Algebra worksheet — GCSE Foundation

1.Solve 5x + 2 = 17.

2.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

3.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

4.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.

5.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

6.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

7.Make x the subject of the formula y = 5x + 3.

8.Which of these is a factor of 15x + 20?

9.n = 3. Work out the value of (2n)².

10.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

11.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

12.Which of these equations gives a straight-line graph when plotted?

13.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

14.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.

15.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.