Algebra worksheet — GCSE Foundation

1.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.

2.Make x the subject of the formula y = (x − 4)/5.

3.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.

4.Work out the value of 2x² when x = −3

5.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

6.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

7.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

8.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

9.Solve 2x² − 32 = 0.

10.Solve (2x + 1)/3 = 5

11.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

12.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.

13.Solve 2x − 2 = 2

14.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

15.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.