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.
Non-calculator
Geometry and measures worksheet — GCSE Foundation
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- 1.A ladder rests against a wall, making an angle of 60° with the ground. The ladder is 2 m long. Using the exact value of sin 60°, work out how high up the wall the ladder reaches, giving your answer in centimetres.
- 2.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.
- 3.An isosceles trapezium has exactly one pair of parallel sides, and its two non-parallel sides are equal in length. How many lines of symmetry does it have?
- 4.A vertical line passes through the point (5, 2). Write down the equation of this line.
- 5.How many vertices does a square-based pyramid have?
- 6.In triangle PQR and triangle STU, PQ = ST, QR = TU and PR = SU. Write down the congruence condition that proves the two triangles are congruent.
- 7.The midpoint of the line segment AB is (3, 5). A is the point (1, 3). Work out the coordinates of B.
- 8.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.
- 9.A plumber charges a £45 call-out fee, plus £28 for each hour worked. She works on a job for 3 hours 30 minutes, and her hours are billed by rounding up to the next whole hour. Work out the total amount she charges.
- 10.The diagram shows the plan, front elevation and side elevation of a solid. Which of these solids matches all three views?
- 11.A builder props a straight plank against a vertical wall to reach a window ledge. The foot of the plank is 2.1 m from the base of the wall, and the plank is 3.5 m long. Work out how high up the wall the plank reaches.
- 12.A bearing is described as being exactly halfway between north and east, measured clockwise. What is the three-figure bearing?
- 13.Point C is at (2, 3). It is rotated 90° clockwise about the origin. Work out the coordinates of the image of point C.
- 14.A regular polygon has 5 lines of symmetry. What is the order of rotational symmetry of this polygon?
- 15.A solid has 6 faces and 8 vertices. Using the formula F + V − E = 2, work out how many edges it has.
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