EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Loci
Loci · Transformations and constructions · Lesson 8 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 ruler and compasses and show all construction lines.
Question 1 DRAW (2 marks)
P is a point. Draw the locus of all the points that are 3 cm from P.
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(Total for Question 1 = 2 marks)
Question 2 CONSTRUCT (3 marks)
A and B are two points 6 cm apart. Using ruler and compasses only, construct the locus of points that are the same distance from A and from B.
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(Total for Question 2 = 3 marks)
Question 3 CONSTRUCT (4 marks)
The diagram shows a rectangle ABCD. The scale is 1 cm to 1 m. A tree will be planted nearer to AB than to AD and less than 4 m from C. Shade the region where the tree can be planted.
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(Total for Question 3 = 4 marks)
Question 4 DESCRIBE (2 marks)
A robot moves so that it is always 2 m from a straight fence 6 m long. Describe the shape of its path.
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(Total for Question 4 = 2 marks)
Question 5 CONSTRUCT (3 marks)
Two straight roads meet at a point O. A phone mast must be the same distance from both roads. Describe how to find the possible positions of the mast on a map.
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(Total for Question 5 = 3 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 (2 marks)
A circle of radius 3 cm with centre P.
• A circle drawn, centre P M1
• Radius 3 cm A1
Question 2 (3 marks)
The perpendicular bisector of AB, with construction arcs.
• Equal arcs from A and B M1
• Crossings joined M1
• A correct line with arcs shown A1
Question 3 (4 marks)
The bisector of angle DAB is drawn from A, a circle of radius 4 cm is drawn centred on C, and the region inside the rectangle below the bisector and inside the circle is shaded.
• Bisector of angle DAB M1
• Circle of radius 4 cm centred on C M1
• Correct side of each locus M1
• Correct region shaded A1
Question 4 (2 marks)
A racetrack: two straight lines parallel to the fence, 2 m from it, joined by a semicircle of radius 2 m at each end.
• Two parallel lines 2 m from the fence B1
• Semicircular ends B1
Question 5 (3 marks)
Construct the bisector of the angle between the two roads. The mast can be anywhere on this line.
• Angle bisector B1
• Construction method: arcs from O, then from the crossings M1
• The mast can be anywhere on the bisector A1