Algebra worksheet — GCSE Foundation

1.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

2.Solve the inequality 2(x − 1) ≤ 8.

3.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.

4.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.

5.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.

6.Make x the subject of the formula y = x + 7.

7.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

8.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?

9.Which expression means 'add 3 to n, then multiply the result by 4'?

10.Which expression is equivalent to 7x − 3(2x − 6)?

11.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

12.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.

13.Solve x² − 100 = 0.

14.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

15.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.