Algebra worksheet — GCSE Foundation

1.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

2.A taxi company charges a £2.50 booking fee plus £1.80 per mile. A journey costs £15.10 in total. Work out the number of miles travelled.

3.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

4.The graph of P = 480 ÷ V shows how the pressure, P pascals, of a gas depends on its volume, V cm³, at constant temperature. Use the relationship to work out the volume when the pressure is 32 pascals, and then work out by how much the volume increases when the pressure drops to 24 pascals.

5.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.

6.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

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

8.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

9.Which of these equations is equivalent to 5x − 2 = 3x + 8?

10.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

11.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

12.Solve 4x + 3 = 19

13.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

14.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.

15.Solve 5x − 9 = 16