Algebra worksheet — GCSE Foundation

1.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.

2.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

3.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

4.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.

5.Solve x² − 2x − 24 = 0.

6.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

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

8.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

9.Solve x² − 5x + 6 = 0 by factorising.

10.Which expression means the same as a × a × a?

11.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

12.Expand 7(a + 8)

13.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

14.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

15.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.