Algebra worksheet — GCSE Higher

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

2.n = 3. Work out the value of (2n)².

3.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

4.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

5.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

6.A geometric sequence has first term 4 and common ratio √2. Work out the sum of the first three terms of the sequence, giving your answer in the form a + b√2.

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

8.Factorise fully 56x − 24

9.The nth term of a sequence is n² + 2n − 4. Work out the 7th term.

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

11.A circle has centre (0, 0) and passes through the point (12, 35). Work out the equation of the circle.

12.The graph of y = f(x) crosses the x-axis at x = −3 and x = 7, and crosses the y-axis at (0, 21). A second graph crosses the x-axis at x = −7 and x = 3, and crosses the y-axis at the same point, (0, 21). The second graph is y = g(x). Which of these could be the equation of g(x)?

13.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.

14.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.

15.Solve 3x + 14 = 8x − 6