Geometry and measures worksheet — GCSE Foundation

1.A bead starts at position (2, −1) on a grid, in centimetres. It is moved by the column vector u, with top number 3 and bottom number 5, and then moved by the column vector v, with top number −7 and bottom number 2. Work out the coordinates of the bead's final position.

2.A car's windscreen wiper blade is 40 cm long and sweeps through an angle of 110° as it wipes the glass. Using π = 3.14, work out the area of glass it wipes, to the nearest cm².

3.A sector of a circle has angle 120° and an arc length of 31.4 cm. Using π = 3.14, work out the radius of the circle.

4.A hiker walks on a bearing of 065°. She then turns clockwise through 90° and continues walking in a straight line. What bearing is she now walking on?

5.In a right-angled triangle one of the other two angles is 45°, and the side opposite that 45° angle is 7 cm. Work out the length of the hypotenuse. Give your answer to 1 decimal place.

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

7.A sector of a circle has radius 10 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector, to 1 decimal place.

8.A solid ball has a radius of 7 cm. Work out the surface area of the ball. Use π = 3.14.

9.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?

10.A footpath is 3750 m long. Work out this distance in kilometres.

11.A sector of a circle has radius 10 cm and angle 72°. Using π = 3.14, work out the arc length of the sector.

12.A rectangular tile measures 4.5 cm by 6 cm. Work out the area of the tile.

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

14.A cylindrical water tank has a solid hemispherical dome on top, both with radius 2 m. Work out the volume of the hemispherical dome alone. Use π = 3.14 and give your answer correct to 3 decimal places.

15.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?