## Transcribed Text

Question.1
A rectangular picture frame is to be made.
It is 30 centimetres high
and 22.5 centimetres wide, as shown.
To check that the frame is rectangular,
d
30 cm
the diagonal, d, is measured.
It is 37.3 centimetres long.
Y
Is the frame rectangular ?
22-5 cm
Question.2
The central semi-circular archway
under a bridge is to be strengthened.
While the work is being carried out,
2 metal beams are to be set in place
to support the archway.
For safety reasons, the beams have
to just meet on the circumference
of the arch.
4-1 m
Will the beams fit this archway which is 4.1 metres wide ?
Question.3
The diagram shows the design of an earring.
The earring consists of a circle
inside an equilateral triangle.
The sides of the triangle are tangents to the circle.
The radius of the circle is 8 mm
The distance from the centre of the circle
to each vertex of the triangle is 17mm.
Calculate the perimeter of the triangle.
Question.4
The road joining A to B is
A
300 m
B
parallel to the road joining
C to D in the diagram.
180 m
240 m
X
AB = 300 metres,
Brock
Burn
AX = 180 metres,
T
BX = 240 metres
and CD = 750 metres.
C
750 m
D
a)
Prove that the two roads AX and BX are at right angles to one another
b)
The Brock Burn burst its banks at T and the road became impassable.
An alternative route had to be found in order to travel from A to D.
Question.5
Trigonometry
1.
In the diagram
Angle STV = 34°
S
Angle VSW = 25°
13.1con
25°
Angle SVT = Angle SWV = 90°
W
ST = 13.1 centimetres
34°
Calculate the length of SW
T
V
Question.6
A cat is trapped in a tree and a ladder is placed against the tree in an
attempt
to
rescue
it.
The ladder rests against the tree making an angle of
60° with the horizontal and reaching 14 metres up
1 4m
the tree, allowing the rescuer to reach the cat.
60'
o
I
1m
Just as the cat is about to be rescued, it jumps to a
branch 1 metre above its original resting place.
Calculate the size of the angle, to the nearest degree,
that the ladder now has to make with the horizontal
to allow the rescuer to reach the cat.
Question.7
Two support cables, from the
T
A
4h
top (T) of a motorway light,
are attached to a pair of points,
A and B, on the ground,
as shown in the diagram.
13.5 m
a)
Calculate the distance
from B to C.
b)
Calculate the distance
40°
70°
O
a
from A to B.
A
B
C
Question.8
The diagram shows the design
of a swimming pool 50 metres
in length.
1 metre
The pool is 1 metre deep at one
50 metres
4
1 metre
end and its base slopes downwards
d metres
at an angle of 3° to the horizontal.
3°
Calculate the depth, d metres, of
7
the other end of the pool, giving
your answer to 2 significant figures.
Do not use a scale drawing.
Question.9
Two boats leave port together.
Nort
Boat D sails on a course of 057°
at 13 miles per hour.
Boat E sails on a bearing of 104°
D
at 15 miles per hour.
After 45 minutes Boat D receives
a distress call from Boat E requesting
Port
their help as soon as possible.
E
How far, to the nearest mile, would Boat D have to travel to reach Boat E?
Question.10
N
The radio masts, Kangaroo (K), Wallaby (W)
and Possum (P) are situated
in the Australian outback.
W
Kangaroo is 250 kilometres due south of Wallaby.
250 km
Wallaby is 410 kilometres from Possum
410 km
Possum is on a bearing of 130° from Kangaroo.
Calculate the bearing of Possum from Wallaby.
K
Do not use a scale drawing.
P

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