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Common Mistakes

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Pre-calculus · AP · Trigonometric and Polar Functions

Focus

Periodic Phenomena

This topic is assessed on the AP Exam.

Frequent mistakes

### 1. Angle mode error

What it looks/sounds like: Calculator is in degrees when radians are required (or vice versa).

Why it happens: Mode is not checked at the start.

How to fix: Write ‘degrees’ or ‘radians’ on the page before evaluating.

### 2. Period/amplitude mix-up

What it looks/sounds like: Horizontal shrink is confused with vertical stretch.

Why it happens: Coefficients on x and y are not separated.

How to fix: Identify b for period and a for amplitude before graphing.

### 3. Correct work, wrong question

What it looks/sounds like: The algebra is fine but answers a different quantity than the stem asks for.

Why it happens: Attention locks onto the first operation instead of the final ask.

How to fix: Underline the final question; after solving, verify the boxed answer matches it.

### 4. Notation and justification gaps

What it looks/sounds like: Missing units, limit language, or ‘because’ statements AP graders expect.

Why it happens: Notation is treated as decoration rather than part of the score.

How to fix: Add one justification phrase per major step (definition, theorem, or rule).

How to avoid them

1. Sketch one period by hand before using technology. 2. Use exact unit-circle values when the exam expects radicals. 3. Label amplitude, period, and phase on graphs.

Quick self-check

[ ] Can find one exact trig value
[ ] Can read period/amplitude from an equation
[ ] Can catch a mode error quickly

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