Algebra worksheet — GCSE Higher

1.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

2.Solve x² − 8x + 3 = 0 by completing the square. Give your answers in surd form.

3.Work out the value of 2(x + 2) when x = −5

4.The table shows some values of f(x): when x = 0, f(x) = 5; when x = 1, f(x) = 8; when x = 2, f(x) = 4; when x = 3, f(x) = 1. Work out the value of f(x − 1) when x = 2.

5.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

6.Work out the gradient of a line that is perpendicular to the line with equation 2x + 3y = 6.

7.Expand and simplify (x + 1)(x + 2)(x + 3).

8.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?

9.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

10.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

11.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

12.The point (−4, 3) lies on the circle x² + y² = 25, which has centre (0, 0). Work out the equation of the tangent to the circle at (−4, 3), giving your answer in the form y = mx + c.

13.A circle has centre (0, 0) and equation x² + y² = 25. Work out the x-coordinates of the two points where the circle crosses the line y = 3.

14.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

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