Geometry and measures worksheet — GCSE Foundation

1.A rhombus has all four sides equal in length, but it is not a square — its angles are not all 90°. How many lines of symmetry does this rhombus have?

2.A student draws a net using 5 identical squares arranged in a row of four with one extra square attached to the side of one of them. Can this net be folded to make a closed cube?

3.A goat is tied by a rope 7 m long to a post at a corner of a rectangular field, where two fences meet at a right angle. The goat can reach anywhere inside the field that the rope allows. Using π = 3.14, work out the area the goat can graze, to the nearest square metre.

4.A composite solid is made from a cylinder of radius 3 cm and height 10 cm, with a cone of the same radius and vertical height 4 cm fixed on top, apex upward. Work out the total volume of the solid. Use π = 3.14 and give your answer correct to 1 decimal place.

5.A ship sails 12 km on a bearing of 070° from a harbour to a buoy. It then sails a further 9 km, still on a bearing of 070°, from the buoy to a lighthouse. How far is the lighthouse from the harbour, in kilometres?

6.A regular hexagon is divided into six identical triangles by joining its centre to each of the six vertices. Work out the size of the angle of one of these triangles at the centre of the hexagon.

7.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.

8.The column vector r has top number 2 and bottom number 6. Which of these column vectors is parallel to r?

9.In this question, a curved surface counts as a face. How many faces does a sphere have?

10.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.

11.Write down the mathematical name for a quadrilateral that has exactly one pair of parallel sides.

12.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.

13.For two triangles to be proved congruent using SAS, which two facts must be true about both triangles?

14.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

15.A raised garden bed is a prism whose cross-section is a triangle with a base of 1.2 m and a perpendicular height of 0.8 m. The bed is 3 m long. Work out the volume of soil needed to fill it, in m³.