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 sector of a circle has radius 10 cm and angle 72°. Using π = 3.14, work out the arc length of the sector.
(a)25.12 cm
(b)6.28 cm
(c)62.8 cm
(d)12.56 cm
2.A shopkeeper builds a display from two cuboid boxes, shown in the diagram. She wants to cover the front of the display with coloured paper. Work out the total area of the front elevation, in square centimetres.
(a)4700 cm²
(b)2000 cm²
(c)7200 cm²
(d)2700 cm²
3.A circular decoration has a radius of 10 cm. A ribbon costs £0.50 per centimetre and is fixed along the curved edge (the arc) of a sector-shaped section with an angle of 90°. Using π = 3.14, work out the cost of the ribbon for this section.
(a)£157.00
(b)£31.40
(c)£7.85
(d)£15.70
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 shop stacks identical storage crates in a display. The diagram shows the plan of the floor positions used, with one corner position marked. Every floor position is filled with crates stacked 3 high, except the marked corner position, which is left completely empty. Work out how many crates are used in total.
(a)33
(b)11
(c)36
(d)35
6.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.
(a)125 g
(b)1025 g
(c)1000 g
(d)1250 g
7.In a phone game, a character starts at the point (−5, 2) on a grid. It moves by the vector $(- 9 6)$ to collect a coin. The player now wants the character's next single move to finish at the point (3, 0). Write down the column vector of that second move.
(a) $(- 2 8)$
(b) $(- 7 - 2)$
(c) $(7 2)$
(d) $(- 7 4)$
8.A running track has a straight section and a semicircular bend. The bend is a semicircle with radius 32 m. Work out the length of the curved part of the bend, to 1 decimal place. (Use π = 3.14.)
(a)201.0 m
(b)64.0 m
(c)100.5 m
(d)50.2 m
9.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)
10.A fish tank is a cuboid measuring 40 cm long, 25 cm wide and 30 cm high. Water is poured in to a depth of 20 cm. Work out the volume of water in the tank, in litres.
(a)20 litres
(b)20000 litres
(c)0.02 litres
(d)30 litres
11.A bus journey takes 2.5 hours. Work out how many minutes this is.
(a)170 minutes
(b)120 minutes
(c)150 minutes
(d)250 minutes
12.A textbook contains the instruction 'Draw AB' and, on the next line, the statement 'AB = 5 cm'. Which statement about the notation AB is correct?
(a)The length must be written as |AB|, not AB
(b)A different symbol is needed for the length
(c)AB means the segment or its length, shown by context
(d)AB can only mean the segment, never a length
13.A trapezium-shaped garden bed has parallel sides of 2.5 m and 4.5 m, and a perpendicular width of 3 m. A gardener wants to know the area of the bed before ordering topsoil. Work out the area of the garden bed.
(a)3.5 m²
(b)10.5 m²
(c)6.75 m²
(d)21 m²
14.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
15.A rectangular garden bed measures 5 m by 3 m. A semicircular flower border is attached along one of the 3 m-wide ends, on the outside of the rectangle, so that the 3 m side is the diameter of the semicircle. Work out the total perimeter of the combined shape (the two long sides, the one remaining short side, and the curved edge). Use π = 3.14.
(a)16 m
(b)22.42 m
(c)17.71 m
(d)20.71 m

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