Algebra worksheet — GCSE Higher

1.A tap's flow rate, in litres per minute, is plotted against time, in minutes, on a graph. What are the units of the area under this graph?

2.A population of bacteria doubles every 3 hours. It starts at 800. Work out the population after 9 hours.

3.The trapezium rule is used to estimate the area under a curve between x = 2 and x = 6. The curve is concave up (it curves upwards, like the inside of a bowl) throughout this interval. Which statement about the estimate is correct?

4.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.

5.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

6.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

7.Work out the integer values of x that satisfy x² − 2x − 8 ≤ 0.

8.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

9.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

10.Work out the gradient of the straight line with equation 3y = 12 − 6x.

11.The table shows the speed, in m/s, of a cyclist at times, in seconds, 1 second apart: 0 at t = 0, 7 at t = 1, 12 at t = 2, 15 at t = 3, 16 at t = 4, 14 at t = 5, 9 at t = 6. Using the trapezium rule with strip width 1 second, estimate the distance the cyclist travels between t = 2 and t = 5 only.

12.Simplify (x² − 9) ÷ (x² + 5x + 6).

13.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

14.A car's velocity–time graph is a straight line from (0 s, 4 m/s) rising to (6 s, V m/s), followed by a straight line falling from (6 s, V m/s) to (9 s, 0 m/s). The gradient of the second line is −8 m/s². Work out the total distance travelled between t = 0 and t = 9 seconds.

15.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.