Course Overview:
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.
Note: This course is not designed for ELL (English Language Learners) students. ELL students may enroll in this course ONLY if they have adequate mentor support at their home school and are able to fulfill all course requirements.
Prerequisites:
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
