Algebra worksheet — GCSE Foundation

1.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

2.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

3.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?

4.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

5.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

6.a = 2 and b = 5. Work out the value of ab².

7.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

8.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

9.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

10.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

11.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

12.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.

13.Factorise fully 56x − 24

14.Which of these values of x is a solution of x² + 2x − 15 = 0?

15.Solve 5x² − 15x = 0.