# Pre-Calculus 40S

## Scroll  Down to find the latest (by date) Video Tutorial.

If you need a copy of the Unit 4: Quadratic Functions booklet, you could pick up one from the box that’s outside the front door of the school.

## Booklets and Assignments

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## Assignments from “Example Booklets” – to be submitted for marks.

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## 6b Trigonometry Part 2 Example Booklet

• From Chapter 6 Trigonometry Part 1 and Part 2 Example Booklets (click link above for copy).

### From Booklet: 6a Trigonometry Part 1 Example Booklet

1.  Pages 4 t0 6: Lesson 1 Examples. (Due on Friday, May 22nd, 2020.)
2. Pages 7 to 9: Unit Circle – Examples. (Due on Friday, May 29th, 2020)
3. Pages 10 to 14: Lesson 2 Examples. (Due on Tuesday, June 2nd, 2020)
4. Pages 15 to 17:  Lesson 3 Examples. ( Due on Wednesday, June 3rd, 2020.)
5. Pages 18 to 26: Lesson 3 Examples. (Due on  Friday, June 5th, 2020.)
6. Pages 27 to 28: Lessons 5 Examples.  (Due on  Monday June 8th, 2020.)

### From Booklet: 6b Trigonometry Part 2 Example Booklet

1.  Pages 4 t0 7: Lesson 1 Examples. (Due on Tuesday, June 9th, 2020.)
2. Pages 12 to 14: Lesson 3 Examples. (Due on Thursday, June 11th, 2020.)
3. Pages 15 to 16: Lesson 4 Examples. (Due on Friday, June 10th, 2020.)

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## Chapter 5 Exponents & Logarithms  Examples Booklet

From Chapter 5 Example Booklet (click link above for copy), complete the following:

1.  Lesson 1 Examples on pages 5 to 9. (Due on Wednesday, April 22, 2020.)
2. Lesson 3 Examples on pages 13 to 15 ( Due on Monday, April 27, 2020.) NOTE: Changed date.
3. Lesson 4 Examples on pages 16 to 17. (Due on Wednesday, April 29, 2020.) NOTE: Changed date.
4. Lessons 5 & 6 Examples on pages 18 to  24. (Due on Monday, May 4th, 2020.) NOTE: Changed date.
5. Lesson 2 Examples on pages 10 to 12. (Due on Monday, May 10th, 2020) NOTE: Changed date.
6. Lessons 7 Examples on pages 25-26 (Due on Thursday, May 14th , 2020.)

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## Chapter 4 Example Booklet- Combining Functions

From Chapter 4 Example Booklet (click link above), complete the following:

#### 4. Practice Test from Textbook: – Questions 3, 4, 7 and 9 on pages 335 to 338. (Must show all work.)

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# Friday, June 12th, 2020

### Lesson 6.6: Combining Transformations of Sinusoidal Functions (p. 529-539)

###### (Goals: Using Transformation to sketch a graph of a Trigonometric Function. Writing the Equation of the Graph of a trigonometric Function)

Completed Solutions to Questions 3 to 11 on pages 534 t0 536 of Textbook.

• Students will use this time to complete the final assessment: “Sketching transformation of Graphs”; and, “Determining equations given a sine and cosine graph”.

• ### To be Submitted for marks.

• Pages 15 to 16: Lesson 4 – Chapter 6 Part 2 Examples Booklet. (Due on Monday, June 15th, 2020.)

### Learning Notes:

#### 1. Student Assessment:

Practice Assessment:

• #2 on page 533 of textbook.
• ‘Exercises” # 5, # 6, # 7, and #10 on pages 535 to 539 of textbook

To be submitted for marks.

### From: 6a Trigonometry Part 1 Example Booklet

• Pages 15 to 17:  Lesson 3 Examples. ( Due on Friday, June 5th, 2020.)
• Pages 27 to 28: Lessons 5 Examples.  (Due on  Monday June 8th, 2020.)

### From Booklet: 6b Trigonometry Part 2 Example Booklet

• Pages 4 t0 7: Lesson 1 Examples. (Due on Tuesday, June 9th, 2020.)
• Pages 12 to 14: Lesson 3 Examples. (Due on Thursday, June 11th, 2020.)
• Pages 15 to 16: Lesson 4 Examples. (Due on Friday, June 10th, 2020.

# Thursday, June 11th, 2020

### Video Tutorial

###### (Goals: Using Transformation to sketch a graph of a Trigonometric Function. Writing the Equation of the Graph of a trigonometric Function)

Completed Solutions to Questions 3 to 11 on pages 534 t0 536 of Textbook.

### Learning Notes:

#### 1. Student Assessment:

Practice Assessment:

• #2 on page 533 of textbook.
• ‘Exercises” # 5, # 6, # 7, and #10 on pages 535 to 539 of textbook

To be submitted for marks.

### From: 6a Trigonometry Part 1 Example Booklet

• Pages 15 to 17:  Lesson 3 Examples. ( Due on Friday, June 5th, 2020.)
• Pages 27 to 28: Lessons 5 Examples.  (Due on  Monday June 8th, 2020.)

### From Booklet: 6b Trigonometry Part 2 Example Booklet

• Pages 4 t0 7: Lesson 1 Examples. (Due on Tuesday, June 9th, 2020.)
• Pages 12 to 14: Lesson 3 Examples. (Due on Thursday, June 11th, 2020.)
• Pages 15 to 16: Lesson 4 Examples. (Due on Friday, June 10th, 2020.

# Wednesday, June 10th, 2020

## Video Tutorial

###### (Goal: Using Transformation to sketch a graph of a Trigonometric Function.)

Completed Solutions to Questions 3 to 11 on pages 534 t0 536 of Textbook.

