Algebra II

US High School

Course Overview

Lessons & Practice

I. Welcome

1. Review of Basic Functions

26min

1.1.1. Properties of Parent Functions10 min

1.1.2. Practice (Level 1)2 min

1.1.3. Practice (Level 1)3 min

1.1.4. Practice (Level 2)38 sec

1.1.5. Practice (Level 2)1 min

1.1.6. Practice (Level 3)2 min

1.1.7. Reference Sheet: Basic Graphs

1.2.1. Example2 min

1.2.2. Practice Level 140 sec

1.2.3. Practice Level 23 min

1.2.4. Practice Level 32 min

2. Transformations of Functions

1.3hr

2.I. Chapter Intro

2.1.1. Vertical Translations2 min

2.1.2. Horizontal Translations3 min

2.1.3. Example 4 min

2.1.4. Example 3 min

2.1.5. Practice Level 12 min

2.1.6. Practice Level 22 min

2.1.7. Practice Level 21 min

2.1.8. Practice Level 32 min

2.2.1. Vertical Reflections1 min

2.2.2. Horizontal Reflections2 min

2.2.3. Example3 min

2.2.4. Example3 min

2.2.5. Practice Level 12 min

2.2.6. Practice Level 22 min

2.2.7. Practice Level 32 min

2.3.1. Vertical Expansions & Compressions3 min

2.3.2. Horizontal Expansions & Compressions2 min

2.3.3. Example7 min

2.3.4. Example7 min

2.3.5. Practice Level 12 min

2.3.6. Practice Level 25 min

2.3.7. Practice Level 32 min

2.4.1. Combining Transformations4 min

2.4.2. Example4 min

2.4.3. Practice Level 12 min

2.4.4. Practice Level 1

2.4.5. Practice Level 23 min

2.4.6. Cheatsheet

3. Quadratic Equations & Complex Numbers

2.2hr

3.1.1. Completing the Square (

x^2+bx+c

3.1.2. Example4 min

3.1.3. Practice Level 15 min

3.1.4. Practice Level 25 min

3.1.5. Practice Level 34 min

3.1.6. Extra Completing the Square Practice Drill 💪

3.1.7. Completing the Square (

ax^2+bx+c

3.1.8. Example4 min

3.1.9. Practice Level 14 min

3.1.10. Practice Level 25 min

3.1.11. Practice Level 37 min

3.1.12. Extra Completing the Square Practice Drill 💪

3.2.1. Basics of Complex Numbers4 min

3.2.2. Operations With Complex Numbers13 min

3.2.3. Example9 min

3.2.4. Practice5 min

3.3.1. Quadratic Formula3 min

3.3.2. Example3 min

3.4.1. Solving Quadratic Inequalities in One Variable7 min

3.4.2. Example4 min

3.4.3. Practice Level 13 min

3.4.4. Practice Level 23 min

3.4.5. Practice Level 3

3.5.1. Solving Quadratic Inequalities in Two Variables5 min

3.5.2. Example3 min

3.5.3. Practice Level 13 min

3.5.4. Practice Level 23 min

3.6.1. Systems of Quadratic Equations7 min

3.6.2. Example4 min

3.6.3. Practice Level 14 min

3.6.4. Practice Level 24 min

4. Polynomial Functions

2.9hr

4.1.1. Basic of Polynomials4 min

4.1.2. Example2 min

4.1.3. Practice Level 13 min

4.2.1. Polynomial Graphs & Characteristics4 min

4.2.2. Example2 min

4.2.3. Practice Level 12 min

4.3.1. Factoring 5 min

4.3.2. Factoring a Difference & Sum of Cubes3 min

4.3.3. Example2 min

4.3.4. Practice Level 146 sec

4.3.5. Practice Level 22 min

4.3.6. Practice Level 32 min

4.4.1. Factoring & Graphing Polynomials4 min

4.4.2. Example3 min

4.4.4. Example2 min

