Algebra worksheet — GCSE Foundation

1.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

2.Make x the subject of the formula y = 4(x − 6).

3.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

4.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.

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

6.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

7.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

8.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

9.Factorise x² − 3x − 10.

10.Which of these is an equation, rather than an expression, a formula or an identity?

11.Solve x/4 + 1 = 3

12.Which expression means the same as 3 × a × b?

13.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

14.Work out the y-intercept of the graph of y = x² + 3x − 10.

15.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.