Algebra worksheet — GCSE Foundation

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

2.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

3.Make p the subject of the formula n = p/3.

4.Solve the inequality 9 − 2x ≥ 1.

5.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

6.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

7.Solve 2x² = 18.

8.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

9.Make c the subject of the formula k = 6c.

10.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

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

12.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

13.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.

14.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.

15.Which of these statements is an equation with exactly one solution?