Algebra worksheet — GCSE Foundation

1.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

2.Write down the first four terms of the sequence with nth term 6n − 5.

3.Expand 2(x + 12)

4.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

5.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.

6.Solve 4x − (2x − 6) = 18

7.A number machine adds 5 to its input. Work out the output when the input is 0.

8.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

9.Solve 3x − 1 = 8

10.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

11.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

12.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.

13.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

14.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.

15.p = 4. Work out the value of 2p³.