Geometry and measures worksheet — GCSE Foundation

1.Which of these correctly compares a 'line' with a 'line segment'?

2.A solid has one curved surface and two flat circular faces of equal size, one at each end. What is the name of this solid?

3.A zip wire is fixed at an angle of 50° to the horizontal, running from a high platform down to the ground. The zip wire itself, from the platform to the ground, is 12 m long. Work out the horizontal distance covered by the zip wire. Give your answer correct to 1 decimal place.

4.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.

5.A photograph is 10 cm wide and 15 cm tall. It is enlarged to make a similar poster that is 40 cm wide. The poster costs £0.80 per centimetre of its height to print, based on its full height. Work out the cost of printing the poster.

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

7.A flower bed in the shape of a parallelogram has a base of 3.5 m and a perpendicular height of 2 m. Compost costs £4.80 per m². Work out the total cost of covering the flower bed with compost.

8.A regular nonagon has 9 sides. Work out the sum of its interior angles.

9.Write down the exact value of cos 60°.

10.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.

11.Two straight lines cross at a point. Which statement about a pair of vertically opposite angles is always true?

12.A shape is made by joining two rectangles edge to edge, with no overlap. One rectangle measures 12 cm by 4 cm and the other measures 4 cm by 8 cm. Work out the total area of the shape.

13.A tank holds 3.2 m³ of water. Work out this volume in litres.

14.Point A is at (5, 2). It is translated by the vector (−3, 4) to give point A′. Work out the coordinates of A′.

15.p is the column vector with top number 5 and bottom number 1. q is the column vector with top number −2 and bottom number 3. Work out p − 2q, giving your answer as a column vector in the form (top, bottom).