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Intermediate Algebra Topics

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1. Adding and Subtracting Integers

1.1

Introduction to integer addition

1.2

Adding integers

1.3

Introduction to integer subtraction

1.4

Subtracting integers

1.5

Application of integer operations

2. Multiplying and Dividing Integers

2.1

Understanding integer multiplication

2.2

Multiplying integers

2.3

Understanding integer division

2.4

Dividing integers

2.5

Applications of integer operations

3. Operations with Decimals

3.1

Adding and subtracting decimals

3.2

Multiplying decimals

3.3

Dividing decimals

3.4

Order of operations (BEDMAS)

4. Adding and Subtracting Fractions

4.1

Using models to add and subtract fractions

4.2

Adding fractions with like denominators

4.3

Subtracting fractions with like denominators

4.4

Adding and subtracting fractions with unlike denominators

4.5

Adding and subtracting mixed numbers

5. Multiplying and Dividing Fractions

5.1

Multiplying fractions and whole numbers

5.2

Dividing fractions with whole numbers

5.3

Multiplying proper fractions

5.4

Multiplying improper fractions and mixed numbers

5.5

Dividing fractions and mixed numbers

5.6

Applications of fraction operations

6. Introduction to Variables and Expressions

6.1

Evaluating algebraic expressions

7. Coordinates, Quadrants, and Transformations

7.1

Cartesian plane

7.2

Draw on coordinate planes

7.3

Introduction to transformations

7.4

Horizontal and vertical distances

8. Number System

8.1

Understanding the number systems

8.2

Prime factorization

8.3

Greatest Common Factors (GCF)

8.4

Least Common Multiple (LCM)

8.5

Rational vs. Irrational numbers

8.6

Converting repeating decimals to fractions

9. Set Theory

9.1

9.2

Set builder notation

9.3

Intersection and union of 2 sets

9.4

Intersection and union of 3 sets

10. Solving Linear Equations

10.1

Solving linear equations using multiplication and division

10.2

Solving two-step linear equations: ax + b = c, x/a + b = c

10.3

Solving linear equations using distributive property: a(x + b) = c

10.4

Solving linear equations with variables on both sides

10.5

Solving literal equations

11. Introduction to Relations and Functions

11.1

Relationship between two variables

11.2

Understand relations between x- and y-intercepts

11.3

Domain and range of a function

11.4

Identifying functions

11.5

Function notation

12. Linear Functions

12.1

Distance formula:

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

12.2

Midpoint formula:

M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)

12.3

Slope equation:

m = \frac{y_2-y_1}{x_2- x_1}

12.4

Slope intercept form: y = mx + b

12.5

General form: Ax + By + C = 0

12.6

Point-slope form:

y - y_1 = m (x - x_1)

12.7

12.8

Graphing linear functions using table of values

12.9

Graphing linear functions using x- and y-intercepts

12.10

Graphing from slope-intercept form y=mx+b

12.11

Graphing linear functions using a single point and slope

12.12

Word problems of graphing linear functions

12.13

Parallel and perpendicular lines in linear functions

12.14

Applications of linear relations

13. Linear Equations

13.1

Introduction to linear equations

13.2

Introduction to nonlinear equations

13.3

Special case of linear equations: Horizontal lines

13.4

Special case of linear equations: Vertical lines

13.5

Parallel line equation

13.6

Perpendicular line equation

13.7

Combination of both parallel and perpendicular line equations

13.8

Applications of linear equations

14. Absolute Value

14.1

Absolute value functions

14.2

Solving absolute value equations

14.3

Solving absolute value inequalities

15. Systems of Linear Equations

15.1

Solving systems of linear equations by graphing

15.2

Using elimination method to solve systems of equations

15.3

Using substitution method to solve systems of equations

15.4

Solving 3 variable systems of equations by substitution

15.5

Solving 3 variable systems of equations by elimination

15.6

Solving 3 variable systems of equations with no or infinite solutions

15.7

Word problems relating 3 variable systems of equations

15.8

Solving linear systems using Cramer's Rule

15.9

Solving linear systems using 2 x 2 inverse matrices

16. Inequalities in One Variable

16.1

Express linear inequalities graphically and algebraically

16.2

Solving one-step linear inequalities

16.3

Solving multi-step linear inequalities

16.4

Compound inequalities

16.5

Solving quadratic inequalities

17. Inequalities in Two Variables

17.1

Graphing linear inequalities in two variables

17.2

Graphing systems of linear inequalities

17.3

What is linear programming?

