Algebra worksheet — GCSE Foundation

1.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

2.Make p the subject of the formula n = p/3.

3.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

4.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

5.Write down the gradient of the line with equation y = 7x − 2.

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

7.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

8.Expand and simplify 2(a + 6) − 2(a − 7)

9.x = 5. Work out the value of 3x² − 4.

10.Write down the expression that means the same as (x + 7) ÷ 4.

11.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

12.Solve 2x + 1 = 9

13.Write down the number of terms in the expression 4x² − 7x + 3.

14.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

15.Expand 2(x + 12)