Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A recipe for pastry uses flour and butter in the ratio 3:2. A baker has 180 g of butter and wants to make pastry using all of it. Work out the total mass of pastry the baker can make.

2.A window cleaner charges a call-out fee plus an amount per window. The total charge, C pounds, is shown on a straight-line graph against the number of windows cleaned, w. The line passes through the points (2, 14) and (6, 26). Work out the gradient of the line.

3.A tank is filled at a rate of 3 litres every 2 minutes. Given that 1 litre = 1000 cm³, work out the flow rate in cm³ per minute.

4.Three numbers are in the ratio 1:2:3. The three numbers add up to 72. Work out the largest of the three numbers.

5.A straight-line graph shows the number of pages printed, p, plotted against the time in minutes, t, since a printer started a print job. The line passes through the points (2, 30) and (5, 90). Work out the gradient of the line.

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

7.A journey to school takes 12 minutes. A journey to the gym takes 20 minutes. Write the time for the journey to school as a fraction of the time for the journey to the gym, giving your answer in its simplest form.

8.A straight line passes through the points (1, 20) and (5, 8). Work out the gradient of the line.

9.£5000 is invested in an account paying 4% compound interest each year. Work out the total interest earned after 3 years.

10.£2000 is invested in a savings account that pays 5% compound interest each year. Work out the value of the investment at the end of 2 years.

11.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.

12.A garden centre has 90 rose bushes in stock. It receives a delivery that increases its stock of rose bushes by 20%. In the same week it sells 150 lavender bushes. Work out the new number of rose bushes, then write it as a fraction of the number of lavender bushes sold, giving your answer in its simplest form.

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

14.y is inversely proportional to x, so y = k ÷ x. When x = 5, the value of y is 8. Work out the value of k.

15.Write the ratio 2/3 : 1/2 as a ratio of whole numbers, in its simplest form.