Algebra worksheet — GCSE Foundation

1.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.

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

3.Write down the expression that means the same as 3 × y × y.

4.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

5.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

6.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

7.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.

8.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

9.Make a the subject of the formula b = 20 − a.

10.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

11.In which quadrant does the point (−3, 0.5) lie?

12.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

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

14.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

15.Work out the value of (x − 4)/2 + 3 when x = 10