Geometry and measures worksheet — GCSE Higher

1.A surveyor marks two fixed points A and B, with position vectors OA = a and OB = b (in km) from a base station O. A relay mast P is to be placed on the line AB such that AP : PB = 3 : 2. Express the vector OP in terms of a and b.

2.A footpath sign shows a distance of 0.45 km to the next village. Work out this distance in metres.

3.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.

4.A circle has two straight radii drawn from the centre to the edge, together with the arc between them. Write down the name of the region enclosed by these two radii and the arc.

5.A sector of a circle has radius 15 cm and angle 216°. Using π = 3.14, work out the arc length of the sector.

6.Two hikers walk from a campsite A to a lookout B, a distance of 14 km on a bearing of 038°. From B they walk to a shelter C, a distance of 20 km on a bearing of 142°. Work out the direct distance from A to C. Give your answer to 1 decimal place.

7.Sam says: '3.2 litres is the same as 320 ml, because you multiply by 100.' Which statement about Sam's claim is correct?

8.A garden flower bed is in the shape of a trapezium. Its two parallel edges are 3.5 m and 6.5 m long, and the perpendicular distance between them is 4 m. Bedding plants cost £2.50 per square metre to cover the bed. Work out the total cost of the bedding plants.

9.A mast stands vertically on level ground and its top is 60 m above the ground. Amelia and Noah stand on the ground on the same side of the mast, in line with its foot. The angle of elevation of the top of the mast is 30° from where Amelia stands and 60° from where Noah stands. Work out the distance between Amelia and Noah. Give your answer to 1 decimal place.

10.A window is made from a rectangle with a semicircle on top. The rectangle is 40 cm wide and 60 cm tall. The semicircle has the same width as the rectangle. Work out the total area of the window. Use π = 3.14. Give your answer to the nearest whole number.

11.In triangle ABC the angle at C is 90°, AC = 8 cm and the angle at A is 30°. Work out the length of BC. Give your answer to 1 decimal place.

12.In triangle ABC, AB = 8.6 cm, AC = 11.4 cm and angle BAC = 47°. Work out the area of triangle ABC. Give your answer to 1 decimal place.

13.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.

14.A rhombus-shaped floor tile has sides of length 12 cm and an interior angle of 55°. Work out the area of the tile. Give your answer to 1 decimal place.

15.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.