Algebra worksheet — GCSE Higher

1.Work out the value of n² − n when n = −3

2.A geometric sequence has first term 3 and common ratio √3. Work out the position of the first term of the sequence that exceeds 30.

3.Make x the subject of the formula y = 2x − 9.

4.Which expression is equivalent to 3(2x − 5) + 4x?

5.Solve the inequality 5 − x ≤ 2.

6.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

7.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

8.(2x + 3)(x + a) ≡ 2x² + 11x + 12 is an identity. Work out the value of a.

9.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.

10.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

11.The curve y = x² − 3x. Use the chord between x = 1 and x = 4 to estimate the gradient of the curve at x = 2.5.

12.A garden path runs along the line 4x + y = 12. A drainage pipe must be laid perpendicular to the path, passing through the point (3, 1) where a sprinkler sits. Work out the equation of the pipe's line, giving your answer in the form y = mx + c.

13.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?

14.When a number is added to its square the result is 30. Work out the possible values of the number.

15.y = 5 − 2x. Work out the value of x when y = 11.