Algebra worksheet — GCSE Foundation

1.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

2.Solve 2x − 2 = 2

3.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.

4.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

5.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

6.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

7.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

8.y = 3x − 2. Work out the value of y when x = 4.

9.Factorise fully 5x + 5y − 5

10.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

11.A market stall's cost of hiring n tables is modelled by two formulas: Formula A: C = 3(2n + 5); Formula B: C = 6n + 15, where C is in pounds. A stallholder says the two formulas always give the same cost. Work out the cost given by each formula when n = 4, and use your results to decide whether the stallholder is correct.

12.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

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

14.The point B has coordinates (−2, −2). In which quadrant is B?

15.Factorise fully 12x² + 18x.