Algebra worksheet — GCSE Foundation

1.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

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

3.Which of these statements is an identity?

4.A number machine multiplies its input by 5. Work out the output when the input is −1.

5.A cyclist's journey is shown on a distance–time graph. The graph is a straight line from (0 minutes, 0 km) to (40 minutes, 12 km). Work out her speed in kilometres per hour.

6.Solve 4x − (2x − 6) = 18

7.Write down the first four terms of the sequence with nth term 6n − 5.

8.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.

9.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.

10.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

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

12.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.

13.Write down the expression that means the same as (x + 7) ÷ 4.

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

15.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.