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Algebra 2 Topics

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1. Linear Equations

1.1

Introduction to linear equations

1.2

Applications of linear equations

1.3

Solving absolute value equations

2. Inequalities

2.1

Graphing linear inequalities in two variables

2.2

Graphing quadratic inequalities in two variables

2.3

Solving absolute value inequalities

2.4

Graphing systems of quadratic inequalities

3. Functions

3.1

Identifying functions

3.2

Domain and range of a function

3.3

Function notation

3.4

Slope intercept form: y = mx + b

3.5

Graphing from slope-intercept form y=mx+b

3.6

Application of linear relations

4. Systems of Equations

4.1

Determining number of solutions to linear equations

4.2

Solving systems of linear equations by graphing

4.3

Using elimination method to solve systems of equations

4.4

Using substitution method to solve systems of equations

4.5

Money related questions in linear equations

4.6

Unknown number related questions in linear equations

4.7

Distance and time related questions in linear equations

4.8

Rectangular shape related questions in linear equations

4.9

System of quadratic-quadratic equations

4.10

Solving 3 variable systems of equations by substitution

4.11

Solving 3 variable systems of equations by elimination

4.12

Solving 3 variable systems of equations with no solution, infinite solutions

4.13

Word problems relating 3 variable systems of equations

5. Systems of Inequalities

5.1

What is linear programming?

5.2

Linear programming word problems

6. Complex Numbers

6.1

Introduction to imaginary numbers

6.2

Complex numbers and complex planes

6.3

Adding and subtracting complex numbers

6.4

Complex conjugates

6.5

Multiplying and dividing complex numbers

6.6

Distance and midpoint of complex numbers

6.7

Angle and absolute value of complex numbers

7. Factoring

7.1

Multiplying monomial by monomial

7.2

Factoring polynomials by grouping

7.3

Factor by taking out the greatest common factor

7.4

Factor by grouping

7.5

7.6

Factoring difference of cubes

7.7

Factoring sum of cubes

8. Quadratic Functions

8.1

Characteristics of quadratic functions

8.2

Solving quadratic equations by factoring

8.3

Solving quadratic equations by completing the square

8.4

Using quadratic formula to solve quadratic equations

8.5

Nature of roots of quadratic equations: the discriminant

9. Polynomials

9.1

Characteristics of polynomials

9.2

Adding and subtracting polynomials

9.3

Multiplying polynomial by polynomial

9.4

Polynomial long division

9.5

Polynomial synthetic division

9.6

Remainder theorem

9.7

Rational zeroes theorem

9.8

Characteristics of polynomial graphs

9.9

Repeated factors (Multiplicities) in polynomials

9.10

Imaginary zeros of polynomials

9.11

Determining the equation of a polynomial function

9.12

Pascal's triangle

9.13

Binomial theorem

9.14

What is a polynomial function?

9.15

Applications of polynomial functions

9.16

Solving polynomial inequalities

9.17

Fundamental theorem of algebra

9.18

Descartes' rule of signs

10. Radical Functions and Expressions

10.1

Squares and Square Roots

10.2

Cubic and Cube Roots

10.3

Evaluating and simplifying radicals

10.4

Multiplying and dividing radicals

10.5

Adding and subtracting radicals

10.6

Rationalize the denominator

10.7

Basic radical functions

10.8

Transformations of radical functions

10.9

Solving radical equations

10.10

Operations with radicals

10.11

Conversion between entire radicals and mixed radicals

10.12

Adding and subtracting radicals

10.13

Multiplying radicals (advanced)

11. Rational Exponents

11.1

Power of a power rule

11.2

Rational exponents

12. Rational Functions and Expressions

12.1

Quotient rule of exponents

12.2

Power of a product rule

12.3

Power of a quotient rule

12.4

Negative exponent rule

12.5

What is a rational function?

12.6

Point of discontinuity

12.7

Vertical asymptote

12.8

Horizontal asymptote

12.9

Slant asymptote

12.10

Solving rational equations

12.11

Solving rational inequalities

12.12

Simplifying rational expressions and restrictions

12.13

Adding and subtracting rational expressions

12.14

Multiplying rational expressions

12.15

Dividing rational expressions

12.16

Applications of rational equations

12.17

Simplifying complex fractions

12.18

Partial fraction decomposition

13. Reciprocal Functions

13.1

Graphing reciprocals of linear functions

13.2

Graphing reciprocals of quadratic functions

14. Function Operations

14.1

Inverse functions

14.2

System of linear-quadratic equations

15. Families of Functions

15.1

Transformations of functions: Horizontal translations

15.2

Transformations of functions: Vertical translations

15.3

Reflection across the y-axis: y = f(-x)

15.4

Reflection across the x-axis: y = -f(x)

15.5

Horizontal stretches in transformations

15.6

Vertical stretches in transformations

15.7

Combining transformations of functions

15.8

Even and odd functions

16. Variation

16.1

Direct variation

17. Piecewise Functions

17.1

Evaluating piecewise functions

17.2

Graphing piecewise linear functions

17.3

Graphing piecewise non-linear functions

18. Logarithms

18.1

What is a logarithm?

