Algebra worksheet — GCSE Foundation

1.The first five terms of a sequence are 2, 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

2.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.

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

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

5.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

6.Solve x² = 49.

7.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.

8.Expand 7(a + 8)

9.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

10.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.

11.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

12.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

13.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

14.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?

15.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.