Pre Calculus

Basic Math Skills 2
05
Jan

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

Total learning: 63 lessons Time: 10 weeks
  • Functions and Graphs
    8
    • Lecture1.1
      Modeling and Equation Solving
    • Lecture1.2
      Functions and Their Properties
    • Lecture1.3
      Twelve Basic Functions
    • Lecture1.4
      Building Functions from Functions
    • Lecture1.5
      Parametric Relations and Inverses
    • Lecture1.6
      Graphical Transformations
    • Lecture1.7
      Modeling with Functions
    • Lecture1.8
      Chapter TEST Functions and Graphs
  • Polynomial, Power, and Rational Functions
    9
    • Lecture2.1
      Linear and Quadratic Functions and Modeling
    • Lecture2.2
      Power Functions with Modeling
    • Lecture2.3
      Polynomial Functions of Higher Degree with Modeling
    • Lecture2.4
      Real Zeros of Polynomial Functions
    • Lecture2.5
      Complex Zeros and the Fundamental Theorem of Algebra
    • Lecture2.6
      Graphs of Rational Functions
    • Lecture2.7
      Solving Equations in One Variable
    • Lecture2.8
      Solving Inequalities in One Variable
    • Lecture2.9
      Chapter TEST Polynomial, Power, and Rational Functions
  • Exponential, Logistic, and Logarithmic Functions
    7
    • Lecture3.1
      Exponential and Logistic Functions
    • Lecture3.2
      Exponential and Logistic Modeling
    • Lecture3.3
      Logarithmic Functions and Their Graphs
    • Lecture3.4
      Properties of Logarithmic Functions
    • Lecture3.5
      Equation Solving and Modeling
    • Lecture3.6
      Mathematics of Finance
    • Lecture3.7
      Chapter TEST Exponential, Logistic, and Logarithmic Functions
  • Trigonometric Functions
    9
    • Lecture4.1
      Angles and Their Measures Preview
    • Lecture4.2
      Trigonometric Functions of Acute Angles Preview
    • Lecture4.3
      Trigonometry Extended: The Circular Functions
    • Lecture4.4
      Graphs of Sine and Cosine: Sinusoids
    • Lecture4.5
      Graphs of Tangent, Cotangent, Secant, and Cosecant
    • Lecture4.6
      Graphs of Composite Trigonometric Functions
    • Lecture4.7
      Inverse Trigonometric Functions
    • Lecture4.8
      Solving Problems with Trigonometry
    • Lecture4.9
      Chapter TEST Trigonometric Functions
  • Analytic Trigonometry
    7
    • Lecture5.1
      Fundamental Identities
    • Lecture5.2
      Proving Trigonometric Identities
    • Lecture5.3
      Sum and Difference Identities
    • Lecture5.4
      Multiple-Angle Identities
    • Lecture5.5
      The Law of Sines
    • Lecture5.6
      The Law of Cosines
    • Lecture5.7
      Chapter TEST Analytic Trigonometry
  • Applications of Trigonometry
    7
    • Lecture6.1
      Vectors in the Plane
    • Lecture6.2
      Dot Product of Vectors
    • Lecture6.3
      Parametric Equations and Motion
    • Lecture6.4
      Polar Coordinates
    • Lecture6.5
      Graphs of Polar Equations
    • Lecture6.6
      De Moivre’s Theorem and nth Roots
    • Lecture6.7
      Chapter TEST Applications of Trigonometry
  • Systems and Matrices
    6
    • Lecture7.1
      Solving Systems of Two Equations
    • Lecture7.2
      Matrix Algebra
    • Lecture7.3
      Multivariate Linear Systems and Row Operations
    • Lecture7.4
      Partial Fractions
    • Lecture7.5
      Systems of Inequalities in Two Variables
    • Lecture7.6
      Chapter TEST Systems and Matrices
  • Discrete Mathematics
    10
    • Lecture8.1
      Basic Combinatorics
    • Lecture8.2
      The Binomial Theorem
    • Lecture8.3
      Probability
    • Lecture8.4
      Sequences
    • Lecture8.5
      Series
    • Lecture8.6
      Mathematical Induction
    • Lecture8.7
      Statistics and Data (Graphical)
    • Lecture8.8
      Statistics and Data (Algebraic)
    • Lecture8.9
      Statistical Literacy
    • Lecture8.10
      Chapter TEST Discrete Mathematics

About the Instructor

David David

David is a professor of mathematics education at the Aphy School. His research focuses on social and cultural factors as well as educational policies and practices that facilitate mathematics engagement, learning, and performance, especially for underserved students. Alphy School collaborates with teachers, schools, districts, and organizations to promote mathematics excellence and equity for young people.
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