Algebra worksheet — GCSE Foundation

1.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

2.The diagram shows the graph of a quadratic function. Which equation could it represent?

3.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

4.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

5.Expand 4(2x − 3).

6.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

7.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

8.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

9.Simplify 5a/6 − a/3

10.A number machine multiplies its input by 3. The output is 15. Work out the input.

11.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.

12.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

13.Solve 7x − 5 = 3x + 11

14.Work out the value of 2(x + 2) when x = −5

15.Solve the inequality 5 − x ≤ 2.