Algebra worksheet — GCSE Foundation

1.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.

2.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

3.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

4.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

5.The point B has coordinates (−2, −2). In which quadrant is B?

6.Solve the inequality 2(3x − 1) ≥ 4x + 8.

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

8.Which of these quadratic graphs does NOT cross the x-axis at all?

9.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

10.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

11.Solve 3x + 14 = 8x − 6

12.Work out the value of 3n − 2 when n = 1

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

14.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

15.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.