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- Created on Monday, 09 September 2013 03:56
- Last Updated on Friday, 31 May 2019 17:30
- Written by Amory KC Wong
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# Welcome to Mr. Wong's Calculus 12 Class!

Click for Course Outline 2018-2019, Intro, and Schedule.

## Bonus

**Policy Clarifications:**

- Rules can be exempted by me on a case by case basis. I am not obligated to give reasons as some issues may be private matters concerning the individual student.
- Students must be following the school code of conducts to get bonus marks or test re-writes.
- Excessive lateness or unexcused absences will disqualify a student from bonus marks or re-writes for their current chapter.
- In order to qualify for test re-writes, half of the assigned work must be completed a day before the test schedule.
- In order to qualify for bonus marks, all of the assigned work must be completed a day before the test schedule.
- For test re-writes, you must complete all assigned work from the chapter and correct all answers on the test.
- Bonus marks cannot be added to any re-written tests. They can only be added to the original test score.
- The videos are meant to be public so that students can view them through the links on my website. Do not make the videos private.
- Students caught cheating will disqualify them from bonus marks for the remainder of the year.
- Students not working on their assigned work during class will be disqualified from bonus marks for their current chapter.
- Bonus marks and test re-writes must be submitted a week before the end of the term otherwise it will not be recorded for that term.
- All bonuses and re-tests are subject to change at my discretion with notice.

Bonus marks for writing good solutions on Math Stack Exchange Socratic.org; Socratic no longer accepts new questions and answers. You can log in using **Google** or **Facebook**; I don't recommend creating a Math Stack Exchange account. **5 good answers** will be a 10% bonus towards a test, so **2% per question**. Email me the link. Try to answer questions that are related to the chapter that you are doing. Put "$" around expressions so they get formatted as math expressions. Click on this link Click on this link for more formatting instructions; this forum uses a markup language called LaTeX. **Marks will not be given for easy questions or incorrect formatting.** It's a good idea to do one Math Stack Exchange question and get it approved before doing more on your own.

If you want homework help, you can ask the question on Math Stack Exchange Socratic and email me the link to solve (no bonus marks for asking questions).

Alternative bonus marks: You can create **up to 2 videos** related to questions solved incorrectly for an exam. Choose a similar question from the homework or test and **modify** the numbers to create a new question. Show me the question, then write up the solution. Show me the solution, then proceed with creating the video. Failure to follow these procedures can result in a loss of marks.

- You will get up to
**5%**for each video applied to the exam from where the question was chosen. - The exam grade will be capped at
**90%**when applying the bonus marks. - You may work in pairs, but each person must contribute to speaking on the video.
- Marks will be deducted if there is no spoken description.
- Marks will be deducted if the errors (spoken or written) are not edited from the video.
- Videos should be approximated 2-3 minutes.
- Marks will be deducted if the question is not sufficiently difficult.
- Report card marks are cumulative, so you may go back to any test from the year.
- Marks will be deducted for not following the Creating Videos.

**2 Reference Sheets** (front and page are one sheet) are permitted for tests; if you have more than 2, I will make you choose only 2. Reference sheets must be hand-written, so you are NOT permitted to use the notes template. It may contain formulas and homework questions. You are not permitted to make any changes to reference sheets for re-tests; so if you did not make reference sheets for the original test, you will not be allowed to have reference sheets for the re-test. Re-tests will have a cap of **95%**.

## Chp 1

- Chp 1.1 Notes - Different Line Forms
- Chp 1.2 Notes - Functions
- Chp 1.3 Notes - Exponential Functions
- Chp 1.4 Notes - Parametric Equations
- Chp 1.5 Notes - Inverse and Logarithmic Functions
- Chp 1.6 Notes - Trigonometric Functions
- Chp 1 Review

## Assigned Work

## Student Videos

- Inverse Trig of a Special Angle by Mehran Z. - Example of arccos(-sqrt(3)/2)
- Solving linear systems by David P. and Jonald C. - Where does Fahrenheit degrees match Celcius degrees.
- Solving exponential equations by Sepher M. and Arvin A. - Solving a quadratic exponential equation using the quadratic formula and logarithms.

