Algebra worksheet — GCSE Foundation

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

2.x = 5. Work out the value of 3x² − 4.

3.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

4.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

5.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

6.Make p the subject of the formula n = p/3.

7.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

8.Factorise x² − 64.

9.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.

10.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

11.Solve x² − 5x + 6 = 0 by factorising.

12.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

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

14.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

15.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.