Geometry and measures worksheet — GCSE Foundation

1.Two similar triangles have lengths in the ratio 2 : 5. The sides of the smaller triangle are 4 cm, 6 cm and 8 cm. Work out the length of the longest side of the larger triangle.

2.In an isosceles triangle each of the two base angles is 46°. Work out the size of the angle at the apex.

3.In pentagon PQRST, which of the following correctly names the interior angle at vertex R, using standard three-letter angle notation?

4.The diagram shows a solid built from identical cubes. How many squares are in its plan view, the view looking straight down from above?

5.A ship's radar shows a lighthouse at the point (12, −4) on a grid measured in nautical miles. The ship is at (2, 5). The ship sails along the vector that takes it directly to the lighthouse, then sails along that same vector again. Work out the ship's final position.

6.A bus journey takes 2.5 hours. Work out how many minutes this is.

7.Three of these are rational numbers and one is irrational. Write down the one that is irrational.

8.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.

9.Triangle T has a vertex at (2, 1). It is enlarged by a scale factor of 3, centre (0, 0). Work out the coordinates of the image of this vertex.

10.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?

11.Write down the column vector that describes a translation of 4 units to the right and 4 units up.

12.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.

13.A sector of a circle has an angle of 150°. Work out what fraction of the circle's area the sector is.

14.A path goes from A(1, 1) to B(1, 5), then from B to C(6, 5). Work out the total length of the path from A to C.

15.A drone flies from its base in three stages, each stage measured in metres east and north as a column vector. Stage 1 is the column vector with top number 30 and bottom number 40. Stage 2 is the column vector with top number −10 and bottom number 20. Stage 3 is the column vector with top number 15 and bottom number −5. Work out the column vector that would take the drone in a single straight flight back to its base from where it ends up.