Algebra worksheet — GCSE Higher

1.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

2.Two expressions are 4(x + 3) and 4x + 3. A student checks whether they are equivalent by substituting x = 2. Which statement correctly interprets the result?

3.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.

4.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

5.Subtract, giving your answer as a single fraction in its simplest form: 4/(x − 1) − 2/(x + 3)

6.Which line of algebra shows that the sum of two consecutive odd numbers is always a multiple of 4?

7.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

8.The graph of y = f(x) has a minimum turning point at (3, −5), crosses the x-axis at x = 1, and crosses the y-axis at (0, −2). Exactly one of these statements about the graph of y = −f(x + 2) is true. Which statement is true?

9.f(x) = 2x + 1. Work out the value of x for which f⁻¹(x) = 5.

10.Simplify (5x² + 3x − 2) − (2x² − x + 5)

11.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

12.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

13.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

14.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.

15.Write down the first four terms of the sequence with nth term 6n − 5.