EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Constructions 2
Constructions 2 · Transformations and constructions · Lesson 7 of 8 · 16 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 and compasses. Show all construction lines.
Question 1 CONSTRUCT (2 marks)
The diagram shows an angle ABC. Using ruler and compasses only, construct the bisector of angle ABC. Show all your construction lines.
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(Total for Question 1 = 2 marks)
Question 2 CONSTRUCT (3 marks)
Point P is 4 cm above a horizontal line. Using ruler and compasses only, construct the perpendicular from P to the line. Show all your construction lines.
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(Total for Question 2 = 3 marks)
Question 3 CONSTRUCT (3 marks)
Using ruler and compasses only, construct an angle of 60° at the end A of a line AB.
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(Total for Question 3 = 3 marks)
Question 4 CONSTRUCT (3 marks)
Using ruler and compasses only, construct an angle of 30° at the end A of a line AB.
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(Total for Question 4 = 3 marks)
Question 5 CONSTRUCT (3 marks)
Q is a point on a straight line. Using ruler and compasses only, construct the perpendicular to the line at Q.
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(Total for Question 5 = 3 marks)
Question 6 EXPLAIN (2 marks)
Explain why the line through the crossing arcs is the bisector of the angle in the angle bisector construction.
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(Total for Question 6 = 2 marks)
TOTAL FOR PAPER = 16 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (2 marks)
An arc from B crossing both arms, two equal arcs from those points crossing inside the angle, and a line from B through the crossing.
• Arcs from B and from the two crossing points M1
• A correct bisector with arcs shown A1
Question 2 (3 marks)
An arc centred on P cutting the line twice; equal arcs from those two points crossing below the line; a line from P to the crossing.
• Arc from P crossing the line twice M1
• Equal arcs from the two points M1
• A correct perpendicular A1
Question 3 (3 marks)
An arc centred on A crossing AB; the same radius centred on that crossing; a line from A through the crossing of the arcs.
• Arc centred on A M1
• Second arc with the same radius M1
• Line completed and angle correct A1
Question 4 (3 marks)
Construct 60° at A, then bisect it to make 30°.
• 60° constructed M1
• Bisector constructed M1
• Angle of 30° A1
Question 5 (3 marks)
An arc centred on Q cutting the line on both sides; equal larger arcs from those points crossing above; a line from Q through the crossing.
• Arc centred on Q M1
• Equal arcs from both points M1
• Correct perpendicular A1
Question 6 (2 marks)
The point where the arcs cross is the same distance from the two points on the arms, and both points are the same distance from the vertex, so the two triangles are congruent (a kite) and the angles are equal.
• Equal distances used M1
• Congruent triangles or kite symmetry C1