Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

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

4.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.

5.A number machine multiplies its input by 3. The output is 15. Work out the input.

6.A quadratic graph has equation y = (x − 4)². A student says this graph crosses the x-axis at two different points. Explain why the student is wrong.

7.Solve 2(x + 3) = 10

8.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.

9.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.

10.Which expression means 'triple c, then add double d'?

11.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

12.Write down the coefficient of p in the expression 7 − 4p + 9q.

13.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

14.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

15.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.