Algebra worksheet — GCSE Foundation

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

2.Write down the expression that means the same as p + p + p + q.

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

4.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

5.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.

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

7.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

8.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

9.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

10.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.

11.Which expression means 'add 3 to n, then multiply the result by 4'?

12.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

13.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

14.The point A lies on the x-axis. Which statement about A must be true?

15.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.