Algebra worksheet — GCSE Foundation

1.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

2.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.

3.Which expression means the same as 3 × a × b?

4.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.

5.Write down the coefficient of p in the expression 7 − 4p + 9q.

6.Solve the inequality 9 − 2x ≥ 1.

7.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?

8.Solve the inequality 5x − 3 > 2x + 9.

9.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

10.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

11.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

12.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

13.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

14.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

15.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.