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Office Hours

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Video Lessons

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Week 3: Sept 14th - 18th 2020

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Lesson 1: Limits

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.

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Lesson 2: Limits and continuity

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.

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

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Lesson 3 - Rates of change and derivatives

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.

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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.

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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.

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Week 5: Sept 28th - Oct 2nd, 2020

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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

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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

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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.

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Week 6: Oct. 5th - Oct. 9th

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Paper 1 & Paper 2 Correction

HL1:

October 6th

HL 2:

October 7th

For this lesson you will need:

- Paper 1 and Paper 2

- Formula booklet

- Calculator

In this lesson you will be given time to work on questions:

Paper 1: 1, 4, 6, 7

Paper 2: TBD

In addition to these problems, you might want to practice with this set.

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Lesson 6: Increasing and decreasing functions and other derivatives

October 8th

In this lesson you will learn:

- the derivative of inverse trigonometric functions

- to determine growth of a function using the first derivative

INSTRUCTIONS

Before you come to class

- Read: MAAHL by Oxford. Page 262-265.

- Watch: Please watch this session's video lesson Lesson 6.

Part *I* - Further differentiation and normal lines

Part II - Increasing and decreasing functions

In class:

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

- Do: From MAAHL textbook by Oxford Exercise 4M page 264

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Week 9: Oct. 26 - Oct 30 (Week A)

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Differentiation Review

October 27th

In this lesson you will review:

- The concept of derivative.

- The rules for differentiation.

- The derivatives of basic families of functions.

- The derivative as the gradient of a function.

- Tangent lines to a function.

- the relation between the graphs of the function, first derivative and second derivative.

INSTRUCTIONS

Before you come to class

- Read: Review your notes.

- Watch: If needed go through any of the past videos you need reviewing.

- Write: write down any questions, items that need clarifying in class.

In class:

- Do: If you brought any prepared questions, please share them at this time.

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Paper 3

On Wednesday October 28th, we will have the first Paper 3.

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Lesson 7: Implicit differentiation

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Week 10: Nov 2nd ~ Nov 6th (Week B)

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Lesson 8: Rates of change

November 3rd TBD

In this lesson you will learn:

- The concept of related rates.

- How to use implicit differentiation to find a related rate.

- How to use related rates to find rates of change applied to real world problems.

INSTRUCTIONS

Before you come to class

- Read: Review your notes.

- Watch: If needed go through any of the past videos you need reviewing.

- Write: write down any questions, items that need clarifying in class.

In class:

- Do: If you brought any prepared questions, please share them at this time.