4.4.5. Practice Level 12 min

4.4.6. Practice Level 23 min

4.4.7. Practice Level 3

4.5.1. Dividing Polynomials - Long Division6 min

4.5.2. Example3 min

4.5.3. Dividing Polynomials - Synthetic Division8 min

4.5.4. Example2 min

4.5.5. Practice Level 12 min

4.5.6. Practice Level 2

4.5.7. Practice Level 33 min

4.6.1. Remainder Theorem, Factor Theorem, & Rational Root Theorem5 min

4.6.2. Factoring Polynomials (Degree 3+)6 min

4.6.3. Example5 min

4.6.4. Practice Level 154 sec

4.6.5. Practice Level 27 min

4.6.6. Practice Level 34 min

4.7.1. Fundamental Theorem of Algebra5 min

4.7.2. Practice Level 12 min

4.8.1. Transformations of Cubic3 min

4.8.2. Example2 min

4.8.3. Transformations of Quartic Functions3 min

4.8.4. Example3 min

4.8.5. Practice Level 12 min

4.8.6. Practice Level 2

4.8.7. Practice Level 32 min

4.9.1. Solving General Polynomial Equations6 min

4.9.2. Example5 min

4.9.3. Practice Level 11 min

4.9.4. Practice Level 2

4.9.5. Practice Level 33 min

4.10.1. Solving Polynomial Inequalities using a Number Line3 min

4.10.2. Example5 min

4.10.3. Practice Level 1

4.10.4. Practice Level 24 min

4.10.5. Practice Level 33 min

4.11.1. Solving Polynomial Inequalities Using a Graph5 min

4.11.2. Example2 min

4.11.3. Practice Level 1

4.11.4. Practice Level 2

4.11.5. Practice Level 32 min

4.12.1. Example4 min

4.12.2. Example6 min

4.12.3. Practice Level 14 min

4.12.4. Practice Level 24 min

4.Q. Checkpoint Quiz5 Qns

5. Radical Expressions and Functions

1.7hr

5.1.1. Radical Expressions5 min

5.1.2. Multiplying Radicals6 min

5.1.3. Example2 min

5.1.4. Practice Level 12 min

5.1.5. Practice Level 25 min

5.1.6. Practice Level 34 min

5.2.1. Rationalizing the Denominator5 min

5.2.2. Simplifying Radicals7 min

5.2.3. Example4 min

5.2.4. Practice Level 12 min

5.2.5. Practice Level 25 min

5.2.6. Practice Level 33 min

5.3.1. Solving Radical Equations5 min

5.3.2. Example5 min

5.3.3. Example6 min

5.3.4. Practice Level 16 min

5.3.5. Practice Level 23 min

5.3.6. Practice Level 38 min

5.4.1. Radical Functions59 sec

5.4.2. Transformations of Radical Functions3 min

5.4.3. Example: Transformations of Radical Functions2 min

5.4.4. Practice Level 11 min

5.4.5. Practice Level 23 min

5.4.6. Practice Level 3

5.5.1. Example3 min

5.5.2. Practice Level 11 min

5.5.3. Practice Level 22 min

6. Logarithmic Functions

34min

6.1.1. Basics of Logarithms3 min

6.1.2. Example3 min

6.1.3. Practice Level 1

6.1.4. Practice Level 2

6.1.5. Practice Level 3

6.2.1. Logarithm Laws4 min

6.2.2. Example2 min

6.2.3. Example 2 min

6.2.4. Practice Level 1

6.2.5. Practice Level 2

6.2.6. Practice Level 32 min

6.3.1. Solving Logarithmic Equations2 min

6.3.2. Example2 min

6.3.3. Practice Level 1

6.3.4. Practice Level 22 min

6.3.5. Practice Level 31 min

6.4.1. Using Logarithms to Solve Exponential Equations1 min

6.4.2. Example58 sec

6.4.3. Practice Level 1

6.4.4. Practice Level 2

