Algebra worksheet — GCSE Foundation

1.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.

2.Write down the expression that means 5 more than half of n.

3.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

4.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

5.a = 2 and b = 5. Work out the value of ab².

6.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

7.Solve (2x + 1)/3 = 5

8.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

9.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.

10.Solve 2x + 7 = x + 13

11.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

12.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

13.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

14.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

15.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.