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##### 1Basic Algebra

- 1.1Patterns
- 1.2Evaluating algebraic expressions
- 1.3Solving one - step equations:
*x + a = b* - 1.4Model and solve one-step linear equations:
*ax = b*,*x/a = b* - 1.5Solving two-step linear equations using addition and subtraction:
*ax + b = c* - 1.6Solving two-step linear equations using multiplication and division:
*x/a + b = c* - 1.7Solving two-step linear equations using distributive property:
*a(x + b) = c* - 1.8Solving literal equations

- 1.1Patterns
##### 2Exponents

- 2.1Introduction to Exponents
- 2.2Using exponents to describe numbers
- 2.3Exponent rules
- 2.4Order of operations with exponents
- 2.5Using exponents to solve problems
- 2.6Product rule of exponents
- 2.7Quotient rule of exponents
- 2.8Power of a product rule
- 2.9Power of a quotient rule
- 2.10Power of a power rule
- 2.11Negative exponent rule
- 2.12Combining the exponent rules
- 2.13Scientific notation
- 2.14Solving for exponents
- 2.15Exponents: Product rule
*(a^x)(a^y) = a^(x+y)* - 2.16Exponents: Division rule (a^x / a^y) = a^(x-y)
- 2.17Exponents: Power rule
*(a^x)^y = a^(x * y)* - 2.18Exponents: Negative exponents
- 2.19Exponents: Zero exponent:
*a^0 = 1* - 2.20Exponents: Rational exponents

- 2.1Introduction to Exponents
##### 3Radicals

- 3.1Squares and square roots
- 3.2Estimating square roots
- 3.3Square and square roots
- 3.4Cubic and cube roots
- 3.5Evaluating and simplifying radicals
- 3.6Converting radicals to mixed radicals
- 3.7Converting radicals to entire radicals
- 3.8Adding and subtracting radicals
- 3.9Multiplying and dividing radicals
- 3.10Rationalize the denominator
- 3.11Convert between radicals and rational exponents
- 3.12Operations with radicals
- 3.13Conversion between entire radicals and mixed radicals
- 3.14Adding and subtracting radicals (Advanced)
- 3.15Multiplying radicals (Advanced)

- 3.1Squares and square roots
##### 4Unit Conversion

##### 5Linear Equations

- 5.1Graphing linear relations
- 5.2Identifying proportional relationships
- 5.3Understanding graphs of linear relationships
- 5.4Understanding tables of values of linear relationships
- 5.5Applications of linear relationships
- 5.6Representing patterns in linear relations
- 5.7Reading linear relation graphs
- 5.8Solving linear equations by graphing
- 5.9Solving linear equations using multiplication and division
- 5.10Solving two-step linear equations:
*ax + b = c*,*x/a + b = c* - 5.11Solving linear equations using distributive property:
*a(x + b) = c* - 5.12Solving linear equations with variables on both sides
- 5.13Introduction to linear equations
- 5.14Introduction to nonlinear equations
- 5.15Special case of linear equations: Horizontal lines
- 5.16Special case of linear equations: Vertical lines
- 5.17Parallel line equation
- 5.18Perpendicular line equation
- 5.19Combination of both parallel and perpendicular line equations
- 5.20Applications of linear equations

- 5.1Graphing linear relations
##### 6Linear Functions

- 6.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 6.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 6.3Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 6.4Slope intercept form: y = mx + b
- 6.5General form: Ax + By + C = 0
- 6.6Point-slope form: $y - y_1 = m (x - x_1)$
- 6.7Rate of change
- 6.8Graphing linear functions using table of values
- 6.9Graphing linear functions using x- and y-intercepts
- 6.10Graphing linear functions using various forms
- 6.11Graphing linear functions using a single point and slope
- 6.12Word problems of graphing linear functions
- 6.13Parallel and perpendicular lines in linear functions
- 6.14Applications of linear relations

- 6.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 7Introduction to Polynomials

##### 8Operations with Polynomials

- 8.1Adding and subtracting polynomials
- 8.2Multiplying and dividing monomials
- 8.3Multiplying polynomials by monomials
- 8.4Dividing polynomials by monomials
- 8.5Multiplying monomial by monomial
- 8.6Multiplying monomial by binomial
- 8.7Multiplying binomial by binomial
- 8.8Multiplying polynomial by polynomial
- 8.9Applications of polynomials
- 8.10Solving polynomial equations
- 8.11Word problems of polynomials