6.4.5. Practice Level 3

6.5.1. Characteristics of Logarithmic Functions2 min

6.5.2. Example57 sec

6.5.3. Practice Level 1

6.5.4. Practice Level 2

6.5.5. Practice Level 3

6.6.1. Transformations of Logarithmic Functions2 min

6.6.2. Example2 min

6.6.3. Practice Level 1

6.6.4. Practice Level 2

6.6.5. Practice Level 3

6.7.1. Applications of Logarithmic Functions30 sec

6.7.3. Practice Level 1

6.7.4. Practice Level 2

6.7.5. Practice Level 3

6.Q. Checkpoint Quiz5 Qns

7. Exponential Functions

1.8hr

7.1.1. Review: Exponent Rules (Laws of Exponents)2 min

7.2.1. Investigating Integer Exponents6 min

7.2.2. Integer Exponents1 min

7.2.3. Practice1 min

7.2.4. Practice4 min

7.2.5. Practice3 min

7.3.1. Investigating Rational Exponents5 min

7.3.2. Rational Exponents2 min

7.3.3. Practice Level 19 min

7.3.4. Practice Level 24 min

7.3.5. Practice Level 34 min

7.4.1. Exponent Rules4 min

7.4.2. Example5 min

7.4.3. Practice Level 14 min

7.4.4. Practice Level 25 min

7.4.5. Practice Level 23 min

7.4.6. Practice Level 32 min

7.5.1. Solving Exponential Equations1 min

7.5.2. Example2 min

7.5.3. Practice Level 1

7.5.4. Practice Level 2

7.5.5. Practice Level 3

7.6.1. Characteristics of Exponential Functions2 min

7.6.2. Example53 sec

7.6.3. Practice Level 12 min

7.6.4. Practice Level 22 min

7.7.1. Transformations of Exponential Functions3 min

7.7.2. Example3 min

7.7.3. Practice Level 12 min

7.7.4. Practice Level 23 min

7.7.5. Practice Level 29 min

7.8.1. Applications of Exponential Functions1 min

7.8.2. Example2 min

7.8.3. Practice Level 14 min

7.8.4. Practice Level 25 min

7.8.5. Practice Level 33 min

8. Rational Functions

2.9hr

8.1.1. Rational Expressions & Functions7 min

8.1.2. Practice Level 13 min

8.1.3. Practice Level 24 min

8.1.4. Practice Level 25 min

8.1.5. Practice Level 34 min

8.2.1. Multiplying & Dividing Rational Expressions6 min

8.2.2. Practice Level 13 min

8.2.3. Practice Level 26 min

8.2.4. Practice Level 35 min

8.3.1. Adding and Subtracting Rational Expressions5 min

8.3.2. Practice Level 14 min

8.3.3. Practice Level 1

8.3.4. Practice Level 25 min

8.3.5. Practice Level 34 min

8.4.1. Solving Rational Equations3 min

8.4.2. Example5 min

8.4.3. Practice Level 152 sec

8.4.4. Practice Level 26 min

8.4.5. Practice Level 3

8.5.1. Reciprocal Functions2 min

8.5.2. Graphing Reciprocal Functions7 min

8.5.3. Example4 min

8.5.4. Example5 min

8.5.5. Example3 min

8.5.6. Practice Level 12 min

8.5.7. Practice Level 23 min

8.5.8. Practice Level 33 min

8.6.1. Graphs of Rational Functions4 min

8.6.2. Example3 min

8.6.3. Example2 min

8.6.4. Example3 min

8.6.5. Practice Level 12 min

8.6.6. Practice Level 22 min

8.6.7. Practice Level 3

8.7.1. Graphing Rational Functions6 min

8.7.2. Example5 min

8.7.3. Example5 min

8.7.4. Example6 min

8.7.5. Practice Level 12 min

8.7.6. Practice Level 2

8.7.7. Practice Level 22 min

8.7.8. Practice Level 33 min

