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Loci and Construction: Name

This document provides instructions for a test on loci and construction. It explains that students should use black or blue ink, answer all questions in the spaces provided, and show all working out. It provides the mark allocation for each question to guide students on time spent. The document contains 12 questions testing students' abilities to accurately construct geometric shapes and lines using only a ruler and compass, and to solve problems involving loci.

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carolinethami13
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492 views8 pages

Loci and Construction: Name

This document provides instructions for a test on loci and construction. It explains that students should use black or blue ink, answer all questions in the spaces provided, and show all working out. It provides the mark allocation for each question to guide students on time spent. The document contains 12 questions testing students' abilities to accurately construct geometric shapes and lines using only a ruler and compass, and to solve problems involving loci.

Uploaded by

carolinethami13
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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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 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)

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