Algebra worksheet — GCSE Foundation

1.Which expression means 'y squared, multiplied by 3'?

2.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

3.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.

4.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

5.A square tile has an area of 144 cm². Work out the side length of the tile.

6.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

7.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

8.Solve 6x − 5 = 3x + 13.

9.Solve x² − 2x − 24 = 0.

10.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

11.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.

12.Which of these is a formula, rather than an expression, an equation, or an identity?

13.A ferry's distance-time graph is a straight line from (0 minutes, 0 km) to (25 minutes, 15 km). Work out the ferry's speed in kilometres per hour.

14.Write down the number of terms in the expression 4x² − 7x + 3.

15.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.