Algebra worksheet — GCSE Foundation

1.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

2.Work out the value of 3x² − 4x when x = −2.

3.a = 2 and b = 5. Work out the value of a²b.

4.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

5.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

6.Which expression is equivalent to 4(x − 2) + 10?

7.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

8.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

9.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

10.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

11.Make x the subject of the formula y = 2x − 9.

12.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

13.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?

14.Solve 2x + 7 = x + 13

15.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.