Geometry and measures worksheet — GCSE Foundation

1.A solid has 6 faces: one pentagon and five triangles that all meet at a single point above the pentagon. What is the name of this solid?

2.Write down the exact value of cos 30°.

3.Work out the exact value of tan 30° + tan 30°.

4.A hiker walks due west. What is the three-figure bearing for this direction?

5.A sector of a circle has radius 9 cm and angle 40°. Work out the area of the sector, in terms of π.

6.A water tank holds 2.5 m³. Work out this volume in cm³.

7.ABCD is an isosceles trapezium. The sides AB and DC are parallel, and the two sloping sides AD and BC are equal in length. Angle D is 112°. Work out the size of angle B.

8.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.

9.Two vertical masts stand on level ground, 40 m apart. One mast is 30 m tall and the other is 50 m tall. Work out the straight-line distance between the tops of the two masts. Give your answer to 1 decimal place.

10.Triangles ABE and CDE share the vertex E, where lines AC and BD cross at E. AE equals CE, and BE equals DE. Angle AEB and angle CED are formed as vertically opposite angles where the lines cross. Which condition proves that triangle ABE is congruent to triangle CDE?

11.Work out the exact value of (cos 45°)² + (sin 45°)².

12.A model car is built to a scale of 1 : 24. The real car is 4.32 m long. Work out the length of the model, in centimetres.

13.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.

14.A tile is described as having two pairs of parallel sides, four equal sides, and diagonals that cross at right angles but are not equal in length. Give a reason why this tile cannot be a square.

15.A rectangular photograph has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.