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 hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?
(a)320
(b)180
(c)295
(d)310
2.A parallelogram has a base of 9 cm and a perpendicular height of 6 cm. Work out the area of the parallelogram.
(a)30 cm²
(b)54 cm²
(c)15 cm²
(d)27 cm²
3.A sector of a circle is bounded by two straight edges and one curved edge. Write down the mathematical term for each of the two straight edges.
(a)Chord
(b)Diameter
(c)Radius
(d)Arc
4.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.
(a)Major arc
(b)Minor segment
(c)Chord
(d)Minor arc
5.A circular table mat has diameter 20 cm. Yasmin has a 70 cm length of ribbon and sews it around the edge of the mat with no overlap. Using π = 3.14, work out how much ribbon is left over after going around the mat once.
(a)7.2 cm
(b)50 cm
(c)20 cm
(d)62.8 cm
6.A translation is described by the column vector $(- 5 6)$ . Write down the column vector of the translation that undoes it.
(a) $(6 - 5)$
(b) $(- 5 - 6)$
(c) $(5 - 6)$
(d) $(5 6)$
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.A right-angled triangle has angles of 90°, 40° and x°. Work out the value of x.
(a)45
(b)130
(c)90
(d)50
9.A bead starts at position (2, −1) on a grid, in centimetres. It is moved by the column vector u, with top number 3 and bottom number 5, and then moved by the column vector v, with top number −7 and bottom number 2. Work out the coordinates of the bead's final position.
(a)(−5, 1)
(b)(5, 4)
(c)(−4, 7)
(d)(−2, 6)
10.A triangular prism has two triangular end faces and three rectangular faces joining them. How many faces does it have in total?
(a)5
(b)6
(c)3
(d)9
11.Write down the name given to a quadrilateral that has exactly one pair of parallel sides.
(a)Kite
(b)Rhombus
(c)Trapezium
(d)Parallelogram
12.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°
13.A dog is tied by a lead 4 m long to a fixed ring on a straight garden wall. The wall extends much further than the lead can reach in both directions, and the dog cannot cross through it. Describe the region the dog can reach.
(a)A rectangle 4 m wide, running along the wall.
(b)A semicircle of radius 4 m, away from the wall.
(c)A full circle of radius 4 m.
(d)A quarter circle of radius 4 m.
14.Work out the exact value of sin 45° × cos 45°.
(a)√2
(b)1
(c)1/2
(d)√2/2
15.Triangle ABC is translated by the column vector with top number 3 and bottom number −5 to form triangle A′B′C′. Triangle A′B′C′ is then translated by the column vector with top number −7 and bottom number 2 to form triangle A″B″C″. Work out the single column vector that translates triangle ABC directly to triangle A″B″C″.
(a)(10, −7)
(b)(4, −3)
(c)(−4, 3)
(d)(−4, −3)

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