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Algebra II Academic Library

Second Semester

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Algebra II Online 

Algebra II is a full-year, high school math course intended for the student who has successfully completed the prerequisite course Algebra I. This course focuses on algebraic techniques and methods in order to develop student understanding of advanced number theory, concepts involving linear, quadratic and polynomial functions, geometric concepts, basic trigonometric identities, and pre-calculus theories.

Working together to provide the most comprehensive helps to our students, NFC Academy provides this Academic Library of videos which give to the student additional examples and instruction of daily concepts.

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Algebra II Online Second Semester

UNIT 7 – REAL NUMBERS
  1. Real Numbers
    1. Rational and Irrational Numbers  
    2. Converting Decimals to Fractions 2  
    3. Converting a Fraction to a Repeating Decimal  
    4. Converting Repeating Decimal to a Fraction
    5. Convert Repeating Decimals to Fractions 2
    6. Square Root and Real Numbers  
    7. Recognizing Irrational Numbers 
  2. Law of Radicals (There are likely more instructional presentations than will be needed and students should use as many as they need to come to a good understanding of the concepts)
    1. Simplifying Radicals  
    2. Introduction to Radicals
    3. ​Multiply and Simplify A Radical Expression 1  
    4. Subtract and Simplifying Radicals  
    5. Adding and Simplifying Radicals  
    6. Multiply and Simplify A Radical Expression 2   
    7. Operations with Radical Expressions- Multiplication and Division
    8. Multiply and Divide Radical Expressions
    9. Operations on Radical Expressions
    10. Algebra 2 – Radical Equations
  3. Conjugates
    1. Dividing Radicals Using Conjugates
    2. Algebra 1 11.9b – Conjugates
    3. Rationalize Denominators using conjugates
  4. Radical Equations
    1. Solving Radical Equations 
    2. Extraneous Solutions to Radical Equations
    3. Solving Radical Equations 2  
    4. Solving Radical Equations 3  
  5. Quiz 1: Real Numbers
  6. Standard Form of Quadratic Function
    1. Graphing parabolas intro  
    2. Worked Example: Quadratic Formula  
    3. Graphing quadratics: standard form 
    4. Graphing Quadratic Functions – Example 1
  7. Quadratic Equations
    1. Solve quadratic equations by square root property
  8. Factoring Quadratic Equations
    1. Solving a Quadratic Equation by Factoring  
    2. Solve Quadratic by Factoring  
  9. Completing the Square
    1. Solving Quadratic Equations by Completing the Square  
    2. Example 1 Completing the Square  
    3. Example 2 Completing the Square  
    4. Example 3 Completing the Square
  10. Quiz 2: Quadratic Solutions
  11. Quadratic Formula
    1. Quadratic Formula ​
    2. Ex: Solve Quadratic Equations Using Square Roots
  12. Graphs of Quadratic Functions
    1. Graphing Quadratics: Vertex Function  
    2. Solving Quadratic Equations by Factoring Part 1 of 4
    3. Solving Quadratic Equations by Factoring Part 2 of 4
    4. Solving Quadratic Equations by Factoring Part 3 of 4
    5. Solving Quadratic Equations by Factoring Part 4 of 4
    6. How to Factor any Quadratic Equation
    7. Solving Simple Quadratic Equations  
    8. Order of Steps Exercise Example  
  13. Word Problems Involving Quadratic Equations
    1. Example 4 – Applying the Quadratic Formula  
    2. How to Solve Word Problems Using Quadratic Formula
  14. Sum and Product of Roots
    1. Example: Complex Roots for a Quadratic 
    2. Sum and Product of Roots of Quadratic Equation
    3. How to find Sum and Product of roots of a quadratic equation
  15. Imaginary Numbers
    1. Introduction to i and Imaginary Numbers 
    2. Algebra 2 – Complex Numbers – part 1 of 3
    3. Algebra 2 – Complex Numbers – Part 2 of 3
  16. Complex Solutions
    1. Using the Discriminant for Quadratic Equations
  17. The Fundamental Theorem of Algebra
    1. The Fundamental Theorem of Algebra  
  18. Quiz 3: Quadratic Formula
  19. Test
  20. Alternate Test
  21. Glossary and Credits
