Algebra worksheet — GCSE Foundation

1.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

2.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

3.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

4.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

5.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

6.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

7.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

8.a = 3 and b = 5. Work out the value of a²b.

9.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.

10.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

11.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

12.y = 5x − 1. Work out the value of y when x = 3.

13.Solve 2x² − 32 = 0.

14.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

15.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.