Algebra worksheet — GCSE Foundation

1.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

2.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

3.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

4.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

5.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.

6.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

7.In which quadrant does the point (−3, 0.5) lie?

8.y = 5 − 2x. Work out the value of x when y = 11.

9.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

10.Solve x² − x − 12 = 0.

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

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

13.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

14.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

15.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.