Geometry and measures worksheet — GCSE Foundation

1.Shape S has a vertex at (9, 6). It is enlarged by a scale factor of 1/3, centre the origin. Work out the coordinates of the image of this vertex.

2.A market stall sells apples at £2.40 per kilogram. Which of these expressions gives the cost, in pounds, of buying m kilograms of apples?

3.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.

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

5.Triangle ABC has AB = 9 cm, BC = 6 cm and angle A = 35°. Triangle DEF has DE = 9 cm, EF = 6 cm and angle D = 35°. Which of the following correctly identifies the condition shown here?

6.The bearing of a campsite B from a walker's position A is 070°. What is the bearing of A from B?

7.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.

8.Two straight lines cross at a point. To find the points that are the same distance from both lines, which construction should be used?

9.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.

10.A shop stacks tins in a display block. The front elevation of the block is 4 tins wide and 3 tins high. The side elevation shows the block is 2 tins deep. Every position in the block is filled. How many tins are used in total?

11.Quadrilateral PQRS has angle P = 92°, angle Q = 84° and angle R = 106°. Work out the size of angle S.

12.Two straight lines AB and CD cross at point O. Angle AOC = 74°. Work out angle AOD.

13.A cyclist rides around a perfectly circular track with centre O. At every moment of the ride, the distance from O to the cyclist is exactly the same. Which term names this fixed distance?

14.A television cable runs in a straight line from the edge of a flat roof 20 m above the ground to a bracket on a wall 5 m above the ground. The horizontal distance between the roof edge and the bracket is 15 m. Work out the length of the cable. Give your answer to 1 decimal place.

15.A right-angled triangle has a hypotenuse of 10 cm and one of its other angles is 45°. Work out the length of one of the two shorter sides. Give your answer to 1 decimal place.