Printable · GCSE Higher · ages 14-16

Geometry and measures worksheet — GCSE Higher

Fifteen questions across the geometry and measures statements at Higher 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 Higher

Maths · GCSE Higher · Geometry and measures · 15 questions

MathsUKwww.geekhero.co.uk

1.A regular polygon has an exterior angle of 45°. Work out the number of sides of the polygon.
(a)4
(b)45
(c)8
(d)315
2.A rectangular gate is braced with a diagonal strut. The gate is 1.2 m wide and 0.9 m tall. Work out the exact length of the diagonal strut.
(a)2.1 m
(b)0.3 m
(c)2.25 m
(d)1.5 m
3.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°
4.A solid has 6 faces and 8 vertices. Using the formula F + V − E = 2, work out how many edges it has.
(a)14
(b)10
(c)16
(d)12
5.The top of a clock tower is 25 m above level ground. Oliver stands on the ground 25 m from the foot of the tower. Work out the angle of elevation of the top of the tower from the point where Oliver stands.
(a)50°
(b)1°
(c)45°
(d)90°
6.A chord divides a circle into two regions, one larger than the other. Write down the term used for the smaller of these two regions.
(a)major segment
(b)arc
(c)minor segment
(d)sector
7.A regular hexagon has sides of length 8 cm. By splitting the hexagon into 6 identical triangles that meet at its centre, work out the area of the hexagon. Give your answer to 1 decimal place.
(a)192.0 cm²
(b)166.3 cm²
(c)138.6 cm²
(d)27.7 cm²
8.In triangle ABC, AB = 6 cm, AC = 8 cm and angle BAC = 60°. Work out the exact area of triangle ABC, giving your answer in the form $a 3$ .
(a) $93$ cm²
(b) $243$ cm²
(c) $123$ cm²
(d) $163$ cm²
9.A cyclist's journey from her house to the shop is represented by the column vector with top number 2 and bottom number 5, where each unit is 1 km east and 1 km north. She then cycles from the shop to the park, represented by the column vector with top number 4 and bottom number −3. What single column vector represents her journey from her house directly to the park?
(a)(2, −8)
(b)(6, 2)
(c)(6, 8)
(d)(−2, 8)
10.A circle has two straight radii drawn from the centre to the edge, together with the arc between them. Write down the name of the region enclosed by these two radii and the arc.
(a)chord
(b)segment
(c)semicircle
(d)sector
11.A parallelogram has an area of 54 cm² and a base of 9 cm. Work out its perpendicular height.
(a)12 cm
(b)486 cm
(c)6 cm
(d)45 cm
12.Triangle ABC has AB = 5 cm and BC = 7 cm. Triangle DEF has DE = 5 cm and EF = 7 cm. Which extra fact would prove the triangles are congruent by SAS?
(a)angle C = angle F
(b)angle B = angle E
(c)AC = DF
(d)angle A = angle D
13.In triangle ABC and triangle DEF, the angle at A and the angle at D are both 40°, and the angle at B and the angle at E are both 70°. No side lengths are given. Write down whether the two triangles must be similar, with the reason.
(a)No, because the triangles may be different sizes
(b)Yes, by the SSS condition
(c)No, because no side lengths are given
(d)Yes, by the AA condition
14.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°
15.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.
(a)(3, 3)
(b)(4, 0)
(c)(4, 3)
(d)(3.5, 3)

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