Algebra worksheet — GCSE Foundation

1.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.

2.Solve the inequality 2(x − 1) ≤ 8.

3.The graph of W = 840 ÷ L shows how the width, W metres, of a rectangular field of area 840 m² depends on its length, L metres. Use the relationship to work out the width when the length is 35 m, and hence the perimeter of the field.

4.Make x the subject of the formula y = 5x + 3.

5.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

6.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

7.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

8.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

9.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

10.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

11.Solve the inequality 3x − 1 ≤ 11.

12.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

13.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.

14.Work out the value of 5m² + 3m when m = −2.4

15.Solve 6x − 5 = 3x + 13.