This course is designed for IB Standard Level students looking to learn Differentiation. This course can only be purchased by adults. Once purchased, students can then access the contents of the course under the supervision of their parents.

The course is presented in the following manner.

• Course content video explaining the concept

• Downloadable course content notes

• Worksheet and its Solution

• Worksheet solution explanation video

The course is ideal for students looking to learn the difficult concept of differentiation in an easy to understand manner.

Learning Outcomes

1. Limits

• Understanding Gradient of a Function

• Description of Limits

• Left Hand and Right Hand Limits

• Examples

• Vertical Asymptotes

• Horizontal Asymptotes

• Solving of different types of problems pertaining to Limits

  
  

2. Derivative of a Function

• Gradient - Average rate of change

• Derivative - Instantaneous rate of change

• Differentiation - Using First Principles

• Power Rule

• Constant Rule

• Sum/Difference Rule

  
  

3. Differentiation Rules

• Product Rule

• Quotient Rule

• Chain Rule

• Sample Problems

4. Tangents and Normal

• Gradient of a function at a point is the slope of the tangent at that point

• Obtaining the equation of a tangent

• Obtaining the equation of a normal

• Sample Problems

5. Graph

• First Differentiation Test

• Increasing/Decreasing Function

• Critical Points

• Maximum/Minimum

• Second Differentiation Test

• Inflexion Points

• Concavity

• Sketching graphs

6. Application of Differentiation

• Optimization

• Identify the constraint and write the equation

• Identify the expression to be optimized

• Write the expression in one variable using the equation

• Optimize it by differentiating and equating to zero

• Input the optimized parameter in the expression to obtain the optimized value

• Kinematics

• Relationship between Displacement, Velocity and Acceleration

• Converting a displacement equation into velocity equation

• Converting a velocity equation into a displacement equation

  
  

7. Past Paper Questions

• Assorted past paper questions and their solutions

• Video explanation of the solution