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 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
2.A sector of a circle has radius 15 cm and angle 216°. Using π = 3.14, work out the arc length of the sector.
(a)94.2 cm
(b)56.52 cm
(c)28.26 cm
(d)113.04 cm
3.A sector of a circle has radius 10 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector, to 1 decimal place.
(a)72.3 cm
(b)26.2 cm
(c)36.2 cm
(d)46.2 cm
4.A ship leaves port P and sails 24 km on a bearing of 040° to a buoy Q. It then sails 31 km on a bearing of 115° to a lighthouse R. Work out the direct distance from P to R. Give your answer to 1 decimal place.
(a)33.9 km
(b)43.8 km
(c)55.0 km
(d)19.9 km
5.A sector of a circle has radius 6 cm and an area of 4.71 cm². Using π = 3.14, work out the angle of the sector.
(a)3.75°
(b)45°
(c)90°
(d)15°
6.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
7.A shape is translated by the vector (5, −3), and the image is then translated by the vector (−5, 3). Which single transformation has the same overall effect as this combination, for every point?
(a)A reflection in the x-axis
(b)A translation by the vector (10, −6)
(c)A rotation of 180° about the origin
(d)No transformation — every point stays exactly where it was
8.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
9.A solid metal sphere has a radius of 5 cm. It is melted down and recast into a solid cylinder with the same radius, 5 cm. Work out the height of the cylinder, so that its volume equals the volume of the sphere. Use π = 3.14 and give your answer correct to 1 decimal place.
(a)1.7 cm
(b)20.0 cm
(c)5.0 cm
(d)6.7 cm
10.A room measures 4.2 m by 3.6 m. A flooring company needs the area in cm² to order the right amount of vinyl flooring. Work out the area of the room in cm².
(a)15,120 cm²
(b)1,512 cm²
(c)151,200 cm²
(d)15.12 cm²
11.Which of these statements about the area formula Area = 1/2ab sin C is correct?
(a)AB, BC and angle ABC: Area = 1/2 × AB × BC × sin(BAC)
(b)Three sides, no angle: Area still = 1/2 AB×AC×sin(BAC)
(c)AB, AC and angle BAC: Area = 1/2 × AB × AC × sin(BAC)
(d)AB, AC and angle ABC: Area = 1/2 × AB × AC × sin(ABC)
12.A model of a bridge is built to a scale where every length on the model is 1/240 of the matching length on the real bridge. A support beam on the model measures 3.6 cm. Work out the length of the real support beam, giving your answer in metres.
(a)86.4 m
(b)8.64 m
(c)0.0864 m
(d)864 m
13.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
14.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
15.A cuboid-shaped shipping crate has a length of 12 m, a width of 5 m, and a volume of 360 m³. Work out the height of the crate, in metres.
(a)30 m
(b)6 m
(c)300 m
(d)72 m

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