Algebra 2

Algebra 2 Alphy School
05
Jan

Credit Value: Full Year Course (1 credit)

Anticipated Grade Level(s): 10 and 11

Prerequisites: Satisfactory completion of Geometry and Algebra I.  In exceptional situations with teacher approval, this course can be taken simultaneously with Geometry after the completion of Algebra I.

Course Description: 

This Algebra 2 course is organized around families of functions; linear, quadratic, exponential, logarithmic, radical, and rational functions. Students will learn about these functions, and the rules, techniques, and procedures necessary to manipulate and solve problems with these functions. In conjunction with this technical knowledge, students will develop skills in critical thinking and creative problem solving as they apply these mathematic concepts to real-world situations.

Course Content

Total learning: 78 lessons Time: 10 weeks
  • Quadratic Functions and Factoring
    10
    • Lecture1.1
      Graph Quadratic Functions in Standard Form
    • Lecture1.2
      Graph Quadratic Functions in Vertex or Intercept Form
    • Lecture1.3
      Solve x^2 + bx + c = 0 by Factoring
    • Lecture1.4
      Solve ax^2 + bx + c = 0 by Factoring
    • Lecture1.5
      Solve Quadratic Equations by Finding Square Roots
    • Lecture1.6
      Perform Operations with Complex Numbers
    • Lecture1.7
      Complete the Square
    • Lecture1.8
      Use the Quadratic Formula and the Discriminant
    • Lecture1.9
      Graph and Solve Quadratic Inequalities
    • Lecture1.10
      Chapter TEST Quadratic Functions and Factoring
  • Polynomials and Polynomial Functions
    9
    • Lecture2.1
      Use Properties of Exponents
    • Lecture2.2
      Evaluate and Graph Polynomial Functions
    • Lecture2.3
      Add, Subtract, and Multiply Polynomials
    • Lecture2.4
      Factor and Solve Polynomial Equations
    • Lecture2.5
      Apply the Remainder and Factor Theorems
    • Lecture2.6
      Find Rational Zeros
    • Lecture2.7
      Apply the Fundamental Theorem of Algebra
    • Lecture2.8
      Analyze Graphs of Polynomial Functions
    • Lecture2.9
      Chapter TEST Polynomials and Polynomial Functions
  • Rational Exponents and Radical Functions
    7
    • Lecture3.1
      Evaluate nth Roots and Use Rational Exponents
    • Lecture3.2
      Apply Properties of Rational Exponents
    • Lecture3.3
      Perform Function Operations and Composition
    • Lecture3.4
      Use Inverse Functions
    • Lecture3.5
      Graph Square Root and Cube Root Functions
    • Lecture3.6
      Solve Radical Equations
    • Lecture3.7
      Chapter TEST Rational Exponents and Radical Functions
  • Exponential and Logarithmic Functions
    8
  • Rational Functions
    8
  • Data Analysis and Statistics
    7
    • Lecture6.1
      The Fundamental Counting Principle and Permutations
    • Lecture6.2
      Use Combinations and the Binomial Theorem Preview
    • Lecture6.3
      Construct and Interpret Binomial Distributions
    • Lecture6.4
      Use Normal Distributions
    • Lecture6.5
      Select and Draw Conclusions from Samples
    • Lecture6.6
      Compare Surveys, Experiments, and Observational Studies
    • Lecture6.7
      Chapter TEST Data Analysis and Statistics
  • Sequences and Series
    6
    • Lecture7.1
      Define and Use Sequences and Series
    • Lecture7.2
      Analyze Arithmetic Sequences and Series
    • Lecture7.3
      Analyze Geometric Sequences and Series
    • Lecture7.4
      Find Sums of Infinite Geometric Series
    • Lecture7.5
      Use Recursive Rules with Sequences and Functions
    • Lecture7.6
      Chapter TEST Sequences and Series
  • Quadratic Relations and Conic Sections
    8
    • Lecture8.1
      Apply the Distance and Midpoint Formulas
    • Lecture8.2
      Graph and Write Equations of Parabolas
    • Lecture8.3
      Graph and Write Equations of Circles
    • Lecture8.4
      Graph and Write Equations of Ellipses
    • Lecture8.5
      Graph and Write Equations of Hyperbolas
    • Lecture8.6
      Translate and Classify Conic Sections
    • Lecture8.7
      Solve Quadratic Systems
    • Lecture8.8
      Chapter TEST Quadratic Relations and Conic Sections
  • Trigonometric Ratios and Functions
    7
    • Lecture9.1
      Use Trigonometry with Right Triangles
    • Lecture9.2
      Define General Angles and Use Radian Measure
    • Lecture9.3
      Evaluate Trigonometric Functions of Any Angle
    • Lecture9.4
      Evaluate Inverse Trigonometric Functions
    • Lecture9.5
      Apply the Law of Sines
    • Lecture9.6
      Apply the Law of Cosines
    • Lecture9.7
      Chapter TEST Trigonometric Ratios and Functions
  • Trigonometric Graphs, Identities, and Equations
    8
    • Lecture10.1
      Graph Sine, Cosine, and Tangent Functions
    • Lecture10.2
      Translate and Reflect Trigonometric Graphs
    • Lecture10.3
      Verify Trigonometric Identities
    • Lecture10.4
      Solve Trigonometric Equations
    • Lecture10.5
      Write Trigonometric Functions and Models
    • Lecture10.6
      Apply Sum and Difference Formulas
    • Lecture10.7
      Apply Double-Angle and Half-Angle Formulas
    • Lecture10.8
      Chapter TEST Trigonometric Graphs, Identities, and Equations

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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Aims & Goals:

  • Students will have a fundamental understanding of algebra and its practical applications.
  • Students will be able to represent functional relationships graphically, numerically, analytically, and with words and will be able to navigate between these various representations.
  • Students will understand the linear, quadratic, exponential, logarithmic, radical, and rational functions.
  • Students will be able to model real-world situations using functions in order to solve problems arising from those situations.
  • Students will be able to think critically about mathematics and the application of mathematics to real-world situations.
  • Students will be prepared to study higher-level mathematics.
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