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.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) $(- 7 4)$
2.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
3.A sector of a circle has radius 9 cm and angle 120°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.
(a)56.5 cm
(b)37.7 cm
(c)9.4 cm
(d)18.8 cm
4.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
5.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.
(a)zero
(b)negative
(c)cannot be determined
(d)positive
6.A warehouse stores identical cube-shaped crates. Its plan view is a 2 by 4 rectangle of crate positions, and every position is filled to a height of 3 crates, except one corner position, which has only 2 crates stacked on it because a delivery was incomplete. How many crates are there in total?
(a)22
(b)23
(c)21
(d)24
7.A room measures 4.2 m by 3.6 m. A flooring company needs the area in cm² to order the right amount of vinyl flooring. Work out the area of the room in cm².
(a)15,120 cm²
(b)1,512 cm²
(c)151,200 cm²
(d)15.12 cm²
8.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
9.Two identical ladders lean against the same vertical wall from opposite sides, each making an angle of 58.2° with the ground. The two ladders and the ground form a triangle. Work out the size of the angle between the two ladders at the top, where they meet.
(a)121.8
(b)58.2
(c)116.4
(d)63.6
10.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
11.In a right-angled triangle one of the other two angles is 45°, and the side opposite that 45° angle is 7 cm. Work out the length of the hypotenuse. Give your answer to 1 decimal place.
(a)7.0 cm
(b)14.0 cm
(c)9.9 cm
(d)5.0 cm
12.A sector of a circle has an angle of 90° and an arc length of 15.7 cm. Using π = 3.14, work out the radius of the circle.
(a)20 cm
(b)10 cm
(c)5 cm
(d)2.5 cm
13.An angle is measured with a protractor as 47°. What type of angle is this?
(a)Reflex
(b)Acute
(c)Obtuse
(d)Right angle
14.A shop stacks tins in a display block. The front elevation of the block is 4 tins wide and 3 tins high. The side elevation shows the block is 2 tins deep. Every position in the block is filled. How many tins are used in total?
(a)24
(b)6
(c)12
(d)9
15.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

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