Algebra worksheet — GCSE Foundation

1.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

2.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

3.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

4.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

5.Which of these numbers is a cube number?

6.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.

7.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

8.The graph of y = x² − 2x − 8 crosses the x-axis at x = −2 and x = 4. Work out the x-coordinate of the turning point of the curve, using the symmetry of the graph.

9.Solve 2x + 1 = 9

10.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

11.Solve the inequality 9 − 2x ≥ 1.

12.The graph of a straight line has equation y = 4x − 5. Beth says the y-intercept is 4. Work out the correct y-intercept.

13.Solve x² − 2x − 24 = 0.

14.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

15.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.