Algebra worksheet — GCSE Higher

1.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.

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

3.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

4.Factorise 3x² + 10x − 8.

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

6.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

7.Line L has equation y = 3x − 2. Work out the gradient of a line perpendicular to L.

8.The curve y = x² − 3x. Use the chord between x = 1 and x = 4 to estimate the gradient of the curve at x = 2.5.

9.The first five terms of a sequence are 7, 9, 13, 19, 27. By finding the second difference, work out the coefficient of n² in the nth term.

10.The discriminant of a quadratic equation is greater than zero. Which statement about the solutions of that equation is correct?

11.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

12.Solve the inequality 9 − 2x ≥ 1.

13.Work out the smallest positive value of x, in degrees, for which y = tan x is undefined.

14.Work out the value of 2(x + 2) when x = −5

15.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.