Mochi does Maths!

Ms Carolina's Math class

Topic 5 - Calculus

Office Hours

Office hours will happen on a rotation basis during a cycle. 

Week A - Tuesday 7:00 - 8:00 PM JST
Week B - Wednesday 7:00 - 8:00 PM JST

Video Lessons

The structure of the lessons is as follows:

1. Assigned reading.
2. Video
3. Video and classroom examples
4. Class work.

Videos may  contain additional examples or content that may not be in the textbook. However, if you can't watch the videos, you should not worry, you still have access to all the textbooks and tasks via our classroom and mochidoesmaths.com.
Essential understandings: 
Calculus describes rates of change between two variables and the accumulation of limiting areas. Understanding these rates of change and accumulations allow us to model, interpret and analyze real-world problems and situations. Calculus helps us to understand the behaviour of functions and allows us to interpret the features of their graphs. 

Suggested concepts embedded in this topic: 
Change, patterns, relationships, approximation, generalization, space, modelling. 
AHL: Systems, quantity. 

Content-specific conceptual understandings: 
• The derivative may be represented physically as a rate of change and geometrically as the gradient or slope function. 
• Areas under curves can be can be approximated by the sum of the areas of rectangles which may be calculated even more accurately using integration. 
• Examining rates of change close to turning points helps to identify intervals where the function increases/decreases, and identify the concavity of the function. 
• Numerical integration can be used to approximate areas in the physical world. 
• Mathematical modelling can provide effective solutions to real-life problems in optimization by maximizing or minimizing a quantity, such as cost or profit. 
• Derivatives and integrals describe real-world kinematics problems in two and three-dimensional space by examining displacement, velocity and acceleration. 
AHL 
• Some functions may be continuous everywhere but not differentiable everywhere. 
• A finite number of terms of an infinite series can be a general approximation of a function over a limited domain. 
• Limits describe the output of a function as the input approaches a certain value and can represent convergence and divergence. 
• Examining limits of functions at a point can help determine continuity and differentiability at a point.

Week 3: Sept 14th - 18th 2020

Lesson 1: Limits

HL1
September 15th

HL2

September 16th


For this lesson you will need:

- Thorough knowledge and understanding of a diverse range of families of functions and their graphs.

- Factorization

- Properties of exponents and radicals.


In this lesson you will learn:

- the concept of limit.

- to calculate a limit using a table of values.

- to calculate a limit by direct evaluation.

- to calculate a limit with algebraic manipulation.


INSTRUCTIONS

Before you come to class

- Read: This week's reading will be from this chapter. This is a pre-calculus textbook that goes deeper into the concept of limit than IB textbooks do. It is very important that you get this concept clearly and quickly. Pages 897 - 911

- Watch: Please watch this session's video lessons: 

   Part I -  Limits using tables

   Part II - Limits with algebraic manipulation

   Part III - Limits from graphs

In class:

- Do: If there are any questions regarding the materials, please ask them at this time.

- Further examples

- Do: From the chapter shared above, complete from exercise 13.1questions 5-16.

- Additional practice: From MAAHL textbook by Oxford Exercise 4A, page 223.

Lesson 2: Limits and continuity

September 17th


For this lesson you will need:

- Thorough knowledge and understanding of a diverse range of families of functions and their graphs.

- Factorization

- Properties of exponents and radicals.


In this lesson you will learn:

- the concept of lateral limit.

- the concept of continuity.

- to use limits to assess continuity of a function.

- Limits to infinity

- Convergence


INSTRUCTIONS

Before you come to class

- Read: - Read: This week's reading will be from this chapter. This is a pre-calculus textbook that goes deeper into the concept of limit than IB textbooks do. It is very important that you get this concept clearly and quickly. Pages 911-913

- Watch: Please watch this session's video lesson Lesson 2 - Calculus - Limits and continuity.

   Part I - Lateral limits and continuity

   Part II - Limits to infinity and convergence

In class:

- Do: If there are any questions regarding the materials, please ask them at this time.

