Intermediate Algebra That Makes sense

Introduction to integer addition

Adding integers

Introduction to integer subtraction

Subtracting integers

Application of integer operations

Understanding integer multiplication

Multiplying integers

Understanding integer division

Dividing integers

Applications of integer operations

Adding and subtracting decimals

Multiplying decimals

Dividing decimals

Order of operations (BEDMAS)

Using models to add and subtract fractions

Adding fractions with like denominators

Subtracting fractions with like denominators

Adding and subtracting fractions with unlike denominators

Adding and subtracting mixed numbers

Multiplying fractions and whole numbers

Dividing fractions with whole numbers

Multiplying proper fractions

Multiplying improper fractions and mixed numbers

Dividing fractions and mixed numbers

Applications of fraction operations

Evaluating algebraic expressions

Cartesian plane

Draw on coordinate planes

Introduction to transformations

Horizontal and vertical distances

Understanding the number systems

Prime factorization

Greatest Common Factors (GCF)

Least Common Multiple (LCM)

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Set notation

Set builder notation

Intersection and union of 2 sets

Intersection and union of 3 sets

Solving linear equations using multiplication and division

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

Solving linear equations using distributive property: <i>a(x + b) = c</i>

Solving linear equations with variables on both sides

Solving literal equations

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

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

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: \(y - y_1 = m (x - x_1)\)

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

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

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 functions

Solving absolute value equations

Solving absolute value inequalities

Solving systems of linear equations by graphing

Using elimination method to solve systems of equations

Using substitution method to solve systems of equations

Solving linear systems using Cramer's Rule

Solving linear systems using 2 x 2 inverse matrices

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

Word problems relating 3 variable systems of equations

Solving 3 variable systems of equations with no or infinite solutions

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

Solving multi-step linear inequalities

Solving quadratic inequalities

Compound inequalities

Graphing linear inequalities in two variables

Graphing systems of linear inequalities

What is linear programming?

Linear programming word problems

Function notation

Composite functions

Inverse functions

Direct variation

Scientific notation

Exponents: Product rule <i>(a^x)(a^y) = a^(x+y)</i>

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

Exponents: Power rule <i>(a^x)^y = a^(x * y)</i>

Exponents: Negative exponents

Exponents: Zero exponent: <i>a^0 = 1</i>

Exponents: Rational exponents

Solving exponential equations using exponent rules

Multiplying monomial by monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Polynomial long division

Polynomial synthetic division

Adding and subtracting polynomials

Factor by taking out the greatest common factor

Factor by grouping

Factoring difference of squares: <i>x^2 - y^2</i>

Factoring trinomials

Introduction to quadratic functions

Transformations of quadratic functions

Quadratic function in general form: <i>y = ax^2 + bx + c</i>

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

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

Completing the square

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

Square and square roots

Rationalize the denominator

Solving radical equations

Conversion between entire radicals and mixed radicals

Adding and subtracting radicals

Multiplying radicals

Operations with radicals

Evaluating and simplifying radicals

Solving rational equations

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Multiplying rational expressions

Dividing rational expressions

Applications of rational equations

Simplifying complex fractions

Partial fraction decomposition

What is a polynomial function?

Remainder theorem

Factor theorem

Rational zero theorem

Characteristics of polynomial graphs

Determining the equation of a polynomial function

Applications of polynomial functions

Multiplicities of polynomials

Imaginary zeros of polynomials

Solving polynomial inequalities

Fundamental theorem of algebra

Descartes&apos; rule of signs

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

Exponential growth and decay by percentage

Solving logarithmic equations

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

Graphing logarithmic functions

Finding a logarithmic function given its graph

Conics - Parabola

Conics - Circle

Conics - Ellipse

Conics - Hyperbola

Introduction to imaginary numbers

Complex numbers and complex planes

Adding and subtracting complex numbers

Complex conjugates

Multiplying and dividing complex numbers

Binomial theorem

Arithmetic sequences

Arithmetic series

Geometric sequences

Geometric series

Infinite geometric series

Sigma notation