18.2

Converting from logarithmic form to exponential form

18.3

Evaluating logarithms without a calculator

18.4

Common logarithms

18.5

Evaluating logarithms using change-of-base formula

18.6

Natural log: ln

18.7

Converting from exponential form to logarithmic form

18.8

Product law of logarithms

18.9

Solving logarithmic equations

18.10

Logarithmic scale: Richter scale (earthquake)

18.11

Logarithmic scale: pH scale

18.12

Logarithmic scale: dB scale

18.13

Finance: Future value and present value

19. Exponential and Logarithmic Functions

19.1

Graphing exponential functions

19.2

Graphing transformations of exponential functions

19.3

Finding an exponential function given its graph

19.4

Graphing logarithmic functions

19.5

Finding a logarithmic function given its graph

19.6

Finance: compound interest

19.7

Continuous growth and decay

19.8

Solving exponential equations with logarithms

20. Angle Measures

20.1

Converting between degrees and radians

20.2

Angle in standard position

20.3

Coterminal angles

20.4

Reference angle

21. Trigonometry

21.1

Solving first degree trigonometric equations

21.2

Determining non-permissible values for trig expressions

21.3

Solving second degree trigonometric equations

21.4

Solving expressions using 45-45-90 special right triangles

21.5

Solving expressions using 30-60-90 special right triangles

21.6

Find the exact value of trigonometric ratios

21.7

ASTC rule in trigonometry (All Students Take Calculus)

21.8

Solving trigonometric equations involving multiple angles

21.9

Solving trigonometric equations using pythagorean identities

21.10

Solving trigonometric equations using sum and difference identities

21.11

Solving trigonometric equations using double-angle identities

21.12

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

21.13

Using cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

21.14

Use tangent ratio to calculate angles and sides (Tan =

\frac{o}{a}

21.15

Combination of SohCahToa questions

21.16

Pythagorean theorem

21.17

21.18

21.19

21.20

Word problems relating ladder in trigonometry

21.21

Word problems relating guy wire in trigonometry

21.22

Other word problems relating angles in trigonometry

22. Bearings

22.1

Introduction to bearings

22.2

Bearings and direction word problems

22.3

Angle of elevation and depression

23. Graphing Trigonometric Functions

23.1

Sine graph: y = sin x

23.2

Cosine graph: y = cos x

23.3

Tangent graph: y = tan x

23.4

Cotangent graph: y = cot x

23.5

Secant graph: y = sec x

23.6

Cosecant graph: y = csc x

23.7

Graphing transformations of trigonometric functions

23.8

Determining trigonometric functions given their graphs

24. Trigonometric Identities

24.1

Quotient identities and reciprocal identities

24.2

Sum and difference identities

24.3

Pythagorean identities

24.4

Double-angle identities

25. Sequences and Series

25.1

Arithmetic sequences

25.2

Geometric sequences

25.3

Arithmetic series

25.4

Infinite geometric series

25.5

Geometric series

25.6

26. Probability

26.1

Fundamental counting principle

26.2

26.3

Path counting problems

26.4

Permutation vs. Combination

26.5

26.6

26.7

Probability of independent events

26.8

Probability with Venn diagrams

27. Statistics

27.1

Influencing factors on data collection

27.2

Median and mode

27.3

27.4

Range and outliers

27.5

Application of averages

28. Parabolas

28.1

Introduction to quadratic functions

28.2

Quadratic function in general form: y =

ax^2 + bx+c

28.3

Quadratic function in vertex form: y = a(x-p)^2 + q

28.4

Converting from general form to vertex form by completing the square

28.5

Graphing parabolas for given quadratic functions

28.6

Finding the quadratic functions for given parabolas

29. Introduction to Conic Sections

29.1

Conics - Circle

29.2

Conics - Parabola

30. Introduction to Matrices

30.1

Notation of matrices

30.2

Adding and subtracting matrices

30.3

Scalar multiplication

30.4

Matrix multiplication

30.5

The three types of matrix row operations

31. Properties of Matrices

31.1

31.2

Identity Matrix

31.3

Properties of matrix addition

31.4

Properties of scalar multiplication

31.5

Properties of matrix multiplication

32. Determinants and Inverses of Matrices

32.1

The determinant of a 2 x 2 matrix

32.2

The determinant of a 3 x 3 matrix (General & Shortcut Method)

32.3

The inverse of a 2 x 2 matrix

32.4

The inverse of 3 x 3 matrices with matrix row operations

32.5

The inverse of 3 x 3 matrix with determinants and adjugate

32.6

2 x 2 invertible matrix

32.7

Solving linear systems using Cramer's Rule

32.8

Solving linear systems using 2 x 2 inverse matrices

33. Transformations with Matrices

33.1

Transforming vectors with matrices

33.2

Transforming shapes with matrices

33.3

Finding the transformation matrix

33Chapters

224Topics

1377Videos

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