- Do: Kahoot! Let's all go to https://kahoot.it/ for a quick game!

- Do: From the chapter shared above, complete from exercise 13.1 questions 17-20, 19-32.

- Additional practice: From MAAHL textbook by Oxford Exercise 4B, page 227.

Week 4: Sept 21st - Sept 25th, 2020

Lesson 3 - Rates of change and derivatives

September 22nd


For this lesson you will need:

- Thorough understanding of limits.


In this lesson you will learn:

- to find average rates of change.

- to find instantaneous rates of change.

- the equation of the tangent line to a function at some value of x.

- to differentiate a function from first principles.


INSTRUCTIONS

Before you come to class

- Read: MAAHL by Oxford. Page 236-243.

- Watch: Please watch this session's video lesson Lesson 3 - Rates of change and derivatives.

   Part I - Average and Instantaneous Rates of change

   Part II - Derivation from first principles


In class:

- Do: If there are any questions regarding the materials, please ask them at this time.

- Do: Kahoot! Let's all go to https://kahoot.it/ for a quick game!

- Do: From MAAHL textbook by Oxford Exercise 4E, page 241 and Exercise 4F, page 243.

Paper 1

September 23rd.


This day you will sit a cumulative test Paper 1.


The Exam will be 70~75 minutes long. 

You will not be allowed a calculator for this test. 

Please bring a printed copy of your Formula booklet.

Section A: Short questions. Please answer on the spaces provided only.

Section B: Long questions. Please answer on a separate piece of paper.

Lesson 4 - Differentiation rules Part I

HL1: September 24th

HL2: September 25th


For this lesson you will need:

- Thorough understanding of limits.

- Thorough understanding of the concept of derivative.


In this lesson you will learn:

- learn the rule to differentiate power functions.

- learn the derivatives of common functions.

- understand the concept of differentiability.

- learn the product and quotient rules.


INSTRUCTIONS

Before you come to class

- Read: MAAHL by Oxford. Page 244-251 and 255-258.

- Watch: Please watch this session's video lesson Lesson 4 - Differentiation rules Part I.

   Part I - Derivatives of common functions

   Note - Differentiability

   Part II - The product and quotient rules for differentiation


In class:

- Do: If there are any questions regarding the materials, please ask them at this time.

- Do: From MAAHL textbook by Oxford Exercise 4G, page 248; Exercise 4H, page 252; Exercise 4J page 256 and Exercise 4K page 258.


Week 5: Sept 28th - Oct 2nd, 2020

Lesson 5 - Differentiation rules Part II

September 29th


For this lesson you will need:

- Thorough understanding of the concept of derivative.

- Thorough understanding of the derivation rules

- Thorough understanding of composite and inverse functions.


In this lesson you will learn:

- the chain rule to differentiate composite functions

- to calculate and write higher order derivatives using appropriate notation.


INSTRUCTIONS

Before you come to class

- Read: MAAHL by Oxford. Page 522-255, page 259-261.

- Watch: Please watch this session's video lesson Lesson 5 - Differentiation rules II

   Part III - Chain Rule

   Part IV - Higher order derivatives and examples

   Note - Proof of chain rule


In class:

- Do: If there are any questions regarding the materials, please ask them at this time.

- Do: From MAAHL textbook by Oxford Exercise 4J, page 256; Exercise 4L page 261

Paper 2

September 30th.


This day you will sit a cumulative* test Paper 2.


The Exam will be 70~75 minutes long. 

You will be allowed a calculator for this test. 

Please bring a printed copy of your Formula booklet.

Section A: Short questions. Please answer on the spaces provided only.

Section B: Long questions. Please answer on a separate piece of paper.


*Chain rule may be included

IA 

October 2nd


Please use the time of this lesson to work on the first draft of your Math IA.

Remember the deadline to submit this work is October 9th. 

Week 6: Oct. 5th - Oct. 9th

Week 9: Oct. 26 - Oct 30