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Exam Strategy

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Readiness Check

You are ready when you can:

  • Convert points both directions with correct theta.
  • Plot/locate points from either form.
  • Write complex numbers in a+bi and polar trig form.
  • Explain multiple polar representations when relevant.

On the AP Exam

  • MCQ: conversion, quadrant angle, complex modulus/argument.
  • FRQ: convert with justification (skills 1.B, 2.A).

Tactics

1. Label quadrant before finding theta. 2. Compute r = sqrt(x^2+y^2) first when going rect to polar. 3. For x>0, theta = arctan(y/x); adjust with +pi or +pi/2 rules as needed. 4. Check: x should equal r cos theta and y equal r sin theta. 5. Complex: r = |a+bi| = sqrt(a^2+b^2).

Common Traps

  • Wrong quadrant theta.
  • Using degrees vs radians inconsistently.
  • Forgetting i in complex polar sine term.
  • Assuming polar coordinates are unique.

Quick Checklist

  • [ ] Formulas correct
  • [ ] Quadrant checked
  • [ ] r nonnegative if required
  • [ ] Back-substitution verified
  • [ ] Complex forms complete

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