Name: ___________________________
GCSE (1 – 9)
Loci and Construction
Instructions
• Use black ink or ball-point pen.
• Answer all Questions.
• Answer the Questions in the spaces provided
– there may be more space than you need.
• Diagrams are NOT accurately drawn, unless otherwise indicated.
• You must show all your working out.
Information
• The marks for each Question are shown in brackets
– use this as a guide as to how much time to spend on each Question.
Advice
• Read each Question carefully before you start to answer it.
• Keep an eye on the time.
• Try to answer every Question.
• Check your answers if you have time at the end
mathsgenie.co.uk
1 ABC is a triangle.
C
6 cm
8 cm
AB = 10 cm
BC = 8 cm A B
AC = 6 cm 10 cm
Use ruler and compasses to construct an accurate drawing of triangle ABC.
You must show all your construction lines.
(Total for Question 1 is 3 marks)
2 A stadium is going to be built.
It must be no more than 10 km from town A and no more than 8 km from town B.
1 cm represents 2 km
Shade the region on the diagram where the stadium can be built.
× Town A
×
Town B
(Total for Question 2 is 2 marks)
3 In the space below, use a ruler and compasses to construct an equilateral triangle with side
length 6 cm.
You must show all your construction lines.
(Total for Question 3 is 3 marks)
4 Use ruler and compasses to construct the perpendicular from point C to the line AB.
You must show all your construction lines.
× C
(Total for Question 4 is 2 marks)
5 Use ruler and compasses to construct the perpendicular from point P to the line AB.
You must show all your construction lines.
× P
A B
(Total for Question 5 is 2 marks)
6 Use ruler and compasses to construct the bisector of angle BAC.
You must show all your construction lines.
(Total for Question 6 is 2 marks)
7 Use ruler and compasses to construct the bisector of angle DEF.
You must show all your construction lines.
(Total for Question 7 is 2 marks)
8 Use ruler and compasses to construct a perpendicular bisector of the line AB.
You must show all your construction lines.
A B
(Total for Question 8 is 2 marks)
9 In the space below, use a ruler and compasses to construct a 30° angle.
You must show all your construction lines.
(Total for Question 9 is 4 marks)
10 Here is a scale drawing of a garden.
The scale is 1 cm to 2 m
A tree is going to be planted.
The tree must be more than 4 m from the patio.
The tree must be more than 6 m from the pond.
Shade the region where the tree can be planted.
Patio
×
Pond
(Total for Question 10 is 2 marks)
11 Here is a scale drawing of a room.
The scale is 1 cm to 2 m.
A chair is going to be placed in the room.
The chair must be closer to AB than BC.
The chair must be less than 14 m from D.
Shade the region where the chair can be placed.
A D
B C
(Total for Question 11 is 2 marks)
12 A, B and C are three points on a map.
1cm represents 100 metres.
×B
A
×
×
C
Point P is 300 metres from A.
Point P is equidistant from B and C.
On the map, show the possible positions of P.
(Total for Question 12 is 3 marks)
