Algebra worksheet — GCSE Higher

1.f(x) = x³ − 3x² − 4. Work out the pair of consecutive integers between which the solution of f(x) = 0 lies.

2.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

3.Write down the expression that means the same as (x + 7) ÷ 4.

4.f(x) = x³ − 5x − 6. Given that f(2.6) = −1.424 and f(2.7) = 0.183, work out what this shows about the equation x³ − 5x − 6 = 0.

5.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

6.A student claims: 'For every positive integer n, n² + n + 1 is a prime number.' Which value of n shows that this claim is false?

7.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

8.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

9.f(x) = 2x − 1. Work out ff(x).

10.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.

11.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

12.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

13.Solve x² − 100 = 0.

14.Solve 5(x + 3) = 40

15.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.