 K12 Curriculum
 1 (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

Functions and Graphs
8
Lecture1.1Modeling and Equation Solving

Lecture1.2Functions and Their Properties

Lecture1.3Twelve Basic Functions

Lecture1.4Building Functions from Functions

Lecture1.5Parametric Relations and Inverses

Lecture1.6Graphical Transformations

Lecture1.7Modeling with Functions

Lecture1.8Chapter TEST Functions and Graphs


Polynomial, Power, and Rational Functions
9
Lecture2.1Linear and Quadratic Functions and Modeling

Lecture2.2Power Functions with Modeling

Lecture2.3Polynomial Functions of Higher Degree with Modeling

Lecture2.4Real Zeros of Polynomial Functions

Lecture2.5Complex Zeros and the Fundamental Theorem of Algebra

Lecture2.6Graphs of Rational Functions

Lecture2.7Solving Equations in One Variable

Lecture2.8Solving Inequalities in One Variable

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


Exponential, Logistic, and Logarithmic Functions
7
Lecture3.1Exponential and Logistic Functions

Lecture3.2Exponential and Logistic Modeling

Lecture3.3Logarithmic Functions and Their Graphs

Lecture3.4Properties of Logarithmic Functions

Lecture3.5Equation Solving and Modeling

Lecture3.6Mathematics of Finance

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


Trigonometric Functions
9
Lecture4.1

Lecture4.2

Lecture4.3Trigonometry Extended: The Circular Functions

Lecture4.4Graphs of Sine and Cosine: Sinusoids

Lecture4.5Graphs of Tangent, Cotangent, Secant, and Cosecant

Lecture4.6Graphs of Composite Trigonometric Functions

Lecture4.7Inverse Trigonometric Functions

Lecture4.8Solving Problems with Trigonometry

Lecture4.9Chapter TEST Trigonometric Functions


Analytic Trigonometry
7
Lecture5.1Fundamental Identities

Lecture5.2Proving Trigonometric Identities

Lecture5.3Sum and Difference Identities

Lecture5.4MultipleAngle Identities

Lecture5.5The Law of Sines

Lecture5.6The Law of Cosines

Lecture5.7Chapter TEST Analytic Trigonometry


Applications of Trigonometry
7
Lecture6.1Vectors in the Plane

Lecture6.2Dot Product of Vectors

Lecture6.3Parametric Equations and Motion

Lecture6.4Polar Coordinates

Lecture6.5Graphs of Polar Equations

Lecture6.6De Moivre’s Theorem and nth Roots

Lecture6.7Chapter TEST Applications of Trigonometry


Systems and Matrices
6
Lecture7.1Solving Systems of Two Equations

Lecture7.2Matrix Algebra

Lecture7.3Multivariate Linear Systems and Row Operations

Lecture7.4Partial Fractions

Lecture7.5Systems of Inequalities in Two Variables

Lecture7.6Chapter TEST Systems and Matrices


Discrete Mathematics
10
Lecture8.1Basic Combinatorics

Lecture8.2The Binomial Theorem

Lecture8.3Probability

Lecture8.4Sequences

Lecture8.5Series

Lecture8.6Mathematical Induction

Lecture8.7Statistics and Data (Graphical)

Lecture8.8Statistics and Data (Algebraic)

Lecture8.9Statistical Literacy

Lecture8.10Chapter TEST Discrete Mathematics

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