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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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Differentiation

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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)

HL1 Nov 3rd / HL 2 Nov 4th

In this lesson you will learn:

- The concept of implicit differentiation.

INSTRUCTIONS

Before you come to class

- Read: Oxford. Mathematics Analysis and Approaches HL. Pages 288 - 293

- Watch: Lesson 7 - Implicit differentiation Part I, Part II

In class:

- Quiz

- Worked examples

- Practice questions

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Lesson 8: Derivatives of logarithms and inverse trigonometric functions

HL1 Nov 4th / HL2 Nov 5th

In this lesson you will learn:

- To deduce the derivatives of logarithmic and inverse trigonometric functions.

INSTRUCTIONS

Before you come to class

- Read: Oxford. Mathematics Analysis and Approaches HL. Pages 483 - 488

- Watch: Video Lesson part III, part IV

In class:

- Worked examples

- Practice questions

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Lesson 9: Related rates of change

HL1 Nov 5th / HL2 Nov 6th

In this lesson you will learn:

- To apply implicit differentiation to real world problems

- To identify ligatures and related rates

INSTRUCTIONS

Before you come to class

- Read: Oxford. Mathematics Analysis and Approaches HL. Pages 288 - 293

- Watch: Part I

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Week 11: Nov 9th ~ Nov 13th (Week C)

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Related Rates further practice

HL2 :November 9th

HL1: November 10th

In this lesson you will apply the concept of related rates practicing with past IB questions.

INSTRUCTIONS

Before you come to class

- Review the materials for lesson 9.

During class:

- Download and work on the exercises included in this file.

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Lesson 10: Optimization I

HL1: November 11th

HL2: November 12th

In this lesson you will learn:

- To use differentiation in optimization problems

INSTRUCTIONS

Before you come to class

- Read: Pearson. Mathematics Analysis and Approaches HL page 677-682

- Watch: Video Lesson

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Week 12: Nov 16th ~ Nov 20th (Week A)

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Optimization - Practice

HL1: November 17th

HL2: November 18th

In this lesson you will practice:

- Optimization and differentiation problems

INSTRUCTIONS

Before you come to class

- Review our previous lesson

During class

- Please work on the following task.

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Lesson 11 - L'Hôpital's Rule

HL1: November 18th

HL2: November 19th

In this lesson you will learn:

- L'Hôpital's rule for undetermined limits

INSTRUCTIONS

Before you come to class

- Review differentiation methods

- Read: Mathematics Analysis and Approaches HL. Oxford. Page 550-553

- Video lesson: Part I, Part II

During class

- Investigation 9, MAA HL Oxford page 550.

- MAA HL Oxford page 553. Exercise 8J.

- If you are interested in a more formal proof please read this document.

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Lesson 12 - Maclaurin Series I

HL1: November 19th

HL2: November 20th

In this lesson you will learn:

- To expand functions using Maclaurin Series

INSTRUCTIONS

Before you come to class

- Review differentiation methods

- Read: Mathematics Analysis and Approaches HL. Oxford. Page 554-562

- Video lesson: Part I, part II

During class

- Investigation 10, MAA HL Oxford page 554.

- MAA HL Oxford page 556. Exercise 8K.

- Kignity Assignment - Maclaurin series practice

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Week 13: Nov 23rd ~ Nov 27th (Week B)

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Lesson 13 - Maclaurin Series II

HL1: November 24th

HL2: November 26th

In this lesson you will learn:

- Maclaurin expansion of composite functions

INSTRUCTIONS

Before you come to class

- Review differentiation methods

- Read: this section

- Watch: Video lesson

During class

- MAA HL Cambridge page 112, exercise 4C.

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Paper 1 (2)

On november 25th you will sit a paper 1 exam.

This is a non-calculator test.

Use black or blue ink to write, you may use pencil for graphs and diagrams only.

Please bring a printed copy of your formula booklet.

If English is not your first language, you can bring a paper copy of a your-language/English dictionary.

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Lesson 14 - Binomial Series and Applications

HL1: November 26th

HL2: November 27th

In this lesson you will learn:

- To find the binomial series

- To apply Maclaurin series to calculate limits.

INSTRUCTIONS

Before you come to class

- Review differentiation methods

- Video Lesson: part I

- Read: MAA HL Oxford page 558-561

During class

- MAA HL Oxford page 562 Exercise 8L

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Week 15: Dec 7th ~ Dec 11th (Week A)

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Integration

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Lesson 15 - Antiderivatives

HL1: December 8th

HL2: December 9th

In this lesson you will learn:

- The concept of antiderivative/anti-differentiation

- How to use initial values to find integration constants

INSTRUCTIONS

Before you come to class

- Review differentiation methods

- Video Lesson: part I, part II

- Read: MAAHL Pearson page 698 - 701.

MAAHL Oxford page 444 - 450.

During class

- Investigation 3. MAAHL Oxford page 448.

- MAA HL Oxford page 450 Exercise 7A.

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Lesson 16 - Integration by Substitution

HL1: December 9th

HL2: December 10th

In this lesson you will learn:

- To integrate functions in composition with linear functions

- To integrate using the method of substitution

INSTRUCTIONS

Before you come to class

- Review differentiation methods

- Video Lesson: part I

- Read: MAAHL Pearson page 702 - 707. (shorter)

MAAHL Oxford page 448 - 450; 488 - 499. (more detailed)

During class

- Investigation 16. MAAHL Oxford page 490.

- MAA HL Oxford page 495 Exercise 7G.

