CAIE A-Level Further Mathematics 1.5.2 Polar Curves

Practise sketching polar curves over a stated interval, labelling the pole and symmetry, then differentiating the relevant coordinate to locate an exact maximum distance.

Exam points

sketch the correct loop or branch over the stated interval and label the pole and symmetry line
express the requested distance as r, x or y, then differentiate it with respect to the angle
test the stationary value against endpoints and report the exact greatest distance requested

[Maximum number: 3]

Sketch C and state the equation of the line of symmetry.

B1

Initial line drawn and one loop in the first quadrant.

Figure for Answer to Question 1.5.2—Polar curves question 1 — CAIE A-Level Further Math AS

B1

Correct shape at extremities.

$\theta=\frac{1}{8} \pi$

B1

States the equation of the line of symmetry.

3

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1.5.2—Polar curves question 1