Algebra worksheet — GCSE Foundation

1.y = x + 4. Work out the value of y when x = 3.

2.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

3.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.

4.A ferry's distance-time graph is a straight line from (0 minutes, 0 km) to (25 minutes, 15 km). Work out the ferry's speed in kilometres per hour.

5.Solve the inequality 9 − 2x ≥ 1.

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

7.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

8.Solve x² − 100 = 0.

9.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

10.Which expression means 'add 3 to n, then multiply the result by 4'?

11.Make b the subject of the formula a = 5b.

12.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

13.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.

14.Factorise fully 5x + 5y − 5

15.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.