Algebra worksheet — GCSE Foundation

1.Work out the gradient of the straight line with equation y = (2x/5) − 3.

2.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

3.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

4.A number machine multiplies its input by 3. The output is 15. Work out the input.

5.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

6.Solve 2(x + 3) = 10

7.Solve the inequality 2(x − 1) ≤ 8.

8.Make x the subject of the formula y = 4x − 3.

9.Factorise x² − 3x − 10.

10.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

11.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

12.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.

13.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

14.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

15.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.