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 · 15 questions

MathsUKwww.geekhero.co.uk

1.A wooden block is a cuboid measuring 2 cm by 10 cm by 15 cm. Work out the volume of the block.
(a)27 cm³
(b)400 cm²
(c)150 cm³
(d)300 cm³
2.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
3.Point A and point B are 5 cm apart. How many points are exactly 4 cm from A and exactly 3 cm from B?
(a)4
(b)0
(c)2
(d)1
4.A garden water trough is a prism whose cross-section is a right-angled triangle with base 40 cm and height 30 cm. The trough is 120 cm long. Work out the volume of water needed to fill the trough completely.
(a)36 000 cm³
(b)72 000 cm³
(c)144 000 cm³
(d)720 cm³
5.A polygon has 9 sides. What is the name of this polygon?
(a)Octagon
(b)Nonagon
(c)Heptagon
(d)Decagon
6.Write down the exact value of tan 45°.
(a)0
(b)√3
(c)√3/3
(d)1
7.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)
8.The column vector $(2 - 6)$ describes a translation. Write down the movement it represents.
(a)6 left, 2 up
(b)6 left, 2 down
(c)2 left, 6 up
(d)6 right, 2 up
9.A tap fills a tank at a rate of 18 litres per minute. The tank holds 0.45 m³. Work out how long the tap takes to fill the tank.
(a)8100 minutes
(b)25 minutes
(c)2.5 minutes
(d)25 000 minutes
10.A straight transversal crosses a pair of parallel lines. At one crossing point, the angle between the transversal and a parallel line is 118°. Work out the size of the co-interior (allied) angle at the other crossing point.
(a)59°
(b)118°
(c)62°
(d)236°
11.A kite string makes an angle of 30° with the ground. The kite is flying at a height of 6 m directly above a point on the ground. Using the exact value of sin 30°, work out the exact length of the kite string.
(a)4√3 m
(b)12 m
(c)6√3 m
(d)3 m
12.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.
(a)(−2, 6)
(b)(−2, −2)
(c)(7, −3)
(d)(8, 6)
13.A shape is translated by the vector $(3 - 8)$ , and one vertex of the image is at the point (1, 6). The original shape is instead translated by the vector $(- 5 2)$ . Work out the coordinates of the image of that same vertex under this second translation.
(a)(7, 8)
(b)(11, 3)
(c)(3, 1)
(d)(11, −2)
14.Point B is at (3, 5). It is reflected in the line y = 2. Work out the coordinates of the image of point B.
(a)(3, −4)
(b)(3, −1)
(c)(3, −5)
(d)(−3, 5)
15.A straight fence is 5 m long. Describe the shape of the region made up of every point on the ground within 2 m of any part of the fence.
(a)a rounded rectangle: 5 m by 4 m with semicircular ends
(b)a circle of radius 2 m
(c)a rectangle, 9 m by 4 m
(d)a rectangle, 5 m by 2 m

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