Algebra worksheet — GCSE Foundation

1.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.

2.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

3.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

4.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.

5.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

6.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?

7.Simplify k + k + k + k + k.

8.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

9.y = 3x − 2. Work out the value of y when x = 4.

10.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.

11.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.

12.Which expression means the same as a × a × a?

13.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.

14.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

15.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.