Pre-Calculus 40S

Contents

Note: Please email  any assignments to me at:  bdabie@wsd1.org

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.

 The Final Class will be on Friday, June 12th, 2020

All assignments must be submitted by June 17th, 2020.

Booklets and Assignments

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Example Booklets – Click links to download.

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

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Chapter 6 – Trigonometry

Click on link below for Chapter 6a & 6b Booklets.

6a Trigonometry Part 1 Example Booklet

6b Trigonometry Part 2 Example Booklet

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

Complete the following:

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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Click on link below for Chapter 5 Booklet.

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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Click on link below for Chapter 4 Booklet.

Chapter 4 Example Booklet- Combining Functions

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

1. Lesson 1 and Lesson 2:  due April 7th, 2020

2. Lesson 3; due  April 9, 2020

3. Lesson 4; due April 14th, 2020.

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 

Unit 6 Trigonometry  p. 445 to 570.

 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: 

  • Click on link below to view notes on combining transformation of Sinusoidal Function.

Learning Notes for Lesson 6.6 Combining Transformation of Sinusoidal Functions

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 

Unit 6 Trigonometry  p. 445 to 570.

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

 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: 

  • Click on link below to view notes on combining transformation of Sinusoidal Function.

Learning Notes for Lesson 6.6 Combining Transformation of Sinusoidal Functions

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 

Unit 6 Trigonometry  p. 445 to 570.

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

 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: 

  • Click on link below to view notes on combining transformation of Sinusoidal Function.

Learning Notes for Lesson 6.6 Combining Transformation of Sinusoidal Functions

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 

Unit 6 Trigonometry  p. 445 to 570.

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

 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.

Learning Notes: 

  • Click on link below to view notes on combining transformation of Sinusoidal Function.

Learning Notes for Lesson 6.6 Combining Transformation of Sinusoidal Functions

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 

Unit 6 Trigonometry  p. 445 to 570.

 Lesson 6.5 – Trigonometric Functions – p. 513-511

 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:

  • Practice Questions: # 2, # 3. # 4 on pages 517 to 519 of textbook. And, from ‘Exercises” # 3, # 4, # 6 on pages 521 to 523 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.

Friday, June 5th, 2020 

Unit 6 Trigonometry  p. 445 to 570.

 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.

Today’s Class:

  • Students will use this time to complete Practice Questions: # 2, # 3. # 4 on pages 517 to 519 of textbook. And, Exercises: Questions # 3, # 4, # 6 on pages 521 to 523 of textbook.

  • These questions will be taken up at the next (class) session (Monday, June 8th, 2020).

Student Assessment:

  • To be submitted for marks.

  • Pages 4 to 7: Lesson 1 – Chapter 6 Part 2 Examples Booklet. (Due on Friday, June 5th, 2020.) 

Thursday, June 4th, 2020 

Unit 6 Trigonometry  p. 445 to 570.

 Lesson 6.5 – Trigonometric Functions – p. 513-511

 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.

 

1. Student Assessment: 

Practice Assessment:

  • Questions #1 on page 516; #2 0n page 517; and, #3 on page 518 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 

Unit 6 Trigonometry  p. 445 to 570.

 Lesson 6.4 – Graphing Trigonometric Functions – p. 510-511

 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.

 

1. Student Assessment: 

  • Practice Assessment: Questions: 1 -4  on page 512 of Textbook.

To be submitted for marks.

Tuesday, June 2nd, 2020 

Unit 6 Trigonometry  p. 445 to 570.

 Lesson 6.3 – Radian Measure – Determining Angles Measures Given a Terminal Point  (Part 4)

 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.

 

1. Student Assessment: 

  • Practice Assessment: Questions: #4 on page 493; and,  #10 , #11 on pages 508 -509 of Textbook.

To be submitted for marks.

Monday, June 1st, 2020 

Unit 6 Trigonometry  p. 445 to 570.

 Lesson 6.3 – Radian Measure – Trig. Ratios of Angles in Radians – pages 491-492 (Part 3)

 Video Tutorial

(Determining Trig. Ratios of Angles in Radians Problem Solving Involving Radians and Trig Ratios – Part 3 )

 

1. Student Assessment: 

  • Practice Assessment: Questions: #2, #3 on pages 491, 492; and,  #9, #10 on page 508 of Textbook.

