Printable · GCSE Foundation · ages 14-16

Geometry and measures worksheet — GCSE Foundation

Fifteen questions across the geometry and measures statements at Foundation tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.

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Geometry and measures worksheet — GCSE Foundation

Maths · GCSE Foundation · Geometry and measures · 15 questions

MathsUKwww.geekhero.co.uk

1.A sector of a circle has an angle of 90° at the centre. Write down what fraction of the whole circle this sector represents.
(a)3/4
(b)1/2
(c)1/4
(d)1/8
2.Triangle ABC has a right angle at B. Triangle DEF has a right angle at E. The hypotenuse of triangle ABC equals the hypotenuse of triangle DEF, and side AB equals side DE. Which condition proves that the two triangles are congruent?
(a)ASA
(b)SAS
(c)SSS
(d)RHS
3.The diagram shows a cuboid. Work out the area of its front elevation, in square centimetres.
(a)12 cm²
(b)20 cm²
(c)24 cm²
(d)18 cm²
4.A vertical flagpole casts a shadow 6 m long at the same time as a 1.2 m vertical post casts a shadow 1.8 m long. The flagpole and the post are both vertical, and the triangles formed by each object, its shadow, and the sun's ray are similar. Work out the height of the flagpole.
(a)5.4 m
(b)4 m
(c)9 m
(d)7.2 m
5.Three angles meet at a single point on one side of a straight line. Two of the angles are 48° and 65°. Work out the third angle.
(a)113°
(b)48°
(c)67°
(d)180°
6.The angle between north and a footpath is 35°, measured clockwise from north. What is the three-figure bearing of the footpath?
(a)035°
(b)325°
(c)350°
(d)215°
7.A gardener wants to plant a tree so that it is the same distance from two straight garden walls that meet at a corner, and also the same distance from two ornamental posts standing 4 m apart. Which construction locates this point?
(a)where the angle bisector meets the posts' perpendicular bisector
(b)where the angle bisector meets the line joining the posts
(c)the perpendicular bisector of the posts, alone
(d)the angle bisector of the corner, alone
8.m is the column vector with top number 4 and bottom number 6. n is the column vector with top number −6 and bottom number −9. Given that n = k × m for some number k, work out the value of k.
(a)1.5
(b)−10
(c)−1.5
(d)−24
9.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?
(a)A smaller circle
(b)A triangle
(c)The same size circle as the base
(d)An ellipse
10.Work out the distance between the point (0, 0) and the point (5, 12).
(a)12
(b)13
(c)17
(d)7
11.A drone starts at the point (2, −3) on a coordinate grid. It flies by the vector $(4 6)$ and then by the vector $(- 9 - 1)$ . Write down the column vector that would take the drone straight back to its starting point.
(a) $(- 5 - 5)$
(b) $(5 - 5)$
(c) $(- 5 5)$
(d) $(- 13 - 7)$
12.Two metal window frames are checked before installation. Frame A has edges of 40 cm and 65 cm, with a marked angle of 35° at the far end of the 65 cm edge, away from where the two given edges meet. Frame B has matching edges of 40 cm and 65 cm, with a matching 35° angle in the same position. The fitter wants to know if these measurements alone guarantee the two frames are congruent. What should the fitter be told?
(a)No — the angle is not between the two sides
(b)Yes — SSS, since three measurements are given
(c)Yes — SAS, since two sides and an angle match
(d)No — because only two sides were measured
13.A solid has 6 faces: one pentagon and five triangles that all meet at a single point above the pentagon. What is the name of this solid?
(a)Hexagonal pyramid
(b)Triangular pyramid
(c)Pentagonal pyramid
(d)Pentagonal prism
14.A solid has one curved surface and two flat circular faces of equal size, one at each end. What is the name of this solid?
(a)Triangular prism
(b)Sphere
(c)Cone
(d)Cylinder
15.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.
(a)159
(b)283
(c)182
(d)77

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