Algebra worksheet — GCSE Foundation

1.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

2.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

3.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.

4.Solve x² = 49.

5.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.

6.Solve the inequality 5 − x ≤ 2.

7.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

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

9.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.

10.Solve 5x + 2 = 17.

11.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.

12.Work out the value of 5m² + 3m when m = −2.4

13.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

14.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

15.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.