Ratio, proportion and rates of change worksheet — GCSE Higher

1.The exchange rate is £1 = 1.28 US dollars. Convert £350 into US dollars.

2.A car travels at a constant speed. It travels 150 miles in 3 hours. At the same speed, work out how far it travels in 5 hours.

3.A shop's number of online orders is proportional to its number of in-store orders. Last month there were 45 in-store orders and 180 online orders. Write the ratio of online orders to in-store orders, in its simplest form.

4.A greenhouse's temperature, in °C, is recorded every hour during the day: 09:00, 15.0; 10:00, 18.4; 11:00, 20.1; 12:00, 19.8; 13:00, 17.2. Work out between which two consecutive readings the instantaneous rate of change of the temperature is most likely to have been zero.

5.A photo is enlarged so that its new width is 1.4 times its original width. Write the multiplier that would scale the new width back down to the original width, as a fraction in its simplest form.

6.The population of a town, P thousand, is plotted against time, t years, since 2020. A tangent to the graph at t = 6 has gradient 2.5. What does this gradient represent?

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

8.2.4 kg of cheese costs £36. Work out the cost of 1.5 kg of the same cheese.

9.Two numbers are in the ratio 3 : 7. Their sum is 60. Work out the positive difference between the two numbers.

10.y is directly proportional to x. When x = 7, the value of y is 21. Work out the value of x when y = 12.

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

12.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.

13.Two cars travel at constant speeds. Car A travels 150 km in 3 hours. Car B travels 180 km in 4 hours. Which car is faster, and what is its speed?

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

15.A dog walker's charge, C pounds, for walking a dog for m minutes is shown on a straight-line graph. The line passes through the points (20, 14) and (50, 26). Work out the charge for a 65-minute walk.