### Learning Notes:

#### 1. Student Assessment:

Practice Assessment:

• #2 on page 533 of textbook.
• ‘Exercises” # 5, # 6, # 7, and #10 on pages 535 to 539 of textbook

To be submitted for marks.

### From: 6a Trigonometry Part 1 Example Booklet

• Pages 15 to 17:  Lesson 3 Examples. ( Due on Friday, June 5th, 2020.)
• Pages 27 to 28: Lessons 5 Examples.  (Due on  Monday June 8th, 2020.)

### From Booklet: 6b Trigonometry Part 2 Example Booklet

• Pages 4 t0 7: Lesson 1 Examples. (Due on Tuesday, June 9th, 2020.)
• Pages 12 to 14: Lesson 3 Examples. (Due on Thursday, June 11th, 2020.)
• Pages 15 to 16: Lesson 4 Examples. (Due on Friday, June 10th, 2020. # Tuesday, June 9th, 2020

## Video Tutorial

###### (Goal: Describe how a graph  change  with Transformation. Using Transformation to sketch a graph of a Trigonometric Function.)

Completed Solutions to Questions 3 to 11 on pages 534 t0 536 of Textbook.

### 1. Student Assessment:

Practice Assessment:

• #1 on page 532 of textbook.
• ‘Exercises” # 3, # 4, # 8 on pages 534, 535, and 537 of textbook

To be submitted for marks.

### From: 6a Trigonometry Part 1 Example Booklet

• Pages 15 to 17:  Lesson 3 Examples. ( Due on Friday, June 5th, 2020.)
• Pages 27 to 28: Lessons 5 Examples.  (Due on  Monday June 8th, 2020.)

### From Booklet: 6b Trigonometry Part 2 Example Booklet

• Pages 4 t0 7: Lesson 1 Examples. (Due on Tuesday, June 9th, 2020.)
• Pages 12 to 14: Lesson 3 Examples. (Due on Thursday, June 11th, 2020.)
• Pages 15 to 16: Lesson 4 Examples. (Due on Friday, June 10th, 2020. # Monday, June 8th, 2020

## Video Tutorial

###### (Determining the Amplitude and Period, Phase Shift, and Vertical Translation of a Trigonometric Function – pages 510-511.)

Completed Solutions to Questions 3 to 11 on pages 521 to 526 of textbook.

### 1. Student Assessment:

Practice Assessment:

## To be submitted for marks.

• ### From: 6a Trigonometry Part 1 Example Booklet

• Pages 15 to 17:  Lesson 3 Examples. ( Due on Friday, June 5th, 2020.)
• Pages 27 to 28: Lessons 5 Examples.  (Due on  Monday June 8th, 2020.)

### From Booklet: 6b Trigonometry Part 2 Example Booklet

• Pages 4 t0 7: Lesson 1 Examples. (Due on Tuesday, June 9th, 2020.)
• Pages 12 to 14: Lesson 3 Examples. (Due on Thursday, June 11th, 2020.)
• Pages 15 to 16: Lesson 4 Examples. (Due on Friday, June 10th, 2020. # Friday, June 5th, 2020

### Lesson 6.5 – Trigonometric Functions – p. 513-519

###### (Determining the Amplitude and Period, Phase Shift, and Vertical Translation of a Trigonometric Function – pages 510-511.)

Completed Solutions to Questions 3 to 11 on pages 521 to 526 of textbook.

# Thursday, June 4th, 2020

## Video Tutorial

###### (Determining the Amplitude and Period of a Trigonometric Function – pages 510-511.)

Completed Solutions to Questions 3 to 11 on pages 521 to 526 of textbook.

### To be submitted for marks.

• #### From: 6a Trigonometry Part 1 Example Booklet

• Pages 15 to 17:  Lesson 3 Examples. ( Due on Friday, June 5th, 2020.)
• Pages 27 to 28: Lessons 5 Examples.  (Due on  Monday June 8th, 2020.)
• Pages 4 t0 7: Lesson 1 Examples. (Due on Tuesday, June 9th, 2020.)
• Pages 12 to 14: Lesson 3 Examples. (Due on Thursday, June 11th, 2020.)
• Pages 15 to 16: Lesson 4 Examples. (Due on Friday, June 10th, 2020.) # Wednesday, June 3rd, 2020

## Video Tutorial

###### (Sketch the graphs of  y=sin x; y= cos x, y=tan x and determine their characteristics – pages 510-511.)

Completed Solutions to Questions 1 to 4 on page 512 of textbook.

### To be submitted for marks.

• #### From: 6a Trigonometry Part 1 Example Booklet

• Pages 10 to 14: Lesson 2 Examples. (Due on Tuesday, June 2nd, 2020)
• Pages 15 to 17:  Lesson 3 Examples. ( Due on Friday, June 5th, 2020.) # Tuesday, June 2nd, 2020

## Video Tutorial

###### (Determining Angle Measures Given a Terminal Point  – page 493)

Completed Solutions to questions 4 to 15 on pages 494 to 500 of textbook.

