Algebra worksheet — GCSE Foundation

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

2.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

3.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.

4.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

5.Simplify 5a/6 − a/3

6.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

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

8.Solve the inequality 5 − x ≤ 2.

9.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

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.A cinema sells adult tickets and child tickets. On one evening, 40 tickets are sold in total. There are 8 more adult tickets sold than child tickets. Work out the number of child tickets sold.

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

13.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

14.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

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