Precalculus

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Overview

Precalculus provides the mathematical foundation for calculus. This section covers functions, trigonometry, and the algebraic skills you’ll need before starting MATH 161.

Source Material: OpenStax Precalculus (CC BY 4.0)

Course Structure

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    subgraph MATH141["MATH 141: Precalculus I"]
        A1["Ch 1: Functions"]
        A2["Ch 2: Linear Functions"]
        A3["Ch 3: Polynomial & Rational"]
        A4["Ch 4: Exponential & Log"]
    end

    subgraph MATH142["MATH 142: Precalculus II"]
        B1["Ch 5: Trig Functions"]
        B2["Ch 6: Periodic Functions"]
        B3["Ch 7: Trig Identities"]
        B4["Ch 8: Applications of Trig"]
        B5["Ch 9: Systems"]
        B6["Ch 10: Conics"]
        B7["Ch 11: Sequences & Series"]
    end

    subgraph Bridge["Bridge to Calculus"]
        C1["Ch 12: Intro to Calculus"]
    end

    A1 --> A2 --> A3 --> A4
    A4 --> B1 --> B2 --> B3 --> B4
    B4 --> B5
    B4 --> B6
    B4 --> B7
    B7 --> C1

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    style A4 fill:#d1fae5
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MATH 141: Precalculus I

Foundation for calculus: functions, polynomials, exponentials, and logarithms.

Chapter 1: Functions

The language of calculus starts here.

• Functions and Function Notation
• Domain and Range
• Rates of Change and Behavior of Graphs
• Composition of Functions
• Transformation of Functions
• Absolute Value Functions
• Inverse Functions

Chapter 2: Linear Functions

Linear models and rate of change.

• Linear Functions
• Graphs of Linear Functions
• Modeling with Linear Functions
• Fitting Linear Models to Data

Chapter 3: Polynomial and Rational Functions

Building toward calculus with polynomials.

• Complex Numbers
• Quadratic Functions
• Power Functions and Polynomial Functions
• Graphs of Polynomial Functions
• Dividing Polynomials
• Zeros of Polynomial Functions
• Rational Functions
• Inverses and Radical Functions
• Modeling Using Variation

Chapter 4: Exponential and Logarithmic Functions

Essential for calculus applications.

• Exponential Functions
• Graphs of Exponential Functions
• Logarithmic Functions
• Graphs of Logarithmic Functions
• Logarithmic Properties
• Exponential and Logarithmic Equations
• Exponential and Logarithmic Models
• Fitting Exponential Models to Data

MATH 142: Precalculus II

Trigonometry, sequences, and preparation for calculus.

Chapter 5: Trigonometric Functions

The circular functions that model periodic behavior.

• Angles
• Unit Circle: Sine and Cosine Functions
• The Other Trigonometric Functions
• Right Triangle Trigonometry

Chapter 6: Periodic Functions

Graphing and transforming trig functions.

• Graphs of the Sine and Cosine Functions
• Graphs of the Other Trigonometric Functions
• Inverse Trigonometric Functions

Chapter 7: Trigonometric Identities and Equations

Manipulating trig expressions.

• Solving Trigonometric Equations with Identities
• Sum and Difference Identities
• Double-Angle, Half-Angle, and Reduction Formulas
• Sum-to-Product and Product-to-Sum Formulas
• Solving Trigonometric Equations
• Modeling with Trigonometric Functions

Chapter 8: Further Applications of Trigonometry

Polar coordinates, vectors, and more.

• Non-right Triangles: Law of Sines
• Non-right Triangles: Law of Cosines
• Polar Coordinates
• Polar Coordinates: Graphs
• Polar Form of Complex Numbers
• Parametric Equations
• Parametric Equations: Graphs
• Vectors

Chapter 9: Systems of Equations and Inequalities

Systems and matrices.

• Systems of Linear Equations: Two Variables
• Systems of Linear Equations: Three Variables
• Systems of Nonlinear Equations and Inequalities
• Partial Fractions
• Matrices and Matrix Operations
• Solving Systems with Gaussian Elimination
• Solving Systems with Inverses
• Solving Systems with Cramer’s Rule

Chapter 10: Analytic Geometry

Conic sections in depth.

• The Ellipse
• The Hyperbola
• The Parabola
• Rotation of Axes
• Conic Sections in Polar Coordinates

Chapter 11: Sequences, Probability and Counting Theory

Sequences, series, and discrete math.

• Sequences and Their Notations
• Arithmetic Sequences
• Geometric Sequences
• Series and Their Notations
• Counting Principles
• Binomial Theorem
• Probability

Bridge to Calculus

Chapter 12: Introduction to Calculus

Preview of calculus concepts.

• Finding Limits: Numerical and Graphical Approaches
• Finding Limits: Properties of Limits
• Continuity
• Derivatives

What Precalculus Unlocks

After mastering precalculus, you’re ready for:

• MATH 161: Calculus I (Limits, Derivatives, Integrals)
• MATH 162: Calculus II (Integration Techniques, Series)
• MATH 163: Calculus III (Vectors, Multivariable)