Algebra worksheet — GCSE Foundation

1.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

2.The braking distance of a car, in metres, is estimated using the formula d = 0.4v² + 6, where v is the speed in mph. A car travelling at 35 mph brakes. Work out the estimated braking distance.

3.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

4.Simplify x + x + 4

5.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

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

7.Solve the inequality x − 10 < −3.

8.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.

9.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

10.Work out the value of (x − 4)/2 + 3 when x = 10

11.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

12.Expand 2(x + 12)

13.Solve x² = 49.

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

15.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.