Algebra worksheet — GCSE Foundation

1.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

2.Work out the equation of the straight line through the points (−2, 1) and (0, 7).

3.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

4.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

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.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

7.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

8.Solve 7x − 5 = 3x + 11

9.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

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

11.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

12.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

13.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

14.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.

15.Which of these values of x is a solution of x² + 2x − 15 = 0?