Algebra worksheet — GCSE Higher

1.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

2.Write down the expression that means the same as (x + 7) ÷ 4.

3.A cyclist's speed-time graph is described as follows: speed increases steadily from 0 m/s to 8 m/s over the first 4 seconds, stays constant at 8 m/s for the next 6 seconds, then decreases steadily to 0 m/s over the final 2 seconds. Work out the total distance travelled.

4.n is an integer. Which of these expressions is always an even number?

5.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

6.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

7.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

8.Solve the inequality 9 − 2x ≥ 1.

9.Solve 2x + 7 = x + 13

10.Which expression means 'add 3 to n, then multiply the result by 4'?

11.f(x) = x + 3 and g(x) = 2x. Work out fg(x).

12.By completing the square, find the turning point of the curve y = x² − 4x + 9.

13.A circle has centre (0, 0) and equation x² + y² = 50. Work out the radius of the circle, giving your answer as a surd in its simplest form.

14.For 0 ≤ x ≤ 360, the equation sin x = 0.5 has two solutions. What are they?

15.a = 2 and b = 5. Work out the value of a²b.