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 · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.A patio plan states: 'Side AB of the patio is parallel to side DC, and AB is longer than DC. Sides BC and AD are not parallel to each other and are not equal in length.' The four sides measure AB = 5.1 m, BC = 3.2 m, DC = 2.8 m and AD = 4.5 m. The tiler needs to order edging strip only for the sides that are not parallel to any other side. What total length of edging strip, in metres, should the tiler order?
(a)7.7 m
(b)4.5 m
(c)7.6 m
(d)15.4 m
2.A tent is shaped like a triangular prism: two triangular end faces and three rectangular faces. One of the rectangular faces lies flat on the ground as the groundsheet. How many of the tent's faces are above the ground, not touching the ground?
(a)5
(b)4
(c)3
(d)2
3.A chocolate bar is a prism. Its cross-section is a triangle with a base of 6 cm and a perpendicular height of 5 cm, and the bar is 12 cm long. Work out the volume of the bar.
(a)180 cm³
(b)66 cm³
(c)15 cm³
(d)360 cm³
4.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.
(a)8π cm
(b)8 cm
(c)16π cm
(d)4π cm
5.In triangle ABC, angle A is 2x°, angle B is 3x° and angle C is 4x°. Work out the size of angle B.
(a)60°
(b)20°
(c)120°
(d)80°
6.The vector $(- 2 5)$ describes a translation. A student writes it as $(5 - 2)$ by mistake. Write down what error the student has made.
(a)Doubled the x component
(b)Reversed both signs
(c)Swapped the x and y components
(d)Reversed only the y sign
7.The interior angles of a pentagon are 100°, 110°, 120°, x° and x°. Work out the size of each of the two angles marked x°.
(a)105°
(b)55°
(c)108°
(d)210°
8.In an isosceles triangle each of the two base angles is 46°. Work out the size of the angle at the apex.
(a)92°
(b)134°
(c)46°
(d)88°
9.In triangle ABC and triangle DEF, AB = DE, angle ABC = angle DEF and BC = EF. Write down the congruence condition that proves the two triangles are congruent.
(a)SSS
(b)SAS
(c)ASA
(d)RHS
10.A shop sells a scale model of a van. The model and the real van are similar shapes, with lengths in the ratio 1 : 24. The model is 18.5 cm long. Work out the length of the real van, giving your answer in metres.
(a)444 m
(b)44.4 m
(c)0.77 m
(d)4.44 m
11.A quadrilateral has all four sides equal in length and all four interior angles equal to 90°. Its diagonals are equal in length and bisect each other at right angles. Which quadrilateral matches this description exactly?
(a)Rectangle
(b)Square
(c)Kite
(d)Rhombus
12.A fan-shaped rug is in the shape of a sector of a circle with radius 4 m and angle 180°. It costs £4 per square metre to make. Using π = 3.14, work out the total cost of the rug.
(a)£50.24
(b)£25.12
(c)£200.96
(d)£100.48
13.A solid pyramid has a square base of side 10 cm and four identical triangular faces. Its apex is directly above the centre of the base, at a vertical height of 12 cm, and the slant height of each triangular face — the distance from the apex to the midpoint of a base edge — is 13 cm. Work out the total surface area of the pyramid.
(a)340 cm²
(b)360 cm²
(c)620 cm²
(d)260 cm²
14.A parallelogram has a base of 9 cm and a perpendicular height of 4 cm. Work out its area.
(a)72 cm²
(b)18 cm²
(c)36 cm²
(d)26 cm²
15.A student says the reverse of the translation vector $(- 9 4)$ is $(9 4)$ . Write down the correct reverse translation vector.
(a) $(- 9 - 4)$
(b) $(- 9 4)$
(c) $(9 - 4)$
(d) $(9 4)$

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