Edexcel GCSE Maths · G1–G15

Properties and constructions

50 maths questions with worked answers with answers for G1–G15 Properties and constructions in Edexcel GCSE Maths (spec 1MA1). Practise with flashcards, a topic quiz, a random quiz across the course, 5 crosswords, or read every question and answer below. Not official Pearson material.

All 50 questions and answers

Question 1 · Constructions · G2
How do you construct the perpendicular bisector of a line AB?
Answer:
With compasses set more than half of AB, draw arcs from A and from B on both sides.
Join the two crossing points.
Question 2 · Constructions · G2
How do you bisect an angle with compasses?
Answer:
Draw an arc from the vertex cutting both arms. From each cut, draw arcs that cross.
Join the vertex to the crossing point.
Question 3 · Loci · G2
Describe the locus of points 3 cm from a fixed point P.
Answer:
All points at the same distance from P.
A circle with centre P and radius 3 cm.
Question 4 · Loci · G2
Describe the locus of points equidistant from two points A and B.
Answer:
Points the same distance from A and B.
The perpendicular bisector of AB.
Question 5 · Loci · G2
Describe the locus of points equidistant from two intersecting lines.
Answer:
Points the same distance from both lines.
The bisectors of the angles between the lines.
Question 6 · Angle facts · G3
Angles on a straight line are 3x and 2x. Find x.
Answer:
3x + 2x = 180.
x = 36°.
Question 7 · Angle facts · G3
Angles around a point are 110°, 95° and x. Find x.
Answer:
Angles at a point sum to 360°.
x = 360 − 205 = 155°.
Question 8 · Parallel lines · G3
What is the relationship between alternate angles on parallel lines?
Answer:
They form a Z shape.
Alternate angles are equal.
Question 9 · Parallel lines · G3
What is the relationship between co-interior angles on parallel lines?
Answer:
They form a C (or U) shape.
They add up to 180°.
Question 10 · Triangles · G3
Two angles of a triangle are 48° and 67°. Find the third.
Answer:
Angles in a triangle sum to 180°.
180 − 115 = 65°.
Question 11 · Isosceles triangles · G3
An isosceles triangle has one angle of 40° between its two equal sides. Find the other two angles.
Answer:
180 − 40 = 140.
Each is 70°.
Question 12 · Polygons · G3
Find the sum of the interior angles of a hexagon.
Answer:
(n − 2) × 180 with n = 6.
4 × 180 = 720°.
Question 13 · Polygons · G3
Find the size of each exterior angle of a regular octagon.
Answer:
Exterior angles sum to 360°.
360 ÷ 8 = 45°.
Question 14 · Polygons · G3
Each interior angle of a regular polygon is 150°. How many sides does it have?
Answer:
Exterior angle = 180 − 150 = 30°.
360 ÷ 30 = 12 sides.
Question 15 · Quadrilaterals · G3
Three angles of a quadrilateral are 85°, 100° and 70°. Find the fourth.
Answer:
Angles in a quadrilateral sum to 360°.
360 − 255 = 105°.
Question 16 · Quadrilaterals · G4
State two properties of a rhombus.
Answer:
Any two from:
All four sides are equal. Opposite angles are equal. Diagonals bisect each other at right angles.
Question 17 · Quadrilaterals · G4
What is the difference between a kite and a parallelogram?
Answer:
A kite has two pairs of equal adjacent sides and one line of symmetry.
A parallelogram has two pairs of parallel, equal opposite sides.
Question 18 · Symmetry · G4
How many lines of symmetry does a regular pentagon have?
Answer:
A regular polygon has as many lines of symmetry as sides.
5.
Question 19 · Congruence · G5
State the four conditions for triangles to be congruent.
Answer:
SSS, SAS, ASA (or AAS) and RHS.
RHS = right angle, hypotenuse, side.
Question 20 · Congruence · G5
Is AAA a valid condition for congruence? Explain.
Answer:
Three equal angles only show the triangles are the same shape.
No; the triangles are similar but may be different sizes.
Question 21 · Proof · G6 · Higher only
Prove that the angles in a triangle add up to 180°.
Answer:
Draw a line through one vertex parallel to the opposite side.
The two alternate angles and the vertex angle lie on a straight line, so they sum to 180°.
Question 22 · Similar triangles · G6
Triangles ABC and DEF are similar. AB = 5 cm, DE = 15 cm and BC = 7 cm. Find EF.
Answer:
Scale factor = 15 ÷ 5 = 3.
EF = 7 × 3 = 21 cm.
Question 23 · Reflections · G7
Reflect the point (3, 5) in the y-axis.
Answer:
The x-coordinate changes sign.
(−3, 5).
Question 24 · Reflections · G7
Reflect the point (2, −4) in the line y = x.
Answer:
Swap the coordinates.
(−4, 2).
Question 25 · Rotations · G7
Rotate (4, 1) by 90° clockwise about the origin.
Answer:
(x, y) becomes (y, −x).
(1, −4).
Question 26 · Rotations · G7