### To be submitted for marks.

• #### From: 6a Trigonometry Part 1 Example Booklet

• Pages 10 to 14: Lesson 2 Examples. (Due on Tuesday, June 2nd, 2020)
• Pages 15 to 17:  Lesson 3 Examples. ( Due on Friday, June 5th, 2020.) # Monday, June 1st, 2020

## Video Tutorial

### To be submitted for marks.

• #### From: 6a Trigonometry Part 1 Example Booklet

• Pages 7 to 9: Unit Circle Examples. (Due on Friday, May 29th 2020.)
• Pages 10 to 14: Lesson 2 Examples. (Due on Tuesday, June 2nd, 2020)
• Pages 15 to 17:  Lesson 3 Examples. ( Due on Friday, June 5th, 2020.) # Friday, May 29th, 2020

## Video Tutorial

### To be submitted for marks.

• #### From: 6a Trigonometry Part 1 Example Booklet

• Pages 7 to 9: Unit Circle Examples. (Due on Friday, May 29th 2020.)
• Pages 10 to 14: Lesson 2 Examples. (Due on Tuesday, June 2nd, 2020)
• Pages 15 to 17:  Lesson 3 Examples. ( Due on Friday, June 5th, 2020.) # Thursday, May 28th, 2020

## Video Tutorial

### To be submitted for marks.

• #### From: 6a Trigonometry Part 1 Example Booklet

• Pages 7 to 9: Unit Circle Examples. (Due on Friday, May 29th 2020.) # Wednesday, May 27th, 2020

## Video Tutorial

### To be submitted for marks.

• #### From: 6a Trigonometry Part 1 Example Booklet

• Pages 7 t0 9: Unit Circle Examples. (Due on Friday, May 29th 2020.)

# Notes on Arc Length # Tuesday, May 2th, 2020

## Video Tutorial (To be posted later.)

### To be submitted for marks.

• #### From: 6a Trigonometry Part 1 Example Booklet

• Pages 7 t0 9: Unit Circle Examples. (Due on Friday, May 29,th 2020.)

# Notes on Unit Circle, Reference Triangles, Trig. Ratios      # Monday, May 25th, 2020

## Video Tutorial

### To be submitted for marks.

• #### From: 6a Trigonometry Part 1 Example Booklet

• Pages 7 t0 9: Unit Circle Examples. (Due on Friday, May 29, 2th020.)

# Notes on Unit Circle, Reference Triangles, Trig. Ratios      # Friday, May 22nd, 2020

## Video Tutorial

### To be submitted for marks.

• #### From: 6a Trigonometry Part 1 Example Booklet

• Pages 4 t0 6: Lesson 1 Examples. (Due on Friday, May 22nd, 2020.)

# Notes on Unit Circle, Reference Triangles, Trig. Ratios      # Thursday, May 21st, 2020

## Video Tutorial

### 1. Student Assessment:

#### Practice Questions:  “Check your Understanding”, Question 3 on page 472; Questions 8, 9 on  p. 477 and 478.

To be submitted for marks.

• #### From: 6a Trigonometry Part 1 Example Booklet

• Pages 4 t0 6: Lesson 1 Examples. (Due on Friday, May 22nd, 2020.)

# Wednesday, May 20th, 2020

## Video Tutorial

###### ( Determining and Sketching Angles in Standard Position, Co-terminal Angles, and Reference Angles. Using Assignment Questions 1 to 5. )

1. Student Assignment: To be submitted for marks.

• #### From: 6a Trigonometry Part 1 Example Booklet

• Pages 4 t0 6: Lesson 1 Examples. (Due on Friday, May 22nd, 2020.)

# Tuesday, May 19th, 2020

## Video Tutorial

###### (Determining and Sketching Angles in Standard Position and  Co-terminal Angles.)

1. Student Assignment:

• Practice Questions: Check Your Understanding – Q. 1 on pages 469 of textbook.

Students will complete: “Exercises” – Questions  3, 4, and 5  on pages 474 and 475 of textbook.

2. To be submitted for marks.

• #### From: 6a Trigonometry Part 1 Example Booklet

• Pages 4 t0 6: Lesson 1 Examples. (Due on Friday, May 22nd, 2020.)

# Friday, May 15th, 2020

## Video Tutorial

###### (Solving a Problem involving Future Value. Solving a Problem Involving the Richter Scale.)

1. Student Assignment:

• Practice Questions. Students will complete: “Check Your Understanding”

Questions 1 and 3 on pages 431 and 433 of  textbook.

# Thursday, May 14th, 2020

## Video Tutorial

###### (Solving logarithm and exponential equations  algebraically. Questions  11, 12, 13, 14 on pages 425 to 426 of textbook.)

1. Student Assignment. To be submitted for marks.

# Wednesday, May 13th, 2020

## Video Tutorial

###### (Solving logarithm and exponential equations  algebraically.)

1. Student Assignment:

• Practice Questions:

Students will complete: “Exercises” – Questions  11, 12, 13, 14 on pages 425 to 426 of textbook.

# Tuesday, May 12th, 2020

## Video Tutorial

###### (Solving logarithm and exponential equations  algebraically.)

1.Student Assignment:

Practice Questions: Students will complete: “Exercises” – Questions 3, 4, 5, 7, 9, 10 on pages 422 to 424.

# Monday, May 11th, 2020

## Video Tutorial

###### (Solving logarithm and exponential equations  algebraically.)

1.Student Assignment:

Practice Questions: Students will complete:  “Check Your Understanding” 1,2,3 on pages 418 to 420.

# Thursday, May 7th, 2020

## Video Tutorial

##### (Use the Change of Base Formula to find the value of a logarithm. Sketch the transformation graph of a Logarithmic function.)

• Student Assignment:

Students will complete: Questions 9, 10, 11, and 12 on pages 407 and 409.

#### To be submitted for marks.

# Wednesday, May 6th, 2020

## Video Tutorial

##### (Use the Change of Base Formula to find the value of a logarithm. Sketch the transformation graph of a Logarithmic function.)