- 8.1Adding and subtracting polynomials
##### 9Factoring Polynomials

- 9.1Common factors of polynomials
- 9.2Factoring polynomials by grouping
- 9.3Solving polynomials with unknown coefficients
- 9.4Solving polynomials with unknown constant terms
- 9.5Factoring polynomials:
*x^2 + bx + c* - 9.6Applications of polynomials:
*x^2 + bx + c* - 9.7Solving polynomials with the unknown "b" from $ax^2 + bx + c$
- 9.8Factoring polynomials: $ax^2 + bx + c$
- 9.9Factoring perfect square trinomials:
*(a + b)^2 = a^2 + 2ab + b^2*or*(a - b)^2 = a^2 - 2ab + b^2* - 9.10Find the difference of squares:
*(a - b)(a + b) = (a^2 - b^2)* - 9.11Factor by taking out the greatest common factor
- 9.12Factor by grouping
- 9.13Factoring difference of squares:
*x^2 - y^2* - 9.14Factoring trinomials
- 9.15Factoring difference of cubes
- 9.16Factoring sum of cubes

- 9.1Common factors of polynomials
##### 10Polynomial Functions

- 10.1What is a polynomial function?
- 10.2Polynomial long division
- 10.3Polynomial synthetic division
- 10.4Remainder theorem
- 10.5Factor theorem
- 10.6Rational zero theorem
- 10.7Characteristics of polynomial graphs
- 10.8Multiplicities of polynomials
- 10.9Imaginary zeros of polynomials
- 10.10Determining the equation of a polynomial function
- 10.11Applications of polynomial functions
- 10.12Fundamental theorem of algebra
- 10.13Pascal's triangle
- 10.14Binomial theorem
- 10.15Descartes' rule of signs

- 10.1What is a polynomial function?
##### 11Quadratic Functions

- 11.1Introduction to quadratic functions
- 11.2Transformations of quadratic functions
- 11.3Quadratic function in general form:
*y = ax^2 + bx + c* - 11.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 11.5Completing the square
- 11.6Converting from general to vertex form by completing the square
- 11.7Shortcut: Vertex formula
- 11.8Graphing parabolas for given quadratic functions
- 11.9Finding the quadratic functions for given parabolas
- 11.10Applications of quadratic functions

- 11.1Introduction to quadratic functions
##### 12Quadratic Equations

- 12.1Solving quadratic equations by factoring
- 12.2Solving quadratic equations by completing the square
- 12.3Solving quadratic equations using the quadratic formula
- 12.4Nature of roots of quadratic equations: The discriminant
- 12.5Solving polynomial equations by iteration
- 12.6Applications of quadratic equations

- 12.1Solving quadratic equations by factoring
##### 13System of Equations

- 13.1Determining number of solutions to linear equations
- 13.2Solving systems of linear equations by graphing
- 13.3Solving systems of linear equations by elimination
- 13.4Solving systems of linear equations by substitution
- 13.5Money related questions in linear equations
- 13.6Unknown number related questions in linear equations
- 13.7Distance and time related questions in linear equations
- 13.8Rectangular shape related questions in linear equations
- 13.9System of linear equations
- 13.10System of linear-quadratic equations
- 13.11System of quadratic-quadratic equations
- 13.12Solving 3 variable systems of equations by substitution
- 13.13Solving 3 variable systems of equations by elimination
- 13.14Solving 3 variable systems of equations with no or infinite solutions
- 13.15Word problems relating 3 variable systems of equations

- 13.1Determining number of solutions to linear equations
##### 14Inequalities

- 14.1Express linear inequalities graphically and algebraically
- 14.2Solving one-step linear inequalities
- 14.3Solving multi-step linear inequalities
- 14.4Compound inequalities
- 14.5Solving quadratic inequalities
- 14.6Inequalities of combined functions
- 14.7Solving polynomial inequalities
- 14.8Solving rational inequalities
- 14.9What is linear programming?
- 14.10Linear programming word problems

- 14.1Express linear inequalities graphically and algebraically
##### 15Inequalities in Two Variables

