Algebra worksheet — GCSE Foundation

1.Solve x² = 81.

2.A wall is tiled in rows, and every row uses the same number of tiles. One row uses 10 tiles, two rows use 20 tiles and three rows use 30 tiles. Work out how many tiles are needed for 7 rows.

3.y = x + 4. Work out the value of y when x = 3.

4.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.

5.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.

6.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

7.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

8.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

9.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

10.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

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

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.Make x the subject of the formula y = x/2 − 5.

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

15.Solve the inequality 6.3x + 1.8 ≤ 40. Hence write down the greatest number with exactly one decimal place that satisfies the inequality.