Algebra worksheet — GCSE Foundation

1.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

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

3.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.

4.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

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

6.Which expression is equivalent to 2(x + 6)?

7.Make x the subject of the formula y = 3(x + 2).

8.Which of these equations gives a straight-line graph when plotted?

9.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

10.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

11.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.

12.The formula for converting a temperature in Fahrenheit, F, to Celsius, C, is C = 5(F − 32) ÷ 9. Work out C, to 1 decimal place, when F = 98.6.

13.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

14.Solve x² = 49.

15.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.