UNIT 8 – QUADRATIC RELATIONS AND SYSTEMS
  1. Distance Formula
    1. Finding the Distance Between Two Points  
    2. The Distance Formula and Finding the Distance Between Two Points 
    3. Distance Formula ​Circl
  2. Circle
    1. ​Introduction to Conic Sections
    2. Equation of a Circle  
    3. Equation of Circle 1
    4. Equation of Circle 2 
  3. Ellipse
    1. 6-3 derivation of ellipse formula  
    2. Foci of an Ellipse  
    3. Conic Section: Introduction to Ellipses
  4. ​Ellipse Continued
    1. Conic Section: Introduction to Ellipses
  5. ​Quiz 1: Conics and the Coordinate Plane
  6. Conic Sections: Parabola
    1. Conic Sections: Parabola 1 of 2  
    2. Conic Sections: Parabola 2 of 2   
    3. Algebra 2 – Focus and Directrix of a Parabola  
    4. Conic Sections – Parabola  
  7. Conic Sections: Parabola Continued
    1. Conic Sections: Parabola 1 of 2 
    2. Conic Sections: Parabola 2 of 2  
    3. Algebra 2 – Focus and Directrix of a Parabola  
    4. Conic Sections – Parabola  
  8. Conic Sections: Hyperbola
    1. Conic Section: Intro to Hyperbola  
    2. Conic Section Hyperbola 2    
    3. Conic Section Hyperbola 3  
    4. Foci of Hyperbola  
    5. Conic Sections: The Hyperbola part 1 of 2  
    6. Conic Sections: The Hyperbola part 2 of 2  
  9. Conic Sections: Hyperbola Continued
    1. Conic Sections: The Hyperbola part 1 of 2  
    2. Conic Sections: The Hyperbola part 2 of 2  
  10. Identifying Conic Sections (Use previous presentations as needed for review)
  11. Quiz 2: Conics
  12. Systems of Equations
    1. Systems of 2nd Degree Equations  
    2. Systems of 2nd Degree Equations  
    3. Solving Systems of Conic by Graphing 
    4. Solving Systems of Conics by Graphing Video  
  13. Solutions of Inequalities
    1. Systems of 2nd Degree Equations  
    2. Graphing Quadratic Inequalities  
    3. Graphing Quadratic Inequalities  
  14. Applications of Conic Sections–Part 1  (Use your instructional presentations in this section for completion of Parts 1-3 as needed)
  15. Applications of Conic Sections–Part 2
  16. Applications of Conic Sections–Part 3
  17. ​​Constant of Proportionality
    1. Proportionality Constant for Direct Variation  
    2. Direct and Inverse Variation  
    3. Recognizing Direct and Inverse Variation  
  18. Quiz 3: Application of Conics
  19. ​​Test
  20. Alternate Test
  21. Glossary and Credits​ 
UNIT 9 – FUNCTIONS
  1. Absolute Value Functions
    1. Algebra 2: Absolute Value Functions and Graphs (2-7)  
  2. Exponential Functions
    1. Exponent Rules Part 1 – Review  
    2. Exponent Rules Part 2 – Review  
    3. Negative Exponents  
    4. Exponent Rules Math Learning Upgrade (If you like music then this presentation should help you with exponents)
    5. Algebra 2 – Rules of Exponents  
  3. Fractional Exponents
    1. Basic Fractional Exponents  
    2. Solving for Fractional Exponents 
    3. Zero, Negative, and Fractional Exponents  
  4. Radical Functions
    1. Graphs of square root functions  
    2. Transforming the square root function  
  5. Graphs of Piece-Wide Defined Functions
    1. Introduction to piecewise functions  
    2. Worked example: evaluating piecewise function  
  6. Exponential Equations
    1. Solving Exponential Equations  
  7. Graphing Exponential Functions
    1. Graphing Exponential Functions  
    2. Graphing Exponential Functions   
  8. Exponential Applications (Use as needed the instructional presentations as needed to complete this application assignment)
  9. Solving Equations by Graphing Functions
    1. Solving an Advanced Equation by Graphing f(x)=g(x)  
    2. fx)=g(x) Find values  
  10. Quiz 1: Exponential Functions 
  11. Logarithmic Functions
    1. Logarithms
    2. Introduction to Logarithms  
    3. Properties of Logarithms  
  12. Evaluation of Logarithms​
    1. Ex 1: Evaluate Logarithm without a calculator – Whole  
    2. Ex 2: Evaluate a Logarithm without a calculator  
    3. Evaluate Common Logarithms on a calculator  
    4. Fancier Logarithm Expressions  
  13. Evaluating Exponential Functions, Common Logarithms, and Natural Logarithms
    1. Basic Properties of Common Logarithms  
    2. Algebra 2 – Common and Natural Logarithms  
