Ratio, proportion and rates of change worksheet — GCSE Higher

1.A river 120 km long is drawn as a line 6 cm long on a map. Work out the scale of the map.

2.The ratio of y to x is always 3 : 4. Write down which equation could represent this relationship.

3.A beaker holds 500 g of a salt solution of concentration 12%. Pure water is added until the concentration falls to 8%. Work out the mass of water added.

4.A concert hall has 54 seats in total, of which 24 are reserved and the rest are free. Write the number of free seats as a fraction of the number of reserved seats. Give your answer in its simplest form.

5.A footpath is drawn 3 cm long on a map with a scale of 1 : 50 000. Work out the real length of the footpath, in metres.

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

7.The height of a candle, in cm, is measured as it burns: t = 0 min, height = 20.0; t = 3 min, height = 18.7; t = 5 min, height = 17.5; t = 6 min, height = 16.6; t = 7 min, height = 15.4; t = 9 min, height = 13.4. Which pair of readings gives the best estimate of the instantaneous rate of change of the height at t = 6 minutes, and why?

8.Leah puts £4000 into a savings account paying 3% compound interest each year. At the end of 2 years she takes out all of the money and spends £1500 of it on a laptop. Work out how much of the money she has left.

9.A fruit squash is made by mixing squash and water. In a jug, 2/9 of the total volume is squash. A caterer makes up 4.5 litres of the squash mixture. Work out how many litres of squash are in the mixture.

10.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?

11.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?

12.Two quantities, P and Q, are in inverse proportion. A graph is drawn with P on the vertical axis and Q on the horizontal axis. Write down which description fits the shape of this graph.

13.Write £3.60 : £2.40 as a ratio in its simplest form.

14.In a class, 50% of the students study French, 30% study Spanish and the rest study German. Write down the ratio of French : Spanish : German students, in its simplest form.

15.Work out the value of x when 4/x = 2/5.