- K-12 Curriculum
- 1 (Registered)
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Credit Value: 1
Anticipated Grade Level(s): 11th or 12th
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 post-study Checkup activity that provides them the opportunity to hone their computational skills in a low-stakes 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
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Functions and Graphs
8-
Lecture1.1Modeling and Equation Solving
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Lecture1.2Functions and Their Properties
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Lecture1.3Twelve Basic Functions
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Lecture1.4Building Functions from Functions
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Lecture1.5Parametric Relations and Inverses
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Lecture1.6Graphical Transformations
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Lecture1.7Modeling with Functions
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Lecture1.8Chapter TEST Functions and Graphs
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Polynomial, Power, and Rational Functions
9-
Lecture2.1Linear and Quadratic Functions and Modeling
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Lecture2.2Power Functions with Modeling
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Lecture2.3Polynomial Functions of Higher Degree with Modeling
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Lecture2.4Real Zeros of Polynomial Functions
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Lecture2.5Complex Zeros and the Fundamental Theorem of Algebra
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Lecture2.6Graphs of Rational Functions
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Lecture2.7Solving Equations in One Variable
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Lecture2.8Solving Inequalities in One Variable
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Lecture2.9Chapter TEST Polynomial, Power, and Rational Functions
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Exponential, Logistic, and Logarithmic Functions
7-
Lecture3.1Exponential and Logistic Functions
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Lecture3.2Exponential and Logistic Modeling
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Lecture3.3Logarithmic Functions and Their Graphs
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Lecture3.4Properties of Logarithmic Functions
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Lecture3.5Equation Solving and Modeling
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Lecture3.6Mathematics of Finance
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Lecture3.7Chapter TEST Exponential, Logistic, and Logarithmic Functions
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Trigonometric Functions
9-
Lecture4.1
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Lecture4.2
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Lecture4.3Trigonometry Extended: The Circular Functions
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Lecture4.4Graphs of Sine and Cosine: Sinusoids
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Lecture4.5Graphs of Tangent, Cotangent, Secant, and Cosecant
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Lecture4.6Graphs of Composite Trigonometric Functions
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Lecture4.7Inverse Trigonometric Functions
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Lecture4.8Solving Problems with Trigonometry
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Lecture4.9Chapter TEST Trigonometric Functions
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Analytic Trigonometry
7-
Lecture5.1Fundamental Identities
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Lecture5.2Proving Trigonometric Identities
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Lecture5.3Sum and Difference Identities
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Lecture5.4Multiple-Angle Identities
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Lecture5.5The Law of Sines
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Lecture5.6The Law of Cosines
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Lecture5.7Chapter TEST Analytic Trigonometry
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Applications of Trigonometry
7-
Lecture6.1Vectors in the Plane
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Lecture6.2Dot Product of Vectors
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Lecture6.3Parametric Equations and Motion
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Lecture6.4Polar Coordinates
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Lecture6.5Graphs of Polar Equations
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Lecture6.6De Moivre’s Theorem and nth Roots
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Lecture6.7Chapter TEST Applications of Trigonometry
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Systems and Matrices
6-
Lecture7.1Solving Systems of Two Equations
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Lecture7.2Matrix Algebra
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Lecture7.3Multivariate Linear Systems and Row Operations
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Lecture7.4Partial Fractions
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Lecture7.5Systems of Inequalities in Two Variables
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Lecture7.6Chapter TEST Systems and Matrices
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Discrete Mathematics
10-
Lecture8.1Basic Combinatorics
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Lecture8.2The Binomial Theorem
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Lecture8.3Probability
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Lecture8.4Sequences
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Lecture8.5Series
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Lecture8.6Mathematical Induction
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Lecture8.7Statistics and Data (Graphical)
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Lecture8.8Statistics and Data (Algebraic)
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Lecture8.9Statistical Literacy
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Lecture8.10Chapter TEST Discrete Mathematics
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About the Instructor
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