Algebra worksheet — GCSE Higher

1.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

2.Work out the coordinates of the reflection of (6, −3) in the y-axis.

3.Points A(8, 15) and B(−8, 15) both lie on the circle x² + y² = 289, which has centre (0, 0). Work out the length of the chord AB.

4.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

5.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

6.How many turning points does the graph of y = x² − 7x + 10 have?

7.By completing the square, find the turning point of the curve y = x² − 10x + 30.

8.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?

9.Simplify (2x² + 7x + 3) ÷ (x² − 9), giving your answer as a single fraction.

10.By completing the square, find the turning point of the curve y = x² − 4x + 9.

11.The point (3, 6) lies on the circle x² + y² = 45. The tangent to the circle at (3, 6) crosses the x-axis at the point P. Work out the coordinates of P.

12.f(x) = 3x − 2. Find f⁻¹(x).

13.The graph of y = f(x) has a minimum point at (4, −1). Write down the coordinates of the corresponding turning point on the graph of y = −f(x).

14.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

15.Solve the simultaneous equations y = x + 1 and x² + y² = 25, giving both pairs of solutions.