Source: Questions from Complete International Mathematics For Cambridge IGCSE - David Rayner, Jim Fenson
1. In the cube shown, find:
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a) BD
b) AS
c) BS
d) the angle SBD
e) the angle ASB.
(a) | ![]() |
(b) | ![]() |
(c) | ![]() |
(d) | ![]() |
(e) | ![]() |
2. In the wedge shown, PQRS is perpendicular to ABRQ.
PQRS and ABRQ are rectangles with AB = QR = 6 m, BR = 4 m, RS = 2 m. Find :
a) BS
b) AS
c) Angle BSR
d) Angle ASR
e) Angle PAS
(a) | PQRS is perpendicular to ABRQ Hence SR is perpendicular to BR ![]() |
(b) | ABRQ is a rectangle. Hence ∠ABR = 90° ![]() |
(c) | ![]() |
(d) | ![]() |
(e) | ![]() |
3. In the diagram A, B and O are points in a horizontal plane and P is vertically above O.
OP = h m. A is due West of O, B is due South of O and AB = 60 m.
The angle of elevation of P from A is 25° and the angle of elevation of P from B is 33°.
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b) Find the length of BO in terms of h.
c) Find the value of h.
(a) | In △ AOP, ∠AOP = 90°![]() |
(b) | In △BPO, ∠BOP = 90°![]() |
(c) | ![]() |
4. An observer at the top of a tower of height 15 m sees a man due West of him at an angle of depression of 31°.
He sees another man due South at an angle of depression 17°.
Find the distance between the men.
![]() | Let Tower = OA = 15 m Man due West = P Angle of depression = 31° Hence angle with tower = 59° Man due South = Q Angle of depression = 17° Hence angle with tower = 73° Distance between men = PQ OP is west and OQ south. ∠POQ = 90° ![]() |
5. The figure shows a triangular pyramid on a horizontal base ABC.
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Point M is the mid-point of AC. Calculate the size of angle VMB.
V Is vertically above B.
Hence VBA id perpendicular to ABC