• Student Assignment:

Students will complete: Questions 1, 3 on pages 402 and 403.

Questions 3, 4, 5 on pages 405, 406 of student textbook.

# Tuesday, May 5th, 2020

## Video Tutorial

(Writing a Log. as a sum or Difference of  Logarithms. Using the laws of Logarithm to Evaluate Logarithmic Expression.)

# Friday, May 1st, 2020

## Video Tutorial

(Writing a Log. as a sum or Difference of  Logarithms. Using the laws of Logarithm to Evaluate Logarithmic Expression)

# Thursday, April 30th, 2020

## Video Tutorial

(Writing a Log. as a sum or Difference of  Logarithms. Using the laws of Logarithm to Evaluate Logarithmic Expressions.)

### A.  Student Assignments:

#### Questions: 3 and 4 on page 391 t0 393 of Textbook.

Questions: 9, 10, 11, 12, 13 and 18 on pages 394 to 398 of Textbook.

# Wednesday, April 29th, 2020

## Video Tutorial

(Use the Law of Logarithm to Simplify Expressions. Apply the laws of Logarithm to Logarithm with Base 10.)

### A.  Student Assignments:

#### Questions: 1 and 2 on page 390 t0 391  of Textbook.

Questions: 5, 6, and 8 on pages 394 to 395 of Textbook.

# Tuesday, April 28th, 2020

## Video Tutorial

(Writing Expressions in Different Forms; Evaluating Logarithms; Using Benchmarks to estimate the value of a Logarithm; and, Characteristics  of the Graphs of Logarithmic Functions.)

# Monday, April 27th, 2020

## Video Tutorial

(Using Benchmarks to estimate the value of a Logarithm; Characteristics  of the Graphs of Logarithmic Functions.)

### A.  Student Assignments:

#### Questions: 3 and 4 on page 379 of Textbook.

Questions: 4 to 11 on pages 381 to 383 of Textbook.

# Friday, April 24th, 2020

## Video Tutorial

(Writing Expressions in different forms; Evaluating Logarithms.)

# Thursday, April 23rd, 2020

## Video Tutorial

(Graphing Exponential Functions; Transformation of Exponential Functions; and, Solving Exponential Equations.)

# Wednesday, April 22nd, 2020

## Video Tutorial

(Solving: Exponential Equations using Common Bases; Exponential Equations involving Radicals.)

1. ### Student Assignments:

a).  Practice Assignments: Questions 3 t0 5 on page 364; and Question 10 on page 366 of textbook.

•    Lesson 3 Examples on pages 13 to 15 ( Due on Friday, April 24, 2020.) NOTE: Changed date.

# Tuesday, April 21st, 2020

## Video Tutorial

(Sketching Graphs of Transformation of Exponential Functions including Real-World Situations)

1. ### Student Assignments:

a).  Practice Assignment: Students to complete Questions 9;  10 c; and 13 on p. 352 to 355 of textbook.

Lesson 1 Examples on pages 5 to 9. (Due today, April 22, 2020.)

# Monday, April 20th, 2020

## Video Tutorial

(Examples of  Transformation of Exponential Functions)

1. ### Student Assignments:

a).  Practice Assignment: Students to complete Questions 3, 4, 5, 6, 7, on p. 349 to 353 of textbook.

Lesson 1 Examples on pages 5 to 9. (Due Wednesday, April 22, 2020.)

# Friday, April 17th, 2020

### No-online Classes

Staff Professional Development Day

# Thursday, April 16th, 2020

## Video Tutorial

(Sketching exponential functions; transformation of  Exponential Functions.)

• Student Assignment:

1. “Check your Understanding” – Q. 1 on page 345 and – Q. 2 on page 347.

# Wednesday, April 15th, 2020

## Video Tutorial

(Describing the graph of Exponential Function.)

1. Student Assignment: Page 341
2. Students to complete: “Assess Your Understanding”; Question  1.

# Tuesday, April 14th, 2020

## Video Tutorial

(Introduction: Review Powers; Exponent Laws. )

1. Students to complete Assignment 1 – Exponential Functions – Pre-requisite Skills.

• Complete Questions 1 to 7, and 9.

(Click Link below for copy of Assignment.)

# Monday, April 13th, 2020

Unit 4: Combining Functions  p. 266 to 338.

## Video Tutorial

#### on Review Questions

Questions: 1. a;  3 ; 6 ; 7; and 10  on pages 327 to 332.

### Students to Complete and submit (for marks)

(due Tuesday, April 14th, 2020)

1. #### Lesson 4  Questions – from 4 Example Booklet Combining Functions.

2. Practice Test from Textbook: – Questions 3, 4, 7 and 9 on pages 335 to 338. (Must show all work.)

# Thursday, April 9th, 2020

Unit 4: Combining Functions  p. 266 to 338.

## Video Tutorial

#### on

Questions: 3, 4  on pages 312, 313.

Questions: 3 c, d; 4 a, b; 6 a; 8 a; 10 a; on pages 314 to 319

### Students to Complete and submit (for marks)

(due next week Tuesday, April 14th)

1. #### Lesson 4  Questions – from 4 Example Booklet Combining Functions.

2. Practice Test from Textbook: – Questions 3, 4, 7 and 9 on pages 335 to 338. (Must show all work.)

# Wednesday, April 8th, 2020

Unit 4: Combining Functions  p. 266 to 338.

