EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Constructions 1
Constructions 1 · Transformations and constructions · Lesson 6 of 8 · 14 marks · 30 minutes
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Instructions
• Answer all the questions.
• Write your answers in the spaces provided.
• The marks for each question are shown in brackets - use this as a guide to how much to write.
• The answers are on separate pages at the back. Attempt every question before you look at them.
• Answer all questions. Use a sharp pencil, a ruler, compasses and a protractor. Show all construction lines.
Question 1 CONSTRUCT (3 marks)
Using ruler and compasses only, construct a triangle with sides of length 6 cm, 5 cm and 4 cm. Show all your construction lines.
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(Total for Question 1 = 3 marks)
Question 2 CONSTRUCT (2 marks)
The line AB is 6 cm long. Using ruler and compasses only, construct the perpendicular bisector of the line AB. Show all your construction lines.
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(Total for Question 2 = 2 marks)
Question 3 EXPLAIN (2 marks)
Explain why it is not possible to construct a triangle with sides of length 3 cm, 4 cm and 8 cm.
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(Total for Question 3 = 2 marks)
Question 4 CONSTRUCT (3 marks)
Construct a triangle ABC with AB = 7 cm, AC = 5 cm and angle BAC = 40°.
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(Total for Question 4 = 3 marks)
Question 5 MEASURE (2 marks)
In the triangle with sides 6 cm, 5 cm and 4 cm, measure the size of the largest angle.
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(Total for Question 5 = 2 marks)
Question 6 DECIDE (2 marks)
For each set of lengths, state whether a triangle can be constructed. (a) 5 cm, 6 cm, 7 cm (b) 2 cm, 3 cm, 6 cm
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(Total for Question 6 = 2 marks)
TOTAL FOR PAPER = 14 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (3 marks)
Draw a line of 6 cm. From one end draw an arc of radius 5 cm and from the other draw an arc of radius 4 cm, crossing above the line. Join the crossing to each end.
• A 6 cm line drawn accurately B1
• Both arcs drawn correctly M1
• Triangle completed and arcs shown A1
Question 2 (2 marks)
Equal arcs from A and B, with radius more than 3 cm, crossing above and below; a straight line through the two crossings.
• Arcs of equal radius from A and B M1
• Correct crossings, both sides A1
Question 3 (2 marks)
The two shorter sides add up to 3 + 4 = 7 cm, which is less than 8 cm, so the arcs would not meet.
• 3 + 4 = 7 M1
• 7 < 8, so the arcs do not meet C1
Question 4 (3 marks)
Draw AB = 7 cm. Measure 40° at A. Mark C 5 cm from A along the line. Join B to C.
• AB drawn accurately B1
• Angle of 40° at A M1
• AC = 5 cm and triangle completed A1
Question 5 (2 marks)
The largest angle is opposite the 6 cm side and is about 83° (accept 81° to 85°).
• Identifying the angle opposite the 6 cm side M1
• 83 (within the range) A1
Question 6 (2 marks)
(a) Yes, because 5 + 6 = 11 > 7. (b) No, because 2 + 3 = 5 < 6.
• (a) Yes B1
• (b) No B1