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Pre-algebra
Arithmetics
Comparing whole numbers
Addition
Subtraction
Multiplication
Division
Order of operations
Integers
Opposite and absolute value
Addition
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Multiplication
Division
Order of operations
LCM and GCF
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Prime numbers
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Prime factorization
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LCM
Decimals
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Identify fractions
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Power of a power
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Calculate the % of a number
Determine the %
Percentage increases
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Calculate the inital capital
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Proportional reasoning
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Mixture problems
Uniform motion problems
Equal shares
Radical expressions
Adding and subtracting
Rationalizing
Radical equation
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Plotting points and naming quadrants
Definition of slope
Positive or negative slope
Algebra
Monomials
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Multiplication
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Polynomials
Polynomial Vocabulary
Addition
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Multiplication (FOIL)
Multiplication
Special products
Long division
Synthetic division
Remainder theorem
Roots and factors
Polynomial Function
Factoring
Factoring
Factoring Trinomials a=1
Factoring trinomials a not equal to 1
Difference of Perfect Squares
Perfect Trinomial Squares
Factoring by grouping
Factoring the Sum or Difference of Cubes
Factoring Complicated Expressions
Solving equations by Factoring
Linear Equations
Solving equations
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Radical equations
Word problems
Mixture problems
Time and distance problems
Equal shares
Graphs of linear equations
Rectangular Coordinate System
Midpoint Formula
Definition of Slope
Positive and negative slope
Determine the slope of a line
Equations of lines
Slope-Intercept Form
Point-Slope Form
Standard Form
Equation of lines (from graph)
Applications of linear equations
Inequalities
Linear inequalities
Multistep inequalities I
Multistep inequalities II
Quadratic equations
Quadratic formula
Solve factoring
Solve completing the square
Incomplete quadratic equation
The discriminant
Applications
Quadratic function
Equations in quadratic form
Graphs of quadratic equations
Exploring Quadratic Graphs
Graphing Quadratic Equations
Using a table to graph a Quadratic Equation
Vertical and Horizontal Shifts of Quadratic Graphs
Vertical Stretching and Shrinking of Quadratic Graphs
Vertex and Intercepts of a Quadratic Graph
Applications
Absolute Value
Definition
Absolute Value Equations
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Absolute Value Graphs
Radical expressions
Adding and subtracting
Rationalizing
Radical equations
Exponential equations
Logarithmic equations
System of equations
Introduction
Substitution
Elimination
Graphing
Using the augmented matrix
Using the inverse matrix
Word problems
System of 3 variables
Graphs and functions
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Interpreting Graphs
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Function Notation
Writing a Linear Equation from a Table
Writing a Linear Equation to describe a Graph
Direct Variation
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Domain and range
Definitions
Polynomial function
Rational function
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Trigonometric function I
Trigonometric function II
Trigonometric function III
Sequences and series
Introduction to sequences
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Arithmetic sequences
Arithmetic series
Geometric sequences
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Recursion Sequence
Matrices
Concept of matrix
Definitions
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Multiplication properties
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Solve linear systems (augmented matrix)
Solve linear system (inverse matrix method)
Matrix equations
Inverse of a matrix
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Geometry
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Isosceles Triangle
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SSS and SAS
ASA and AAS
HL
CPCTC
Isosceles Triangle Property
Polygons
Interior Angles Sum
Equiangular Polygon Sums
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Kite Properties
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Parallelogram Properties
Rhombus Properties
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2-D Shapes
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Rectangle
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Kyte and Rhombus
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Regions between circles and squares
Surface area of Prisms
Surface area of Cylinders
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Surface area of a Cone
Surface area of Joined Solids
Volume
Volume of prisms
Volume of pyramids
Volume of cylinders
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Pythagorean Theorem
Pythagorean theorem
Proofs
Solve right angles (find hypotenuse)
Solve right angles (find missing legs)
Word problems
Space Diagonals
Converse of the Pythagorean Theorem
Pythagorean Triples
45-45-90 Triangles
Angles
Building Blocks
Point, Line and Plane
Line segment and ray
Congruent segments and midpoints
Midpoint
Parallel and skew lines
Parallel lines and planes
Angles
Complementary and supplementary angles
Using a protractor
Angle bisector
Polygons
Regular polygons
Concave and convex polygon
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Vertex and diagonal
Perimeter
Parts of a circle
Concentric circles
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Geometry Transformations
Transformations and Isometries
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Reflections
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Symmetry
- Reflectional symmetry
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Enlargements (Dilations)
Parallel, coincident and intersepting lines
Distances in the plane
Between two points
From a point to a line
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Lines in space
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Intersection 2 lines
Plane in space
Planes in the Space
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Intersection of Two Planes
Intersection of Three Planes
Sheaf of Planes
Angles in the space
Line-Line angle
Line-Plane angle
Plane-Plane Angle
Exercises
Distances in the space
Point-Line Distance
Point-Plane Distance
Line-Line Distance
Plane-Plane Distance
Similarity
Precalculus
Sequences and series
Introduction to sequences
Series and Summation Notation
Arithmethic sequences
Arithmetic series
Geometric sequences
Geometric series
Recursion Sequences
Graphs
Graphs
Definition of slope
Positive or negative slope
Determine the slope of a line
Equation of a line (slope-intercept form)
Equation of a line (point slope form)
Equation of a line from graph
Domain and range
Definitions
Polynomial function
Rational function
Radical function
Trigonometric function I
Trigonometric function II
Trigonometric function III
Quadratic function
Limits (approaches a constant)
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Asymptotes
Continuity and discontinuities
Parallel, coincident and intersepting lines
Introduction to Functions
Seven Basic Functions
Limits
Limit of a function
Limits approaches a constant
Limits approaches infinity
Evaluating limits
One-Sided Limits
Continuity
Continuity
Discontinuities
Asymptotes
Vertical Asymptote
Horizontal Asymptote
Slant Asymptote
Trigonometry
Trigonometric ratios
Sine
Cosine
Tangent
The reciprocal trigonometric ratios
Cosecant
Secant
Cotangent
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Trigonometric ratios of related angles
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Supplementary angles
Angles that differ by 180º
Opposite angles
Trigonometric identities
Solving right angles
Two sides knowed
One side and one angle
Law of sines
Law of cosines
Domain of trigonometric functions
Statistics
Mean
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Mode
Quartiles
Deciles
Percentiles
Mean deviation
Variance
Standard Deviation
Coefficient of variation
Skewness
kurtosis
Frequency distribution
Previous concepts
Ungrouped data
Grouped data
Graphing statistics & Data
Bar chart
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Pie chart
Frequency Polygon
Pictogram
Cartogram
Factorial
Variations without repetition
Variations with repetition
Permutations without repetition
Permutation with repetition
Circular permutation
Binomial coefficient
Combinations without repetition
Combinations with repetition
Radical expressions
Adding ans subtracting radical expressions
Rationalization
Radical equation
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Adding and subtracting radical expressions
To add algebraically two or more radicals, reduce each radical to simplest form and combine terms with similar radicands. Thus:
Simplify
Simplify:
