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Pre-Calculus – Semester 2

 
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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:

 

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

 

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