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.A surveyor marks two fixed points A and B, with position vectors OA = a and OB = b (in km) from a base station O. A relay mast P is to be placed on the line AB such that AP : PB = 3 : 2. Express the vector OP in terms of a and b.
(a)(3/5)a + (2/5)b
(b)a + (3/5)b
(c)(1/2)a + (1/2)b
(d)(2/5)a + (3/5)b
2.A footpath sign shows a distance of 0.45 km to the next village. Work out this distance in metres.
(a)45 m
(b)4500 m
(c)450 m
(d)0.45 m
3.Two traffic cones are geometrically similar. The smaller cone has height 6 m and the larger cone has height 9 m. Work out the ratio of the volume of the smaller cone to the volume of the larger cone, giving your answer in the form a : b in its simplest form.
(a)4 : 9
(b)8 : 27
(c)2 : 3
(d)27 : 8
4.In triangle OAB, OA = a and OB = b. P lies on AB such that AP is twice PB. Express the vector OP in terms of a and b.
(a)a + (2/3)b
(b)(1/2)a + (1/2)b
(c)(1/3)a + (2/3)b
(d)(2/3)a + (1/3)b
5.In triangle ABC, AB = 7.4 cm, AC = 5.9 cm and angle BAC = 68°. Work out the length of BC. Give your answer to 1 decimal place.
(a)7.5 cm
(b)56.9 cm
(c)11.1 cm
(d)2.9 cm
6.A sector of a circle has radius 6 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector.
(a)15.7 cm
(b)21.7 cm
(c)27.7 cm
(d)31.4 cm
7.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.
(a)65 cm²
(b)1,000 cm²
(c)500 cm²
(d)2,000 cm²
8.A sector of a circle has radius 9 cm and angle 40°. Work out the area of the sector, in terms of π.
(a)2π cm²
(b)9π cm²
(c)81π cm²
(d)18π cm²
9.A tent has the cross-section of a right-angled triangle. The sloping side of the cross-section is 10 m long, and it makes an angle of 60° with the horizontal ground. Using the exact value of cos 60°, work out the horizontal distance covered by the sloping side.
(a)8.7 m
(b)20 m
(c)5 m
(d)10 m
10.Sam says: '3.2 litres is the same as 320 ml, because you multiply by 100.' Which statement about Sam's claim is correct?
(a)Wrong: 1 litre = 100 ml, so his number is off.
(b)Wrong: 1 litre = 1000 ml, so 3.2 l = 3200 ml.
(c)Wrong, but only because 3.2 should round to 3.
(d)Correct: ×100 converts litres to millilitres.
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.A circle has a diameter of 24 cm. A sector of this circle has an angle of 90°. Using π = 3.14, work out the area of the sector.
(a)9.42 cm²
(b)113.04 cm²
(c)18.84 cm²
(d)452.16 cm²
13.A furniture catalogue drawing uses a scale of 1 cm to 1.5 m. A sofa in the drawing is measured as 7 cm long. What is the real length of the sofa, in metres?
(a)8.5
(b)10.5
(c)3.5
(d)14
14.A cube has edges of length 5 cm. Work out the length of the diagonal that runs from one corner of the cube to the opposite corner. Give your answer as a surd in its simplest form.
(a)5√2 cm
(b)75 cm
(c)5√3 cm
(d)15 cm
15.The area of triangle ABC is 42 cm². AB = 9.5 cm and angle BAC = 61°. Work out the length of AC. Give your answer to 1 decimal place.
(a)10.1 cm
(b)7.7 cm
(c)18.2 cm
(d)5.1 cm

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