Algebra worksheet — GCSE Foundation

1.p = 4. Work out the value of 2p³.

2.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

3.Write down 0.2x with its coefficient written as a fraction in its simplest form.

4.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

5.Work out the gradient of the straight line with equation y = (2x/5) − 3.

6.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

7.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

8.Work out the value of 4p² − 3 when p = 2.5

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

10.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.

11.Solve the inequality 3x + 6 ≤ 0.

12.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

13.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

14.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

15.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.