1.
Here is a sketch of a triangle.
5.7 cm
4.2 cm
6.3 cm
In the space below, use ruler and compasses to construct this triangle accurately. You must
show all construction lines.
(Total 3 marks)
2.
The diagram shows a sketch of triangle ABC.
Diagram NOT
accurately drawn
B
7. 3
A
cm
38°
8 cm
C
BC = 7.3 cm.
AC = 8 cm.
Angle C = 38°.
queen elizabeth's mercian school
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(a)
Make an accurate drawing of triangle ABC. The line AC has been accurately drawn.
A
C
(2)
(b)
Measure the size of angle A on your diagram.
.........................°
(1)
(Total 3 marks)
3.
Use ruler and compasses to construct an angle of 45 at A.
You must show all construction lines.
A
(Total 3 marks)
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4.
Diagram NOT accurately drawn
A
8 cm
B
6 cm
10 cm
C
ABC is a triangle.
AB = 8 cm.
AC = 6 cm.
BC = 10 cm.
(a)
Use ruler and compasses to construct an accurate drawing of triangle ABC.
The line BC has been drawn for you.
You must show all your construction lines.
B
C
(2)
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(b)
Use ruler and compasses to construct the perpendicular bisector of the line PQ.
You must show all your construction lines.
P
Q
(2)
(Total 4 marks)
5.
N
Diagram NOT
accurately drawn
N
Hospital
Cinema
72°
Art
gallery
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The diagram shows the position of each of three buildings in a town.
The bearing of the Hospital from the Art gallery is 072.
The Cinema is due East of the Hospital.
The distance from the Hospital to the Art gallery is equal to the distance from the Hospital to
the Cinema.
Work out the bearing of the Cinema from the Art gallery.
……………………
(Total 3 marks)
6.
The diagram shows the position of a farm F and a bridge B on a map.
(a)
Measure and write down the bearing of B from F.
....................................... º
(1)
A church C is on a bearing of 155º from the bridge B.
On the map, the church is 5 cm from B.
(b)
Mark the church with a cross (
) and label it C.
(2)
(Total 3 marks)
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7.
The diagram shows the position of two airports, A and B.
A plane flies from airport A to airport B.
N
N
A
x
B
Scale: 1 cm represents 50 km
(a)
Measure the size of the angle marked x.
................................ °
(1)
(b) Work out the real distance between airport A and airport B.
Use the scale 1 cm represents 50 km.
............................. km
(2)
Airport C is 350 km on a bearing of 060° from airport B.
(c)
On the diagram, mark airport C with a cross (×).
Label it C.
(2)
(Total 5 marks)
8.
Comptown
N
7.4 km
Ambletown
9.6 km
Bowtown
Diagram NOT accurately drawn
queen elizabeth's mercian school
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Ambletown, Bowtown and Comptown are three towns.
Ambletown is 9.6 km due west of Bowtown.
Bowtown is 7.4 km due south of Comptown.
Calculate the bearing of Ambletown from Comptown.
Give your answer correct to one decimal place.
……………………………
(Total 4 marks)
9.
N
Q
P
(a)
Measure and write down the bearing of Q from P.
............................................
(1)
N
T
(b)
R
Find the bearing of T from R.
............................................
(1)
(Total 2 marks)
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10.
A
B
D
C
ABCD is a rectangle.
Shade the set of points inside the rectangle which are both
and
more than 4 centimetres from the point A
more than 1 centimetre from the line DC.
(Total 4 marks)
11.
Draw the locus of all points which are equidistant from the points A and B.
A
B
(Total 2 marks)
12.
Draw the locus of all points that are exactly 3 cm from the line PQ.
P
___________________________________
Q
(Total 2 marks)
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