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Exam Strategy

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Readiness Check

You are ready when you can:

  • Define tan as slope and as sin/cos.
  • State period pi and asymptote locations.
  • Read transforms on y = a tan(b(theta + c)) + d.
  • Sketch one branch with asymptotes labeled.

On the AP Exam

  • MCQ: period, asymptotes, undefined values, transform readout.
  • FRQ: describe characteristics with precision (skills 2.A, 3.A, 1.C).

Tactics

1. Write asymptotes first: solve b(theta + c) = pi/2 + k pi. 2. Period = pi/|b|; phase = -c for tan(theta + c) form. 3. Check cos = 0 for undefined tan values. 4. |a| is vertical scale; d shifts the inflection line. 5. One-branch sketches beat messy multi-branch attempts.

Common Traps

  • Confusing tangent period with sine period.
  • Wrong asymptote spacing.
  • Sign error on phase shift.
  • Evaluating tan where cos = 0.

Quick Checklist

  • [ ] Slope/ratio definition stated
  • [ ] Period pi/|b|
  • [ ] Asymptotes correct
  • [ ] Phase -c
  • [ ] Undefined values identified

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