Free Pythagoras’ theorem questions for IGCSE Mathematics (0580), part of Trigonometry. Each question has the answer and the marking points an examiner would look for.
Generate a full Pythagoras’ Theorem worksheet →All Trigonometry questionsThe diagram shows a cuboid. It has a horizontal base measuring 6 cm by 8 cm and a height of 9 cm. Find the length of the longest diagonal of the cuboid and the angle it makes with the base.
| Part | Answer and marking points | Marks |
|---|---|---|
| 13.5 cm; 42° √(62 + 82 + 92) oe (base diagonal √(100) then 3D step) M1 13.5 cm A1 tan θ = 9 ÷ base diagonal M1 42° A1 | 4 |
A ladder of length 5 m leans against a vertical wall. The foot of the ladder is on horizontal ground, 1.6 m from the wall.
The top of the ladder slides 0.8 m down the wall.
Calculate how far the foot of the ladder moves away from the wall.
| Part | Answer and marking points | Marks |
|---|---|---|
| 1.48 m original height √(52 − 1.62) = 4.737 M1 new height 3.937 M1 new distance √(52 − 3.9372) = 3.082 M1 1.48 A1 | 4 |
A ladder 7 m long leans against a vertical wall. The foot of the ladder is 2 m from the wall. How high up the wall does the ladder reach?
| Part | Answer and marking points | Marks |
|---|---|---|
| 6.71 m 72 − 22 M1 square root M1 6.71 A1 | 3 |
The diagram shows a right-angled triangle ABC.
Calculate the length of AC.
| Part | Answer and marking points | Marks |
|---|---|---|
| 14.6 cm 42 + 142 M1 14.6 A1 | 2 |
A rectangle measures 9 cm by 12 cm. Find the length of its diagonal.
| Part | Answer and marking points | Marks |
|---|---|---|
| 15 cm √(92 + 122) M1 15 A1 | 2 |
ABCDEFGH is a cuboid. The base ABCD is a horizontal rectangle with AB = 8 cm and BC = 6 cm. The vertical edges AE, BF, CG and DH are 5 cm long. M is the midpoint of AB.
Calculate the length of the diagonal AG.
Calculate the angle between AG and the base ABCD.
Calculate the angle between the line MG and the base ABCD.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 11.2 cm AC² = 8² + 6², then AG² = AC² + 5² M1 11.2 A1 | 2 |
| (b) | 26.6° tan = 5 ÷ AC M1 26.6 A1 | 2 |
| (c) | 34.7° MC² = 4² + 6² M1 tan = 5 ÷ MC M1 34.7 A1 | 3 |
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Meet Riyaz →Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in