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 

Unit 6 Trigonometry  p. 445 to 570.

 Lesson 6.3 – Radian Measure

 Video Tutorial

(Converting between Degrees and Radian Measures. Part 2 – Assignment Questions 1, 4 -8  from Textbook)

 

1. Student Assessment: 

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 

Unit 6 Trigonometry  p. 445 to 570.

 Lesson 6.3 – Radian Measure

 Video Tutorial

(Converting between Degrees and Radian Measures. Part 1)

 

 

1. Student Assessment: 

  • Practice Assessment: Questions: #1 on page 489; #5, #6  on pages 494 and 495 of Textbook.

To be submitted for marks.

 

Wednesday, May 27th, 2020 

Unit 6 Trigonometry  p. 445 to 570.

 Lesson 6.2 – Angles in Standard Position and Arc Length

 Video Tutorial

(Determining the arc length and radius of a circle.)

 

1. Student Assessment: 

  • Practice Assessment: Questions 2 c, d; 3 b, c; 4 c, d  on pages 485 and 486 of Textbook.

To be submitted for marks.

Notes on Arc Length (Clink on link below.)

Notes on Arc Length

 

 

Tuesday, May 2th, 2020 

Unit 6 Trigonometry  p. 445 to 570.

 Lesson 6.1 – Trigonometric Ratios for Any Angle in Standard Position -Part 5

 Video Tutorial (To be posted later.)

(Lesson Review: Determining All Trigonometric Ratios for any Angle – when given the coordinates of a point on the Terminal Arm and/or Given one Trig. Ratio.)

 

1. Student Assessment: 

  • Practice Assessment: Questions 10,11 on page 478 of Textbook.

To be submitted for marks.

Notes on Unit Circle, Reference Triangles, Trig. Ratios

 

 

 

Monday, May 25th, 2020 

Unit 6 Trigonometry  p. 445 to 570.

 Lesson 6.1 – Trigonometric Ratios for Any Angle in Standard Position -Part 4

 Video Tutorial

( Determining All Trigonometric Ratios and Angle Measures  Given One Trig. Ratio.

1. Student Assessment: 

  • Practice Assessment: Question 4 on page 473; Questions 8,9, 10, 11 on pages 478 & 479 of textbook.

To be submitted for marks.

Notes on Unit Circle, Reference Triangles, Trig. Ratios

 

 

 

Friday, May 22nd, 2020 

Unit 6 Trigonometry  p. 445 to 570.

 Lesson 6.1 – Trigonometric Ratios for Any Angle in Standard Position -Part 4

 Video Tutorial

(Unit Circle,  Determining Six Trigonometric Ratios and Angle Measures  Given One Trig. Ratio .

1. Student Assessment: 

  • Practice Assessment: Question 4 on page 473; Questions 10, 11 on pages 478 & 479 of textbook.

To be submitted for marks.

Notes on Unit Circle, Reference Triangles, Trig. Ratios

 

 

 

Thursday, May 21st, 2020 

Unit 6 Trigonometry  p. 445 to 570.

 Lesson 6.1 – Trigonometric Ratios for Any Angle in Standard Position -Part 3

 Video Tutorial

(Equation of a Circle in Standard Form  (x – h)2 + (y – k)2 = r2 ; Unit Circle; Determining Six Trigonometric Ratios Given the Coordinates of a Point on the Terminal Arm.

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.

 

 

 

Wednesday, May 20th, 2020 

Unit 6 Trigonometry  p. 445 to 570.

 Lesson 6.1 – Trigonometric Ratios for Any Angle in Standard Position -Part 2

 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.

Tuesday, May 19th, 2020 

Unit 6 Trigonometry  p. 445 to 570.

 Lesson 6.1 – Trigonometric Ratios for Any Angle in Standard Position – Part 1.

 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.

Tuesday, May 12th, 2020 

Friday, May 15th, 2020 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

 Lesson 5.8 – Solving Problems with Logarithms & Exponents.

 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 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

 Lesson 5.7 – Solving Logarithmic & Exponential Functions – Part 4  (Assignment Questions)

 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 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

 Lesson 5.7 – Solving Logarithmic & Exponential Functions – Part 3  (Assignment Questions)

 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.

