Algebra worksheet — GCSE Foundation

1.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.

2.Write down the expression that means the same as w ÷ 6.

3.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

4.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

5.y = 5 − 2x. Work out the value of x when y = 11.

6.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?

7.Solve x² + 3x − 10 = 0.

8.Solve 3(2x − 1) = 27

9.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

10.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

11.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

12.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.

13.Solve 5x − 9 = 16

14.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

15.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?