Algebra worksheet — GCSE Foundation

1.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

2.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

3.Make x the subject of the formula y = 5x + 3.

4.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

5.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.

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

7.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.

8.Which of these statements is an equation with exactly one solution?

9.Simplify (5x² + 3x − 2) − (2x² − x + 5)

10.Simplify 5x + 3y − 2x + y.

11.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.

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

13.Factorise fully 5x + 5y − 5

14.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

15.Work out the value of 2x² when x = −3