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 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
2.A kitchen scale is marked in equal divisions of 20 g. The pointer rests three divisions past the 400 g mark. Work out the reading on the scale.
(a)60 g
(b)430 g
(c)460 g
(d)403 g
3.A raised garden bed is a prism whose cross-section is a triangle with a base of 1.2 m and a perpendicular height of 0.8 m. The bed is 3 m long. Work out the volume of soil needed to fill it, in m³.
(a)3.6 m³
(b)2.88 m³
(c)1.44 m³
(d)0.48 m³
4.A quadrilateral has both pairs of opposite sides parallel and equal in length, but none of its angles are right angles. Which statement about this quadrilateral is correct?
(a)It is a trapezium
(b)It must be a rhombus
(c)It is a parallelogram but not a rectangle
(d)It must be a rectangle
5.An ice cream is made from a cone of radius 3 cm and height 10 cm, topped with a hemisphere of the same radius sitting exactly on top of the cone. Work out the total volume of the ice cream. Use π = 3.14. Give your answer to the nearest whole number. Volume of a cone = 1/3 × πr²h. Volume of a sphere = 4/3 × πr³.
(a)151 cm³
(b)94 cm³
(c)339 cm³
(d)207 cm³
6.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?
(a)65
(b)0.65
(c)650
(d)6.5
7.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
8.A sector of a circle has radius 6 cm and an arc length of 15.7 cm. Using π = 3.14, work out the angle of the sector.
(a)150°
(b)300°
(c)42°
(d)157°
9.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
10.A gardener wants to buy edging trim to go all the way around a circular flower bed with a diameter of 8 m. Work out the length of edging trim needed, using π = 3.14. Give your answer to the nearest metre.
(a)50 m
(b)201 m
(c)25 m
(d)13 m
11.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.
12.A sector of a circle has radius 12 cm and angle 45°. Using π = 3.14, work out the area of the sector.
(a)9.42 cm²
(b)452.16 cm²
(c)56.52 cm²
(d)4.71 cm²
13.A sector of a circle has radius 4 cm and angle 90°. Using π = 3.14, work out the area of the sector.
(a)3.14 cm²
(b)12.56 cm²
(c)6.28 cm²
(d)50.24 cm²
14.A crane's hook starts at the point (3.4, 9.5) on a construction site plan measured in metres. It moves along the vector $(- 4.5 - 1.2)$ to pick up a beam, then along the vector $(- 2.5 0.8)$ to place it. Work out the single column vector that describes the hook's overall movement from its start position to where it places the beam.
(a) $(- 2 - 2)$
(b) $(- 7 - 0.4)$
(c) $(7 - 0.4)$
(d) $(- 7 2)$
15.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

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