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Algebra Topics

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Basic Algebra

Evaluating algebraic expressions

Model and solve one-step linear equations:

ax = b

\frac{x}{a} = b

(free lessons)

Solving two-step linear equations using addition and subtraction:

ax + b = c

Solving two-step linear equations using multiplication and division:

\frac{x}{a} + b = c

Solving two-step linear equations using distributive property:

\;a\left( {x + b} \right) = c

Solving literal equations

Exponents

Introduction to exponents

Using exponents to describe numbers (free lessons)

Order of operations with exponents

Using exponents to solve problems

Product rule of exponents (free lessons)

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule (free lessons)

Negative exponent rule

Combining the exponent rules

Scientific notation

Solving for exponents

Exponents: Product rule

(a^x)(a^y)=a^{(x+y)}

(free lessons)

Exponents: division rule

{a^x \over a^y}=a^{(x-y)}

Exponents: Power rule

(a^x)^y = a^{(x \cdot y)}

(free lessons)

Exponents: Negative exponents

Exponents: Zero exponent:

a^0 = 1

Exponents: Rational exponents

Radicals

Squares and square roots (free lessons)

Estimating square roots (free lessons)

Square and square roots (free lessons)

Cubic and cube roots

Evaluating and simplifying radicals

Converting radicals to mixed radicals

Converting radicals to entire radicals (free lessons)

Adding and subtracting radicals

Multiplying and dividing radicals

Rationalize the denominator

Convert between radicals and rational exponents (free lessons)

Operations with radicals (free lessons)

Conversion between entire radicals and mixed radicals

Adding and subtracting radicals (free lessons)

Multiplying radicals

Unit Conversion

Metric systems (free lessons)

Imperial systems

Conversions between metric and imperial systems

Conversions involve squares and cubic

Linear Equations

Understanding graphs of linear relationships (free lessons)

Understanding tables of values of linear relationships

Applications of linear relationships (free lessons)

Representing patterns in linear relations

Reading linear relation graphs

Solving linear equations by graphing

Solving linear equations using multiplication and division (free lessons)

Solving two-step linear equations:

ax + b = c

{x \over a} + b = c

Solving linear equations using distributive property:

a(x + b) = c

(free lessons)

Solving linear equations with variables on both sides

Introduction to linear equations (free lessons)

Introduction to nonlinear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel line equation (free lessons)

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Applications of linear equations

Linear Functions

Distance formula:

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

(free lessons)

Midpoint formula:

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

(free lessons)

Slope equation:

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

Slope intercept form: y = mx + b (free lessons)

General form: Ax + By + C = 0 (free lessons)

Point-slope form:

y - y_1 = m (x - x_1)

(free lessons)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts (free lessons)

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 (free lessons)

Applications of linear relations

Introduction to Polynomials

Characteristics of polynomials (free lessons)

Equivalent expressions of polynomials

What is a polynomial? (free lessons)

Polynomial components

Evaluating polynomials

Using algebra tiles to solve polynomials

Operations with Polynomials

Adding and subtracting polynomials

Multiplying and dividing monomials (free lessons)

Multiplying polynomials by monomials

Dividing polynomials by monomials

Multiplying monomial by monomial

Multiplying monomial by binomial

Multiplying binomial by binomial (free lessons)

Multiplying polynomial by polynomial

Applications of polynomials

Solving polynomial equations (free lessons)

Word problems of polynomials

Factoring Polynomials

Common factors of polynomials (free lessons)

Factoring polynomials by grouping

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

Factoring polynomials:

x^2 + bx + c

(free lessons)

Applications of polynomials:

x^2 + bx + c

Solving polynomials with the unknown "b" from

{ax^2+bx+c}

Factoring polynomials:

ax^2 + bx + c

Factoring perfect square trinomials:

(a + b)^2 = a^2 + 2ab + b^2

(a - b)^2 = a^2 - 2ab + b^2

(free lessons)

Find the difference of squares:

(a - b)(a + b) = (a^2 - b^2)

Factor by taking out the greatest common factor (free lessons)

Factor by grouping

Factoring difference of squares:

x^2 - y^2

Factoring trinomials

Factoring difference of cubes

Factoring sum of cubes

Polynomial Functions

Polynomial functions (free lessons)

Polynomial long division (free lessons)

