Algebra worksheet — GCSE Foundation

1.Solve 4(x − 3) = 2x + 6.

2.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

3.Solve 2x + 1 = 9

4.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

5.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

6.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?

7.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.

8.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.

9.Simplify 5a/6 − a/3

10.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

11.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

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

13.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

14.A geometric sequence starts at 4, and each term after that is found by multiplying the term before it by 3. Write down the first four terms of the sequence.

15.Solve the inequality 2(3x − 1) ≥ 4x + 8.