Algebra worksheet — GCSE Higher

1.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

2.The graph of y = f(x) has a minimum point at (4, −1). Write down the coordinates of the corresponding turning point on the graph of y = −f(x).

3.How many turning points does the graph of y = x² − 7x + 10 have?

4.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

5.Work out the value of m² + 3m when m = −2

6.Ben is asked to find the inverse of f(x) = 4 − 3x. He writes f⁻¹(x) = (4 − x)/3. Which statement about Ben's answer is correct?

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

8.Which expression means 'y squared, multiplied by 3'?

9.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.

10.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

11.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

12.For 0 ≤ x ≤ 360, the equation sin x = 0.5 has two solutions. What are they?

13.Line L has equation y = 3x + 1. Which of these lines is perpendicular to L?

14.Solve x² − 5x + 6 = 0 by factorising.

15.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.