## Video

#### on

(Determining a Composition of a Radical Function and a Quadratic Function; Writing a Function as Composition of Two Functions)

### Check Your Understanding  (from Textbook)

• Question # 3  a, b on page 312.
• Question # 4 a, b  on page 313

### Exercises (from Textbook)

• Question  # 6   (a, b, c, d) on pages 316 -317.
• Question  # 8  (a on page 315
• Question  # 10  (a, b, c, d) on page 319

# Tuesday, April 7th, 2020

Unit 4: Combining Functions  p. 266 to 338.

## on

(Domain & Range of  f(g(x)); Composition of a Linear and a Quadratic Function; Reciprocal Function and a Quadratic Function)

### Practice Assignment (not for marks – do not submit)

• Question # 1  a, b on page 308.
• Question # 2 a, b  on page 311

Exercises (from Textbook)

• Question  # 3   a, b, c, d on page 314
• Question  # 4  a, b, c, d on page 315
• Question  #5  a, b on page 316

# Monday, April 6th, 2020

Unit 4: Combining Functions  p. 266 to 338.

## Video Tutorial

on

(Check Your Understanding # 3 and #4 on Pages 296 and 297 of Textbook.)

(Exercises: # 4 a,b;    #5 a,b;  # 6 c,d;     #10 a,b )

### 1. Practice Assignment (not for marks – do not submit)

• From Textbook: Pages 298 to 301
• # 4 a, b;  #5 c,d;  #6 a,b;  #7 a,b;  #8 b;  #9 a,b,d; #10 a,b,d; #11 a,b,c)

### 2. To be submitted for marks.

• From Example Booklet: Lesson 3: #1 to #4 on  pages 9 to 10.

Click below for copy of Example Booklet – Combining Functions

# Friday, March 27th, 2020

Unit 4: Combining Functions  p. 266 to 338.

## Video Tutorial

• ### From Textbook  – Pages 294- 297

#1 on page 294

# 2 on page 295

# 3 on page 296

# 4 on page 297

### From Textbook  – Pages 288 to 290.

• Question 2   a, b, c, d – Pages  288 to 289
• Question 4   a, b, c  – Pages 289 to 290
• Question 5  a, b, c, d – Page 290

# Thursday, March 26th, 2020

Unit 4: Combining Functions  p. 266 to 338.

# Video Tutorial

### 1. Student Hand-in Assignment

#### To be submitted by Friday, March 27th, 2020:

• From “Example Booklet”: Lesson 2

Students to complete Lesson 2: Examples 1 to 4 on pages 7  and 8.

# Wednesday, March 25th, 2020

Unit 4: Combining Functions  p. 266 to 338.

## Video Tutorial: Combining Functions Algebraically

### 1. Student Assignment: From Textbook  – Pages 274- 277

#1 on page 274

# 2 on page 275

# 3 on page 276

# 4 on page 277

# Tuesday, March 24th, 2020

Unit 4: Combining Functions  p. 266 to 338.

## Video Tutorial: Assess Your Understanding  – p.268 to 271.

### 1. Student Assignment:

• From Example Booklet:

Complete Lesson 1: Examples 1 to 4 on pages 4, 5, and 6.

# Monday, March 23rd, 2020

Unit 4: Combining Functions  p. 266 to 338.

### 1. Student Assignment:

• Complete Questions 1 to 3 on pages 268 to 271.

# Friday, March 20th, 2020

### Transforming Graphs of Functions

Unit 3 Review of Inverse of Relations

• Today, we will complete the final lesson of Unit 3: Transforming Graphs of Functions.
• Examples Booklet-  Lesson 5: Inverses of Relations.

# Unit Test

Unit 3: Transforming Graphs of Functions

# Wednesday, March 18th, 2020

Unit 3: Transforming Graphs of Functions  p. 161 to 264.

### See below for answers to today’s assignments.

Questions 4 and 5 page 243 # Tuesday, March 17th, 2020

Unit 3: Transforming Graphs of Functions  p. 161 to 264.

# Monday, March 16th, 2020

Unit 3: Transforming Graphs of Functions  p. 161 to 264.

No Classes

# Thursday, March 12th, 2020

Unit 3: Transforming Graphs of Functions  p. 161 to 264.

# Wednesday, March 11th, 2020

Unit 3: Transforming Graphs of Functions  p. 161 to 264.

# Tuesday, March 10th, 2020

Unit 3: Transforming Graphs of Functions  p. 161 to 264.

# Monday, March 9th, 2020

Unit 3: Transforming Graphs of Functions  p. 161 to 264.

# Friday, March 6th, 2020

Unit 3: Transforming Graphs of Functions  p. 161 to 264.

### Today we will continue  Unit 3: Transforming Graphs of Functions

1. Transformation.

# Thursday, March 5th, 2020

Unit 3: Transforming Graphs of Functions  p. 161 to 264.

### Today we will begin Unit 3: Transforming Graphs of Functions

1. We will review the prerequisite skills for Transforming Graphs of Functions.

Students will complete ” Chapter 2: Pre-requisite skills” assignment. See link below for copy.

# Tuesday, March 3rd, 2020

Unit 2: Graphing Radical &  Rational  Functions p. 82 to 156.

# Monday, March 2nd, 2020

Unit 2: Graphing Radical &  Rational  Functions p. 82 to 156.

## 1. Take up the the following:

• ### “Constructing Understanding” example on pages 129 and 130.

• Example 2 on page 131.

### 2.  Assignments:

• #### Textbook:

• Page 143, question 3
• Page 135, Question 4
• Page 135, Question 5
• Page 136, Question 6
• Page 139 Question 8

# Friday, February 28th, 2020

Unit 2: Graphing Radical &  Rational  Functions p. 82 to 156.

## 2. Completed the following:

• ### “Constructing Understanding” example on pages 129 and 130.

