Algebra worksheet — GCSE Foundation

1.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

2.Which of these statements is an identity?

3.Solve 2(x + 3) = 10

4.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

5.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.

6.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

7.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.

8.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

9.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

10.A square has sides of length y cm. Write down an expression for the perimeter of the square.

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

12.Solve the inequality 6x ≥ 18.

13.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

14.Write down the expression that means the same as m² × m × 3.

15.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.