Algebra worksheet — GCSE Foundation

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

2.Make x the subject of the formula y = (x − 4)/5.

3.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

4.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

5.A quadratic graph has equation y = (x − 4)². A student says this graph crosses the x-axis at two different points. Explain why the student is wrong.

6.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

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

8.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.

9.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.

10.Solve x² − 6x = 0.

11.A straight line has equation y = 5x. Work out the value of y when x = 3.

12.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

13.Mia buys 3 identical notebooks and a pen costing £1.50. She pays a total of £9.90. Form an equation using n for the cost of one notebook, and solve it to find n.

14.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

15.Which expression is equivalent to 6x − (2x − 5)?