Algebra worksheet — GCSE Foundation

1.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.

2.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

3.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

4.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

5.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

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

7.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

8.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

9.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

10.Solve 2x + 1 = 9

11.Expand 7(a + 8)

12.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

13.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?

14.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

15.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.