Algebra worksheet — GCSE Foundation

1.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

2.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

3.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

4.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

5.Factorise fully 12x² + 18x.

6.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

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 plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

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.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

11.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.

12.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

13.Solve 4x² − 9 = 0.

14.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

15.Solve (3x + 2)/5 = (x + 4)/3