Algebra worksheet — GCSE Foundation

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

2.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

3.How many turning points does the graph of y = x² − 7x + 10 have?

4.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.

5.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

6.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.

7.Work out the y-intercept of the graph of y = x² + 3x − 10.

8.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.

9.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

10.Solve x − 4 = −9

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

12.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

13.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

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

15.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.