Algebra worksheet — GCSE Foundation

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

2.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

3.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

4.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

5.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

6.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

7.Solve x² − x − 12 = 0.

8.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

9.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.

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

11.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

12.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

13.Write down the expression that means the same as m × m × m × n.

14.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

15.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.