Polynomial synthetic division

Remainder 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

Fundamental theorem of algebra

Pascal's triangle

Binomial theorem

Descartes’ rule of signs

Quadratic Functions

Characteristics of quadratic functions (free lessons)

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 (free lessons)

Converting from general to vertex form by completing the square

Shortcut: Vertex formula (free lessons)

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas (free lessons)

Applications of quadratic functions

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

System of Equations

Determining number of solutions to linear equations (free lessons)

Solving systems of linear equations by graphing

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

Money related questions in linear equations (free lessons)

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

System of linear equations

System of linear-quadratic equations (free lessons)

System of quadratic-quadratic equations

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

Solving 3 variable systems of equations (no solution, infinite solutions)

Word problems relating 3 variable systems of equations

Inequalities

Express linear inequalities graphically and algebraically (free lessons)

Solving one-step linear inequalities (free lessons)

Solving multi-step linear inequalities (free lessons)

Solving quadratic inequalities

Inequalities of combined functions

Solving polynomial inequalities

Solving rational inequalities

What is linear programming?

Linear programming word problems

Inequalities in Two Variables

Graphing linear inequalities in two variables (free lessons)

Graphing systems of linear inequalities (free lessons)

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Applications of inequalities

Absolute Value

Absolute value functions (free lessons)

Solving absolute value equations

Solving absolute value inequalities

Set Theory

Set builder notation

Relations and Functions

Relationship between two variables (free lessons)

Understand relations between x- and y-intercepts

Domain and range of a function (free lessons)

Identifying functions

Function notation (free lessons)

Function notation (advanced) (free lessons)

Operations with functions

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Composite functions (free lessons)

Inverse functions (free lessons)

One to one functions

Difference quotient: applications of functions

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis:

y = f(-x)

(free lessons)

Reflection across the x-axis:

y = -f(x)

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Combining transformations of functions

Even and odd functions

Rational Equations and Expressions

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions (free lessons)

Multiplying rational expressions

Dividing rational expressions

Solving rational equations

Applications of rational equations

Simplifying complex fractions

Partial fraction decomposition

Rational Functions

What is a rational function? (free lessons)

Point of discontinuity

Vertical asymptote

Horizontal asymptote

Slant asymptote

Graphs of rational functions

Radical Functions and Equations

Basic radical functions

Radical functions and transformations

Square root of a function

Solving radical equations

Piecewise Functions

Evaluating piecewise functions

Graphing piecewise linear functions

Graphing piecewise non-linear functions

Exponential Functions

Solving exponential equations using exponent rules

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

Exponential growth and decay by a factor

Exponential decay: Half-life (free lessons)

Exponential growth and decay by percentage

Finance: Compound interest

Continuous growth and decay

Finance: Future value and present value

Logarithm

What is a logarithm?

Converting from logarithmic form to exponential form (free lessons)

Evaluating logarithms without a calculator

Common logarithms

Natural log: ln

Evaluating logarithms using change-of-base formula

Converting from exponential form to logarithmic form (free lessons)

Solving exponential equations with logarithms

Product rule of logarithms (free lessons)

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Evaluating logarithms using logarithm rules

Solving logarithmic equations (free lessons)

Graphing logarithmic functions

Finding a logarithmic function given its graph

Logarithmic scale: Richter scale (earthquake)

Logarithmic scale: pH scale

Logarithmic scale: dB scale

Sequences and Series

Arithmetic sequences (free lessons)

Arithmetic series (free lessons)

Geometric sequences

Geometric series

Infinite geometric series

Arithmetic mean vs. Geometric mean

Conic Sections

Conics - Parabola

Conics - Ellipse

Conics - Circle

Conics - Hyperbola

Complex Numbers

Introduction to imaginary numbers (free lessons)

Complex numbers and complex planes (free lessons)

Adding and subtracting complex numbers

Complex conjugates

Multiplying and dividing complex numbers

Distance and midpoint of complex numbers

Angle and absolute value of complex numbers

Polar form of complex numbers

Operations on complex numbers in polar form

Vectors

Introduction to vectors

Magnitude of a vector

Direction angle of a vector

Scalar multiplication of vectors

Equivalent vectors

Adding and subtracting vectors in component form

Operations on vectors in magnitude and direction form

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