Algebra worksheet — GCSE Foundation

1.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

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

3.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.

4.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

5.Factorise fully 12x² + 18x.

6.A taxi company charges a £2.50 booking fee plus £1.80 per mile. A journey costs £15.10 in total. Work out the number of miles travelled.

7.Factorise x² − 3x − 10.

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

9.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

10.How many turning points does the graph of y = x² − 7x + 10 have?

11.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

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

13.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

14.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

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