 Mathematics
 327 (Registered)

Credit Value: 1
Anticipated Grade Level(s): 11^{th} or 12^{th}
Precalculus is a comprehensive course that weaves together the previous study of algebra, geometry, and functions into a preparatory course for calculus. The course focuses on the mastery of critical skills and exposure to new skills necessary for success in subsequent math courses. The first semester includes linear, quadratic, exponential, logarithmic, radical, polynomial, and rational functions; systems of equations; and conic sections. The second semester covers trigonometric ratios and functions; inverse trigonometric functions; applications of trigonometry, including vectors and laws of cosine and sine; polar functions and notation; and arithmetic of complex numbers.
Within each Precalculus lesson, students are supplied with a poststudy Checkup activity that provides them the opportunity to hone their computational skills in a lowstakes problem set before moving on to formal assessment. Additionally, connections are made throughout the Precalculus course to calculus, art, history, and a variety of other fields related to mathematics.
The course is built to the National Council of Teachers of Mathematics (NCTM) standards and is aligned with state standards.
Course Content

Chapter 1 Functions and Graphs 0/15

Lecture1.1Modeling and Equation Solving

Quiz1.1PreCalculus Quiz 1.1 5 questions20 min

Lecture1.2Functions and Their Properties

Quiz1.2PreCalculus Quiz 1.2 6 questions20 min

Lecture1.3Twelve Basic Functions

Quiz1.3PreCalculus Quiz 1.3 9 questions20 min

Lecture1.4Building Functions from Functions

Quiz1.4PreCalculus Quiz 1.4 5 questions10 min

Lecture1.5Parametric Relations and Inverses

Quiz1.5PreCalculus Quiz 1.5 4 questions10 min

Lecture1.6Graphical Transformations

Quiz1.6PreCalculus Quiz 1.6 3 questions10 min

Lecture1.7Modeling with Functions

Quiz1.7PreCalculus Quiz 1.7 5 questions10 min

Lecture1.8Chapter TEST Functions and Graphs


Chapter 2 Polynomial, Power, and Rational Functions 0/17

Lecture2.1Linear and Quadratic Functions and Modeling

Quiz2.1PreCalculus Quiz 2.1 0 question10 min

Lecture2.2Power Functions with Modeling

Quiz2.2PreCalculus Quiz 2.2 0 question10 min

Lecture2.3Polynomial Functions of Higher Degree with Modeling

Quiz2.3PreCalculus Quiz 2.3 0 question10 min

Lecture2.4Real Zeros of Polynomial Functions

Quiz2.4PreCalculus Quiz 2.4 0 question10 min

Lecture2.5Complex Zeros and the Fundamental Theorem of Algebra

Quiz2.5PreCalculus Quiz 2.5 0 question10 min

Lecture2.6Graphs of Rational Functions

Quiz2.6PreCalculus Quiz 2.6 0 question10 min

Lecture2.7Solving Equations in One Variable

Quiz2.7PreCalculus Quiz 2.7 0 question10 min

Lecture2.8Solving Inequalities in One Variable

Quiz2.8PreCalculus Quiz 2.8 0 question10 min

Lecture2.9Chapter TEST Polynomial, Power, and Rational Functions


Chapter 3 Exponential, Logistic, and Logarithmic Functions 0/13

Lecture3.1Exponential and Logistic Functions

Quiz3.1PreCalculus Quiz 3.1 0 question10 min

Lecture3.2Exponential and Logistic Modeling

Quiz3.2PreCalculus Quiz 3.2 0 question10 min

Lecture3.3Logarithmic Functions and Their Graphs

Quiz3.3PreCalculus Quiz 3.3 0 question10 min

Lecture3.4Properties of Logarithmic Functions

Quiz3.4PreCalculus Quiz 3.4 0 question10 min

Lecture3.5Equation Solving and Modeling

Quiz3.5PreCalculus Quiz 3.5 0 question10 min

Lecture3.6Mathematics of Finance

Quiz3.6PreCalculus Quiz 3.6 0 question10 min

Lecture3.7Chapter TEST Exponential, Logistic, and Logarithmic Functions


Chapter 4 Systems and Matrices 0/11

Lecture4.1Solving Systems of Two Equations

