Algebra worksheet — GCSE Foundation

1.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

2.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.

3.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

4.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

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

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

7.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.

8.Make x the subject of the formula y = 3(x + 2).

9.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

10.Work out the value of n² − n when n = −3

11.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

12.Work out the coordinates of the reflection of (6, −3) in the y-axis.

13.Work out the value of 3b − 4 when b = 6

14.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

15.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.