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.In a right-angled triangle, the two shorter sides are a and b, and the hypotenuse is c. Write down the correct statement of Pythagoras' theorem.
- 2.A right-angled triangle has its two shorter sides equal to 8 cm and 15 cm. Work out the value of cos θ, where θ is the angle opposite the 8 cm side. Give your answer as a fraction.
- 3.Two similar triangular tiles have lengths in the ratio 3 : 5. The longest side of the smaller tile is 9 cm. Work out the length of the longest side of the larger tile.
- 4.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?
- 5.The diagram shows the plan, front elevation and side elevation of a solid. Which solid could this be?
- 6.A hexagonal prism lies on a table. A flat cut is made straight across it, at right angles to its length (so the cut is parallel to the two identical end faces). What shape is the cross-section?
- 7.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.
- 8.Two similar ponds have perimeters in the ratio 4 : 11. The perimeter of the larger pond is 88 m. Work out the perimeter of the smaller pond.
- 9.A garden flower bed is in the shape of a trapezium. Its two parallel edges are 3.5 m and 6.5 m long, and the perpendicular distance between them is 4 m. Bedding plants cost £2.50 per square metre to cover the bed. Work out the total cost of the bedding plants.
- 10.How many vertices does a cuboid have?
- 11.Write down the column vector that describes a translation of 4 units to the right and 4 units up.
- 12.A regular polygon has 5 lines of symmetry. What is the order of rotational symmetry of this polygon?
- 13.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.
- 14.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.
- 15.Point D is at (3, 4). It is rotated 90° clockwise about the origin (0, 0). Work out the coordinates of the image of point D.
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