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Algebra Topics

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Basic Algebra

–Patterns
–Evaluating algebraic expressions
–Model and solve one-step linear equations: ax=bax = b, xa=b\frac{x}{a} = b (free lessons)
–Solving two-step linear equations using addition and subtraction: ax+b=cax + b = c
–Solving two-step linear equations using multiplication and division: xa+b=c\frac{x}{a} + b = c
–Solving two-step linear equations using distributive property: a(x+b)=c\;a\left( {x + b} \right) = c
–Solving literal equations

Exponents

–Introduction to Exponents
–Using exponents to describe numbers (free lessons)
–Exponent rules
–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 (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
–Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
–Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
–Exponents: Negative exponents
–Exponents: Zero exponent: a0=1 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 (Advanced) (free lessons)
–Multiplying radicals (Advanced)

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=cax + b = c, xa+b=c{x \over a} + b = c
–Solving linear equations using distributive property: a(x+b)=ca(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=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
–Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
–Slope equation: m=y2−y1x2−x1m = \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−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
–Rate of change
–Graphing linear functions using table of values
–Graphing linear functions using x- and y-intercepts (free lessons)
–Graphing linear functions using various forms
–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: x2+bx+cx^2 + bx + c (free lessons)
–Applications of polynomials: x2+bx+cx^2 + bx + c
–Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + c
–Factoring polynomials: ax2+bx+cax^2 + bx + c
–Factoring perfect square trinomials: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2 or (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2 (free lessons)
–Find the difference of squares: (a−b)(a+b)=(a2−b2)(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: x2−y2x^2 - y^2
–Factoring trinomials
–Factoring difference of cubes
–Factoring sum of cubes

Polynomial Functions

–What is a polynomial function? (free lessons)
–Polynomial long division (free lessons)
–Polynomial synthetic division
–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
–Fundamental theorem of algebra
–Pascal's triangle
–Binomial theorem

Quadratic Functions

–Introduction to quadratic functions (free lessons)
–Transformations of quadratic functions
–Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
–Quadratic function in vertex form: y = a(x−p)2+qa(x-p)^2 + q
–Completing the square
–Converting from general to vertex form by completing the square
–Shortcut: Vertex formula (free lessons)
–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
–Solving quadratic equations using the quadratic formula
–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
–Solving multi-step linear inequalities
–Solving quadratic inequalities
–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
–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)y = f(-x) (free lessons)
–Reflection across the x-axis: y=−f(x)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
–Solving rational equations

Radical Functions and Equations

–Basic radical functions
–Transformations of radical functions
–Square root of a function
–Solving radical equations

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
–Sigma notation
–Arithmetic mean vs. Geometric mean

Conic Sections

–Conics - Parabola
–Conics - Ellipse
–Conics - Circle
–Conics - Hyperbola

Complex Numbers

–Introduction to imaginary numbers
–Complex numbers and complex planes
–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
–Equivalent vectors
–Adding and subtracting vectors in component form
–Operations on vectors in magnitude and direction form

Matrices

–Notation of matrices
–Adding and subtracting matrices
–Multiplying a matrix by a scalar
–Multiplying a matrix by another matrix
–The three types of matrix row operations
–Representing a linear system as a matrix
–Solving a linear system with matrices using Gaussian elimination
–Zero matrix
–Identity matrix
–Properties of matrix addition
–Scalar multiplication
–Matrix multiplication
–The determinant of a 2 x 2 matrix
–The determinant of a 3 x 3 matrix (General & Shortcut Method)
–The inverse of a 2 x 2 matrix
–The inverse of 3 x 3 matrices with matrix row operations
–The inverse of 3 x 3 matrix with determinants and adjugate
–2 x 2 invertible matrix
–Solving linear systems using Cramer's Rule
–Solving linear systems using 2 x 2 inverse matrices
–Transforming vectors with matrices
–Transforming shapes with matrices
–Finding the transformation matrix
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