17.4

Linear programming word problems

18. Functions

18.1

Function notation

18.2

Composite functions

18.3

Inverse functions

18.4

Direct variation

19. Exponents

19.1

Exponents: Product rule (a^x)(a^y) = a^(x+y)

19.2

Exponents: Division rule (a^x / a^y) = a^(x-y)

19.3

Exponents: Power rule (a^x)^y = a^(x * y)

19.4

Exponents: Negative exponents

19.5

Exponents: Zero exponent: a^0 = 1

19.6

Exponents: Rational exponents

19.7

Solving exponential equations using exponent rules

19.8

Scientific notation

20. Operations with Polynomials

20.1

Adding and subtracting polynomials

20.2

Multiplying monomial by monomial

20.3

Multiplying monomial by binomial

20.4

Multiplying binomial by binomial

20.5

Multiplying polynomial by polynomial

20.6

Polynomial long division

20.7

Polynomial synthetic division

21. Factoring

21.1

Factor by taking out the greatest common factor

21.2

Factor by grouping

21.3

Factoring difference of squares: x^2 - y^2

21.4

Factoring trinomials

22. Quadratic Functions

22.1

Introduction to quadratic functions

22.2

Transformations of quadratic functions

22.3

Quadratic function in general form: y = ax^2 + bx + c

22.4

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

22.5

Completing the square

22.6

Converting from general to vertex form by completing the square

22.7

Shortcut: Vertex formula

22.8

Graphing quadratic functions: General form VS. Vertex form

22.9

Finding the quadratic functions for given parabolas

22.10

Applications of quadratic functions

23. Solving Quadratic Equations

23.1

Solving quadratic equations by factoring

23.2

Solving quadratic equations by completing the square

23.3

Using quadratic formula to solve quadratic equations

23.4

Nature of roots of quadratic equations: The discriminant

23.5

Applications of quadratic equations

24. Radicals

24.1

Square and square roots

24.2

Evaluating and simplifying radicals

24.3

Operations with radicals

24.4

Conversion between entire radicals and mixed radicals

24.5

Adding and subtracting radicals

24.6

Multiplying radicals

24.7

Rationalize the denominator

24.8

Solving radical equations

25. Rational Expressions

25.1

Simplifying rational expressions and restrictions

25.2

Adding and subtracting rational expressions

25.3

Multiplying rational expressions

25.4

Dividing rational expressions

25.5

Solving rational equations

25.6

Applications of rational equations

25.7

Simplifying complex fractions

25.8

Partial fraction decomposition

26. Polynomial Functions

26.1

What is a polynomial function?

26.2

Remainder theorem

26.3

26.4

Rational zero theorem

26.5

Characteristics of polynomial graphs

26.6

Multiplicities of polynomials

26.7

Imaginary zeros of polynomials

26.8

Determining the equation of a polynomial function

26.9

Applications of polynomial functions

26.10

Solving polynomial inequalities

26.11

Fundamental theorem of algebra

26.12

Descartes' rule of signs

27. Exponential Functions

27.1

Graphing exponential functions

27.2

Graphing transformations of exponential functions

27.3

Finding an exponential function given its graph

27.4

Exponential growth and decay by percentage

28. Logarithmic Functions

28.1

What is a logarithm?

28.2

Converting from logarithmic form to exponential form

28.3

Evaluating logarithms without a calculator

28.4

Common logarithms

28.5

Natural log: ln

28.6

Evaluating logarithms using change-of-base formula

28.7

Converting from exponential form to logarithmic form

28.8

Solving exponential equations with logarithms

28.9

Product rule of logarithms

28.10

Quotient rule of logarithms

28.11

Combining product rule and quotient rule in logarithms

28.12

Evaluating logarithms using logarithm rules

28.13

Solving logarithmic equations

28.14

Graphing logarithmic functions

28.15

Finding a logarithmic function given its graph

29. Conics

29.1

Conics - Parabola

29.2

Conics - Ellipse

29.3

Conics - Circle

29.4

Conics - Hyperbola

30. Imaginary and Complex Numbers

30.1

Introduction to imaginary numbers

30.2

Complex numbers and complex planes

30.3

Adding and subtracting complex numbers

30.4

Complex conjugates

30.5

Multiplying and dividing complex numbers

31. Sequences, Series, and Binomial Theorem

31.1

Arithmetic sequences

31.2

Arithmetic series

31.3

Geometric sequences

31.4

Geometric series

31.5

Infinite geometric series

31.6

31.7

Binomial theorem

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