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Exam Prep

AP Precalculus: study sheet

4 units, with a key formula and what each covers, from this hub's syllabus notes. Not yet checked by a teacher: check it against your own notes.

The exam

Section I: 40 multiple-choice questions in 2 hours, 62.5% of the score (Part A: 28 questions, 80 min, no calculator; Part B: 12 questions, 40 min, graphing calculator). Section II: 4 free-response questions in 1 hour, 37.5% (Part A: 2 questions, 30 min, calculator; Part B: 2 questions, 30 min, no calculator). Units 1 to 3 are on the exam; Unit 4 is taught but not examined. Source: College Board, AP Precalculus Course and Exam Description.

Scored 1–5. Unit weightings are the College Board's published ranges for the multiple-choice section.

  1. 1. Unit 1: Polynomial and Rational Functions

    30–40% of exam score

    average rate of change=f(b)−f(a)b−a\text{average rate of change} = \frac{f(b) - f(a)}{b - a}

    • Average rates of change

    • Zeros and end behaviour of polynomials

    • Asymptotes and holes of rational functions

    • Transformations and function models

  2. 2. Unit 2: Exponential and Logarithmic Functions

    27–40% of exam score

    log⁡ba=ln⁡aln⁡b,blog⁡bx=x\log_b a = \frac{\ln a}{\ln b}, \qquad b^{\log_b x} = x

    • Arithmetic and geometric sequences

    • Exponential models

    • Logarithms and their properties

    • Exponential and logarithmic equations

  3. 3. Unit 3: Trigonometric and Polar Functions

    30–35% of exam score

    f(θ)=asin⁡(b(θ+c))+d,period 2π∣b∣f(\theta) = a\sin(b(\theta + c)) + d, \quad \text{period } \tfrac{2\pi}{|b|}

    • The unit circle and periodic functions

    • Sinusoidal transformations and models

    • Inverse trig functions and identities

    • Polar coordinates and polar graphs

  4. 4. Unit 4: Functions Involving Parameters, Vectors, and Matrices

    Not on the AP exam

    det⁡(abcd)=ad−bc\det\begin{pmatrix} a & b \\ c & d \end{pmatrix} = ad - bc

    • Parametric functions

    • Conic sections

    • Vectors and their operations

    • Matrices and linear transformations