8.8.1. Solving Rational Inequalities 5 min

8.8.2. Example5 min

8.8.3. Practice Level 11 min

8.8.4. Practice Level 2

8.8.5. Practice Level 3

8.9.1. Example3 min

8.9.2. Practice Level 12 min

8.9.3. Practice Level 23 min

8.9.4. Practice Level 35 min

8.Q. Checkpoint Quiz6 Qns

9. Combination of Functions

28min

9.1.1. Combining Families of Functions2 min

9.1.2. Example2 min

9.1.3. Practice Level 1

9.1.4. Practice Level 21 min

9.1.5. Practice Level 31 min

9.2.1. Sum & Difference1 min

9.2.2. Example60 sec

9.2.3. Practice Level 13 min

9.2.4. Practice Level 2

9.2.5. Practice Level 3

9.3.1. Product & Quotient of Functions2 min

9.3.2. Example2 min

9.3.3. Practice Level 1

9.3.4. Practice Level 22 min

9.3.5. Practice Level 31 min

9.4.1. Composition of Functions2 min

9.4.2. Example2 min

9.4.3. Practice Level 1

9.4.4. Practice Level 2

9.4.5. Practice Level 31 min

9.5.1. Solving Equations & Inequalities Graphically2 min

9.5.2. Example54 sec

9.5.3. Practice Level 1

9.5.4. Practice Level 245 sec

9.5.5. Practice Level 341 sec

9.Q. Checkpoint Quiz5 Qns

10. Trigonometric Ratios (Radians)

53min

10.1.1. Radians vs. Degrees4 min

10.1.2. Converting Between Degrees and Radians2 min

10.1.3. Example1 min

10.1.4. Practice Level 11 min

10.1.5. Practice Level 1

10.1.6. Practice Level 1

10.1.7. Practice Level 22 min

10.1.8. Practice Level 3

10.2.1. Trigonometric Ratios in Radians9 min

10.2.2. Example4 min

10.2.3. Practice Level 13 min

10.2.4. Practice Level 22 min

10.2.5. Practice Level 32 min

10.3.1. Special Angles & Unit Circle in Radians3 min

10.3.2. Reciprocal Trigonometric Ratios: Special Angles & Unit Circle2 min

10.3.3. Example3 min

10.3.4. Practice Level 1

10.3.5. Practice Level 22 min

10.3.6. Practice Level 32 min

10.4.1. Solving Simple Trigonometric Equations3 min

10.4.2. Example2 min

10.4.3. Example 3 min

10.4.4. Practice Level 1

10.4.5. Practice Level 21 min

10.4.6. Practice Level 31 min

10.Q. Checkpoint Quiz5 Qns

11. Trigonometric (Sinusoidal) Graphs

42min

11.1.1. Graphs of Sinusoidal Functions3 min

11.2.1. Transformations of Sinusoidal Functions (Pt 1)5 min

11.2.2. Example3 min

11.2.3. Transformations of Sinusoidal Functions (Pt 2)4 min

11.2.4. Example2 min

11.2.5. Practice Level 13 min

11.2.6. Practice Level 2

11.2.7. Practice Level 32 min

11.3.1. Graphs of Reciprocal Trigonometric Functions3 min

11.3.2. Example2 min

11.3.3. Example 3 min

11.3.4. Practice Level 11 min

11.3.5. Practice Level 2

11.3.6. Practice Level 32 min

11.4.1. Equivalent Sinusoidal Functions (Radians)3 min

11.4.2. Example3 min

11.4.3. Practice Level 1

11.4.4. Practice Level 2

11.4.5. Practice Level 3

11.5.1. Applications of Trigonometric Functions19 sec

11.5.2. Example2 min

11.5.3. Practice Level 1

11.5.4. Practice Level 2

11.5.5. Practice Level 3

11.Q. Checkpoint Quiz5 Qns

12. Trigonometric Identities & Proofs

1.2hr

12.1.1. Equivalent Trigonometric Expressions2 min

