Ratio, proportion and rates of change worksheet — GCSE Higher

1.A shop's daily profit, in pounds, is plotted against the price charged for an item, in pounds. A tangent to the profit graph at a price of £15 passes through the points (12, 540) and (18, 480). Work out the instantaneous rate of change of profit with respect to price at £15, and state whether profit is increasing or decreasing there.

2.A sprinter's distance from the start line, in metres, is plotted against time, in seconds. A tangent to the graph at t = 2 seconds has gradient 6. A tangent at t = 8 seconds has gradient 9.5. Which statement correctly compares the sprinter's speed at these two times?

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

4.A metal alloy is made from copper and tin in the ratio 7:3. Work out the mass of tin in 250 g of the alloy.

5.In a fruit bowl, the number of bananas is 3/4 of the number of apples. There are 16 apples in the bowl. Write the number of apples as a fraction of the number of bananas. Give your answer in its simplest form.

6.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?

7.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.

8.A salt solution has a concentration of 10%. The solution contains 50 g of salt. Work out the total mass of the solution.

9.A concrete mix is made from gravel and cement in the ratio 5 : 1 by mass. The mass of cement is c kg and the total mass of the mix is m kg. Write down a formula for m in terms of c.

10.40% of a number is 12 more than 25% of the same number. Work out the number.

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.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?

13.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?

14.Amelia uses 2 kg of flour to bake 5 cakes. Using the same recipe, work out how many cakes she can bake with 6 kg of flour.

15.£1 is worth 1.25 US dollars. Write the ratio of pounds to dollars in its simplest form, using whole numbers.