Algebra worksheet — GCSE Foundation

1.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

2.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

3.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.

4.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.

5.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

6.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?

7.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

8.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

9.y = 5x − 1. Work out the value of y when x = 3.

10.Which of these points lies in the first quadrant?

11.Write down the expression that means the same as m × m × m × n.

12.Solve 2x + 1 = 9

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

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

15.Simplify 5x + 3y − 2x + y.