• Example 2 on page 131.

### 3.  Students were assigned

• #### Example Booklet” – pages 16 to 18.

• Textbook:
•   Page 143, question 3
• Page 135, Question 4
• Page 135, Question 5
• Page 136, Question 6
• Page 139 Question 8

# Thursday, February 27th, 2020

Unit 2: Graphing Radical &  Rational  Functions p. 82 to 156.

## 1.What is a Rational Function?

• ### What is an Asymptote? Click Link   ### –  Point of Discontinuity (Hole)-  a (point) break in the line, when the numerator and denominator have at least one common factor. ### –  Characteristics 1: Non-permissible values of x.

• Non-Permissible Values: values of a variable that make the denominator of a rational expression equal 0.
• See notes (link)  below on Non-permissible values

Notes on Non-Permissible Value

• ### y=0          When the degree of the numerator is less than the degree of the denominator.

• y = a/b      When the degrees of numerator and denominator are the same, then ratio of the leading coefficient is the horizontal asymptote.
• Oblique Asymptotes – When the degree of the numerator is greater than the degree of the denominator.

• ### Lesson 4, pages 10 to 15 of their Example Booklet.

#### Graphing General Polynomials, Radicals, Rationals, and Piecewise Functions

Domain and Range of radical and rational Functions

Video Tutorial

Sketching the Graph of y = √f(x) Given the Graph of a Quadratic  Function  y = f(x)

# Wednesday, February 26th, 2020

Unit 2: Graphing Radical &  Rational  Functions p. 82 to 156.

## p. 100 to 103

### 1. Complete “Get Started” with class on page 100 of textbook.

• Non-Permissible Values: values of a variable that make the denominator of a rational expression equal 0.
• See notes (link)  below on Non-permissible values

Notes on Non-Permissible Value

### 3. Answers to“Construct Understanding ” on pages 100 to 104 of textbook.

Page 101 Page 102 Page 103 Page 104 #### Graphing General Polynomials, Radicals, Rationals, and Piecewise Functions

Domain and Range of radical and rational Functions

Video Tutorial

Sketching the Graph of y = √f(x) Given the Graph of a Quadratic  Function  y = f(x)

# Tuesday, February 25th, 2020

Unit 2: Graphing Radical &  Rational  Functions p. 82 to 156.

## (See Handout)

### 3. Assignment: Check Your Understanding (3 pages).

#### Graphing General Polynomials, Radicals, Rationals, and Piecewise Functions

Domain and Range of radical and rational Functions

Video Tutorial

Sketching the Graph of y = √f(x) Given the Graph of a Quadratic  Function  y = f(x)

# Friday, February 21st, 2020

Unit 2: Graphing Radical &  Rational  Functions p. 82 to 156.

## Lesson 2.1

### 1.  Students  to complete:

• Questions 4, 5, 6, 7, 8, 10, 12 on pages 90 to 95  of  Textbook.

Answers pages 90 to 95 of Textbook          Key Ideas on Sketching a Square Root of  a Function  ## p.  100 to 103

### 1. Complete “Get Started” with class on page 100 of textbook.

• Non-Permissible Values: values of a variable that make the denominator of a rational expression equal 0.
• See notes (link)  below on Non-permissible values

Notes on Non-Permissible Value

### 2. Students complete “Construct Understanding ” on pages 100 to 103 of textbook.

#### Graphing General Polynomials, Radicals, Rationals, and Piecewise Functions

Domain and Range of radical and rational Functions

Video Tutorial

Sketching the Graph of y = √f(x) Given the Graph of a Quadratic  Function  y = f(x)

# Thursday, February 20th, 2020

Unit 2: Graphing Radical &  Rational  Functions p. 82 to 156.

### Today we will continue Unit 2: Properties of Radical Functions – Lesson 2.1

1.  Complete Example 2:

• Sketching the Graph of y = √f(x) Given the Graph of a Quadratic  Function  y = f(x) pages 86 to 87.

2.  Complete Example 3:

• Sketching the Graph of y = √f(x) Given the Graph of a Cubic Function  y = f(x) pages 88.

3.  Square Root of a Function – Key Ideas 3. Students  to complete:

•  Example 2 and Example 3 on pages 6 and 7 of “Radical and Rational Functions Example Booklet”.

• Questions 4, 5, 6, 7, 8, 10, 12 on Pages 90 to95 of Textbook.

#### Graphing General Polynomials, Radicals, Rationals, and Piecewise Functions

Domain and Range of radical and rational Functions

Video Tutorial

Sketching the Graph of y = √f(x) Given the Graph of a Quadratic  Function  y = f(x)

# Wednesday, February 19th, 2020

Unit 2: Graphing Radical &  Rational  Functions p. 82 to 156.

### Today we continued Unit 2: Properties of Radical Functions

1.  Lesson 2.1: Sketching Graph of the Radical Functions y = √xpages 4 and 5 in Example Booklet.

2. Properties of Radical Functions – Example 1 0n pages 84 to 85 of Textbook.

3. Students completed (click on links below):

#### Graphing General Polynomials, Radicals, Rationals, and Piecewise Functions

Domain and Range of radical and rational Functions

Video Tutorial

# Tuesday, February 18th, 2020

Unit 2: Graphing Radical &  Rational  Functions p. 82 to 156.

### Today we will begin Unit 2: Properties of Radical Functions

1. We will review the prerequisite skills for Radical and Rational functions.

Students will complete ” Chapter 2: Pre-requisite skills” assignment. See link below for copy.

