Algebra worksheet — GCSE Foundation

1.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

2.A square tile has an area of 144 cm². Work out the side length of the tile.

3.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.

4.Write down the gradient of the line with equation y = −x + 3.

5.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

6.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

7.Make p the subject of the formula n = p/3.

8.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

9.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

10.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

11.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

12.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

13.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

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

15.The point A is at (5, −3). In which quadrant does A lie?