Ratio, proportion and rates of change worksheet — GCSE Higher

1.A shade of paint is made by mixing blue paint and white paint. To make 5 litres of the shade, 2 litres of blue paint is used and the rest is white paint. Write the ratio of blue paint to white paint in its simplest form.

2.A map has a scale of 2 cm : 5 km. A footpath measures 8 cm on the map. Work out the real length of the footpath, in kilometres.

3.Two mathematically similar hexagonal tiles have areas 18 cm² and 50 cm². Work out the ratio of the side length of the smaller tile to the side length of the larger tile, in simplest form.

4.y is always the same multiple of x. When x = 6, y = 15. Work out the value of y when x = 10.

5.Water flows into a tank at a constant rate. After 8 minutes the tank holds 200 litres. Write the ratio of time in minutes to volume in litres, in its simplest form.

6.A shop sells identical pens. The total cost, C pence, of n pens is given by C = 12n. Write the ratio n : C in its simplest form.

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

8.Two mathematically similar polygons have perimeters in the ratio 2 : 5. Write the ratio of their areas in its simplest form.

9.2.4 kg of cheese costs £36. Work out the cost of 1.5 kg of the same cheese.

10.y is directly proportional to x. When x = 7, the value of y is 21. Work out the value of x when y = 12.

11.Work out the value of x when 4/x = 2/5.

12.Aisha invests £3200 in Account A, which pays 5% compound interest each year. She also invests £3200 in Account B, which pays 3% simple interest each year. Work out how much more Account A is worth than Account B after 2 years.

13.The number of members of a running club increases from 45 to 54. Work out the percentage increase.

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

15.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.