# Intermediate Algebra Help & Practice!

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##### 1Adding and Subtracting Integers

##### 2Multiplying and Dividing Integers

##### 3Operations with Decimals

##### 4Adding and Subtracting Fractions

##### 5Multiplying and Dividing Fractions

##### 6Introduction to Variables and Expressions

##### 7Coordinates, Quadrants, and Transformations

##### 8Number System

##### 9Set Theory

##### 10Solving Linear Equations

##### 11Introduction to Relations and Functions

##### 12Linear Functions

- 12.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 12.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 12.3Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 12.4Slope intercept form: y = mx + b
- 12.5General form: Ax + By + C = 0
- 12.6Point-slope form: $y - y_1 = m (x - x_1)$
- 12.7Rate of change
- 12.8Graphing linear functions using table of values
- 12.9Graphing linear functions using x- and y-intercepts
- 12.10Graphing from slope-intercept form y=mx+b
- 12.11Graphing linear functions using a single point and slope
- 12.12Word problems of graphing linear functions
- 12.13Parallel and perpendicular lines in linear functions
- 12.14Applications of linear relations

- 12.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 13Linear Equations

- 13.1Introduction to linear equations
- 13.2Introduction to nonlinear equations
- 13.3Special case of linear equations: Horizontal lines
- 13.4Special case of linear equations: Vertical lines
- 13.5Parallel line equation
- 13.6Perpendicular line equation
- 13.7Combination of both parallel and perpendicular line equations
- 13.8Applications of linear equations

- 13.1Introduction to linear equations
##### 14Absolute Value

##### 15Systems of Linear Equations

- 15.1Solving systems of linear equations by graphing
- 15.2Using elimination method to solve systems of equations
- 15.3Using substitution method to solve systems of equations
- 15.4Solving 3 variable systems of equations by substitution
- 15.5Solving 3 variable systems of equations by elimination
- 15.6Solving 3 variable systems of equations with no or infinite solutions
- 15.7Word problems relating 3 variable systems of equations
- 15.8Solving linear systems using Cramer's Rule
- 15.9Solving linear systems using 2 x 2 inverse matrices

- 15.1Solving systems of linear equations by graphing
##### 16Inequalities in One Variable

##### 17Inequalities in Two Variables

##### 18Functions

##### 19Exponents

- 19.1Exponents: Product rule
*(a^x)(a^y) = a^(x+y)* - 19.2Exponents: Division rule (a^x / a^y) = a^(x-y)
- 19.3Exponents: Power rule
*(a^x)^y = a^(x * y)* - 19.4Exponents: Negative exponents
- 19.5Exponents: Zero exponent:
*a^0 = 1* - 19.6Exponents: Rational exponents
- 19.7Solving exponential equations using exponent rules
- 19.8Scientific notation

- 19.1Exponents: Product rule
##### 20Operations with Polynomials

##### 21Factoring

##### 22Quadratic Functions

- 22.1Introduction to quadratic functions
- 22.2Transformations of quadratic functions
- 22.3Quadratic function in general form:
*y = ax^2 + bx + c* - 22.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 22.5Completing the square
- 22.6Converting from general to vertex form by completing the square
- 22.7Shortcut: Vertex formula
- 22.8Graphing quadratic functions: General form VS. Vertex form
- 22.9Finding the quadratic functions for given parabolas
- 22.10Applications of quadratic functions

- 22.1Introduction to quadratic functions
##### 23Solving Quadratic Equations

##### 24Radicals

##### 25Rational Expressions

- 25.1Simplifying rational expressions and restrictions
- 25.2Adding and subtracting rational expressions
- 25.3Multiplying rational expressions
- 25.4Dividing rational expressions
- 25.5Solving rational equations
- 25.6Applications of rational equations
- 25.7Simplifying complex fractions
- 25.8Partial fraction decomposition

- 25.1Simplifying rational expressions and restrictions
##### 26Polynomial Functions

- 26.1What is a polynomial function?
- 26.2Remainder theorem
- 26.3Factor theorem
- 26.4Rational zero theorem
- 26.5Characteristics of polynomial graphs
- 26.6Multiplicities of polynomials
- 26.7Imaginary zeros of polynomials
- 26.8Determining the equation of a polynomial function
- 26.9Applications of polynomial functions
- 26.10Solving polynomial inequalities
- 26.11Fundamental theorem of algebra
- 26.12Descartes' rule of signs

- 26.1What is a polynomial function?
##### 27Exponential Functions

##### 28Logarithmic Functions

- 28.1What is a logarithm?
- 28.2Converting from logarithmic form to exponential form
- 28.3Evaluating logarithms without a calculator
- 28.4Common logarithms
- 28.5Natural log: ln
- 28.6Evaluating logarithms using change-of-base formula
- 28.7Converting from exponential form to logarithmic form
- 28.8Solving exponential equations with logarithms
- 28.9Product rule of logarithms
- 28.10Quotient rule of logarithms
- 28.11Combining product rule and quotient rule in logarithms
- 28.12Evaluating logarithms using logarithm rules
- 28.13Solving logarithmic equations
- 28.14Graphing logarithmic functions
- 28.15Finding a logarithmic function given its graph

- 28.1What is a logarithm?
##### 29Conics

##### 30Imaginary and Complex Numbers

##### 31Sequences, Series, and Binomial Theorem