Ratio, proportion and rates of change worksheet — GCSE Higher

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

2.The price of a cycling helmet rises from £80 to £116. Work out the percentage increase.

3.A novel has 312 pages. A comic has 48 pages. Write the number of pages in the novel as a fraction of the number of pages in the comic, giving your answer in its simplest form.

4.A recipe for 8 people needs 320 g of rice. Sanjay scales the recipe down to serve 5 people, then wants to scale his new amount back up to serve 8 people again. Work out the multiplier he should use to scale his amount for 5 people back up to the amount for 8 people.

5.Two mathematically similar circles have radii 4 cm and 20 cm. Write the ratio of the area of the smaller circle to the area of the larger circle in its simplest form.

6.A curve has equation y = 2x² + 5. Work out an estimate for the gradient of the curve at x = 3, using a chord between the points where x = 2 and x = 4.

7.A mobile phone tariff is shown on a straight-line graph with the monthly cost, C pounds, on the vertical axis and the amount of data used, g gigabytes, on the horizontal axis. The line passes through (0, 10) and (8, 26). Work out the gradient and say what it represents.

8.In a fruit squash mix, the ratio of squash to water is 2 : 9. A shop wants to make up the mix using 3.4 litres of squash. Work out how many litres of water are needed.

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

10.A necklace is made using gold beads and silver beads in the ratio 7:3. There are 40 more gold beads than silver beads. Work out the total number of beads in the necklace.

11.The volume of fuel remaining in a storage tank, in thousands of litres, is plotted against time, in hours, since a leak was detected. A tangent to the graph at t = 2 hours has gradient −8.75 thousand litres per hour. A tangent at t = 8 hours has gradient −3.5 thousand litres per hour. Work out by what factor the instantaneous rate of change is greater in size at t = 2 hours than at t = 8 hours.

12.An acid solution has a concentration of 20%. The solution contains 40 g of acid, and the rest of the solution is water. Work out the mass of water in the solution.

13.A loan of £3000 has interest added at 2% each month, and then a fixed repayment of £200 is made. This is modelled by the recurrence B_{n+1} = 1.02B_n − 200, where B_n is the balance after n months and B_0 = 3000. Work out the balance after 2 months.

14.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.

15.A water tank is a cuboid measuring 30 cm × 20 cm × 10 cm. The tank is full of water. Work out how many litres of water it holds.