Circle
A, B, C and D are four points on the circumference of a circle. ABCD is a square with
sides 20 cm long.
Work out the diameter of the circle. Give your answer correct to 3 sig. fig. (4 marks)
Rectangle
The diagram represents a rectangle which is 6 cm long. A diagonal makes an angle of 23
with a 6 cm side.
Calculate the length of a diagonal. Give your answer correct to 3 sig. fig. (3 marks)
Building frame
The diagram represents
the frame for part of a
building
(b) Work out the area of triangle BCD. (2 marks)
(c) Calculate the length BC. Give your answer correct to 3 significant figures.(3 marks)
(d) Calculate the size of the angle marked x .Give your answer correct to 1dp(3 marks)
Ballymena
(a) Calculate the distance of Larne from Ballymena. Give your answer
in kilometres, correct to 1 decimal place. (3 marks)
(b) Calculate the bearing of Ballymena from Woodburn. (4 marks)
Length AB
Calculate the length of AB. Give your answer correct to 1 decimal place
(3 marks)
Nigerian towns
The diagram is part of a map showing the positions of three Nigerian towns.
Kaduna is due North of Aba
(a) Calculate the direct distance between Lagos and Kaduna.
(b) Calculate the distance between Kaduna and Aba.
Give your answers to the nearest kilometre.
(5 marks)
.
Ladder
Sidney places the foot of his ladder on horizontal ground and the top against a
vertical wall.
(a) Work out how high up the wall the ladder reaches.
(b) Work out the angle the base of the ladder makes with the ground.
Give your answers to 3 significant figures.
(6 marks)
Swimming pool
Here is a side view of a swimming pool.
(a) Calculate the length of the line FG.
Give your answer correct to 3 significant
figures.
(b) Calculate the angle that the line GF makes with the horizontal. Give your
answer correct to 1 decimal place. (6 marks)
Triangle
In the diagram AB = 17.9 m, BD = 8.2 m, angle CBD = 37º and angle BDC = 90º.
ADC is a straight line.
(a) Calculate the length of DC. Give your answer,
in metres, correct to 3 sig. fig.
(b) Calculate the size of angle DAB. Give your
answer correct to 1 decimal place.
( 6 marks)
House and garage 1
The diagram shows a house and a garage on level ground.
A ladder is placed with one end at the bottom of the house wall.
The top of the ladder touches the top of the garage wall.
The distance between the garage wall and the house is 1.4 m.
The angle the ladder makes with the ground is 62º
(a) Calculate the height of the garage wall. Give your answer
correct to 3 significant figures.
(3 marks)
.
House and garage 2
The diagram shows a house and a garage on level ground.
A ladder of length 3.5 m is then placed against the house wall.
The bottom of this ladder rests against the bottom of the garage
wall.
(b) Calculate the angle that this ladder makes with the ground.
Give your answer correct to 1 decimal place.
(3 marks)
Diagonal
Calculate the length of a diagonal of this rectangle.
Give your answer in centimetres correct to one decimal place.
(3 marks)
Telephone masts 1
The diagram shows the positions of three telephone masts A, B and C.
(a) Calculate the distance of A from B.
Give your answer in kilometres, correct to 3 significant figures. (3 marks)
Telephone masts 2
The diagram shows the positions of three
telephone masts A, B and C.
(b)
i)Calculate the size of the angle marked x.
ii) Calculate the bearing of A from C.
iii) Calculate the bearing of C from A.
Give your answers correct to one decimal
place. (5 marks)