Algebra worksheet — GCSE Foundation

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

2.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

3.Which of these is a factor of 15x + 20?

4.Solve (2x + 1)/3 = 5

5.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

6.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

7.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

8.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

9.Which expression means 'y squared, multiplied by 3'?

10.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.

11.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

12.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.

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

14.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.

15.Which expression means the same as 3 × a × b?