Algebra worksheet — GCSE Foundation

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

2.The point A is at (5, −3). In which quadrant does A lie?

3.The graph of y = x² − 2x − 8 crosses the x-axis at x = −2 and x = 4. Work out the x-coordinate of the turning point of the curve, using the symmetry of the graph.

4.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

5.Make b the subject of the formula a = 5b.

6.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

7.Work out the value of 2(x + 2) when x = −5

8.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.

9.A number machine adds 5 to its input. Work out the output when the input is 0.

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

11.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

12.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.

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

14.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.

15.Solve x − 4 = −9