Algebra worksheet — GCSE Foundation

1.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.

2.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

3.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

4.A curve has equation y = x² − 9. Which statement about its graph is correct?

5.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

6.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

7.p = 4. Work out the value of 2p³.

8.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

9.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

10.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

11.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

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

13.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

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

15.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.