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 · Calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.Point P has coordinates (2, 1). Transformation A reflects a point in the x-axis. Transformation B translates a point by the vector (0, 4). Work out the coordinates of the image of P when A is applied first, followed by B.
(a)(2, −5)
(b)(2, 3)
(c)(2, 5)
(d)(2, −1)
2.A regular octagonal tabletop has centre O. Each vertex is 30 cm from O. Work out the area of the tabletop. Give your answer to the nearest square centimetre.
(a)1909 cm²
(b)5091 cm²
(c)318 cm²
(d)2546 cm²
3.A triangle has one unknown side or angle, marked x. In which one of these situations should the sine rule, rather than the cosine rule, be used to find x?
(a)Two sides and the included angle; x is the third side
(b)Two sides and the included angle; x is another angle
(c)Two angles and one side are known; x is another side
(d)All three sides are known; x is one of the angles
4.A shop stacks tins in a display block. The front elevation of the block is 4 tins wide and 3 tins high. The side elevation shows the block is 2 tins deep. Every position in the block is filled. How many tins are used in total?
(a)24
(b)6
(c)12
(d)9
5.In triangle PQR, PQ = 11 cm, QR = 7 cm and PR = 13 cm. Work out the size of angle PQR. Give your answer to 1 decimal place.
(a)89.6°
(b)32.6°
(c)90.4°
(d)89.8°
6.In triangle ABC, BC = 8 cm, AC = 10 cm and angle BAC = 40°. Given that angle ABC is acute, work out its size. Give your answer to 1 decimal place.
(a)53.5°
(b)126.5°
(c)73.2°
(d)30.9°
7.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?
(a)080°
(b)100°
(c)180°
(d)440°
8.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.
(a)£24.00
(b)£2.94
(c)£29.40
(d)£2940.00
9.A composite solid is made from a cylinder of radius 3 cm and height 10 cm, with a cone of the same radius and vertical height 4 cm fixed on top, apex upward. Work out the total volume of the solid. Use π = 3.14 and give your answer correct to 1 decimal place.
(a)37.7 cm³
(b)320.3 cm³
(c)282.6 cm³
(d)395.6 cm³
10.A trapezium has an area of 45 cm², a perpendicular height of 5 cm, and one parallel side of length 10 cm. Work out the length of the other parallel side.
(a)18 cm
(b)28 cm
(c)8 cm
(d)4 cm
11.Two straight paths cross at a junction in a park. One of the angles between them, measured with a protractor, is 76°. What is the size of the angle immediately next to it on a straight line?
(a)14
(b)104
(c)76
(d)90
12.A model car is built to a scale of 1 : 24. The real car is 4.32 m long. Work out the length of the model, in centimetres.
(a)432
(b)18
(c)10368
(d)1.8
13.Two similar hexagonal tiles have lengths in the ratio 4 : 7. A side of the smaller tile is 8.4 cm long. Work out the length of the corresponding side of the larger tile.
(a)11.4 cm
(b)4.8 cm
(c)14.7 cm
(d)58.8 cm
14.A trapezium has parallel sides of length 6 cm and 10 cm, and a perpendicular height of 4 cm. Work out its area.
(a)64 cm²
(b)32 cm²
(c)20 cm²
(d)8 cm²
15.In triangle ABC, AB = 11 cm, AC = 9 cm and the area of the triangle is 45 cm². Given that angle BAC is obtuse, work out the size of angle BAC. Give your answer to 1 decimal place.
(a)65.4°
(b)27.0°
(c)153.0°
(d)114.6°

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