Source: Questions from Complete International Mathematics For Cambridge IGCSE - David Rayner, Jim Fenson
1. In the cube shown, find:
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°. a) Find the length AO in terms of h.
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. V is vertically above B where VB = 10 cm, Angle ABC = 90° and AB = BC = 15 cm.
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