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 graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

3.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

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

5.Solve the inequality 6x ≥ 18.

6.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

7.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

8.Which of these is a formula?

9.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.

10.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

11.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?

12.Solve the inequality 5 − x ≤ 2.

13.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.

14.Simplify 2a + 3b − a + 2b − b

15.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?