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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.Point A is at (2, 3). It is translated by the vector (4, −1) to give point A′. Work out the coordinates of A′.
(a)(1, 7)
(b)(6, 4)
(c)(6, 2)
(d)(−2, 4)
2.A trapezium-shaped allotment plot has two parallel sides that face each other, and two sloping sides that are equal in length (an isosceles trapezium). One of the angles next to the shorter parallel side is 118°. Work out the angle next to the other end of the same shorter parallel side.
(a)180°
(b)59°
(c)62°
(d)118°
3.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.
(a)the origin
(b)y-axis
(c)both axes
(d)x-axis
4.A ramp is built from two straight metal supports that rest on the flat ground and meet each other at the top, forming a triangle with the ground. One support meets the ground at 34°. The angle between the two supports where they meet is 71°. Work out the angle between the second support and the ground.
(a)75°
(b)105°
(c)37°
(d)146°
5.A hexagonal prism has 8 faces and 12 vertices. Using F + V − E = 2, work out how many edges it has.
(a)20
(b)22
(c)18
(d)16
6.In kite WXYZ, WX = WZ and XY = ZY (so at each of X and Z, one side from each of the two unequal pairs meets). Angle X = 100°. Work out angle Z.
(a)100°
(b)260°
(c)80°
(d)50°
7.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
8.What does the statement AB = CD mean, where A, B, C and D are all points?
(a)AB is parallel to CD
(b)A, B, C and D all lie on one line
(c)AB and CD are equal in length
(d)AB is perpendicular to CD
9.Triangle ABC has AB = 9 cm, BC = 6 cm and angle A = 35°. Triangle DEF has DE = 9 cm, EF = 6 cm and angle D = 35°. Which of the following correctly identifies the condition shown here?
(a)SSA - not sufficient to prove congruence
(b)ASA - two angles and the included side equal
(c)SAS - two sides and the included angle equal
(d)AAS - two angles and a non-included side equal
10.Triangle DEF has a right angle at E. Angle DFE = 60° and EF = 9 cm. Work out the exact length of DE.
(a)18 cm
(b)3√3 cm
(c)9√3/2 cm
(d)9√3 cm
11.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
12.A circular clock face has a diameter of 18 cm. Work out the circumference of the clock face. Use π = 3.14.
(a)28.26 cm
(b)113.04 cm
(c)1017.36 cm
(d)56.52 cm
13.A rectangular tile measures 4.5 cm by 6 cm. Work out the area of the tile.
(a)10.5 cm²
(b)21 cm²
(c)27 cm²
(d)30 cm²
14.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
15.How many edges does a triangular prism have?
(a)9
(b)5
(c)6
(d)12

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