## Chp 2

- Blank Notes Template
- Chp 2.1 Video - Limits Part 1 - Limit Properties
- Chp 2.2 Video, Casio - Limits Part 2 - Sandwich Theorem, Asymptotes, End Behaviour
- Chp 2.2 Video - Precise Limit Definition (required for most calc for math and science classes)
- Chp 2.3 Part 1 Video - Continuity, Types of Discontinuity
- Chp 2.3 Part 2 Video - Continuous Functions, IVT
- Chp 2.3 Extra - Proof by Contradiction, example of IVT
- Chp 2.4 Video - Rates of Change, Tangent Lines
- Chp 2 Review

## Assigned Work

- 2.1: pp. 62-64: 1-43 (odds), 32; Challenge - 45, 47
- 2.2: p. 64: 53, 55; pp. 71-72: 1-13 (odds), 17, 19, 23, 29-37 (odds), 30, 32; Challenge - 15, 21, 25, 27, 39, 41, use limit def to prove lim x->6 (x/3 + 2) = 4
- 2.3a: pp. 80-81: 1-27 (odds), 24; Challenge - 31, 33
- 2.3b: p. 81: 35-43 (odds), 40; Challenge - 47, 49
- 2.4: pp. 87-89: 1-15 (odds), 19, 29, 14; Challenge - 23, 25

## Student Videos

- Remove a Discontinuity by Kevin P. - Example of a quadratic divided by a quadratic.
- Graphical Limits by Golnar M. - Example of graphical limits without being given actual functions.
- Discontinuity of a Piecewise Function by Mehran Z. - Example of finding discontinuity of a piecewise fn using left and right-sided limits.
- Graphical limits by Jonald C. and David P. - Example of one and two-sided limits.
- Graphical Limits by Sana A. - Example of one and two-sided limits.
- Instantaneous Rate of Change by Tavia W. - Rate of change of falling object using limits (h method).
- Instantaneous Rate of Change by Tavia W. - Calculate normal line at a point on a curve.
- Finding Slope using Limits by Azi E. - Example of finding the slope at a point.
- Finding the Limit by Niknaz M. - Example of finding the limit of trig functions using trig identities.
- Finding the Slope using Limits by Yasaman K. - Example of finding the slope of a quadratic function at a point.
- Average Rate of Change by Saba M. and Kimia M. - Example using a polynomial over a closed interval.
- Remove a Point Discontinuity by Kimia M. and Saba M. - Example using a polynomial rational function.
- Finding Limits at Infinity by Saboura A. - Example using cubic rational functions.
- Finding Limits at a Hole by Saboura A. - An example of a rational function of a cubic divided by a linear binomial.
- Limits - Slope at a Point by Saba M. and Alyssa. E. - Example of finding the point at which a particular slope occurs.
- Rates of Change at a Point by Bosco N. - Example of finding the tangent and normal line at a given point using limits.
- Finding Limit of a Radical Rational by Bosco N. - Example using multiplying by conjugate to find solution.
- Finding the Slope of a Reciprocal Function by Arvin A. and Sepher M. - Example using the limit h method.
- Average Rate of Change by Ramin M. - Example of finding the average rate of change over a closed interval.
- Average Rate of Change by Spencer P. and Andrew L. - Example using a quadratic.

## Chp 3

- Blank Notes Template
- Chp 3.1 Video - Derivative of a Function
- Chp 3.2 Video - Differentiability
- Chp 3.3 Video, (Extra) - Rules for Differentiation
- Chp 3.4 Video - Velocity and Other Rates of Change
- Chp 3.5 Video - Derivatives of Trigonometric Functions
- Chp 3.5 Extra - Quick Review of Trig Functions
- Chp 3.6 Video - Chain Rule
- Chp 3.7 Video - Implicit Differentiation
- Chp 3.8 Video - Derivatives of Inverse Trigonometric Functions
- Chp 3.9 Video - Derivatives of Exponential and Logarithmic Functions
- Chp 3.9 Extra - Quick Review of Exponential and Logarithmic Functions
- Interactive Derivative on desmos
- Chp 3 Part 1 Review
- Chp 3 Part 2 Review

## Assigned Work

- 3.1: pp. 101-103: 1, 3, 5, 7, 9, 11, 15, 18; Challenge - 13, 17
- 3.2: p. 111: 1-21 (odds), 8; Challenge - 25, 29
- 3.3: pp. 120-121: 1-29 (odds), 28; Challenge - 31, 33, 35
- 3.4: pp. 129-133: 1, 3, 5, 9, 13, 23, 29, 6; Challenge - 15, 16
- 3.5: p. 140: 1-23 (odds), 18; Challenge - 25, 29, 33