##### 16Absolute Value

##### 17Set Theory

##### 18Relations and Functions

- 18.1Relationship between two variables
- 18.2Understand relations between x- and y-intercepts
- 18.3Domain and range of a function
- 18.4Identifying functions
- 18.5Function notation
- 18.6Function notation (Advanced)
- 18.7Operations with functions
- 18.8Adding functions
- 18.9Subtracting functions
- 18.10Multiplying functions
- 18.11Dividing functions
- 18.12Composite functions
- 18.13Inverse functions
- 18.14One to one functions
- 18.15Difference quotient: applications of functions
- 18.16Transformations of functions: Horizontal translations
- 18.17Transformations of functions: Vertical translations
- 18.18Reflection across the y-axis:
*y = f(-x)* - 18.19Reflection across the x-axis:
*y = -f(x)* - 18.20Transformations of functions: Horizontal stretches
- 18.21Transformations of functions: Vertical stretches
- 18.22Combining transformations of functions
- 18.23Even and odd functions
- 18.24Direct variation
- 18.25Inverse variation
- 18.26Joint and combined variation

- 18.1Relationship between two variables
##### 19Rational Equations and Expressions

- 19.1Simplifying rational expressions and restrictions
- 19.2Adding and subtracting rational expressions
- 19.3Multiplying rational expressions
- 19.4Dividing rational expressions
- 19.5Solving rational equations
- 19.6Applications of rational equations
- 19.7Simplifying complex fractions
- 19.8Partial fraction decomposition

- 19.1Simplifying rational expressions and restrictions
##### 20Rational Functions

##### 21Radical Functions and Equations

##### 22Reciprocal Functions

##### 23Piecewise Functions

##### 24Exponential Functions

- 24.1Solving exponential equations using exponent rules
- 24.2Graphing exponential functions
- 24.3Graphing transformations of exponential functions
- 24.4Finding an exponential function given its graph
- 24.5Exponential growth and decay by a factor
- 24.6Exponential decay: Half-life
- 24.7Exponential growth and decay by percentage
- 24.8Finance: Compound interest
- 24.9Continuous growth and decay
- 24.10Finance: Future value and present value

- 24.1Solving exponential equations using exponent rules
##### 25Logarithm

- 25.1What is a logarithm?
- 25.2Converting from logarithmic form to exponential form
- 25.3Evaluating logarithms without a calculator
- 25.4Common logarithms
- 25.5Natural log: ln
- 25.6Evaluating logarithms using change-of-base formula
- 25.7Converting from exponential form to logarithmic form
- 25.8Solving exponential equations with logarithms
- 25.9Product rule of logarithms
- 25.10Quotient rule of logarithms
- 25.11Combining product rule and quotient rule in logarithms
- 25.12Evaluating logarithms using logarithm rules
- 25.13Solving logarithmic equations
- 25.14Graphing logarithmic functions
- 25.15Finding a logarithmic function given its graph
- 25.16Logarithmic scale: Richter scale (earthquake)
- 25.17Logarithmic scale: pH scale
- 25.18Logarithmic scale: dB scale

- 25.1What is a logarithm?
##### 26Sequences and Series

##### 27Conic Sections

##### 28Complex Numbers

- 28.1Introduction to imaginary numbers
- 28.2Complex numbers and complex planes
- 28.3Adding and subtracting complex numbers
- 28.4Complex conjugates
- 28.5Multiplying and dividing complex numbers
- 28.6Distance and midpoint of complex numbers
- 28.7Angle and absolute value of complex numbers
- 28.8Polar form of complex numbers
- 28.9Operations on complex numbers in polar form

- 28.1Introduction to imaginary numbers
##### 29Vectors

##### 30Matrices

- 30.1Notation of matrices
- 30.2Adding and subtracting matrices
- 30.3Scalar multiplication
- 30.4Matrix multiplication
- 30.5The three types of matrix row operations
- 30.6Representing a linear system as a matrix
- 30.7Solving a linear system with matrices using Gaussian elimination
- 30.8Zero matrix
- 30.9Identity matrix
- 30.10Properties of matrix addition
- 30.11Properties of scalar multiplication
- 30.12Properties of matrix multiplication
- 30.13The determinant of a 2 x 2 matrix
- 30.14The determinant of a 3 x 3 matrix (General & Shortcut Method)
- 30.15The inverse of a 2 x 2 matrix
- 30.16The inverse of 3 x 3 matrices with matrix row operations
- 30.17The inverse of 3 x 3 matrix with determinants and adjugate
- 30.182 x 2 invertible matrix
- 30.19Solving linear systems using Cramer's Rule
- 30.20Solving linear systems using 2 x 2 inverse matrices
- 30.21Transforming vectors with matrices
- 30.22Transforming shapes with matrices
- 30.23Finding the transformation matrix

- 30.1Notation of matrices