Algebra worksheet — GCSE Higher

1.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

2.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

3.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

4.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?

5.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

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

7.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

8.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

9.A car's speed, in m/s, during a journey is: 0 at t = 0 s, 8 at t = 4 s, and 8 (constant) from t = 4 s to t = 10 s, increasing at a constant rate between t = 0 and t = 4. Estimate the total distance the car travels, using the areas of a triangle and a rectangle.

10.Simplify 5a/6 − a/3

11.Solve the inequality 9 − 2x ≥ 1.

12.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

13.Factorise fully 12x² + 18x.

14.A quadratic graph has equation y = (x − 4)². A student says this graph crosses the x-axis at two different points. Explain why the student is wrong.

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