Algebra worksheet — GCSE Higher

1.The point (18, 24) lies on the circle x² + y² = 900, which has centre (0, 0). The tangent to the circle at (18, 24) crosses the y-axis at the point Q. Work out the y-coordinate of Q.

2.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

3.The nth term of a geometric sequence is given by aₙ = 3 × 2ⁿ⁻¹. Work out the position of the first term that is greater than 1,000.

4.Four sequences are shown below. Sequence P: 3, 6, 12, 24, … Sequence Q: 1, 4, 9, 16, … Sequence R: 2, 4, 8, 14, … Sequence S: 5, 10, 15, 20, … Work out which of the sequences P, Q, R and S is geometric.

5.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.

6.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

7.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

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

9.Expand and simplify (x − 3)²

10.Which expression means 'y squared, multiplied by 3'?

11.Make x the subject of the formula y = 4(x − 6).

12.Solve the inequality 9 − 2x ≥ 1.

13.The formula for the area of a trapezium is A = (a + b)h / 2, where a and b are the parallel side lengths and h is the height. Make h the subject of the formula.

14.Solve 4(x − 3) = 2x + 6.

15.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.