Algebra worksheet — GCSE Foundation

1.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

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

3.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.

4.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

5.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?

6.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

7.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

8.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

9.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.

10.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

11.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

12.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

13.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.

14.Solve 3x − 1 = 8

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