2. To be submitted for marks.

Tuesday, May 12th, 2020 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

 Lesson 5.7 – Solving Logarithmic & Exponential Functions – Part 2  (Assignment Questions)

 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.

2. To be submitted for marks.

Monday, May 11th, 2020 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

 Lesson 5.7 – Solving Logarithmic & Exponential Functions – p. 417-425

 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.

2. To be submitted for marks.

 

Friday, May 8th, 2020 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

 Lesson 5.6 – Part 3: Analyzing Logarithmic Functions – Pages 408 to 410.

 Video Tutorial

(Use the Change of Base Formula to find the value of a logarithm. Sketch the transformation graph of a Logarithmic function.  Questions 10,11, 12) 

To be submitted for marks.

 

 

Thursday, May 7th, 2020 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

 Lesson 5.6 Part 2 – Assignment Questions

Analyzing Logarithmic Functions – Pages 402 to 406.

 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 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

 Lesson 5.6 Part 1

Analyzing Logarithmic Functions – Pages 401 to 404.

 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 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

 Lesson 5.5 Assignment 

Logarithms and the Log. Function –  Pages 393 to 398.

 Video Tutorial

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

A.  Student Assignments:

1.To be submitted for marks.

 

 

 

Monday, May 4th, 2020

No Online class

Teachers’ Professional Development Day

 

 

 

Friday, May 1st, 2020 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

 Lesson 5.5 Part 3 

Logarithms and the Log. Function –  Pages 388 to 394.

 Video Tutorial

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

A.  Student Assignments:

1.To be submitted for marks.

 

 

 

Thursday, April 30th, 2020 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

 Lesson 5.5 Part 2 

Logarithms and the Log. Function –  Pages 388 to 391.

 Video Tutorial

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

A.  Student Assignments:

1. Practice Questions:

     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. 

2. To be submitted for marks.

 

 

Wednesday, April 29th, 2020 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

 Lesson 5.5 

Logarithms and the Log. Function –  Pages 388 to 391.

 Video Tutorial

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

 

A.  Student Assignments:

1. Practice Questions:

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

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

2. To be submitted for marks.

 

Tuesday, April 28th, 2020 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

Complete Lesson 5.4 Assignment Questions

Logarithms and the Log. Function –  Pages 375 to 386.

 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.)

1. To be submitted for marks.

 

 

Monday, April 27th, 2020 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

Complete Lesson 5.4 

Logarithms and the Log. Function –  Pages 379 to 385.

 Video Tutorial

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

 

A.  Student Assignments:

1. Practice Questions:

     Questions: 3 and 4 on page 379 of Textbook.

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

2. To be submitted for marks.

 

 

Friday, April 24th, 2020 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

Today we will continue Exponential & Logarithmic Functions.

We will begin:

Lesson 5.4: Logarithms and the Log. Function –  Pages 375 to 378.

 Video Tutorial

(Writing Expressions in different forms; Evaluating Logarithms.)

 

A.  Student Assignments:

1. Practice Questions: Questions 1 and 2 on page 377 and 378 of Textbook.

2. To be submitted for marks.

 

 

 

Thursday, April 23rd, 2020 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

Today we will continue Exponential & Logarithmic Functions.

We will be reviewing Questions from  Lessons 5.1 to 5.3 –  p. 340  to 366.

 Video Tutorial

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

 

  1. Student Assignments: To be submitted for marks.

 

 

 

Wednesday, April 22nd, 2020 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

Today we will continue Exponential & Logarithmic Functions.

Lesson 5.3: Solving Exponential Equations – p. 358  to 366.

 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.

        b) From Chapter 5 Exponents & Logarithms  Examples Booklet

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

 

 

 

 

Tuesday, April 21st, 2020 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

Today we will continue Exponential & Logarithmic Functions.

Lesson 5.2: Transformation of Exponential Functions – p. 344 to 355.

 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.

        b) From Chapter 5 Exponents & Logarithms  Examples Booklet

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

 

 

 

Monday, April 20th, 2020 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

Today we will continue Exponential & Logarithmic Functions.

Lesson 5.2: Transformation of Exponential Functions – p. 344 to 348.