- 3.6: pp. 146-147: 1-33 (odds), 32; Challenge - 35, 37
- 3.7: p. 155: 3, 9, 11, 17, 19, 23-29 (odds), 28; Challenge - 22
- 3.8: p. 162: 1-19 (odds), 10; Challenge - 21, y=arccos x (use implicit)
- 3.9: p. 170: 1-37 (every other odd), 28; Challenge - 43 (take ln then implicit)

## Student Videos

- Graphing Using First and Second Derivatives by David P and Jonald C - example without explicit functions
- Determine graph features using First and Second Derivatives by Parinaz K - example using a cubic function
- Implicit Differentiation by Ramin M and Mehran Z - example of a second order equation and doing the second derivative
- Implicit Differentiation by Arvin A - example of a trig function
- Implicit Differentiation by Shannon G - example of an exponential and trig function
- Implicit Differentiation by Kiana A and Niki G - example of a rational function
- Implicit Differentiation by Kiana A and Niki G - example of a second derivative
- Deriving a trig derivative by Sana A. - How to derive the derivative of sin x using limits.
- Derivative Rules by Azi E. - Example of using the quotient rule on polynomials.
- Derivatives of Trig Functions by Ramin A. - Prove the derivative of tan x using the quotient rule.
- Derivative Rules by Golnar M. - Example of quotient rule without getting actual functions.
- Application of Derivatives by Jeremy S. - Example of velocity and acceleration word problem.

## Chp 4

- Blank Notes Template
- Chp 4.1 Video - Extreme Values of Functions
- Chp 4.2 Video - Mean Value Theorem
- Chp 4.3 Video - Using f' and f'' to graph f
- Chp 4.3 Extra - Complete Curve Sketching Example
- Chp 4 Part 1 Review
- Chp 4.4 Video - Modelling and Optimization
- Chp 4.5 Part 1 Video - Linearization and Newton's Method
- Chp 4.5 Part 2 Video - Differentials
- Chp 4.6 Video - Related Rates
- Chp 4 Part 2 Review

## Assigned Work

- 4.1: pp. 184-185: 1-29 odds, 46, 48; Challenge - 41, 43
- 4.2: pp. 192: 1-15 odds, 25-29 odds, 38, 39; Challenge - 31
- 4.3: pp. 203-205: 1-21 odds, 37-41 odds, 4; Challenge - 31

- 4.4: pp. 214-215: 5, 7, 9, 11, 15, 17, 22; Challenge - 29, 31
- 4.5a: pp. 229: 1-15 odds, 2; Challenge -
- 4.5b: pp. 230-231: 31-41 odds, 46; Challenge - 43, 45
- 4.6: pp. 237-240: 1, 3, 7, 11, 13, 17, 21, 23, 31, 12; Challenge - 33, 35

## Student Videos

- Finding Critical Points by Mohammad O and Sana A - example of minimizing average cost
- Finding Extrema Analytically by Jock M and Alistair B - example of an exponential function
- Optimization Problems by Tavia W - example of minimizing average cost
- Optimization Problems by Geoffrey W - example of maximizing area
- Antiderivatives by Bosco N - 2 examples of multi-term functions
- Antiderivative by Arvin A - trig and exponential function
- Antiderivative by James G - a polynomial function
- Intervals of Increase by Liam R - example of a rational function
- Intervals of Increase/Decrease and Concavity by Kimia M and Saba M - example with a polynomial
- Intervals of Increase by Justin Y and Devrutt G - example with a rational function
- Graphing with f' by Azi E - example of a polynomial
- Graphing with f' and f'' by Taylor S - example with no explicit function
- Complete Sketch using derivatives by Stefan L and Costner M - example of a polynomial
- Linearization of a Function by Azi E - example of sqrt(x+4)
- Using Linearization to Estimate by Bosco N - example of fourth root of 81.93
- Using Linearization to Estimate by Sana A and Mohammad O - example of cube root of 8.5
- Newton's Method by Mehran Z and Ramin M - example of a trig function
- Related Rates by Tavia W - example of a sphere and radius
- Related Rates by Jonald C and David P - example of a boat being pulled by a rope

## Chp 5

- Blank Notes Template
- Chp 5.1 Video, Casio - Estimating Area Under the Curve.
- RAM/RAML Video for TI-83 - shows you how to enter programs for TI's
- RAM/RAML Video for Casio fx-9750 - shows you how to enter programs for Casio's
- Chp 5.2 Video - Definite Integrals
- Chp 5.3 Video - Definite Integrals and Anti-derivatives
- Chp 5.4 Video - Fundamental Theorem of Calculus
- Chp 5.5 Video - Trapezoidal Rule and Simpson's Rule
- Chp 5 Review

