Ratio, proportion and rates of change worksheet — GCSE Higher

1.A box holds 60 crayons. 25 of the crayons are broken and the rest are unbroken. Write the number of unbroken crayons as a fraction of the number of broken crayons. Give your answer in its simplest form.

2.In a bag the ratio of red counters to blue counters is 7 : 4. Write the number of red counters as a fraction of the number of blue counters.

3.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?

4.The temperature of a chemical reaction, in °C, is modelled by T = 80 − 6t + 0.5t², where t is the time in minutes after the reaction starts. Which of these four statements about the reaction between t = 2 and t = 6 minutes is correct?

5.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?

6.Two mathematically similar water bottles have a volume scale factor of 8 from the smaller bottle to the larger bottle. Work out the surface area scale factor from the smaller bottle to the larger bottle.

7.A machine fills bottles at a constant rate. It fills 18 bottles in 3 minutes. Working at the same rate, work out how many bottles the machine fills in 8 minutes.

8.Two mathematically similar triangular flags have areas in the ratio 4 : 25. The height of the smaller flag is 6 cm. Work out the height of the larger flag.

9.A journey takes 4 hours at an average speed of 60 km/h. The time taken is inversely proportional to the average speed. Work out how long the same journey takes at an average speed of 80 km/h.

10.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.

11.x × y is used to test whether two quantities are in inverse proportion. For the pairs x = 4, y = 15 and x = 6, y = 10, which statement is correct?

12.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.

13.The strength of a radio signal, in units, is inversely proportional to the square of the distance from the transmitter, in km. At a distance of 2 km the signal strength is 20 units. Construct the equation connecting signal strength S and distance d, then work out the distance at which the signal strength is 5 units.

14.A crate exerts a force of 84 N on the floor through a base with an area of 2.4 m². Work out the pressure on the floor, in N/m².

15.In a mix of mortar the ratio of the mass of sand to the mass of cement is 5 : 2. Write the mass of cement as a fraction of the total mass of the mix.