Algebra worksheet — GCSE Foundation

1.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

2.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

3.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

4.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.

5.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

6.Which expression is equivalent to 2(x + 6)?

7.Solve the inequality 3x + 6 ≤ 0.

8.Which expression means 'triple c, then add double d'?

9.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

10.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

11.a = 2 and b = 5. Work out the value of a²b.

12.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

13.Which expression is equivalent to 5x − (x + 3)?

14.Write down the first four terms of the sequence with nth term 6n − 5.

15.Which of these rules generates the sequence 6, 11, 16, 21, …?