Quiz4.1PreCalculus Quiz 4.1 0 question10 min

Lecture4.2Matrix Algebra

Quiz4.2PreCalculus Quiz 4.2 0 question10 min

Lecture4.3Multivariate Linear Systems and Row Operations

Quiz4.3PreCalculus Quiz 4.3 0 question10 min

Lecture4.4Partial Fractions

Quiz4.4PreCalculus Quiz 4.4 0 question10 min

Lecture4.5Systems of Inequalities in Two Variables

Quiz4.5PreCalculus Quiz 4.5 0 question10 min

Lecture4.6Chapter TEST Systems and Matrices


Chapter 5 Trigonometric Functions 0/17

Lecture5.1Angles and Their Measures

Quiz5.1PreCalculus Quiz 5.1 0 question10 min

Lecture5.2Trigonometric Functions of Acute Angles

Quiz5.2PreCalculus Quiz 5.2 0 question10 min

Lecture5.3Trigonometry Extended: The Circular Functions

Quiz5.3PreCalculus Quiz 5.3 0 question10 min

Lecture5.4Graphs of Sine and Cosine: Sinusoids

Quiz5.4PreCalculus Quiz 5.4 0 question10 min

Lecture5.5Graphs of Tangent, Cotangent, Secant, and Cosecant

Quiz5.5PreCalculus Quiz 5.5 0 question10 min

Lecture5.6Graphs of Composite Trigonometric Functions

Quiz5.6PreCalculus Quiz 5.6 0 question10 min

Lecture5.7Inverse Trigonometric Functions

Quiz5.7PreCalculus Quiz 5.7 0 question10 min

Lecture5.8Solving Problems with Trigonometry

Quiz5.8PreCalculus Quiz 5.8 0 question10 min

Lecture5.9Chapter TEST Trigonometric Functions


Chapter 6 Analytic Trigonometry 0/13

Lecture6.1Fundamental Identities

Quiz6.1PreCalculus Quiz 6.1 0 question10 min

Lecture6.2Proving Trigonometric Identities

Quiz6.2PreCalculus Quiz 6.2 0 question10 min

Lecture6.3Sum and Difference Identities

Quiz6.3PreCalculus Quiz 6.3 0 question10 min

Lecture6.4MultipleAngle Identities

Quiz6.4PreCalculus Quiz 6.4 0 question10 min

Lecture6.5The Law of Sines

Quiz6.5PreCalculus Quiz 6.5 5 questions20 min

Lecture6.6The Law of Cosines

Quiz6.6PreCalculus Quiz 6.6 5 questions10 min

Lecture6.7Chapter TEST Analytic Trigonometry


Chapter 7 Applications of Trigonometry 0/13

Lecture7.1Vectors in the Plane

Quiz7.1PreCalculus Quiz 7.1 0 question10 min

Lecture7.2Dot Product of Vectors

Quiz7.2PreCalculus Quiz 7.2 0 question10 min

Lecture7.3Parametric Equations and Motion

Quiz7.3PreCalculus Quiz 7.3 0 question10 min

Lecture7.4Polar Coordinates

Quiz7.4PreCalculus Quiz 7.4 0 question10 min

Lecture7.5Graphs of Polar Equations

Quiz7.5PreCalculus Quiz 7.5 0 question10 min

Lecture7.6De Moivre’s Theorem and nth Roots

Quiz7.6PreCalculus Quiz 7.6 0 question10 min

Lecture7.7Chapter TEST Applications of Trigonometry


Chapter 8 Discrete Mathematics 0/18

Lecture8.1Basic Combinatorics

Quiz8.1PreCalculus Quiz 8.1 0 question10 min

Lecture8.2The Binomial Theorem

Quiz8.2PreCalculus Quiz 8.2 0 question10 min

Lecture8.3Probability

Quiz8.3PreCalculus Quiz 8.3 0 question10 min

Lecture8.4Sequences

Quiz8.4PreCalculus Quiz 8.4 0 question10 min

Lecture8.5Series

Quiz8.5PreCalculus Quiz 8.5 0 question10 min

Lecture8.6Mathematical Induction

Quiz8.6PreCalculus Quiz 8.6 0 question10 min

Lecture8.7Statistics and Data (Graphical)

Lecture8.8Statistics and Data (Algebraic)

Quiz8.7PreCalculus Quiz 8.7 0 question10 min

Lecture8.9Statistical Literacy

Lecture8.10Chapter TEST Discrete Mathematics

Lecture8.11


Chapter 9 An Introduction to Calculus: Limits, Derivatives, and Integrals 0/7

Lecture9.1Polar Equations of Conics

Lecture9.2ThreeDimensional Cartesian Coordinate System

Lecture9.3Limits and Motion: The Tangent Problem

Lecture9.4Limits and Motion: The Area Problem

Lecture9.5More on Limits

Lecture9.6Numerical Derivatives and Integrals

Lecture9.7Chapter TEST An Introduction to Calculus: Limits, Derivatives, and Integrals

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