AP Precalculus study guide
AP Precalculus · Work through your exam, one topic at a time.
AP Precalculus is a College Board Advanced Placement course and exam intended for students who want college-level credit or placement in precalculus-level mathematics before moving on to calculus. The exam measures understanding of the mathematical content in units 1–3 and the ability to apply skills such as algebraically manipulating functions, equations, and expressions; translating mathematical information between representations; and communicating with precise language and rationales. Questions draw on general functions, polynomial and rational functions, exponential and logarithmic functions, and trigonometric and polar functions, presented graphically, numerically, analytically, and verbally, with real-world modeling contexts. The exam is hybrid digital: multiple-choice questions and free-response questions appear in the Bluebook app, while free-response answers are handwritten in paper booklets. The AP Precalculus study guide has 4 sections and about 1,158 words.
01General Functions: Behavior, Composition, and Inverses
General (non-analytical) functions test your ability to reason about functions from their structure rather than from a formula. Core concepts: domain and range restrictions, function notation and evaluation, composition, inverses, transformations, average rate of change, concavity, and symmetry (even/odd).
317 words, about 2 min02Polynomial and Rational Functions: Zeros, End Behavior, and Asymptotes
For polynomials: degree, leading coefficient, end behavior, multiplicity of zeros, and the relationship between factors and x-intercepts. For rational functions: domain exclusions, vertical asymptotes, holes, horizontal or slant asymptotes, and sign analysis.
287 words, about 1 min03Exponential and Logarithmic Functions: Growth, Decay, and Inverses
Exponential functions model constant-percentage change; logarithmic functions are their inverses. Key concepts: base restrictions (b 0, b ≠ 1), domain and range, transformations, properties of logarithms, solving exponential and logarithmic equations, and modeling with exponential growth/decay and half-life or doubling time.
272 words, about 1 min04Trigonometric and Polar Functions: Unit Circle, Identities, and Polar Graphs
Trigonometric functions connect angles to ratios on the unit circle. You need: radian measure, reference angles, signs by quadrant, periodicity, amplitude and midline for sinusoidal models, inverse trig functions and their restricted ranges, fundamental identities, and polar coordinates including conversion to rectangular form and graphing polar curves.
282 words, about 1 min