Edexcel GCSE Maths (1MA1), Higher tier · Geometry and measures
Practise Constructions and loci. 7 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.
Question 1Easy2 marks
The diagram shows the line segment AB. This question should be answered on a printed copy of the diagram.
[object Object]
Use ruler and compasses to construct the perpendicular bisector of AB. You must show all your construction lines.[2]
Show the answer and mark scheme
Answer: A straight line through the two points where arcs of equal radius, centred on A and on B, intersect (one point on each side of AB).
M1 for two pairs of intersecting arcs of equal radius, centred on A and on B, one pair on each side of AB
A1 for a correct perpendicular bisector drawn through the points of intersection of the arcs (within 2 mm of the correct line)
Worked solution: Open the compasses to more than half of AB. Draw arcs centred on A above and below AB. With the same radius, draw arcs centred on B to cross the first arcs. Join the two crossing points with a straight line: this line is the perpendicular bisector of AB.
Question 2Medium3 marks
This question should be answered on plain paper using a ruler, compasses and a protractor.
(a) Use ruler and compasses to construct triangle ABC with AB = 8 cm, AC = 6 cm and BC = 7 cm. You must show all your construction lines.[2]
(b) Measure the size of angle ABC.[1]
Show the answer and mark scheme
(a)Answer: AB drawn 8 cm; arc radius 6 cm centred on A and arc radius 7 cm centred on B, crossing at C.
M1 for AB drawn 8 cm long and an arc of radius 6 cm centred on A or an arc of radius 7 cm centred on B
A1 for a correct triangle with both construction arcs shown (sides within 2 mm)
Worked solution: Draw AB = 8 cm. Set the compasses to 6 cm and draw an arc centred on A. Set the compasses to 7 cm and draw an arc centred on B. The arcs cross at C. Join AC and BC.
(b)Answer: 47° (allow 45° to 49°) °
B1 for an angle in the range 45° to 49°
Worked solution: cos ABC = (8² + 7² − 6²) ÷ (2 × 8 × 7) = 77 ÷ 112, so angle ABC ≈ 46.6°. A careful construction measures about 47°.
Question 3Hard4 marks
This question should be answered on plain paper using a ruler and compasses. ABCD is a rectangle with AB = 8 cm and BC = 5 cm.
Draw rectangle ABCD accurately. A point T lies inside the rectangle. T is nearer to AB than to AD. T is less than 5 cm from C. Shade the region where T could be. You must show all your construction lines.[4]
Show the answer and mark scheme
Answer: The region inside the rectangle that is on the AB side of the bisector of angle DAB and inside the circle of radius 5 cm centred on C.
B1 for rectangle ABCD drawn accurately (AB = 8 cm, BC = 5 cm)
M1 for a construction of the bisector of angle DAB (with arcs)
M1 for an arc of radius 5 cm centred on C
A1 for the correct region shaded
Worked solution: Draw the rectangle. The points that are the same distance from AB and AD lie on the bisector of angle DAB, so construct this bisector: T must be on the same side of it as AB. Draw an arc of radius 5 cm centred on C: T must be inside it. Shade the part of the rectangle that satisfies both conditions.