Algebra worksheet — GCSE Higher

1.The first four terms of a sequence are 2, 2√3, 6, 6√3, ... Work out the next term.

2.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

3.Make x the subject of the formula y = 4x − 3.

4.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.

5.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

6.Simplify (2x² + 7x + 3) ÷ (x² − 9), giving your answer as a single fraction.

7.A graph passes through the point (0, 1). As x increases through positive values, the graph rises more and more steeply, and as x decreases through negative values, the graph gets closer and closer to the x-axis without ever reaching it. Which of these could be the equation of the graph?

8.A population of bacteria doubles every 3 hours. It starts at 800. Work out the population after 9 hours.

9.A company's cost, in £, for producing x items is shown on a graph. The tangent to the curve at x = 50 passes through (30, 400) and (70, 800). Interpret the gradient of this tangent in the context of the company's costs.

10.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.

11.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

12.f(x) = x³ − 3x − 5. Given that f(2.2) = −0.952 and f(2.3) = 0.267, work out what this shows about the equation x³ − 3x − 5 = 0.

13.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.

14.The equation x² = 5x − 3 is to be solved using iteration. Work out which of these iterative formulas comes from a correct rearrangement of the equation.

15.A circular pond has equation x² + y² = 20, with lengths in metres from the centre of the garden. A straight path runs along the line y = 2x, entering the pond and leaving it again. Work out the coordinates of the two points where the path meets the edge of the pond.