Algebra worksheet — GCSE Foundation

1.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

2.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

3.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

4.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

5.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

6.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

7.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

8.Work out the value of 2(x + 2) when x = −5

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

10.Solve x² + 7x = 0.

11.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

12.Write down the gradient of the line with equation y = 6 + 4x.

13.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

14.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

15.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.