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 · Calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.A parallelogram has a base of 9 cm and a perpendicular height of 4 cm. Work out its area.
(a)72 cm²
(b)18 cm²
(c)36 cm²
(d)26 cm²
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.A plan of a car park is drawn to a scale of 1 : 500. A parking bay is drawn as a rectangle measuring 1.2 cm by 0.6 cm. The real width of the bay corresponds to the 0.6 cm side. What is the real width of the bay, in metres?
(a)0.3
(b)3
(c)6
(d)30
4.A sector of a circle has radius 9 cm and angle 60°. Using π = 3.14, work out the area of the sector, to 1 decimal place.
(a)9.4 cm²
(b)4.7 cm²
(c)254.3 cm²
(d)42.4 cm²
5.A parallelogram has an area of 84 cm² and a base of 12 cm. Work out the perpendicular height of the parallelogram.
(a)0.14 cm
(b)1008 cm
(c)3.5 cm
(d)7 cm
6.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.
7.A quadrilateral has angles of 100°, 85° and 95° at three of its vertices. Work out the fourth angle.
(a)260°
(b)280°
(c)70°
(d)80°
8.A sector of a circle has radius 6 cm and angle 60°. Work out the arc length of the sector, in terms of π.
(a)12π cm
(b)6π cm
(c)π cm
(d)2π cm
9.A sector has an angle of 45°. Priti says: 'The area of the sector is one eighth of the area of the full circle, whatever the radius is.' Is Priti correct?
(a)No, because 45 ÷ 360 = 1/6, not 1/8.
(b)Yes, but only because the radius happens to make 45° exactly one eighth of a full turn in this particular circle.
(c)No, because the fraction of the area also depends on the radius, so it is not fixed.
(d)Yes, because 45 ÷ 360 = 1/8, and this fraction applies to any radius.
10.A ship's radar can detect other ships up to 20 km away, over a sector-shaped area with angle 90°. A monitoring company charges £0.50 per square kilometre covered by one radar sweep. Using π = 3.14, work out the total charge for one sweep.
(a)£157.00
(b)£628.00
(c)£7.85
(d)£15.70
11.A robotic arm's tip starts at the point (12.5, −4.25) on a grid measured in centimetres. It moves by the vector $(6.5 - 3.75)$ to pick up a component, then by the vector $(- 1.5 2.25)$ to place it. Work out the coordinates of the tip after both moves.
(a)(0.75, 11)
(b)(8.75, 2.25)
(c)(6.5, 3.75)
(d)(11, 0.75)
12.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
13.A parallelogram has an area of 136 cm² and a base of 17 cm. Work out the perpendicular height of the parallelogram.
(a)2312 cm
(b)8 cm
(c)16 cm
(d)119 cm
14.A sprinkler waters a sector-shaped patch of a garden with radius 8 m and angle 90°. Work out the perimeter of the watered sector, to 1 decimal place. (Use π = 3.14.)
(a)28.6 m
(b)20.6 m
(c)12.6 m
(d)41.1 m
15.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

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