Algebra worksheet — GCSE Foundation

1.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

2.Solve 5x − 9 = 16

3.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

4.Write down the gradient of the line with equation y = 6 + 4x.

5.A tree is 2 metres tall. Each year its height increases by 10% of its height at the start of that year. Work out the height of the tree after 3 years, giving your answer to 1 decimal place.

6.A point lies on the y-axis. What can be said about the x-coordinate of that point?

7.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

8.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

9.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

10.Expand and simplify (x − 3)²

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

12.Expand 2(x − 13)

13.Which of these numbers is a cube number?

14.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.

15.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.