Algebra worksheet — GCSE Foundation

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

2.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

3.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

4.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

5.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

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

7.Solve 4(x − 3) = 2x + 6.

8.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

9.Solve (3x + 2)/5 = (x + 4)/3

10.Factorise x² − 3x − 10.

11.Make x the subject of the formula y = 4(x − 6).

12.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

13.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

14.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

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.