12.1.2. Example1 min

12.1.3. Practice Level 1

12.1.4. Practice Level 2

12.1.5. Practice Level 3

12.2.1. Reciprocal & Quotient Identities2 min

12.2.2. Example57 sec

12.2.3. Practice Level 12 min

12.2.4. Practice Level 23 min

12.2.5. Practice Level 35 min

12.3.1. Pythagorean Identities2 min

12.3.2. Example1 min

12.3.3. Practice Level 13 min

12.3.4. Practice Level 22 min

12.3.5. Practice Level 37 min

12.4.1. Sum & Difference Identities2 min

12.4.2. Example1 min

12.4.3. Practice Level 1

12.4.4. Practice Level 2

12.4.5. Practice Level 2

12.4.6. Practice Level 2

12.4.7. Practice Level 3

12.5.1. Double Angle Identities2 min

12.5.2. Example4 min

12.5.3. Half-Angle Identities3 min

12.5.4. Example2 min

12.5.5. Practice Level 1

12.5.6. Practice Level 2

12.5.7. Practice Level 3

12.6.1. Proofs using Trigonometric Identities2 min

12.6.2. Example2 min

12.6.3. Example4 min

12.6.4. Practice Level 14 min

12.6.5. Practice Level 2

12.6.6. Practice Level 35 min

12.7.1. Inverse Trigonometric Functions4 min

12.7.2. Example3 min

12.7.3. Practice2 min

12.7.4. Practice2 min

12.Q. Checkpoint Quiz5 Qns

13. Sequences & Series

2.1hr

13.1.1. Sequence5 min

13.1.2. Arithmetic Sequence6 min

13.1.3. Practice Level 13 min

13.1.4. Practice Level 13 min

13.1.5. Practice Level 22 min

13.1.6. Practice Level 37 min

13.2.1. Arithmetic Series9 min

13.2.2. Example3 min

13.2.3. Practice Level 13 min

13.2.4. Practice Level 25 min

13.2.5. Practice Level 34 min

13.3.1. Geometric Sequences8 min

13.3.2. Example3 min

13.3.3. Practice Level 13 min

13.3.4. Practice Level 24 min

13.3.5. Practice Level 37 min

13.4.1. Geometric Series6 min

13.4.2. How to derive Geometric Series Formula

13.4.3. Example5 min

13.4.4. Practice Level 13 min

13.4.5. Practice Level 27 min

13.4.6. Practice Level 34 min

13.5.1. Pascal's Triangle and the Binomial Expansion3 min

13.5.2. Example6 min

13.5.3. Practice Level 12 min

13.5.4. Practice Level 28 min

13.5.5. Practice Level 34 min

14. Probability and Counting

2.4hr

14.1.1. Events & Sample Spaces6 min

14.1.2. Types of Probability6 min

14.1.3. Probability Language & Notation4 min

14.1.4. Example3 min

14.1.5. Independent vs. Mutually Exclusive Events4 min

14.1.6. Example2 min

14.1.7. Practice

14.2.1. Venn Diagrams3 min

14.2.2. Tree Diagrams4 min

14.2.3. Two-way Table5 min

14.3.1. Interpretation of Probability2 min

14.3.2. Complement Rule3 min

14.3.3. Practice1 min

14.3.4. The Addition Rule4 min

14.4.1. Probability of Independent Events4 min

14.4.2. Example3 min

14.4.3. Practice2 min

14.5.1. Probability of Dependent Events (Conditional Probability)7 min

14.5.2. Conditional Probability: Tree Diagram5 min

14.5.3. Bayes’ Theorem4 min

14.5.4. Example4 min

14.5.5. Practice3 min

14.6.1. Example6 min

14.6.2. Example7 min

14.6.3. Example7 min

14.6.4. Practice4 min

14.6.5. Practice5 min

14.7.1. Summary of Key Definitions6 min

