Algebra worksheet — GCSE Higher

1.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)?

2.(2x + 3)(x + a) ≡ 2x² + 11x + 12 is an identity. Work out the value of a.

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

4.The function f(x) = x² for all real values of x has no inverse function, but g(x) = x² for x ≥ 0 does have one. Which statement correctly explains this?

5.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

6.A circle has centre (0, 0) and equation x² + y² = 64. Write down the radius of the circle.

7.Work out the value of n² − n when n = −3

8.Expand and simplify (2x − 1)(x + 5)(x − 2). Write down the coefficient of x in your answer.

9.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

10.Make x the subject of the formula y = 2x − 9.

11.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

12.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

13.Write down the expression that means the same as m² × m × 3.

14.Work out the value of 5m² + 3m when m = −2.4

15.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.