# Pre-Calculus – Semester 2

## Pre-Calculus – Semester 2

## Recommended Grade Level: 11 - 12

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.

## Credit: 0.5

## Prerequisites:

**Syllabus:**

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**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