## Assigned Work

- 5.1: pp. 254-255: 1-13 odds, 19, 25, 22; Challenge - 21
- 5.2: pp. 267-268: 7-25 odds, 39, 41, 24; Challenge - 31, 33
- 5.3: pp. 274-275: 1-11 odds, 17, 19, 21, 25, 24; Challenge - 29
- 5.4: pp. 286-287: 1-19 odds, 25, 27, 37, 39, 26; Challenge - 31, 33
- 5.5: pp. 294-295: 1-9 odds, 10ab; Challenge - 13, 17

## Student Videos

- Numeric Integration by Taylor S - example using a table of values and RAM
- Numeric Integration by Geoffrey W - example using a table of values and Trapezoidal
- Definite Integrals using Shapes by Stefan L and Alistair B - example of a semi-circle
- Indefinite Integrals using Antiderivatives by Stefan L and Tate B - examples of polynomials
- Fundamental Theorem of Calculus by Jock M and Kevin K - example of the derivative of a definite integral
- Fundamental Theorem of Calculus by Stefan L and Alistair B - example of the derivative of a definite integral

## Chp 6

- Blank Notes Template
- Chp 6.1 Video - Anti-derivatives and Slope Fields (Here is an online slope field generator)
- Chp 6.2 Video - Integration by Substitution
- Chp 6.3 Video - Integration by Parts
- Chp 6.4 Video - Exponential Growth and Decay
- Chp 6.5 Video - Population Growth
- Chp 6.6 Video - Numerical Methods
- Chp 6 Review

## Assigned Work

- 6.1: pp. 312-313: 7-17 odds, 31-37 odds, 34; Challenge - 25, 57
- 6.2: pp. 321-322: 1-21 odds, 31, 39, 43, 44; Challenge - 41
- 6.3: pp. 328-329: 1-11 odds, 15, 17, integrate(z ln z dz); Challenge - 29
- 6.4: pp. 338-339: 11, 13, 15, 19, 21, 25, 27; Challenge - 23
- 6.5: pp. 347-348: 3, 5, 7, 13, 17, 9-12; Challenge - 19

## Student Videos

- Integral Applications by Stefan L and Jock M - example of Newton's Law of Cooling

## Chp 7

- Blank Notes Template
- Chp 7.1 Video - Integral as Net Change
- Chp 7.2 Video - Areas in the Plane
- Chp 7.3 Video - Volumes Part 1 - Cross Section and Disks
- Chp 7.3 Video - Volumes Part 2 - Washer and Cylindrical Shells
- Chp 7.3 Video extra - Visualizing Volumes by Revolutions
- Chp 7.4 Video - Lengths of Curves
- Chp 7.5 Video - Applications from Sciences and Statistics
- Chp 7 Review

## Assigned Work

- 7.1: pp. 371-372: 1, 3, 7, 9, 11, 17, 19, 21, 29, 20; Challenge - 23, 31
- 7.2: pp. 380-382: 1-7 odds, 11, 13, 19, 21, 27, 20; Challenge - 43
- 7.3a: pp. 390-392: 1, 13-19 odds, integrate volume of cone; Challenge - 11
- 7.3b: pp. 392-393: 21, 23, 25, 39, 41, 43, integrate x=1-y^4, x=0 about x=2; Challenge - 35, 53
- 7.4: pp. 399: 1-15 odds, 2; Challenge - 17
- 7.5: pp. 407-408: 1-11 odds, 3 kg/m cable, 200kg coal, 300m mineshaft, find work; Challenge - 33, 35

## Student Videos

- Integral Applications by Stefan L and Alistair B - example of lifting a fishing net and line
- Volume of Rotated Function by Stefan L and Alistair B - example of using cylindrical shell

## Chp 8

- Blank Notes Template
- Chp 8.2 Full Notes
- Chp 8.1 Video - L'Hopital's Rule
- Chp 8.2 Video - Relative Rates of Growth
- Chp 8.3 Video - Improper Integrals
- Chp 8.4 Video - Partial Fractions and Integral Tables
- Chp 8 Review

- 8.1: pp. 423-424: 1-7 odds, 15-27 odds, 33-39 odds
- 8.2: p. 431: 1-23 odds, 20
- 8.3a: p. 442: 1-21 odds, 14
- 8.3b: p. 442: 27-43 odds, 38
- 8.4: p. 452: 1-13 odds, 17, 18, 21, 25

## Student Videos