Geometry and measures worksheet — GCSE Higher

1.Triangle JKL and triangle MNP are similar, with JK ÷ MN = JL ÷ MP = 2. A student says triangle JKL must be congruent to triangle MNP. Write down why the student is wrong.

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 cylinder has a radius of 5 cm. Its volume is 471 cm³. Using π = 3.14, work out the height of the cylinder.

4.A vertical line passes through the point (5, 2). Write down the equation of this line.

5.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?

6.A ship leaves port P and sails 24 km on a bearing of 040° to a buoy Q. It then sails 31 km on a bearing of 115° to a lighthouse R. Work out the direct distance from P to R. Give your answer to 1 decimal place.

7.A solid rubber ball has a radius of 3 cm. Work out the volume of the ball. Use π = 3.14.

8.A map has a scale of 1 : 25000. A distance between two points measures 2 cm on the map. What is the real distance, in kilometres?

9.A parallelogram has an area of 136 cm² and a base of 17 cm. Work out the perpendicular height of the parallelogram.

10.A scale drawing of a park uses a scale of 1 : 2000. A path is drawn 8.5 cm long on the drawing. A cyclist rides the length of the path and then rides straight back again along the same path. How far does the cyclist travel in total, in metres?

11.Two traffic cones are geometrically similar. The smaller cone has height 6 m and the larger cone has height 9 m. Work out the ratio of the volume of the smaller cone to the volume of the larger cone, giving your answer in the form a : b in its simplest form.

12.In triangle ABC, AB = AC = 9 cm and angle ABC = angle ACB = 65°. Work out the area of triangle ABC. Give your answer to 1 decimal place.

13.A triangular field ABC is to be fenced all the way round. AB = 45 m, AC = 38 m and angle BAC = 110°. Fencing costs £6.50 per metre. Work out the total cost of the fencing. Give your answer to the nearest penny.

14.In triangle ABC, AB = 12 cm, AC = 9 cm and angle BAC = 55°. Work out the size of angle ABC. Give your answer to 1 decimal place.

15.A right-angled triangle has a hypotenuse of 8 cm, and one of its shorter sides is 4 cm. Work out the size of the angle between that 4 cm side and the hypotenuse.