Algebra worksheet — GCSE Foundation

1.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

2.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.

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

4.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

5.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.

6.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

7.Solve 3(2x − 1) = 27

8.Expand 2(x + 12)

9.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

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

11.Solve 2x + 1 = 9

12.Work out the value of a² − 2b when a = −3 and b = 4.

13.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

14.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

15.Make x the subject of the formula y = 2x − 9.