Ratio, proportion and rates of change worksheet — GCSE Higher

1.Two mathematically similar rectangles have widths 5 cm and 10 cm. The perimeter of the smaller rectangle is 18 cm. Work out the perimeter of the larger rectangle.

2.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.

3.A jug of squash is made by mixing water and syrup in the ratio 6:1. Nia wants to make 8.4 litres of squash. Work out how much syrup she needs, in litres.

4.40% of a number is 12 more than 25% of the same number. Work out the number.

5.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.

6.A tangent to a curve at the point where x = 3 passes through the points (1, 4) and (5, 20). Work out the gradient of the tangent at x = 3, and hence the instantaneous rate of change of y with respect to x at that point.

7.A jumper costs £45 at Shop A, where it is reduced by 20%. The same jumper costs £34 at Shop B, where a further 10% reduction is then applied. Work out the difference between the two reduced prices.

8.A fixed job of fitting a solar array is shared between installers, and the time taken is inversely proportional to the number of installers working on it at once. With 4 installers the job takes 18 hours. Construct the equation connecting time T and number of installers n, then work out how long it would take with 6 installers.

9.Two quantities y and z are each in direct proportion to x, and are given by y = 3x and z = 7x. Work out the difference between the value of y and the value of z when x = 4.

10.A rectangular garden has its length and width in the ratio 5:3. Given that the perimeter of the garden is 64 m, work out the width of the garden.

11.There are 84 passengers on a double-decker bus. 35 of the passengers are adults and the rest are children. Write the number of adults as a fraction of the number of children. Give your answer in its simplest form.

12.A map has a scale of 1:25000. A road on the map is 6 cm long. Work out the real-life length of the road, giving your answer in kilometres.

13.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.

14.A worker is paid £13.20 per hour. Work out this rate of pay in pence per minute.

15.A laptop priced at £520 is first increased by 15%, and then the new price is decreased by 20%. Work out the final price of the laptop.