Algebra worksheet — GCSE Foundation

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

2.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

3.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.

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

5.Solve x² − 100 = 0.

6.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?

7.Write down the expression that means the same as 3 × y × y.

8.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.

9.Expand 2(x − 13)

10.Solve the inequality 3x − 1 ≤ 11.

11.Work out the value of 3n − 2 when n = 1

12.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

13.Solve the inequality 5x − 3 > 2x + 9.

14.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

15.Which of these equations gives a straight-line graph when plotted?