Algebra worksheet — GCSE Foundation

1.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

2.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

3.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

4.Solve 5x² − 15x = 0.

5.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

6.Which expression is equivalent to 3(2x − 5) + 4x?

7.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

8.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.

9.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

10.Which of these statements is an equation with exactly one solution?

11.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

12.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

13.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.

14.Solve x² + 3x − 10 = 0.

15.The point A lies on the x-axis. Which statement about A must be true?