Pre-Calculus - Semester - 2

Course Details:

This course builds on Algebra I II and Pre-calculus Semester 1 and lays a solid foundation for a future course in Calculus. Student learns about several important concepts like Vectors, Probability & Distribution and Statistics. This course first provides a detailed introduction to the study of Continuity and later helps the student learn the concepts of Limits & Derivatives. With a firm understanding of Continuity, Limits and Derivatives, the student is well-prepared to handle the challenges of a full-fledged Calculus course.

Prerequisites:

• Algebra I - Semester - 1
• Algebra I - Semester - 2
• Algebra II - Semester - 1
• Algebra II - Semester - 2
• Geometry - Semester - 1
• Geometry - Semester - 2
• Pre-Calculus - Semester - 1

Syllabus:

Section 1: Vectors

• Introduction to Vectors
• Representing Vectors
• Direction and Angle of 2D Vectors
• Trigonometric Functions and 2D Vectors
• Opposite Vectors
• Operations with Vectors – Addition
• Operations with Vectors – Subtraction
• Operations with Vectors – Multiplication with a Scalar
• Unit Vector
• Introduction to 3D Vector
• Operations on 3DVectors

 Section 2: Probability and Probability Distribution

• Introduction to Probability
• Permutation
• Combination
• Uniform Probability Model
• Independent Events
• Conditional Probability
• Probability of a Union
• Probability Distributions
• Binomial Distributions
• Normal Distributions
• Standard Normal Distributions
• Sample Mean
• Central Limit theorem
• Comparing Strategies 

Section 3: Statistics

• Introduction to Statistics
• Mean, Median and Mode
• Standard Deviation
• Correlation
• Residuals
• Regression
• Random Sample
• Experiment Design

Section 4: Continuity

• Introduction to Continuity
• Continuous Functions
• Discontinuous Functions
• Continuous Functions on an open interval
• Continuous Functions on a closed interval
• Continuity of Piecewise Functions
• Intermediate Value Theorem

Section 5: Limits and Derivatives

• Introduction to Limits
• Different types of Limits
• Operations with Limits
• Limit of a Polynomial Function
• Limit of a Rational Function
• Introduction to Derivatives
• Derivative of a Function
• Derivative of a Composite Function