Algebra worksheet — GCSE Foundation

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

2.Which of these numbers is a cube number?

3.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.

4.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

5.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.

6.Solve 6x − 5 = 3x + 13.

7.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

8.Which of these points lies in the first quadrant?

9.Which expression means the same as 3 × a × b?

10.Expand 2(x + 12)

11.Simplify 2b − 1 + 2b − 4 + 2b

12.Work out the gradient of the straight line with equation 2x + y = 8.

13.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

14.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

15.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.