Algebra worksheet — GCSE Higher

1.The first four terms of a sequence are 2, 2√3, 6, 6√3, ... Work out the next term.

2.Work out the value of 2x² when x = −3

3.Describe a sequence of two transformations that maps the graph of y = x² onto the graph of y = −(x − 5)².

4.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.

5.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

6.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

7.Factorise 6x² − 7x − 3.

8.A student is asked to simplify (6x³ − 15x²)/(4x² − 10x) fully. Four attempts are shown below. Which one is correct?

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

10.On a distance-time graph, a horizontal line segment shows a period when the graph's gradient is 0. What does this tell you about the journey during that time?

11.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.

12.The point (6, 8) lies on the circle x² + y² = 100. Work out the gradient of the tangent to the circle at (6, 8).

13.Which of these statements is an equation with exactly one solution?

14.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.

15.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)?