Algebra worksheet — GCSE Higher

1.Solve x² − 6x = 0.

2.A circle has centre (0, 0) and radius 9. Work out the equation of the circle.

3.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?

4.A cyclist's velocity increases from 3 m/s to 11 m/s over 5 seconds, at a constant rate. Work out the cyclist's acceleration, in m/s².

5.A student attempts to prove that the sum of any three consecutive integers is a multiple of 3. Line 1: Let the three consecutive integers be n, n + 1 and n + 2. Line 2: Their sum is n + (n + 1) + (n + 2) = 3n + 2. Line 3: 3n + 2 leaves a remainder of 2 when divided by 3, so it is not a multiple of 3. Line 4: So the sum of three consecutive integers is not always a multiple of 3. Which line contains the FIRST error?

6.A ferry's distance-time graph is a straight line from (0 minutes, 0 km) to (25 minutes, 15 km). Work out the ferry's speed in kilometres per hour.

7.The point (3, 4) lies on the circle x² + y² = 25, which has centre (0, 0). Work out the gradient of the tangent to the circle at (3, 4).

8.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

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

10.A circle has centre (0, 0) and equation x² + y² = 100. A straight line is drawn from the origin through the point P(8, 9). Work out whether P lies inside, on, or outside the circle.

11.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

12.f(x) = 2x + 1. Work out the value of x for which f⁻¹(x) = 5.

13.Solve (3x + 2)/5 = (x + 4)/3

14.Which of these values of x is a solution of x² + 2x − 15 = 0?

15.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?