Algebra worksheet — GCSE Foundation

1.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

2.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

3.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

4.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

5.Expand 7(a + 8)

6.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

7.A cyclist's journey is shown on a distance–time graph. The graph is a straight line from (0 minutes, 0 km) to (40 minutes, 12 km). Work out her speed in kilometres per hour.

8.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

9.y = x + 10. Work out the value of y when x = 0.

10.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

11.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

12.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

13.Solve 2x + 7 = x + 13

14.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

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