 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.

        b) From Chapter 5 Exponents & Logarithms  Examples Booklet

            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 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

Today we will continue Exponential & Logarithmic Functions.

Lesson 5.2: Analyzing  Exponential Functions – p. 344 to 348.

 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 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 416.

Today we will continue Exponential & Logarithmic Functions.

Lesson 5.1: Investigate the graphs of  Exponential Functions – p.340 to 343.

 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 

Unit 5 Exponential & Logarithmic Functions: p. 340 to 338 to 416.

Today we will begin Exponential & Logarithmic Functions.

 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.

Today we will complete Unit 4: Combining Functions.

Review Questions on Combining Functions

 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.

Today we complete:

Lesson 4.4: Determining Restrictions on Composite Functions

 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.

Today we continue:

Lesson 4.4: Determining Restrictions on Composite Functions

-Part 2 (p.312 to 314)

 Video

on

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

 

 

Students to Complete

Practice Assignment (not for marks – do not submit) 

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.

Today we begin 4.4 Determining Restrictions on Composite Functions (p.307)

 Video

on

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

 

 

Students to Complete

Practice Assignment (not for marks – do not submit) 

Check Your Understanding  (from Textbook)

  • 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.

Today we continue 4.3 Introduction to Composite Functions 

 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 )

Students to Complete:

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.

Today we continue 4.3 Introduction to Composite Functions 

 Video Tutorial

 

 

1. Practice Assignment Questions

    (Do not  submit as these are for you to practice.)

  • From Textbook  – Pages 294- 297 

          Check Your Understanding:                           

           #1 on page 294

           # 2 on page 295

           # 3 on page 296

           # 4 on page 297

 

2. Assess Your Understanding (to be submitted by April 6th, 2020). 

     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.

Today we continue 4.2 Combining Functions Algebraically

 Assignment: Exercises 3 to 11; p.278-281.

Video Tutorial

Assignment: Exercises 3 to 11; p.278-281

 

 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.

Today we continue Unit 4: Combining  Functions

4.2 Combining Functions Algebraically  – p. 272 to 271

 

Video Tutorial: Combining Functions Algebraically

 

 

 

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

          Check Your Understanding:                           

           #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.

Today we continue Unit 4: Combining  Functions

4.1 Combining Functions Graphically: Assess Your Understanding  – p. 268 to 271

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.

Today we begin Unit 4: Combining  Functions

4.1 Combining Functions Graphically  – p. 266 to 271

Video Tutorial: Combining Functions Graphically  – p.266 to 268.

 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.

 

 

 

Thursday, March 19th, 2020

Unit Test  

Unit 3: Transforming Graphs of Functions  

 

Wednesday, March 18th, 2020 

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

Today we completed : 3.5 Inverse Relations p. 235 to 264

 1.Teacher to complete “Examples 1, 2, 3 and 4” on pages  237 to 242 of Textbook.

 2.  Students to complete “Check your Understanding” –

        #1 on page 237; # 2 on page 238; and, #3 on page 240.

 

 3. Textbook:

       Students to complete Q. 4 , 5, 6, 7, 9, 11 on pages 243 to 227 of textbook

Transforming Graphs of Functions and review for unit test.

See below for answers to today’s assignments.

Questions 4 and 5 page 243

  • Questions 6 and 7 and b page 244
  • Questions 7 (c and d) and 8  page 245
  • Question 9  page 246

 

 

Tuesday, March 17th, 2020 

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

Today we continue Unit 3: Transforming Graphs of Functions

 

3.5 Inverse Relations p. 235 to 264

 1.Teacher to complete “Examples 1, 2, 3 and 4” on pages  237 to 242 of Textbook.

 2.  Students to complete “Check your Understanding” –

        #1 on page 237; # 2 on page 238; and, #3 on page 240.

 

 3. Textbook:

       Students to complete Q. 4 , 5, 6, 7, 9, 11 on pages 243 to 227 of textbook.

 

4. Example Booklet.

Monday, March 16th, 2020 

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

Today we continue Unit 3: Transforming Graphs of Functions

3.4 Combinations of functions – p. 219 to 233

3.5 Inverse Relations p. 235 to 264

3.4 Combinations of functions – p. 219 to 233

 1. Take up Questions form Textbook:

      Questions: 3, 4 , 5, 6, 9 on pages 226 to 230 of textbook.

