Algebra worksheet — GCSE Foundation

1.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

2.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.

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

4.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

5.Solve the inequality 3x − 1 ≤ 11.

6.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

7.Solve x² + 3x − 10 = 0.

8.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

9.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

10.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

11.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

12.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

13.n = 3. Work out the value of (2n)².

14.Work out the value of a² − 2b when a = −3 and b = 4.

15.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.