Algebra worksheet — GCSE Higher

1.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

2.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

3.The first five terms of a quadratic sequence are −1, 4, 13, 26, 43. Work out an expression, in terms of n, for the nth term.

4.The solution set of a quadratic inequality is {x : x ≤ −3} ∪ {x : x ≥ 5}. Which of these inequalities has this solution set?

5.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

6.One solution of the equation x² − (k + 1)x + k = 0 is x = 3. Work out the value of k.

7.Which of these is a factor of 15x + 20?

8.Which of these equations represents the graph of y = 2ˣ translated by 3 units in the positive y-direction?

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

10.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

11.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

12.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

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

14.Line L has equation y = 2x + 3. Work out the equation of the line perpendicular to L that passes through the point (4, 1), giving your answer in the form x + 2y = c.

15.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.