Algebra worksheet — GCSE Foundation

1.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

2.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

3.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

4.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.

5.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.

6.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.

7.A point lies on the y-axis. What can be said about the x-coordinate of that point?

8.How many turning points does the graph of y = x² − 7x + 10 have?

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

10.Solve x − 4 = −9

11.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

12.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

13.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

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

15.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.