Algebra worksheet — GCSE Foundation

1.Which expression means 'y squared, multiplied by 3'?

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

3.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

4.Make x the subject of the formula y = x + 7.

5.Solve the inequality 5x − 3 > 2x + 9.

6.a = 3 and b = 5. Work out the value of a²b.

7.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

8.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?

9.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

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

11.Work out the value of 3b − 4 when b = 6

12.Factorise fully 56x − 24

13.A ferry's distance-time graph is a straight line from (0 minutes, 0 km) to (25 minutes, 15 km). Work out the ferry's speed in kilometres per hour.

14.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

15.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.