14.8.1. Fundamental Counting Principle6 min

14.8.2. Permutations and Combinations6 min

14.8.3. Practice1 min

14.8.4. Practice54 sec

14.8.5. More Combination Rules3 min

14.8.6. Example4 min

14.8.7. Practice3 min

14.8.8. Practice

14.9.1. Counting and Probability3 min

14.9.2. Example

14.9.3. Practice1 min

16. Sampling and Estimating

1.8hr

16.1.1. Sampling Variability & Sampling Distribution12 min

16.2.1. Central Limit Theorem 5 min

16.2.2. Sampling Distribution for a Mean2 min

16.2.3. Example9 min

16.2.4. Sampling Distribution for a Mean Question5 min

16.3.1. Sampling Distribution of Proportions5 min

16.3.2. Example3 min

16.3.3. Sampling Distribution of Proportions4 min

16.4.1. Drawing Samples From a Finite Population8 min

16.4.2. Example4 min

16.4.3. Practice3 min

16.5.1. Introduction to Confidence Intervals14 min

16.6.1. Confidence Interval for a Mean13 min

16.6.2. Example4 min

16.6.3. Practice3 min

16.7.1. Confidence Interval for a Proportion2 min

16.7.2. Example5 min

16.7.3. Practice4 min

16.8.1. Margin of Error and Sample Size3 min

16.8.2. Practice

18. Matrices (Extension Topic)

1.3hr

18.1.1. Basics of Matrices3 min

18.1.2. Matrix Arithmetic3 min

18.1.3. Example1 min

18.1.4. Practice2 min

18.2.1. Matrix Multiplication6 min

18.2.2. Example1 min

18.2.3. Example4 min

18.2.4. Practice3 min

18.2.5. Practice2 min

18.2.6. Practice

18.3.1. Matrix Transpose3 min

18.3.2. Symmetric Matrices3 min

18.3.3. Example3 min

18.3.4. Practice60 sec

18.3.5. Practice2 min

18.4.1. Matrix Inverse4 min

18.4.2. Example3 min

18.4.3. Practice32 sec

18.4.4. Practice2 min

18.5.1. Matrix Inverse Algorithm3 min

18.5.2. Example2 min

18.5.3. Example2 min

18.5.4. Practice2 min

18.6.1. Solving Matrix Equations2 min

18.6.2. Example52 sec

18.6.3. Example4 min

18.6.4. Practice2 min

18.6.5. Practice54 sec

18.6.6. Practice2 min

18.7.1. Basics of Determinants5 min

18.7.2. Example2 min

18.7.3. Determinant and Area

18.7.4. Practice2 min

18.7.5. Practice3 min

19. Systems of Linear Equations (Extension Topic)

1.5hr

19.I. Chapter Note

19.1.1. Basics of Systems of Linear Equations8 min

19.1.2. Example3 min

19.1.3. Practice2 min

19.1.4. Practice3 min

19.2.1. Augmented Matrix3 min

19.2.2. Example3 min

19.2.3. Example1 min

19.2.4. Practice2 min

19.2.5. Practice2 min

19.3.1. Echelon Forms5 min

19.3.2. Example2 min

19.3.3. Example2 min

19.3.4. Practice

19.3.5. Practice

19.3.6. Practice

19.4.1. Reducing a Matrix5 min

19.4.2. Example3 min

19.4.3. Example7 min

19.4.4. Practice2 min

19.4.5. Practice3 min

19.4.6. Practice

19.5.1. Solving Linear Systems5 min

19.5.2. Homogeneous Systems2 min

19.5.3. Example3 min

19.5.4. Example5 min

19.5.5. Practice2 min

19.5.6. Practice5 min

19.6.1. Method of Inverse52 sec

19.6.2. Example4 min

19.6.3. Practice3 min

19.6.4. Practice2 min

19.6.5. Practice4 min

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