• Construction, Interpretation, and Manipulation of Expressions
• Solutions of Equations and Inequalities

• Definitions, Representations, and Attributes of Functions
• Operations and Transformations with Functions
• Models of Real-World Situations Using Families of Functions

• Lines and Linear Functions
• Exponential and Logarithmic Functions
• Quadratic Functions
  
• Power Functions
• Polynomial Functions
• Rational Functions
• Trigonometric Functions

• Producing and Interpreting Plots
• Producing and Interpreting Plots
• Measures of Center and Variation
• The Normal Distribution

• Scatter Plots and Correlation
• Pearson’s correlation coefficient
• Scatter Plots and Correlation
• Linear Regression
• Least squares regression line

• Data Collection and Analysis
• Simple Random Sampling
• Stratified Random Sampling
• Cluster Sampling
• Surveys
• Completely Randomized and Randomized block designs

• Law of Large Numbers
• Basic Probability Rules
• Law of Total Probability
• Bayes' Theorem
• Random variable and Discrete Probability Distribution
• Effect of a linear transformation of a random variable on its mean and standard deviation.
• Binomial Distribution
• Geometric Distribution
• Hypergeometric Distribution
• Percentiles of normal distributions.
• Simulation
• Central Limit Theorem
• Confidence Intervals
• Control Limits

• Simulation of confidence interval
• t-distribution

• Testing of Hypothesis
• p-value
• Type I and Type II errors
• Chi-squared significance tests of homogeneity and independence
• Goodness-of-fit test

• Statistical model for regression, including linearity, normality of errors, and constancy of error variance.

• Sample space
• Computing the Probability of mutually exclusive, independent, dependent, compound and complementary events
• Conditional Probability
• Venn diagrams
• Combinations and permutations
• Application of Probability concepts to practical situations

• Lines and Angles
• Euclidean and Coordinate Geometry

• Triangles and Their Properties
• Angles, side length, perimeter, and area of triangles.
• Quadratic Functions, Pythagorean Theorem and its applications
  
• Medians, altitudes and perpendicular bisectors, and the angle bisectors of a triangle.

• Quadrilaterals and Their Properties
• Proofs involving quadrilaterals
• Theorems about the interior and exterior angle sums of a quadrilateral.

• Other Polygons and Their Properties
• Perimeter and area of a regular n-gon, interior and exterior angles of a regular n-gon.

• Circles and Their Properties
• Equation of a circle
• Conic Sections and Their Properties
• Identification and Graphs of parabolas, circles, ellipses, and hyperbolas

• Law of Syllogism

• Relationships Between Area and Volume Formulas

• Identification and drawings

• SSS, SAS, ASA and AAS conditions for congruency
• SSS, SAS and AAS conditions for similarity

• Distance-preserving Transformations Isometries
• Shape-preserving Transformations: Dilations and Isometries

• Visualization and Geometric Models
  • Relate graphical and algebraic representations of lines, simple curves and conic sections.
  • Recognize and compare specific shapes and properties in multiple geometries; e.g., plane, spherical and hyperbolic.

• Sine, cosine, and tangent of angles
• Law of Sines and Cosines
• Values of Trigonometric Ratios for 0°, 30°, 45°, 60° angles

• Graphs of transformations of the sine and cosine functions.
• Inverse Trigonometric Functions
• Basic Trigonometric Identities
• Solutions of trigonometric equations
• Radian and Degree Measures

• Definition of a Function
• Algebraic Operations on Functions and apply Transformations.
• Composite Functions

• Relationship between exponential and logarithmic functions
• Graphs of logarithmic functions
• Solution of exponential and logarithmic functions
• Problems involving Exponential growth and decay.

• Solution of quadratic equations by substitution
• Applications of quadratic functions

• Intervals and graphs of polynomial functions
• Solution of polynomial equations and inequalities of degree >=to three
• The Remainder Theorem
• Factor Theorem
• Fundamental Theorem of Algebra

• Solutions of equations and inequalities involving rational functions.
• Vertical and horizontal asymptotes

• Transcendental and Periodic Functions.

• Operations on Vectors
• Operations on Matrices
• Inverse of a matrix
• Determinants
• Gaussian elimination
• Linear Programming

• The sigma and factorial notation.
• Arithmetic sequences
• Geometric sequences
• Mathematical Induction
• Binomial Theorem
• Pascal's Triangle

Polar Coordinates, Parameterizations, And Conic Sections.

• Conversion between polar and rectangular coordinates.
• Graph of functions in polar coordinates.
• De Moivre’s Theorem
• Parametric and Rectangular forms of equations.
• Locus
• Graphs of parabolas, ellipses and hyperbolas