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.
Geometry and measures worksheet — GCSE Foundation
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- 1.Shape S is enlarged by a scale factor of 3, centre the origin. A vertex of S is at (2, 1). Work out the coordinates of the image of this vertex.
- 2.A drone starts at the point (2, −3) on a coordinate grid. It flies by the vector and then by the vector . Write down the column vector that would take the drone straight back to its starting point.
- 3.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.
- 4.In triangle ABC the base BC is 10 cm long and the sloping side AB is 13 cm long. The perpendicular height from A down to BC is 12 cm. Work out the area of triangle ABC.
- 5.A sector of a circle has an angle of 150°. Work out what fraction of the circle's area the sector is.
- 6.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.
- 7.A square tile has sides of length 6 cm. Work out the area of the tile.
- 8.A scale drawing of a park uses a scale of 1 : 2000. A path is drawn 8.5 cm long on the drawing. A cyclist rides the length of the path and then rides straight back again along the same path. How far does the cyclist travel in total, in metres?
- 9.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?
- 10.A sector of a circle has radius 5 cm and angle 72°. Work out the arc length of the sector, in terms of π.
- 11.A sector of a circle has radius 8 cm and takes up three-quarters of the full circle. Work out the perimeter of the sector, in terms of π.
- 12.In this question, a curved surface counts as a face. How many faces does a sphere have?
- 13.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.
- 14.A sector of a circle has radius 6 cm and angle 60°. Work out the arc length of the sector, in terms of π.
- 15.Two sides of a triangle are 9 cm and 15 cm long. Write down which one of these lengths is possible for the third side.
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