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 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
3.A car's windscreen wiper blade is 40 cm long and sweeps through an angle of 110° as it wipes the glass. Using π = 3.14, work out the area of glass it wipes, to the nearest cm².
(a)384 cm²
(b)38 cm²
(c)3070 cm²
(d)1535 cm²
4.A support strut for a shed roof is in the shape of a right-angled triangle. The two shorter sides of the strut are 5 m and 9 m. Work out the length of the sloping strut (the hypotenuse). Give your answer correct to 1 decimal place.
(a)106 m
(b)10.2 m
(c)14 m
(d)10.3 m
5.A television cable runs in a straight line from the edge of a flat roof 20 m above the ground to a bracket on a wall 5 m above the ground. The horizontal distance between the roof edge and the bracket is 15 m. Work out the length of the cable. Give your answer to 1 decimal place.
(a)25.0 m
(b)30.0 m
(c)15.0 m
(d)21.2 m
6.A fan-shaped rug is in the shape of a sector of a circle with radius 4 m and angle 180°. It costs £4 per square metre to make. Using π = 3.14, work out the total cost of the rug.
(a)£50.24
(b)£25.12
(c)£200.96
(d)£100.48
7.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°
8.A scale drawing shows a room that is 5 cm wide. The real room is 15 m wide. Write the scale of the drawing in the form 1 : n.
(a)1 : 3000
(b)1 : 30
(c)1 : 300
(d)1 : 3
9.A vertical flagpole casts a shadow 6 m long at the same time as a 1.2 m vertical post casts a shadow 1.8 m long. The flagpole and the post are both vertical, and the triangles formed by each object, its shadow, and the sun's ray are similar. Work out the height of the flagpole.
(a)5.4 m
(b)4 m
(c)9 m
(d)7.2 m
10.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.
(a)arc
(b)segment
(c)chord
(d)sector
11.A survey team measures the angle between two fences with a protractor and gets a reading of 254°. What type of angle is this?
(a)Right
(b)Acute
(c)Reflex
(d)Obtuse
12.A party hat is in the shape of a cone with a base radius of 6 cm and a slant height of 10 cm. Work out the curved surface area of the party hat. Use π = 3.14 and the formula curved surface area = πrl.
(a)188.4 cm²
(b)376.8 cm²
(c)113.04 cm²
(d)60 cm²
13.A circular clock face has a radius of 9 cm. Work out the circumference of the clock face. Use π = 3.14. Give your answer to 1 decimal place.
(a)28.3 cm
(b)254.3 cm
(c)113.0 cm
(d)56.5 cm
14.A drone starts at the point (3.5, −2) on a grid measured in metres. It flies by the vector $(4.5 - 6.2)$ to check a first sensor. The drone then needs to fly in a straight line to reach the point (−1.7, 9) to check a second sensor. Work out the column vector of this second flight.
(a) $(6.5 1)$
(b) $(- 6.5 - 1)$
(c) $(6.5 - 4.4)$
(d) $(11 - 5.2)$
15.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

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