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Real Numbers and Relation

• Real Numbers
• Real Numbers Line
• Coordinate Plane
• Relation
• Showing the relation in the coordinate plane
• Domain and Range of Relation
• Functions
• Identifying the function from the graph
• Graphs of Basic Functions

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Vectors in Two Dimension

• Introduction to Vectors: Vectors in Two Dimensions
• Equality of Vectors in Two Dimensions
• Scalar Multiplication
• Vector addition and subtraction
• Representation of Addition and Subtraction
• Length of a Vector
• Dot Product and Cross Product
• Parallel vectors
• Orthogonal Vectors
• Parametric Equations and Graphs
• Applications of Vectors

Equations and Inequalities

• Solving Multi-Step Equations
• Slope and Intercepts
• Using Intercepts
• Transforming Linear Functions
• Solving Inequalities
• Graphing Linear Inequalities
• Solving Compound Inequalities
• Solving Absolute Value Equations
• Solving Absolute Value Inequalities
• Graphing Absolute Value Inequalities
• Solving Systems of Equations
• Solving Special Systems
• Systems of Equations Word Problems

Functions

• Evaluating Functions: Function Notation
• Modeling Real-world Situations with Functions
• Adding and Subtracting Functions
• Multiplying and Dividing Functions
• Composite Functions
• Real Zeros
• Average Rate of Changes
• Codomain

Polynomial and Rational Functions

• The Simplest Functions: Constant and Identity
• Polynomial Functions
• Graphing Polynomial Functions
• Writing Polynomials in Standard Form
• Simplifying Polynomials
• Factoring Trinomials
• Solving a Quadratic Equation
• Graphing Quadratic Functions
• Solving Quadratic Inequalities
• Graphing Quadratic Inequalities
• Rational Equations
• Multiplying and Dividing Rational Expressions
• Simplifying Rational Expressions
• Rational Functions
• Graphing Rational Expressions

Exponential Functions and Logarithms

• Exponential Functions: Definition and Properties
• Solving Exponential Equations
• Logarithmic Functions: Definition and Properties
• Evaluating Logarithms
• Properties of Logarithms
• Natural Logarithms
• Solving Logarithmic Equations

Radical and absolute value Functions

• Simplifying Radical Expressions
• Simplifying Radical Expressions Involving Fractions
• Adding and Subtracting Radical Expressions
• Multiplying Radical Expressions
• Radical Equations
• Solving Radical Inequalities
• Domain and Range of Radical Functions
• Graphing Radical Functions
• Absolute Value Functions
• Graphing Absolute Value Functions
• Absolute Value Properties
• Floor Value
• Floor Function
• Graphing Floor Function

Functions Operations

• Positive, Negative, Increasing and Decreasing Functions on Intervals
• Transformations of Functions
• Function Symmetry: Even and Odd
• End Behavior of Polynomial Functions
• One-to-One Function
• Identifying the function one by one from the graph
• Onto (Surjective) Functions
• Function Inverses
• Inverse Function Graph
• Inverse Variation
• Piecewise-defined Functions

Trigonometry

• Degrees, Radians, and Angle Conversions
• Coterminal and Reference Angles
• Angles of Rotation and Unit Circle
• Arc length and Sector Area
• Sine, Cosine, and Tangent
• Reciprocal Functions: Cosecant, Secant, and Cotangent
• Domain and Range of Trigonometric Functions
• Arcsine, Arccosine, and Arctangent
• Applications of Inverse Trigonometric Function
• Fundamental Trigonometric Identities
• Pythagorean Trigonometric Identities
• Co-Function, Even-Odd, and Periodicity Identities
• Double Angle and Half-Angle Formulas
• Sum and Difference Formulas
• Product-to-Sum and Sum-to-Product Formulas

Trigonometric Functions and Graphs

• Graph of the Sine Function
• Graph of the Cosine Function
• Amplitude, Period, and Phase Shift
• Writing the Equation of a Sine Graph
• Writing the Equation of a Cosine Graph
• Graph of the Tangent Function
• Graph of the Cosecant Function
• Graph of the Secant Function
• Graph of the Cotangent Function
• Graph of Inverse of the Sine Function
• Graph of Inverse of the Cosine Function
• Graph of Inverse of the Tangent Function
• Sketching Trigonometric Graphs

Trigonometric Equations

• Basic Techniques for Solving Trigonometric Equations
• Factoring and Simplifying Trigonometric Expressions
• Solving Equations with Multiple Angles

Trigonometric Applications

• Law of Sines: Definition and Applications
• Law of Cosines: Definition and Applications
• Area of a Triangle Using Trigonometry

Analytic Geometry

• Distance and Midpoint Formulas
• Circles
• Finding the Center and the Radius of Circles
• Parabolas
• Finding the Focus, Vertex, and Directrix of a Parabola
• Ellipses
• Hyperbolas
• Classifying a Conic Section (in Standard Form)
• Rotation of Axes and General Form of Conic Sections

Complex Numbers

• Polar Coordinate System
• Converting Between Polar and Rectangular Coordinates
• Introduction to Complex Numbers
• Adding and Subtracting Complex Numbers
• Multiplying and Dividing Complex Numbers
• Rationalizing Imaginary Denominators
• Polar Form of Complex Numbers
• Multiplying and Dividing in Polar Form
• Powers and Roots in Polar Form
• Graphs of Polar Equations

Matrices

• Introduction to Matrices
• Matrix Addition and Subtraction
• Scalar Multiplication
• Matrix Multiplication
• Determinants of Matrices
• Inverse of a Matrix
• Solving Systems of Equations with Matrices

Sequences and Series

• Sequence
• Recursive Formula
• Write a Formula for a Recursive Sequence
• Arithmetic Sequences
• Geometric Sequences
• Sigma Notation
• Arithmetic Series
• Finite Geometric Series
• Infinite Geometric Series
• Convergent and Divergent Series
• The th Term Test for Divergence
• Introduction to the Integral Test
• Comparison, Ratio, and Root Tests
• Alternating Series and Absolute Convergence
• Pascal’s Triangle
• The Binomial Theorem

Limits

• Limits and Function Values
• One-Sided Limits
• Properties of Limits
• Detecting Limits from Graphs
• Nonexistence of Limits
• Calculation of limits of functions
• Indeterminate Form and Vague Limits
• Vague Limits by Change of Function’s Value
• Infinite Limits
• Limits at Infinity
• More about Limits at Infinity
• Removing Ambiguity in Infinite Limits
• Limits Involving Floor and Absolute Value Functions
• The Squeeze Theorem
• Asymptotes: Vertical, Horizontal and Oblique

Continuity

• Continuity at a Point
• Continuity over an Interval
• Types of Continuity
• Properties of Continuity
• Intermediate Value Theorem
• Integral
• Integral Properties
• Basic Integral Formulas
• Definite Integral

Statistics

• Venn diagrams
• Organizing Data
• Types of Data
• Frequency Table and Histograms
• Bar Chart
• Pie Graph
• Scatter Plots
• Mean, Median, Mode, and Range of the Given Data
• Data Distribution
• Measures of Dispersion
• Central Limit Theorem and Standard Error
• Box-and-Whisker Plots

Statistics and Probability

• Theoretical Probability
• Experimental Probability
• Mutually Exclusive Events
• Independent and Dependent Events
• Compound Events
• Permutations and Combinations
• Conditional and Binomial Probabilities
• Random Variables
• Probability Mass Function
• Probability Density Functions
• Expected value and a Random Variable

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