Algebra worksheet — GCSE Foundation

1.A curve has equation y = x² − 9. Which statement about its graph is correct?

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

3.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.

4.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.

5.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

6.A number machine multiplies its input by 3. The output is 15. Work out the input.

7.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

8.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

9.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.

10.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

11.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

12.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

13.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

14.Solve the inequality 3x + 6 ≤ 0.

15.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.