Ratio, proportion and rates of change worksheet — GCSE Higher

1.A charity receives £360 in donations in January and £480 in donations in February. Write the amount received in January as a fraction of the amount received in February, giving your answer in its simplest form.

2.A smoothie recipe combines 350 cm³ of mango juice with 650 cm³ of orange juice. Work out the total volume of the smoothie in litres.

3.A map's scale is given as '1 cm represents 2 km'. Write this scale in the form 1 : n.

4.The width, the length and the height of a box are in the ratio 3:4:5. The length of the box is 16 cm. Work out the height of the box.

5.A car is bought for £12000. Its value falls by 15% in the first year and by 10% in each year after that. Work out the value of the car 3 years after it was bought.

6.A beaker holds 500 g of a salt solution of concentration 12%. Pure water is added until the concentration falls to 8%. Work out the mass of water added.

7.In a science lesson Priya has 10 litres of a solution that is 30% salt. She adds water to make a solution that is 20% salt. Work out how many litres of water she adds.

8.A shop's daily profit, in pounds, is plotted against the price charged for an item, in pounds. A tangent to the profit graph at a price of £15 passes through the points (12, 540) and (18, 480). Work out the instantaneous rate of change of profit with respect to price at £15, and state whether profit is increasing or decreasing there.

9.In a choir of 30 singers, 40% are altos and the rest are sopranos. Write the number of sopranos as a fraction of the number of altos. Give your answer in its simplest form.

10.A metal alloy is made from copper and tin in the ratio 9:1. Write the mass of tin as a fraction of the mass of copper, in its simplest form.

11.Two straight-line graphs represent y = 2x and y = 5x. For the same value of x, where x ≠ 0, write down the ratio of the y-value on the first graph to the y-value on the second graph, in its simplest form.

12.A force of 250 N acts on an area of 0.5 m². Using pressure = force ÷ area, work out the pressure, in pascals.

13.A laptop bag has a mass of 2.4 kg. A school bag has a mass of 3.6 kg. Write the mass of the laptop bag as a fraction of the mass of the school bag, giving your answer in its simplest form.

14.A shop sells fruit juice concentrate that must be diluted with water in the ratio 2 : 5 (concentrate : water) to make squash. Priya has 8 litres of concentrate. Work out how much water she needs to keep the same ratio.

15.The ratio of Josh's savings to Mia's savings is 4:7. Mia has £39 more than Josh. Work out Josh's savings.