 

3.5 Inverse Relations p. 235 to 264

 1.Teacher to complete “Examples 1, 2, 3 and 4” on pages  237 to 242 of Textbook.

 2.  Students to complete “Check your Understanding” –

        #1 on page 237; # 2 on page 238; and, #3 on page 240.

 

 3. Textbook:

       Students to complete Q. 4 , 5, 6, 7, 9, 11 on pages 243 to 227 of textbook.

 

4. Example Booklet

 

Friday, March 12th, 2020 

No Classes

Thursday, March 12th, 2020 

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

Today we continue Unit 3: Transforming Graphs of Functions

3.4 Combinations of functions. 

pages 219 to 233

1. Lesson 3.4 on pages 223 to 226.

 2.Teacher to complete “Examples 1, 2, 3 and 4” on pages  221 to 225.

 3.  Students to complete “Check your Understanding” –

        #1 on page 221; # 2 on page 223; and, #3 on page 224.

 

 4. Textbook:

       Students to complete 3, 4 , 5, 6, 9 on pages 226 to 230 of textbook.

 

Wednesday, March 11th, 2020 

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

Today we continue Unit 3: Transforming Graphs of Functions

3.3 Stretching and Compressing of Functions

pages 195 to 200

1. Lesson 3.3 on pages 195 to 200.

 2.Teacher to complete “Examples 1, 2, 3 and 4” on pages  196 to 200.

 3.  Students to complete “Check your Understanding” –

        #1 on page 196; # 2 on page 198; and, #3 on page 199.

 

 4. Textbook:

       Students to complete 3, 4 , 5, 6, 9 on pages 201 to 205 of textbook.

 

 

 

Tuesday, March 10th, 2020 

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

Today we continue Unit 3: Transforming Graphs of Functions

Reflecting Graphs of Functions

Lesson 3.2 pages 178 to 191

1. Students to complete (in groups) Examples Booklet pages  5, 6 and 8

2. Lesson 3.2 on pages 180 to 182

 Teacher to complete “Examples 1, 2, and 3” on pages 180 to 182.

 3. Textbook:

         Students to complete “Check your Understanding”: 

        #1 on page 180; # 2 on page 181; and, #3 on page 182.

 

 4. Textbook:

       Students to complete 3, 4 , 5, 6, 9 on pages 183 to 187 of textbook.

 

 

Monday, March 9th, 2020 

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

Today we continue Unit 3: Transforming Graphs of Functions

Horizontal and Vertical Translations 3.1

  1. Complete Examples 1, 2, 3 and 4 on pages 165 to 168.

  2. Students to complete “Check your Understanding” #1 on page 165; # 2 on page 166; and #4 o page 167.

 

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.

 

 

 

 

Wednesday, March 4th, 2020 

Test

Unit 2: Graphing Radical &  Rational  Functions 

&

Polynomial Functions

Tuesday, March 3rd, 2020 

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

1. Time will be given to review all assignments and “unit test Review”.

 

 

 

Monday, March 2nd, 2020 

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

Lesson 2.4 –  Sketching Graphs of Rational Functions

p. 129 to 110

  • Today we will review all assignment questions and begin review for unit test on Radical and Rational Functions.

1. Take up the the following:

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

  • Example 2 on page 131.

2.  Assignments:

  • 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

3.  Review for test.

See link below for Test Review on Radical and Rational Functions

 

 

 

Friday, February 28th, 2020 

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

Today we completed Unit 2: Properties of Radical Functions.

Lesson 2.4 –  Sketching Graphs of Rational Functions

p. 129 to 110

1. Students were given time to complete questions from their “Example Booklet” – pages 10 to 15.

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.

Today we will continue Unit 2: Properties of Radical Functions.

Lesson 2.3 –  Analyzing  Rational Functions

p. 105 to 121

Goals:

  • To determine the characteristics of  Rational Functions, and,

  • Solve Rational Equations

 

1.What is a Rational Function?

  • A function that is the ratio of two polynomials.

    It is “Rational” because one is divided by the other, like a ratio.

