Algebra worksheet — GCSE Foundation

1.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

2.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

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

4.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

5.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

6.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.

7.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

8.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

9.n = 3. Work out the value of (2n)².

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

11.Solve x/4 + 1 = 3

12.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

13.The formula for the area of a trapezium is A = (a + b)h / 2, where a and b are the parallel side lengths and h is the height. Make h the subject of the formula.

14.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

15.Work out the value of 4p² − 3 when p = 2.5