2. Lesson 2.1: Sketching Graph of the Radical Functions y = √xpages 2 to 7 of Example Booklet.

3. Properties of Radical Functions – pages 82 to 97 of Textbook.

4. Students to complete: pages 5, 7, 8, 10 and 12 in textbook pages 90 to 92.

5. Completed “Notes”  – to be posted after class.

#### Graphing General Polynomials, Radicals, Rationals, and Piecewise Functions

Domain and Range of radical and rational Functions

Video Tutorial

# Wednesday, February 12th, 2020

## Pre-Calculus 40S: Polynomial Expressions and Functions

• ### Today, we will review how to sketch polynomial.

To sketch a polynomial you will need to know 4 things.

1. The degree of the polynomial

2. The sign of the leading coefficient

3. The Zeros

4. Multiplicity

# Monday, February 10th, 2020

## Pre-Calculus 40S: Polynomial Expressions and Functions

### Today we will complete Lesson 1.4  on pages 37 to 45

1. Lesson 1.4: Relating Polynomial Functions and equations, pages 37  to 45.

2. Review questions from:

Polynomial  Functions Example booklet- pages 17 to 20, Examples 1 to 4.

3. Students to complete: pages 46 to 52, Questions # 5 to 13 of  Textbook.

4. Completed “Notes” from pages 37 to 45 – see links below.

Polynomial Expressions and Functions p 36 and 37

Polynomial Expressions and Functions p 38 and 39

Polynomial Expressions and Functions p 40 and 41

Polynomial Expressions and Functions p 42 and 43

Polynomial Expressions and Functions p 44 and 45

# Steps for Factoring Polynomial Functions

To factor Polynomial Functions and the Integral Zero Theorem:

1. Use the Integral Zero Theorem to list possible possible integer values for the zeros.
2. Next, apply the Factor Theorem to determine one factor.
3. Then, use division to determine the remaining factor.
4. Repeat the above steps until all factors are found.

### Factor Theorem:

• If  x-a is a factor then,  P(a) =0
• If  P(a) = 0, then x-a is a factor of P(a).

### Integral Zero Sum Theorem:

• This describes the relationships between the factors and the constant terns in a polynomial.
• If x-a is a factor of the polynomial P(x) with integral coefficient, then a is a factor of the term P (x) and x = a is an integral zero of P (x).

### Remainder Theorem:

• When a polynomial P (x) is divided by a binomial (x-a), the remainder is P(a).
• If the remainder is zero, then the binomial x-a  is factor of P (x).
• If the remainder is not zero, then the binomial (x-a) is not a factor of P (x).

# Steps for Sketching Graphs of Polynomial Functions

### A. Use:

– x-intercepts,

–   the y-intercepts,

–  the degree of the function, and,

–  the sign of the leading coefficient.

### D. Use the factor theorem  to express a polynomial function factored form. # Multiplicity of a Zero

(How many times a particular number is a zero for a given polynomial.)

• If a polynomial function has a factor of  x-a that is repeated n times, then x-a has a multiplicity of n.

• zero has a “multiplicity“, which refers to the number of times that its associated factor appears in the polynomial. For instance, the quadratic (x + 3)(x – 2) has the zeroes x = –3 and x = 2, each occuring once.
• How many times a particular number is a zero for a given polynomial. For example, in the polynomial function f(x) = (x – 5)4(x – 5)(x – 8)2, the zero 3 has multiplicity 4, 5 has multiplicity 1, and 8 has multiplicity 2. Although this polynomial has only three zeros, we say that it has seven zeros counting multiplicity.

Examples:

• (x – 5)has Zero Multiplicity of 4
• (x – 5)  has Zero Multiplicity of  1
• (x – 8)2 has Zero Multiplicity of 2   ## Solutions to pages 46 to 52, Questions # 3 to 13 of  Textbook.

Polynomial Expressions and Functions p 42 and 43

Polynomial Expressions and Functions p 44 and 45

Polynomial Expressions and Functions p 46 and 47

Polynomial Expressions and Functions p 48 and 49

Polynomial Expressions and Functions p 50 and 51

Polynomial Expressions and Functions p 52 and 53

# Friday, February 7th, 2020

## Pre-Calculus 40S: Polynomial Expressions and Functions

### Today we will continue Unit 1: Polynomial Expressions and Functions

1. Lesson 1.4: Relating Polynomial Functions and equations, pages 37  to 45.

2. Students will work on Whiteboards tables to complete:

– Polynomial  Functions Example booklet- pages 17 to 20, Examples 1 to 4.

3. Students to complete: pages 46 to 52, Questions # 3 to 13 of  Textbook.

4. Completed “Notes” from pages 37 to 45 – see links below.

Polynomial Expressions and Functions p 36 and 37

Polynomial Expressions and Functions p 38 and 39

Polynomial Expressions and Functions p 40 and 41

Polynomial Expressions and Functions p 42 and 43

Polynomial Expressions and Functions p 44 and 45

## Solutions to pages 46 to 52, Questions # 3 to 13 of  Textbook.

Polynomial Expressions and Functions p 42 and 43

Polynomial Expressions and Functions p 44 and 45

Polynomial Expressions and Functions p 46 and 47

Polynomial Expressions and Functions p 48 and 49

Polynomial Expressions and Functions p 50 and 51

Polynomial Expressions and Functions p 52 and 53

# Thursday, February 6th, 2020

## Pre-Calculus 40S: Polynomial Expressions and Functions

### Today we will continue Unit 1: Polynomial Expressions and Functions

1. Lesson 1.2: Factoring Polynomials: Use the Remainder Theorem and Factor Theorem to factor Polynomials,  pages 15 to 19.

