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AP Precalculus: Exam Prep & Study Path

Build function reasoning through symbolic rules, tables, graphs and original worked examples.

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Polynomial and Rational Functions

Function change and transformations

A function pairs each allowed input with one output. Average rate of change compares two outputs over a stated input interval.

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3 domains. One connected path.

Start with the foundations, then build connections.

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Video companions with clear steps, original diagrams, and practice.

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Original diagram: Compare changes before choosing a model. VIDEO → ARTICLE
Gauth · 9 min read

Compare changes before choosing a model.

Connect secant slopes, transformed points and composition through original examples.

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Original diagram: Zeros are only one part of the story. VIDEO → ARTICLE
The Organic Chemistry Tutor · 9 min read

Zeros are only one part of the story.

Use factoring to distinguish intercepts, target outputs, multiplicity and domain restrictions.

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Original diagram: A growth factor needs a clock. VIDEO → ARTICLE
Khan Academy · 10 min read

A growth factor needs a clock.

Compare periods, percentages and inverse questions with an exponential model.

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Original diagram: Inverse sine selects one angle. VIDEO → ARTICLE
Khan Academy · 11 min read

Inverse sine selects one angle.

Use a restricted range to turn a repeating relationship into a function.

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Original diagram: Inverse cosine keeps its range. VIDEO → ARTICLE
Khan Academy · 11 min read

Inverse cosine keeps its range.

A composition can preserve the cosine while changing the angle.

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Original diagram: Translate data into log space. VIDEO → ARTICLE
Khan Academy · 11 min read

Translate data into log space.

A straight line in logarithms describes repeated multiplication in the original quantity.

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A focused foundation pilot. 400 original question variants across 96 families. This is a starting set, not complete AP Precalculus coverage. Explore the coverage map and gaps. Difficulty labels are uncalibrated editorial estimates; independent educator review is pending.