Geometry and measures worksheet — GCSE Foundation

1.What does the statement AB = CD mean, where A, B, C and D are all points?

2.Write down the exact value of tan 45°.

3.A ramp is built from two straight metal supports that rest on the flat ground and meet each other at the top, forming a triangle with the ground. One support meets the ground at 34°. The angle between the two supports where they meet is 71°. Work out the angle between the second support and the ground.

4.Lines AB and CD are parallel. A straight line EF crosses AB at point P and crosses CD at point Q. At P, angle APE = 65°. Angle APE and angle BPQ are vertically opposite. Angle BPQ and angle PQD are co-interior (allied) angles. Work out angle PQD.

5.A cube has all of its edges the same length. How many planes of symmetry does it have?

6.How many vertices does a square-based pyramid have?

7.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.

8.A sector of a circle has radius 12 cm and angle 45°. Using π = 3.14, work out the area of the sector.

9.A cylinder has a volume of 942 cm³ and a height of 12 cm. Using π = 3.14, work out the radius of the cylinder.

10.A trapezium has parallel sides of 5.6 cm and 8.4 cm, and a perpendicular height of 4 cm. Work out the area of the trapezium.

11.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.

12.A quadrilateral has exactly two lines of symmetry, its two pairs of opposite angles are equal, and its diagonals are not equal in length. Write down the name of this quadrilateral.

13.A square tile has sides of length 6 cm. Work out the area of the tile.

14.A cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.

15.In triangle XYZ, the side opposite vertex X is labelled using the standard lowercase-letter convention. Which label is correct?