Algebra worksheet — GCSE Foundation

1.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

2.Solve 2x − 2 = 2

3.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

4.Write down the gradient of the line with equation y = 7x − 2.

5.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.

6.Simplify k + k + k + k + k.

7.Which of these equations describes a vertical line?

8.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

9.Work out the value of 2(x + 2) when x = −5

10.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

11.Solve the inequality 4x + 1 > 2x + 9.

12.Solve 3x − 1 = 8

13.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

14.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.

15.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.