- MAA HL Oxford page 499 Exercise 7H.

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Lesson 17 - Integration by parts

HL1: December 10th

HL2: December 11th

In this lesson you will learn:

- The concept of antiderivative/anti-differentiation

- How to use initial values to find integration constants

INSTRUCTIONS

Before you come to class

- Review differentiation methods

- Video Lesson: part I,

- Read: MAAHL Pearson page 698 - 701.

MAAHL Oxford page 444 - 450.

During class

- Investigation 3. MAAHL Oxford page 448.

- MAA HL Oxford page 450 Exercise 7A.

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Week 17: Jan 10 - Jan 15 (Week C)

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Lesson 18: The definite Integral and area under the curve

Periods 1 and 2

In this lesson you will learn:

- to calculate the area between two curves

- to understand and apply the fundamental theorem of calculus

- to identify definite integrals and their relation to the derivative and the area under the curve.

INSTRUCTIONS

Before you come to class

- Review integration methods and the definite integral

- Read: MAA HL Oxford, page 520-523.

- Watch: Video lesson I

During class

- Work on investigation 1 on page 520 from MAA HL from Oxford.

- Work on questions 1 through 11 from this set. If possible, practice using your GDC to find the areas.

- If you are ready for exam style questions, work on questions 1 through 11 from this set.

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Week 18: Jan 18th ~ Jan 22nd (Week A)

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Lesson 19: Areas between two curves

Period 1

In this lesson you will learn:

- to calculate the area between two curves when they don't intercept

- to calculate the area between two curves when they intercept

INSTRUCTIONS

Before you come to class

- Review integration methods and the definite integral

- Read: MAA HL Oxford, page 520-523.

- Watch: Video Lesson I

- Watch: Video lesson II

During class

- Work on investigation 1 on page 520 from MAA HL from Oxford.

- Work on questions 1 through 11 from this set. If possible, practice using your GDC to find the areas.

- If you are ready for exam style questions, work on questions 1 through 11 from this set.

- Quiz: Visit this link and take the quiz Areas between curves. You will need to create a free account to access the materials. Do not provide any personal information you don't feel comfortable sharing.

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Lesson 20: Volumes of Revolution I

Period 2

In this lesson you will learn:

- to calculate the volume of a solid with rotational symmetry around the x axis or around the y-axis

- to calculate the volume of a solid with rotational symmetry with holes.

INSTRUCTIONS

Before you come to class

- Review integration methods and the definite integral

- Read: MAA HL Oxford, page 520-523.

- Watch: Video Lesson I

During class

- Work on investigation 3 on page 524 from MAA HL from Oxford.

- Work on MAA HL Oxford, page 527, exercise 8C (odd)

- Explore: Geogebra applet by Tim Brzezinski

- If you are ready for exam style questions, work on questions 1 through 9 from this set. Solutions

Bonus materials

- Quiz: Visit this link and take the quiz Volumes of revolution. You will need to create a free account to access the materials. Do not provide any personal information you don't feel comfortable sharing.

- Further reading: link

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Week 18: January 25th - January 29th

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Lesson 21: Kinematics

Period 1

In this lesson you will learn:

INSTRUCTIONS

Before you come to class

- Review integration methods and the definite integral

- Read: MAA HL Oxford, page 528-532.

- Watch: Video Lesson I

During class

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Lesson 22: Integration Revision

Period 2

Please use this opportunity to ask any questions you may have regarding integration and work on the assigned problem set.

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Paper 3

Period 3

In this lesson you will sit a paper 3. Please note the following information:

- Please make sure to keep your camera on at all times.

- Make sure your camera shows your hands and work area.

- You may use a calculator.

- You may use a printed copy of the formula booklet.

- Please submit a pdf of the scan of the test to the google classroom.

- As agreed upon in class, this test is formative.

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Week 19: February 1st - February 5th

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Ordinary Differential Equations

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Lesson 23: Ordinary differential equations: separation of variables

Period 1

In this lesson you will learn:

- to understand what a differential equation is

- how to solve a differential equation using the method of separation of variables.

INSTRUCTIONS

Before you come to class

- Review integration methods and the definite integral

- Read: MAA HL Oxford, page 533-539.

- Watch: Video Lesson I

- Practice: There are two problems in the video left for you to practice at home.

During class

- Worked examples including how to build the equations from word problems.

- Work on questions from this set.

Further resources: Textbook chapter Link

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Week 23: March 1st - 5th (Week A)

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Lesson 25: Homogeneous differential equations

Period 1

In this lesson you will learn:

- to identify homogeneous equation.

- how to use the substitution y=vx to transform the homogeneous equation into one that can be solved by separation of variables..

INSTRUCTIONS

Before you come to class

- Review integration methods and the definite integral

- Read: MAA HL Oxford, page 541 - 543.

- Watch: Video Lesson I

- Practice: There are two problems in the video left for you to practice at home.

During class

- Worked examples including how to build the equations from word problems.

- Work on questions from this set

Further resources: Textbook chapter Link

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Lesson 24: Numerical solution using Euler's Method

Period 2

In this lesson you will learn:

- to draw and interpret

- how to solve a differential equation using the method of separation of variables.

INSTRUCTIONS

Before you come to class

- Review integration methods and the definite integral

- Read: MAA HL Oxford, page 533-539.

- Watch: Video Lesson I

- Practice: There are two problems in the video left for you to practice at home.

During class

- Worked examples including how to build the equations from word problems.

- Work on questions from this set.

Further resources: Textbook chapter Link