Algebra worksheet — GCSE Foundation

1.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.

2.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

3.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.

4.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

5.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

6.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

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

8.Write down the y-intercept of the line with equation y = 3x + 8.

9.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.

10.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

11.Write down the gradient of the line with equation y = 6 + 4x.

12.Given that (x + 2)(x − 7) = 0, write down the two solutions of x.

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

14.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

15.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.