Geometry and measures worksheet — GCSE Foundation

1.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.

2.A circular coin has a diameter of 3 cm. Work out the circumference of the coin. Give your answer in terms of π.

3.A sector of a circle has radius 4 cm and angle 90°. Using π = 3.14, work out the area of the sector.

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

5.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

6.Loose sweets are sold at £1.20 per 100 g. Work out the cost of 350 g of sweets.

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

8.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

9.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.

10.Two similar ponds have perimeters in the ratio 4 : 11. The perimeter of the larger pond is 88 m. Work out the perimeter of the smaller pond.

11.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?

12.Two similar signs have lengths in the ratio 9 : 4. The larger sign has a side of length 14.4 cm. Work out the length of the corresponding side of the smaller sign.

13.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.

14.A flagpole is 12 m tall. Freya stands 9 m from the base of the flagpole on level ground. Work out the angle of elevation of the top of the flagpole from where Freya stands. Give your answer correct to 1 decimal place.

15.A solid metal sphere has a radius of 5 cm. It is melted down and recast into a solid cylinder with the same radius, 5 cm. Work out the height of the cylinder, so that its volume equals the volume of the sphere. Use π = 3.14 and give your answer correct to 1 decimal place.