    3. Basic Properties of Natural Logarithms  
    4. Inverse Properties of Logs  
  14. General Properties of Logarithms
    1. Introduction to Logarithm Properties
    2. Introduction to Logarithm Properties – Part 2  
    3. Sum of Logarithm With Same Base  
  15. Scientific Notation
    1. Scientific Notation  
    2. Introduction to Scientific Notation  
    3. Scientific Notation  
  16. Calculation of Common Logarithms
    1. Change of Base Formula  
    2. Change of Base Formula Proof  
    3. Change of Base Formula for Logarithms 
  17. Graphs of Logarithmic Functions
    1. Graphing Logarithmic Function 
  18. Solving Logarithmic Equations
    1. Solving Logarithmic Equations  
    2. Solving Logarithmic Equations  
    3. Solving logarithmic equations
  19. Graphs of Natural Logarithms
    1. ​Graphing natural logarithm function
  20.  Logarithmic Applications
    1. Solving Exponential Equations – Word Problem involving Finances  
    2. Log Word Problems  
  21. Quiz 2: Logarithmic Functions 
  22. Comparing Functions
    1. Comparing linear functions: equations vs. graph  
    2. Comparing linear functions: table vs. graphs  
  23. Inverse Functions
    1. ​Intro inverse functions    
  24. Matrices
    1. Introduction to Matrix  
    2. Matrix Addition, Subtraction, and Scalar Multiplication  ​
  25. System Solutions with Matrices
    1. Matrices to Solve A System of Equations  
  26. Addition and Multiplication of Matrices
    1. Martrix Addition and Subtraction  
    2. ​Matrix Addition, Subtraction, and Scalar Multiplication  
    3. Matrix Multiplication  
    4. Multiplying Matrices – Example 1  
  27. Quiz 3: Matrices Performance Task 
  28. Test Alternate
  29. Test 
  30. Glossary and Credits
UNIT 10 – COUNTING PRINCIPLES
  1. Progressions: Sequences
    1. Introduction to Sequences  
    2. Arithmetic Sequences  
    3. Geometric Sequences  
    4. Arithmetic Sequences  
    5. Finding the 100th Term In a Sequence  
    6. Geometric Sequence Introduction 
    7. Geometric Sequence  
  2. Arithmetic and Geometric Sequences
    1. Intro to arithmetic sequences  
    2. Using arithmetic sequence formulas  
    3. Intro to geometric sequences   
    4. Extending geometric sequences  
    5. Using explicit geometric formulas of sequence  
  3. Progressions: Series
    1. Arithmetic Series  
    2. Geometric Series
    3. Introduction to Infinite Series  
    4. Formula for Arithmetic Series  
    5. Sigma Notation for Sums  
    6. Writing a Series in Sigma Notation  
  4. Quiz 1: Sequences and Series
  5. Permutations: Factorials
    1. Permutations  
    2. Permutations Formula  
    3. Permutations  
  6. Permutation Formula
    1. Permutation Formula 
    2. Permutations  
  7. Permutations: Applications
    1. Permutations – Counting Using Permutations  
    2. Circular Permutations 
  8. Quiz 2:  Permutations
  9. Combination Formula
    1. Intro to combinations 
    2. Combinations  
    3. Statistics 101: Combinations  
    4. Statistics 101: Permutations vs. Combinations (Repeat – This presentation is a review of both Permutations and Combinations) 
  10. Combinations: Applications
    1. Statistics 101: Combinations  
    2. Permutations and Combinations – Word Problems   
  11. Combinations: Binomial Coefficients
    1. Pascal’s Triangle and the Binomial Coefficients  
    2. Permutations and Combinations Lesson 5 – Pascal’s Triangle and Binomial (This presentation will cover in much greater detail than needed to understand for you lesson assignment) 
  12. Quiz 3:  Combinations
  13. ​Probability: Concepts
    1. Basic Probability  
  14. Probability: Equally Likely Outcomes
    1. Examples, Marbles from a Bag   
  15. Probability: Multiplication Principle
    1. Multiplication Rule (Probability “and”)  
  16. Conditional Probability
  17. Quiz 4: Counting Principles
  18. ​Test
  19. Alternate Test
  20. Glossary and Credits
UNIT 11 – TRIGONOMETRY
  1. Trigonometry Basics​
    1. Basic Trigonometry (Just a little different) 
    2. Basic Trigonometry  
  2. The Unit Circle
    1. Unit Circle Definition of Trig Functions
    2. Sin & Cosine Identities – Symmetry  
    3. A Way to remember the Entire Unit Circle for Trigonometry
  3. Reciprocal Functions
