Algebra worksheet — GCSE Foundation

1.Solve the inequality x − 10 < −3.

2.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

3.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

4.A number machine multiplies its input by 5. Work out the output when the input is −1.

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

6.Write down the expression that means the same as (x + 7) ÷ 4.

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

8.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.

9.Make m the subject of the formula w = m − 8.

10.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

11.Write down the expression that means the same as 3 × y × y.

12.Solve 3x + 14 = 8x − 6

13.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

14.Work out the value of m² + 3m when m = −2

15.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?