SubjectScout
ENAR
Sign inGet matched
Get matched
← Back to interactive practice
Print with marking points
AS & A Level · AS/A Level

Further Mathematics

Polar curves and area

Name: ____________________Date: October 10, 2026
  1. 1.

    Convert the polar point r = 4, theta = pi/3 to Cartesian coordinates. Give its distance from the origin.

    [3 marks] · no calculator
  2. 2.

    Convert r = 6cos theta to Cartesian form and identify its centre and radius.

    [3 marks] · no calculator
  3. 3.

    Find the area swept by r = 2theta for 0 <= theta <= pi/2. Give an exact answer.

    [3 marks] · no calculator
  4. 4.

    For r = 1 + cos theta, find dy/dx at theta = pi/2.

    [3 marks] · no calculator
  5. 5.

    For r = 3cos(2theta), identify the theta interval for the petal centred on the positive x-axis and calculate its area exactly.

    [3 marks] · no calculator
  6. 6.

    Find the area inside r = 1 + cos theta but outside the unit circle. State the intersection angles used.

    [3 marks] · no calculator

Original, unofficial practice questions from SubjectScout — not official past-paper questions.

Marking points are indicative, not an official mark scheme. Accept equivalent valid methods and supported interpretations that address the task; award each mark once without requiring the model wording.