Cambridge International Mathematics

Multi-Topic Questions (Chapter 33) 7

47 Nov 1991, Paper 4

The volume of a regular hexagonal prism is given by the

formula V=2: 6 s^3 , wheresis the length of each edge of

the prism.

a FindVif s=3: 3 cm.

b Makesthe subject of the formula.

ciUse trigonometry to obtain an expression for the

area of the (shaded) hexagon, in terms ofs.

ii Hence show that the original formula is

approximately correct.

48 Nov 1989, Paper 4

In the triangle XYZ, angle XZY=60o,XY=9: 5 cm,

XZ=8cm and YZ=xcm.

aiUse the cosine rule to show that xsatisfies the

equation 4 x^2 ¡ 32 x¡105 = 0.

ii By solving this quadratic equation, find the length

of YZ.

b Calculate angle XYZ.

49

The shape ABCDEF consists of a trapezium ACDF and a

minor segment ABC of a circle centre O. The lines FA and DC

are tangents to the circle at A and C respectively. The radius

of the circle is 2 m. AC=3: 6 m and AF=CD=5m.

a Show that angle AOC is 128 : 3 o, correct to one decimal

place.

b Calculate the area of the sector OABC.

c

d

e Find the area of the trapezium ACDF and hence the area of the whole shape ABCDEF.

50 June 1994, Paper 4

In a fitness exercise, students run across a field from A to B,

then from B to C and then from C to A.

a A student runs from A to B in 10 seconds. Calculate his

speed in

i metres/second ii kilometres/hour

b Another student runs from A to B in 10 : 5 seconds,

from B to C in 13 seconds and from C to A at a

speedof 8 : 5 m/s. Calculate her overall average speed

in metres/second.

c Showing all your working, calculate angle BAC.

d The bearing of B from A is 062 o. Calculate

i the bearing of C from A ii the bearing of A from C

s

s

9.5 8

X

Y x Z

60°

3.6 m

B

A C

O

2m 2m

5m 5m

FED

Calculate the area of the triangle OAC and

hence the area of the minor segment ABC.

Show that the perpendicular distance

between AC and FD is 45 : m.

A

B

C

120 m

80 m

100 m

Adapted from Nov 1990, Paper 4

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