 144, so the other leg is 12 cm	To find a leg, subtract the known leg squared from the hypotenuse squared.

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.