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

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1.The cross-section of a tent is an isosceles triangle. The angle at the top, between the two equal sloping sides, is 62°. The other two angles are equal to each other. Work out the size of each of those two angles.
(a)59°
(b)118°
(c)62°
(d)31°
2.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.
(a)125 g
(b)1025 g
(c)1000 g
(d)1250 g
3.An isosceles triangle ABC has AB equal to AC. AM is a line from vertex A, perpendicular to BC, meeting BC at point M. Which condition proves that triangle ABM is congruent to triangle ACM?
(a)SAS, right angle as included angle
(b)ASA, AB as the included side
(c)SSS, using BM = CM as a fact
(d)RHS, using AM as common side
4.A solid rubber ball has a radius of 3 cm. Work out the volume of the ball. Use π = 3.14.
(a)113.04 cm³
(b)28.26 cm³
(c)37.68 cm³
(d)84.78 cm³
5.A water tank holds 2.5 m³. Work out this volume in cm³.
(a)2500 cm³
(b)2 500 000 cm³
(c)25 000 cm³
(d)250 cm³
6.A polygon has one more side than a heptagon. What is the polygon called?
(a)hexagon
(b)heptagon
(c)octagon
(d)nonagon
7.A circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.
(a)15.7 cm
(b)31.4 cm
(c)62.8 cm
(d)78.5 cm
8.The diagram shows the plan, front elevation and side elevation of a solid. Which solid could this be?
(a)A cuboid
(b)A cone
(c)A square-based pyramid
(d)A cylinder
9.In triangle ABC, point D lies on side AB and point E lies on side AC, so that DE is parallel to BC. AD = 3 cm, DB = 6 cm and DE = 4 cm. Work out the length of BC.
(a)4 cm
(b)8 cm
(c)10 cm
(d)12 cm
10.The point R(−6, 9) is translated by the vector $(- 11 5)$ . Write down the coordinates of the image of R.
(a)(−1, 9)
(b)(−1, −2)
(c)(−6, −2)
(d)(−11, 20)
11.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
12.A wooden cube has edges of length 4 cm. Work out the total surface area of the cube.
(a)96 cm²
(b)24 cm²
(c)16 cm²
(d)64 cm³
13.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) $(- 13 - 7)$
14.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
15.Point D is at (3, 4). It is rotated 90° clockwise about the origin (0, 0). Work out the coordinates of the image of point D.
(a)(−3, −4)
(b)(−4, 3)
(c)(4, −3)
(d)(4, 3)

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