Max. and min. of trigo. expression
1989 FG8.1
If y is the greatest value of
14
, find y.
5 3 sin
1990 FI1.3
If c is the greatest value of
20
, find c.
4 2 cos
1992 HI4
x is an acute angle satisfying
1
1
cos x 5 cos x 2 . Determine the largest
2
2
possib

sin x + cos x = 0.2
1992 HI20 1995 HI5
If sin x cos x
1
and 0 x , find tan x.
5
1993 HG10
If 0 90 and cos sin =
5
, find the value of cos + sin .
3
2007 HI7
Given that sin cos =
1
and 0 < < 180. If tan = B, find the value of B.
5
2007 FI1.4
If cos x + si

Arc and Sector
1983 FI4.4
A wire of c cm is bent to form a sector of radius 1 cm.
What is the angle of the sector in degrees (correct to the
B
nearest degree)?
3 cm
C
O 1 cm
1986 FI1.1
The given figure shows a circle of radius 18 cm, centre O.
If AOB =
an

Area same height different bases
A
1985 FI4.3
In Figure 2, BD = 5, DE 4, EC 3. If the area of
AEC is 24 and the area of ABC is c, find c.
(Figure 2) B
1986 FG10.2
The medians AL, BM, CN of ABC meet at G.
If the area of ABC is 54 cm2 and the area of
ANG is

0.5ah
1983 FG7.2
In the figure shown, ACDE is a square and
AC = BC, ACB = 90. Find the area of
ABC if the area of ACDE is 10 cm2.
A
E
If sin =
B
1984 FG10.1
C
If A is the area of a square inscribed in a circle of diameter 10, find A.
1985 FSG.4
If A is th

0.5absinC
1984 FI4.4
The area of an equilateral triangle is 4 3 cm2. If its perimeter is d cm, find d.
1985 FSI.4
1997 FI3.3
The perimeter and the area of an equilateral triangle are 12 cm and 3R cm2
respectively. Find R.
1999 HI2
The length of a side of

Cosine rule
1992 FG9.2
ABCDEF is a regular hexagon and AB 6 cm, AC y 3 cm, find y.
1994 HG7
The base of a triangle is 80 cm and one of the base angles is 60. The sum of the
lengths of the other two sides is 90 cm. The length of the shortest side of this
t

Compounded angles
1994 FG10.3
It is given that sin 2 = 2 sin cos .
sin 20 cos 20 cos 40 cos 60 cos 80
Find c, if c =
.
sin 160
1994 FG10.4
tan A tan B
. Find d, if
It is given that tan(A + B) =
1 tan A tan B
d = (1 + tan 21)(1 + tan 22)(1 + tan 23)(1 +

3D
1992 FG6
As shown in the figure, ABC and XYZ are
equilateral triangles and are ends of a right prism.
P is the mid-point of BY and BP 3 cm, XY 4 cm.
CP
G6.1 If a =
, find a.
PX
G6.2 If CX = b cm, find b.
X
Y
P
Z
A
c
, find c.
5
C
B
2 d
, find d.
G6.4 I

Mensuration
1986 FI5.4
The base of a pyramid is a triangle with sides 3 cm, 4 cm and 5 cm. If the height
and volume of the pyramid are q cm and 12 cm3 respectively, find q.
1987 FI2.1
The volume of a sphere with radius r is 36, find r.
1989 FG9.2
A cuboid