Algebra worksheet — GCSE Foundation

1.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

2.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.

3.Simplify p + p + p.

4.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

5.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

6.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

7.Solve 3x + 14 = 8x − 6

8.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

9.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.

10.Solve 2x² − 32 = 0.

11.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.

12.Work out the y-intercept of the graph of y = x² + 3x − 10.

13.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.

14.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

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