Algebra worksheet — GCSE Foundation

1.Work out the value of a² − 2b when a = −3 and b = 4.

2.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

3.A sequence begins at 7. Each term after the first is found by adding 6 to the term before it. Work out the 6th term of the sequence.

4.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

5.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

6.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.

7.Make p the subject of the formula n = p/3.

8.Which of these is a factor of 15x + 20?

9.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?

10.Simplify 5x + 3y − 2x + y.

11.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

12.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.

13.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

14.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

15.Make x the subject of the formula y = 2x − 9.