Algebra worksheet — GCSE Foundation

1.Solve 5x − 9 = 16

2.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

3.A number machine adds 5 to its input. Work out the output when the input is 0.

4.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.

5.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

6.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

7.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

8.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

9.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

10.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

11.Which expression is equivalent to 7x − 3(2x − 6)?

12.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.

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

14.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

15.Which of these equations gives a straight-line graph when plotted?