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Intermediate Algebra Topics

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

Midpoint formula:

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

Slope equation:

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

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

Point-slope form:

y - y_1 = m (x - x_1)

Rate of change

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Parallel and perpendicular lines in linear functions

Applications of linear relations

Linear Equations

Introduction to linear equations

Introduction to nonlinear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Applications of linear equations

Absolute Value

Absolute value functions

Solving absolute value equations

Solving absolute value inequalities

Systems of Linear Equations

Solving systems of linear equations by graphing

Using elimination method to solve systems of equations

Using substitution method to solve systems of equations

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

Solving 3 variable systems of equations with no or infinite solutions

Word problems relating 3 variable systems of equations

Solving linear systems using Cramer's Rule

Solving linear systems using 2 x 2 inverse matrices

Inequalities in One Variable

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

Solving multi-step linear inequalities

Compound inequalities

Solving quadratic inequalities

Inequalities in Two Variables

Graphing linear inequalities in two variables

Graphing systems of linear inequalities

What is linear programming?

Linear programming word problems

Functions

Exponents

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

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

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

Exponents: Negative exponents

Exponents: Zero exponent: a^0 = 1

Exponents: Rational exponents

Solving exponential equations using exponent rules

Scientific notation

Operations with Polynomials

Adding and subtracting polynomials

Multiplying monomial by monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Polynomial long division

Polynomial synthetic division

Factoring

Factor by taking out the greatest common factor

Factor by grouping

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

Factoring trinomials

Quadratic Functions

Introduction to quadratic functions

Transformations of quadratic functions

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

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

Completing the square

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Solving Quadratic Equations

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

Radicals

Square and square roots

Evaluating and simplifying radicals

Operations with radicals

Conversion between entire radicals and mixed radicals

Adding and subtracting radicals

Multiplying radicals

Rationalize the denominator

Solving radical equations

Rational Expressions

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Multiplying rational expressions

Dividing rational expressions

Solving rational equations

Applications of rational equations

Simplifying complex fractions

Partial fraction decomposition

Polynomial Functions

What is a polynomial function?

Remainder theorem

Factor theorem

Rational zero theorem

Characteristics of polynomial graphs

Multiplicities of polynomials

Imaginary zeros of polynomials

Determining the equation of a polynomial function

Applications of polynomial functions

Solving polynomial inequalities

Fundamental theorem of algebra

Descartes' rule of signs

Exponential Functions

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

Exponential growth and decay by percentage

Logarithmic Functions

What is a logarithm?

Converting from logarithmic form to exponential form

Evaluating logarithms without a calculator

Common logarithms

Natural log: ln

Evaluating logarithms using change-of-base formula

Converting from exponential form to logarithmic form

Solving exponential equations with logarithms

Product rule of logarithms

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Evaluating logarithms using logarithm rules

Solving logarithmic equations

Graphing logarithmic functions

Finding a logarithmic function given its graph

Conics

Imaginary and Complex Numbers

Introduction to imaginary numbers

Complex numbers and complex planes

Adding and subtracting complex numbers

Complex conjugates

Multiplying and dividing complex numbers

Sequences, Series, and Binomial Theorem

Infinite geometric series

Sigma notation

Binomial theorem

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