Ratio, proportion and rates of change worksheet — GCSE Higher

1.Butter costs £2.40 per kg. Work out the cost of the butter in pence per 100 g.

2.A stall sells bottles of juice. Two bottles cost £3.00, five bottles cost £7.50 and eight bottles cost £12.00. The cost, C pounds, is in a fixed ratio to the number of bottles, n. Write down a formula for C in terms of n.

3.The height of a ball, in metres, above the ground is plotted against time, in seconds, after it is thrown. The tangent to the graph at t = 1.5 seconds has gradient 2. Which of these four statements about the ball at t = 1.5 seconds is correct?

4.The volume of water in a paddling pool, in litres, is plotted against the time since the tap was turned on, in minutes. What are the units of the gradient of a tangent to this graph?

5.A trust fund contains £8000. Each year, 5% interest is added, and then £600 is paid out to a charity. Work out the amount remaining in the fund after 2 years.

6.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.

7.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.

8.A sculptor makes two mathematically similar statues. The smaller statue is 20 cm tall and 80 ml of varnish covers its surface. The larger statue is 50 cm tall. Work out how much varnish is needed to cover the surface of the larger statue.

9.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.

10.A concrete block exerts a force of 45 N on the ground through a base with an area of 0.05 m². Work out the pressure on the ground, in N/m².

11.A gym charges members a joining fee plus a fixed amount per month. The total amount paid, C pounds, is shown on a straight-line graph against the number of months, m. The line passes through the points (3, 130) and (7, 210). Work out the total amount a member will have paid after 12 months.

12.A cyclist's speed, in metres per second, is plotted against time, in seconds, since she sets off. Which statement correctly pairs the gradient of a tangent to this graph, and the area between the graph and the time-axis, with what each one represents?

13.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.

14.A map has a scale of 1 : 40 000. A cycle path measures 7.5 cm on the map. Work out the real length of the cycle path, in kilometres.

15.The density of a type of solid plastic is 0.9 g/cm³. Work out the mass of 0.5 m³ of the plastic, in kilograms.