Algebra worksheet — GCSE Foundation

1.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.

2.Solve 2x² = 18.

3.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

4.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

5.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

6.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

7.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

8.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

9.A point lies on the y-axis. What can be said about the x-coordinate of that point?

10.A cyclist's journey is shown on a distance–time graph. The graph is a straight line from (0 minutes, 0 km) to (40 minutes, 12 km). Work out her speed in kilometres per hour.

11.Which of these is an equation, rather than an expression, a formula or an identity?

12.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?

13.Work out the distance of the point (−6, 4) from the x-axis.

14.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

15.Which expression is equivalent to 5x − (x + 3)?