 

 

 

 

 

 

2. Characteristics of the graph of a rational function.

     –  Vertical Asymptotes –  Vertical line the graph never reach (the non-permissible values; when there there is no common factor).

      –  Horizontal Asymptotes – Horizontal line the graph never reach.

      –  Oblique Asymptotes  – Oblique line the graph never reach.

      –  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

   –  Identifying Non-permissible values of x:

      See Example 1 on page 107 to 108.

 

3. Vertical Asymptotes

     When a rational function has no common factor, the non-permissible values are the vertical asymptotes. It corresponds to the ZEROS of the denominator of a rational function.

4. Hole – is the non-permissible value of a rational function after it has been simplified to remove the denominator by factoring.

5. Horizontal Asymptotes – three “Types”.

  • 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. 

 

6. We will complete  “Examples 1 to 3” on pages 107 to 111.

7. Students complete:

  • Assignment:  # 4, 5, 6, 9, and 10 i) and 10 ii) on pages 114 to to 119 of textbook.

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

 

 

 

Tutorial links to Radical and Rational Functions

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.

Today we will continue Unit 2: Properties of Radical Functions.

Lesson 2.2 –  Graphing Rational Functions

p. 100 to 103

Goal: 

Use technology to investigate non-permissible values of rational functions.

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.

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

Page 101

 

Page 102

 

Page 103

 

Page 104

 

 

 

 

Tutorial links to Radical and Rational Functions

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.

Today we will continue Unit 2: Properties of Radical Functions.

Solving Radical Equations 

 (See Handout)

Goal: Solving Radical Equations Algebraically and Graphically

1. Key Ideas: See  Handout Below.

:2. Working Examples . (See three Handouts Below.)

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

 

 

Tutorial links to Radical and Rational Functions

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.

Today we will continue Unit 2: Properties of Radical Functions.

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

 

 

 

Lesson 2.2 –  Graphing Rational Functions

p.  100 to 103

Goal: 

Use technology to investigate non-permissible values of rational functions.

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.

 

 

 

Tutorial links to Radical and Rational Functions

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.

 

 

 

Tutorial links to Radical and Rational Functions

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.

  • Square Root of a Function – Key Ideas

3. Students completed (click on links below):

 

 

 

Tutorial links to Radical and Rational Functions

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.

 

 

Tutorial links to Radical and Rational Functions

Graphing General Polynomials, Radicals, Rationals, and Piecewise Functions

Domain and Range of radical and rational Functions

Video Tutorial

 

 

Friday, February 14th, 2020 

Test 

Polynomial Expressions and Functions 

 

 

Thursday, February 13th, 2020 

Pre-Calculus 40S: Polynomial Expressions and Functions 

 

Today,time will be given to complete Polynomial test review.

1. Also, time was given to students to complete will complete the following:

    – “Polynomial 1, 2, and  3 Extra Practice”

   –    Practice Test on pages 78 to 79, questions 1 to 6.

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

 

  • Also, time was given to students to complete will complete the following:

  • – “Polynomial 1, 2, and  3 Extra Practice”

  • –    Practice Test on pages 78 to 79, questions 1 to 6.

  • Students will work individually and in groups to complete Polynomial Test Review.

 

     Video

Sketching Polynomial

 

Tuesday, February 11th, 2020 

Pre-Calculus 40S: Polynomial Expressions and Functions 

 

  • Today, time was given to students to complete will complete Questions # 6 to 13 on pages 46 to 52 of the textbook.

  • Group work: Students worked in groups of two to complete two questions from “End of Polynomial Unit Group Activity”.

 

  • Students were assigned Hand-in Assignment 1.

 

 

 

 

 

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.

B. The x-intercepts of the graph of a polynomial function are the roots of the corresponding polynomial equation.

C. Find the ZEROS  a polynomial function from the factors.

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

 

 

Image result for zero multiplicity

 

 

 

 

 

Image result for zero multiplicity

 

 

 

 

Image result for zero multiplicity

 

 

 

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

                   Day 1 Package Handout Pre Calculus 40S Jan 2020 

                            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

  1. Pre-Calculus 12 – My Worktext

  2. Student Workbook

  3. Scientific Calculator

 

 

Reviewing Factoring

1. We will begin the Pre-Calculus 40S with a review assignment.                                             

        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

 

 

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