2. Students will work on Whiteboards tables to complete:

– Polynomial  Functions Example booklet- pages 11 to 14, Examples 1 to 5.

3. Students to complete: pages 20 to 26, Questions # 3 to 9, 11, and 12 of  Textbook.

4. Completed “Notes” from pages 15 to 19 – see links below.

Polynomial Expressions and Functions Lesson 1.2 p 15

Polynomial Expressions and Functions Lesson 1.2 p 16

Polynomial Expressions and Functions Lesson 1.2 p 17

Polynomial Expressions and Functions Lesson 1.2 p 18

Polynomial Expressions and Functions Lesson 1.2 p 19

## Solutions to pages 20 to 26, Questions # 3 to 9, 11, and 12 of  Textbook.

Polynomial Expressions and Functions p 20 and 21

Polynomial Expressions and Functions p 22 and 23

Polynomial Expressions and Functions p 24 and 25

Polynomial Expressions and Functions p 26 and 27

# Steps for Factoring Polynomial Functions

To factor Polynomial Functions and the Integral Zero Theorem:

1. Use the Integral Zero Theorem to list possible possible integer values for the zeros.
2. Next, apply the Factor Theorem to determine one factor.
3. Then, use division to determine the remaining factor.
4. Repeat the above steps until all factors are found.

### Factor Theorem:

• If  x-a is a factor then,  P(a) =0
• If  P(a) = 0, then x-a is a factor of P(a).

### Integral Zero Sum Theorem:

• This describes the relationships between the factors and the constant terns in a polynomial.
• If x-a is a factor of the polynomial P(x) with integral coefficient, then a is a factor of the term P (x) and x = a is an integral zero of P (x).

### Remainder Theorem:

• When a polynomial P (x) is divided by a binomial (x-a), the remainder is P(a).
• If the remainder is zero, then the binomial x-a  is factor of P (x).
• If the remainder is not zero, then the binomial (x-a) is not a factor of P (x).

This section deals with dividing polynomials, synthetic division and the remainder theorem.   The following are some links that may help – the textbook has some great examples, too.

# Wednesday, February 5th, 2020

## Pre-Calculus 40S: Polynomial Expressions and Functions

### Today we will continue Unit 1: Polynomial Expressions and Functions

1. Lesson 1.1: Dividing a Polynomial by a Binomial using “Synthetic Divisions”,  pages 5 to 7.

2. Polynomial  Functions  Example booklet- pages 9 to 10, questions 5, 6, and 7.

3. Students to complete: pages 7 – 12; Questions # 3 to 9, 12  of  Polynomial Expressions and Functions booklet.

4. Completed “Notes” from pages 2 to 6 – see links below.

Polynomial Expressions and Functions p 2

Polynomial Expressions and Functions p 3

Polynomial Expressions and Functions p 4

Polynomial Expressions and Functions p 6

Answers to Exercises: Questions 7 to 14 on pages 8 to 12.

Polynomial Expressions and Functions p 8

Polynomial Expressions and Functions p 9

Polynomial Expressions and Functions p 10

Polynomial Expressions and Functions p 11

Polynomial Expressions and Functions p 12

Polynomial Expressions and Functions p 13

This section deals with dividing polynomials, synthetic division and the remainder theorem.   The following are some links that may help – the textbook has some great examples, too.

# Tuesday, February 4th, 2020

Pre-Calculus 40S:

### Today we will begin Unit 1: Polynomial Expressions and Functions

1. Lesson 1.1: Dividing a Polynomial by a Binomial,  pages 2 to 13.

2. Students to complete: pages 7 – 12; Questions # 3 to 9, 12.

3. Completed “Notes” from pages 2 to 6 – see links below.

# Monday, February 3rd, 2020

This is the first day of class.

We will be looking at the course descriptions and contents, assessment and evaluation, resources required for Pre-Calculus 40S, and the first unit – Polynomial Functions

## Pre-Calculus 40S Course Outline

 Unit Topics Transformations ·         Operations on functions ·         Horizontal and vertical translations ·         Horizontal and vertical stretches and compressions ·         Reflections and Inverses Polynomial Functions ·         Review of factoring ·         Factoring of polynomial functions (up to 5th degree) ·         Graph and analyze polynomial functions (up to 5th degree) Radical Functions ·         Graph and analyze radical functions (one radical) ·         Solve radical equations graphically Rational Functions ·         Graph and analyze rational functions. ·         Connect graphs and equations of rational functions Composite Functions ·         Add, Subtract, Multiply and Divide Functions ·         Composite Functions Trigonometric Angles & Graphs ·         Angles in standard position in degrees and radians ·         Develop and apply the equation of the unit circle ·         Solve problems using six trig ratios in degrees and radians ·         Graph and analyze the primary trig functions Trigonometric Equations & Identities ·         Basic Trig identities ·         Sum and difference identities (sine, cosine, tangent) ·         Double angle identities (sine, cosine, tangent) ·         Solve first and second degree trig equations in degrees and radians Exponential & Logarithms ·         Understanding of logarithms ·         Product, Quotient and Power Laws ·         Graph and analyze exponential and logarithmic functions ·         Solve problems using exponential and logarithmic equations Combinatorics ·         Use Fundamental Counting Principle to solve problems ·         Permutations ·         Combinations ·         Binomial Expansion (natural exponents)

# Student Resources

## Click on the link below.

Day 1 40S PreCal Factoring Review Student Copy

### 2. Lesson 1 (p. 5 and 6) of Chapter 1: Polynomial Functions Example Booklet.

Click on the link below for copy of the booklet.

CHAPTER 1- Polynomial Functions Examples Booklet