Algebra worksheet — GCSE Higher

1.The graph of y = f(x) has roots at x = −1 and x = 4, and crosses the y-axis at (0, −8). Which statement about the graph of y = f(x − 3) is correct?

2.Work out the value of 3a − 2b when a = 5 and b = 4

3.A candidate solves the simultaneous equations y = x − 2 and y = x² − 4x + 2 by substitution. They write: "x − 2 = x² − 4x + 2, so x² − 3x + 4 = 0." Which of these is a correct comment on the candidate's working?

4.Which expression is equivalent to 3(2x − 5) + 4x?

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

6.The graph of y = f(x) has x-intercepts at x = −1 and x = 4. Which statement correctly describes the x-intercepts of y = f(2 − x)?

7.A graph has equation y = −2x² + 5. Which statement about its shape is correct?

8.Which expression is equivalent to 7x − 3(2x − 6)?

9.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

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

11.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

12.A tap's flow rate, in litres per minute, is plotted against time, in minutes, on a graph. What are the units of the area under this graph?

13.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?

14.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

15.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.