Algebra worksheet — GCSE Foundation

1.Solve 2(x + 3) = 10

2.Make a the subject of the formula b = 20 − a.

3.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

4.Simplify 5a/6 − a/3

5.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

6.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

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

8.How many turning points does the graph of y = x² − 7x + 10 have?

9.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

10.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

11.n = 3. Work out the value of (2n)².

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

13.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

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

15.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.