Ratio, proportion and rates of change worksheet — GCSE Higher

1.Write the ratio 2 : 1/4 as a ratio of whole numbers in its simplest form.

2.A water tank has a capacity of 500 litres. It currently holds 350 litres of water. Write the amount of empty space in the tank as a fraction of the tank's capacity. Give your answer in its simplest form.

3.Line P passes through the origin and the point (3, 21). Line Q passes through the origin and the point (5, 45). Both lines represent the distance, in metres, run by an athlete against the time, in seconds. Work out the gradient of the steeper line.

4.A baker uses 450 g of flour and 300 g of butter in a batch of pastry. Write the mass of butter as a fraction of the total mass of flour and butter, in its simplest form.

5.A gardener mixes 300 ml of plant feed concentrate with 1.2 litres of water to make a spray. Write the ratio of concentrate to water in its simplest form.

6.A tangent to a curve at the point where x = 3 passes through the points (1, 2) and (5, 14). A candidate says: "The gradient of the tangent at x = 3 is 3, because 14 − 2 = 12 and 12 ÷ 4 = 3." Which statement is correct?

7.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.

8.1 metre = 100 cm. Work out how many square centimetres there are in 1 square metre.

9.Order these three values from smallest to largest: 3/8, 0.43, 41%.

10.A company's turnover this year is £180,000. Last year's turnover was £120,000. Write down this year's turnover as a percentage of last year's turnover.

11.A metal has a density of 7.8 g/cm³. Work out the density of the metal in kg/m³.

12.The strength of a radio signal, in units, is inversely proportional to the square of the distance from the transmitter, in km. At a distance of 2 km the signal strength is 20 units. Construct the equation connecting signal strength S and distance d, then work out the distance at which the signal strength is 5 units.

13.The ratio of the number of pages Mia has read to the number of pages Leo has read is 7 : 4. Mia has read 84 pages. Work out how many pages they have read altogether.

14.A salt solution has a concentration of 10%. The solution contains 50 g of salt. Work out the total mass of the solution.

15.A dog walker's charge, C pounds, for walking a dog for m minutes is shown on a straight-line graph. The line passes through the points (20, 14) and (50, 26). Work out the charge for a 65-minute walk.