Rotate (3, 2) by 180° about the origin.
Answer:
Both coordinates change sign.
(−3, −2).
Question 27 · Translations · G7
Translate (5, −2) by −34.
Answer:
5 − 3 = 2 and −2 + 4 = 2.
(2, 2).
Question 28 · Enlargements · G7
Enlarge the point (2, 3) by scale factor 3 with centre the origin.
Answer:
Multiply each coordinate by 3.
(6, 9).
Question 29 · Describing transformations · G7
What three details must you give to describe a rotation?
Answer:
Centre, angle and direction.
For example: 90° anticlockwise about (0, 0).
Question 30 · Enlargements · G7 · Higher only
Enlarge the point (4, 6) by scale factor −12 about the origin.
Answer:
Multiply each coordinate by −0.5.
(−2, −3).
Question 31 · Enlargements · G7
What does a fractional scale factor between 0 and 1 do?
Answer:
It makes the shape smaller.
The image is closer to the centre of enlargement.
Question 32 · Combined transformations · G8 · Higher only
What single transformation is a reflection in the x-axis followed by a reflection in the y-axis?
Answer:
(x, y) → (x, −y) → (−x, −y).
A rotation of 180° about the origin.
Question 33 · Invariant points · G8 · Higher only
What is an invariant point?
Answer:
A point that does not move under a transformation.
For example, points on the mirror line in a reflection.
Question 34 · Circle vocabulary · G9
Name the line segment that joins two points on a circle and passes through the centre.
Answer:
It is twice the radius.
The diameter.
Question 35 · Circle vocabulary · G9
What is a chord?
Answer:
A straight line joining two points on the circumference.
The diameter is the longest chord.
Question 36 · Circle theorems · G10 · Higher only
What is the angle in a semicircle?
Answer:
An angle subtended by a diameter at the circumference.
90°.
Question 37 · Circle theorems · G10 · Higher only
The angle at the centre is 140°. Find the angle at the circumference subtended by the same arc.
Answer:
The angle at the centre is twice the angle at the circumference.
70°.
Question 38 · Circle theorems · G10 · Higher only
Opposite angles of a cyclic quadrilateral: one is 105°. Find the other.
Answer:
Opposite angles in a cyclic quadrilateral add to 180°.
75°.
Question 39 · Circle theorems · G10 · Higher only
What is the angle between a tangent and a radius at the point of contact?
Answer:
The tangent meets the radius at a right angle.
90°.
Question 40 · Circle theorems · G10 · Higher only
What does the alternate segment theorem state?
Answer:
The angle between a tangent and a chord is equal to the angle in the alternate segment.
That angle is at the circumference on the other side of the chord.
Question 41 · Circle theorems · G10 · Higher only
What can you say about two tangents drawn from the same external point?
Answer:
They are equal in length.
The line to the centre bisects the angle between them.
Question 42 · Circle theorems · G10 · Higher only
Angles in the same segment: one is 38°. What is another angle in the same segment, subtended by the same chord?
Answer:
Angles in the same segment are equal.
38°.
Question 43 · Constructions · G2
Which compass construction gives a triangle when three side lengths are given?
Answer:
Draw one side, then arcs of the other two lengths from each end.
Join the ends to where the arcs cross.
Question 44 · 3D shapes · G12
How many faces, edges and vertices does a triangular prism have?
Answer:
Two triangles and three rectangles.
5 faces, 9 edges, 6 vertices.
Question 45 · Plans and elevations · G13
What is the plan view of a cylinder standing upright?
Answer:
The view from above.
A circle.
Question 46 · Bearings · G15
What are the three rules for bearings?
Answer:
Measure from north.
Measure clockwise, and write three figures (e.g. 065°).
Question 47 · Bearings · G15
The bearing of B from A is 070°. Find the bearing of A from B.
Answer:
Back bearing = bearing ± 180°.
070 + 180 = 250°.
Question 48 · Bearings · G15
What bearing is due south-west?
Answer:
South is 180° and west is 270°.
225°.
Question 49 · Scale drawings · G15
On a scale drawing 1 cm represents 5 km. A ship sails 35 km. How long is the line?
Answer:
35 ÷ 5.
7 cm.
Question 50 · Coordinate geometry · G11 · Higher only
A(1, 2), B(5, 2) and C(5, 5) form a triangle. Show it is right-angled and find AC.
Answer:
AB is horizontal and BC is vertical, so angle B = 90°.
AC² = 4² + 3² = 25, so AC = 5.

← R1–R16 Ratio, proportion and rates of change G16–G23 Mensuration and calculation →

Properties and constructions

All 50 questions and answers

More Edexcel GCSE Maths topics

Cookies on Knowledge Noodles

Cookie settings