    1. Finding Reciprocal Trig Ratios  
    2. Using Reciprocal Trig Ratios  
    3. Reciprocal Trigonometric Ratios
  4. Radian Measure
    1. Radian Measure
    2. Radians Introduction 
    3. Radians & Degrees 
    4. Degrees to Radians  
    5. Radians to Degrees  
  5. Quiz 1: Unit Circle
  6. Trigonometric Functions on the Unit Circle
    1. Reference Angles
    2. Evaluating Trigonometric Functions at Important Angles, Ex 1
  7. Pythagorean Identity
    1. Proof of Pythagorean Trig Identity  
    2. Using the Pythagorean Identity  
  8. Quiz 2: Trigonometric Functions
  9. Graphs and Amplitude
    1. Graph of y=sin(x) 
    2. Intersection of points of y=sin(x) and y=cos(x)  
    3. How to Graph Sine, Cosine, and Tangent Functions
    4. Graphing the Sin(x) and Cos(X)
  10. Graphs and Modeling
    1. Phase Shift
    2. Finding Amplitude, Period, Horizontal and Vertical Shifts of a Trig Function EX 1
    3. Amplitude & period of sinusoidal functions from equation 
    4. Sinusoidal Functions Part 1 
    5. Sinusoidal Functions Part 2
  11. Quiz 3: Graphs
  12. Review
  13. Test
  14. Alternate Test
  15. Glossary and Credits
​UNIT 12 – STATISTICS
  1. Sample Surveys
    1. AP Statistics: Sample Surveys, Bias, and Sampling Methods (A lengthy introductory video, but helpful) 
    2. AP Stats – 4.1 – Sampling and Surveys (A shorter introductory video) 
    3. Populations vs. Samples
    4. Population vs sample
    5. Population and Sample Statistics
    6. Random sample  (A little accent, but definitions are good)
    7. AP Statistics Chapter 12
  2. Normal Distributions
    1. Normal Distribution – Explained Simply (Part 1) 
    2. Normal Distribution – Explained Simply (Part 2)
    3. Creating a Histogram  
    4. Interpreting a Histogram  
    5. Shapes of Distribution  
  3. Simulations
    1. Chi-square distribution introduction 
    2. Pearson’s Chi-square test 
    3. Chi-squared Test
  4. Experiments
    1. Surveys, Experiments, and Observational Studies
    2. Statistics – Surveys, Observational Studies, and Experiments
    3. Observational Studies and Experiments
    4. Four Principles of an Experiment
  5. Quiz 1: Statistics
  6. Observational Studies
    1. Surveys, Experiments, and Observational Studies
    2. Statistics – Surveys, Observational Studies, and Experiments
    3. Observational Studies and Experiments –
  7. Probability and Decisions
    1. Intro to theoretical probability  
  8. Quiz 2: Statistical Probability
  9. Appropriate Models
    1. Linear, Quadratic, Exponential Models
    2. Exponential, Exponential, Quadratic Models: An Application (Algebra II)
    3. Graphing a cubic function of the form of y=ax(3)
    4. Graphing cubic function
    5. How to Tell if a Table is Linear, Quadratic, or Exponential  
  10. Modeling Functions
    1. Quadratic Model Using T1 calculator
    2. Technology in College Algebra – Quadratic Function – Developing a Model – TI-89
  11. Regression Models
    1. Linear Regression Model Using Graphing Calculator
    2. Linear Regression in Excel
    3. Quadratic Regression Model Graphing Calculator
    4. Quadratic Regression in Excel
    5. Perform Exponential Model Using Graphing Calculator
    6. Exponential Regression in Excel 2010
  12. Quiz 3: Math Models
  13. Review
  14. Test
  15. Alternate Test
  16. Glossary and Credits
UNIT 13 – REVIEW
  1. Integers (For all assignments in this section go back as necessary to review the concepts using all of the material you need)
  2. Integers Continued
  3. Open Sentences
  4. Open Sentences Continued
  5. Graphs
  6. Graphs Continued
  7. Quiz 1: Review
  8. Polynomials
  9. Polynomials Continued
  10. Algebraic Fractions Part 1
  11. Algebraic Fractions Part 2
  12. Algebraic Fractions Part 3
  13. Real Numbers
  14. Real Numbers Continued
  15. Quiz 2: Review
  16. Quadratic Relations and Systems
  17. Quadratics Continued
  18. Exponential Functions
  19. Exponential Functions Continued
  20. Counting Principles
  21. Counting Principles Continued
  22. Quiz 3: Review
  23. Test
  24. Alternate Test
  25. Glossary and Credits
UNIT 14 – SEMESTER REVIEW AND EXAM
  1. Review
  2. Exam
  3. Alternate Exam—Form A
  4. Alternate Exam—Form B

 

UNIT 15 – FINAL EXAM