- K-12 Curriculum
- 1 (Registered)
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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
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Quadratic Functions and Factoring
10-
Lecture1.1Graph Quadratic Functions in Standard Form
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Lecture1.2Graph Quadratic Functions in Vertex or Intercept Form
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Lecture1.3Solve x^2 + bx + c = 0 by Factoring
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Lecture1.4Solve ax^2 + bx + c = 0 by Factoring
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Lecture1.5Solve Quadratic Equations by Finding Square Roots
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Lecture1.6Perform Operations with Complex Numbers
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Lecture1.7Complete the Square
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Lecture1.8Use the Quadratic Formula and the Discriminant
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Lecture1.9Graph and Solve Quadratic Inequalities
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Lecture1.10Chapter TEST Quadratic Functions and Factoring
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Polynomials and Polynomial Functions
9-
Lecture2.1Use Properties of Exponents
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Lecture2.2Evaluate and Graph Polynomial Functions
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Lecture2.3Add, Subtract, and Multiply Polynomials
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Lecture2.4Factor and Solve Polynomial Equations
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Lecture2.5Apply the Remainder and Factor Theorems
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Lecture2.6Find Rational Zeros
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Lecture2.7Apply the Fundamental Theorem of Algebra
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Lecture2.8Analyze Graphs of Polynomial Functions
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Lecture2.9Chapter TEST Polynomials and Polynomial Functions
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Rational Exponents and Radical Functions
7-
Lecture3.1Evaluate nth Roots and Use Rational Exponents
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Lecture3.2Apply Properties of Rational Exponents
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Lecture3.3Perform Function Operations and Composition
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Lecture3.4Use Inverse Functions
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Lecture3.5Graph Square Root and Cube Root Functions
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Lecture3.6Solve Radical Equations
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Lecture3.7Chapter TEST Rational Exponents and Radical Functions
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Exponential and Logarithmic Functions
8-
Lecture4.1
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Lecture4.2
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Lecture4.3
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Lecture4.4
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Lecture4.5
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Lecture4.6
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Lecture4.7
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Lecture4.8Chapter TEST Exponential and Logarithmic Functions
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Rational Functions
8-
Lecture5.1
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Lecture5.2
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Lecture5.3
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Lecture5.4
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Lecture5.5
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Lecture5.6
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Lecture5.7
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Lecture5.8Chapter TEST Rational Functions
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Data Analysis and Statistics
7-
Lecture6.1The Fundamental Counting Principle and Permutations
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Lecture6.2
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Lecture6.3Construct and Interpret Binomial Distributions
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Lecture6.4Use Normal Distributions
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Lecture6.5Select and Draw Conclusions from Samples
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Lecture6.6Compare Surveys, Experiments, and Observational Studies
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Lecture6.7Chapter TEST Data Analysis and Statistics
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Sequences and Series
6-
Lecture7.1Define and Use Sequences and Series
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Lecture7.2Analyze Arithmetic Sequences and Series
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Lecture7.3Analyze Geometric Sequences and Series
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Lecture7.4Find Sums of Infinite Geometric Series
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Lecture7.5Use Recursive Rules with Sequences and Functions
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Lecture7.6Chapter TEST Sequences and Series
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Quadratic Relations and Conic Sections
8-
Lecture8.1Apply the Distance and Midpoint Formulas
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Lecture8.2Graph and Write Equations of Parabolas
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Lecture8.3Graph and Write Equations of Circles
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Lecture8.4Graph and Write Equations of Ellipses
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Lecture8.5Graph and Write Equations of Hyperbolas
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Lecture8.6Translate and Classify Conic Sections
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Lecture8.7Solve Quadratic Systems
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Lecture8.8Chapter TEST Quadratic Relations and Conic Sections
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Trigonometric Ratios and Functions
7-
Lecture9.1Use Trigonometry with Right Triangles
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Lecture9.2Define General Angles and Use Radian Measure
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Lecture9.3Evaluate Trigonometric Functions of Any Angle
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Lecture9.4Evaluate Inverse Trigonometric Functions
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Lecture9.5Apply the Law of Sines
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Lecture9.6Apply the Law of Cosines
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Lecture9.7Chapter TEST Trigonometric Ratios and Functions
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Trigonometric Graphs, Identities, and Equations
8-
Lecture10.1Graph Sine, Cosine, and Tangent Functions
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Lecture10.2Translate and Reflect Trigonometric Graphs
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Lecture10.3Verify Trigonometric Identities
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Lecture10.4Solve Trigonometric Equations
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Lecture10.5Write Trigonometric Functions and Models
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Lecture10.6Apply Sum and Difference Formulas
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Lecture10.7Apply Double-Angle and Half-Angle Formulas
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Lecture10.8Chapter TEST Trigonometric Graphs, Identities, and Equations
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About the Instructor
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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.