MCI45SH GRADE 12 (Honours) INTRODUCTION TO CALCULUS - Semester 2 Feb 2025

Friday Mar 28:  we went over the last quotient rule example from this handout, then we watched this cartoon and had some work time for the Chapter 2 Derivatives workbooklet assignments:   2.4 #1-6,  2.5 #1-7 (2.5 #6 has an answer key typo: it should read (-5,-5) NOT (-5,5)).  Have a great spring break, everyone!

Thursday Mar 27:  Today we went through two of the last three Quotient rule examples (the last two are not in your notebooklet, they are on this handout), we'll go over the last one together tomorrow - try it for yourself before then.   The assignment for that section is 2.5 #1-7 in the  Chapter 2 Derivatives workbooklet.  (2.5 #6 has an answer key typo: it should read (-5,-5) NOT (-5,5))

Wednesday Mar 26:  We went through the lesson on the Product Rule for derivatives, starting on page 17 of the  Unit B: Derivatives Notes Book and getting all the way to the first three examples for Lesson 6: Quotient Law, covering pages 20-22 in the  Unit B: Derivatives Notes Book.  We'll finish up the Quotient law examples tomorrow, but if you want to get a start on the assignment for these two sections, go to the Chapter 2 Derivatives workbooklet and do 2.4 #1-6 and 2.5 #1-7.  We still have some more examples to finish in  tomorrow's class. 

Tuesday March 25:  TEST for 2.2, 2.3, and DIFFERENTIABILITY

Monday Mar 24:  we started by seeing if anyone had any 2.2 or 2.3 homework questions, then let people have time to finish that assignment.    If you are looking for more practice for the test tomorrow, go to page 26 of the workbook and try some of the 4.2 questions.

Friday Mar 21: we started by looking at the differentiability of a rational exponent function (2.1 #15), then a quick discussion on the differentiability of types of curves.  After that, some work time for  2.2 #1-11 and 2.3 #1-3,6-13.  We will test this material and the Differentiability lesson on Tuesday.

Thursday Mar 20:  TEST for 2.1 and GRAPHING DERIVATIVES

Wednesday Mar 19: we started by going over the  differentiability warm up  that I handed out yesterday.  Here is the key if you missed it.  Then we had one last chance to ask for help with the 2.1 assignment from the Chapter 2 Derivatives workbooklet or the  Graphs of Derivatives Worksheets  before we test tomorrow.  If you are looking for extra practice for the test, go to page 23 of the workbook and look at #2-6. 

Tuesday Mar 18:  After I handed out this differentiability warm up (we'll go over it tomorrow),  we started by seeing if anyone had any 2.1 or Graphs of Derivatives Worksheets problems.  Then we finished up the basic derivatives rules examples on page 13 and continuted into a lesson on Differentiability on pages 14-15 of the Unit B: Derivatives Notes Book.   You can now do 2.1 #3 and 15, which finishes your 2.1 assignment.  Make sure you are also done the Graphs of Derivatives Worksheets  (here is the answer key) from last week.  On Thursday, we'll test 2.1 and the Graphing Booklet. If you are looking for extra practice for the test, go to page 23 of the workbook and look at #2-6.   If you are done all that and feel ready for Thursday's test, you can get started on the 2.2 and 2.3 assignments:  2.2 #1-11 and 2.3 #1-3,6-13

Monday Mar 17:   we went over pages 9-13 of the Unit B: Derivatives Notes Book,  covering the lessons: Derivatives-Other Notations and most of the Basic Derivative Rules lesson.   We'll finish off the lesson tomorrow, but for homework, I added #12 to the 2.1 assignment.  The assignment for today's lesson from the Chapter 2 Derivatives Workbook is 2.2 #1-4,7-10,12.  You can start on it tonight if you are all done the 2.1 assignment and the Graphs of Derivatives Worksheets  (here is the answer key).

Thursday Mar 13:  after a quick discussion of what happens when you try to find the derivative of the vertex point of y = abs(x), we went through the graphs on page 8 of the notes booklet.  Then we  had work and ask questions time for  2.1 #2,4-6,8-13,16 in the Chapter 2 Derivatives Workbook and the  Graphs of Derivatives Worksheets  (here is the answer key). If you finish those assignments, you can start working on 2.2 #1-4,7-10,12.

Wednesday Mar 12:  we went through pages 7-13 of the Unit B: Derivatives Notes Book, finishing up our graphing lesson from yesterday and covering the lessons: Derivatives-Other Notations and Basic Derivative Rules. Again, here is  the Desmos file of the examples on pages 5-8, if you want to play with them for yourself.  For homework, keep working on  2.1 #2,4-6,8-13,16 in the Chapter 2 Derivatives Workbook, but I also handed out this Graphs of Derivatives Worksheets  (here is the answer key).  This is quite a bit of work, so I will let you have tomorrow as a work/ask questions period.

Tuesday Mar 11:   we started Unit B: Derivatives today, with the first lesson, covering pages 2-6 in the Unit B: Derivatives Notes Book, the definition of a derivative (first principles of the derivative) and graphing derivatives. I'll leave it for you to do the "you try" example on page 7 and we'll go over it tomorrow.  If you want to play with the Desmos file I was using in the first three examples of the lesson, here it is.  Here is my key for the last page of examples in today's lesson (I already don't like my estimate for the first one - I made it too steep).  Here is the Desmos file of the examples on pages 5-8, if you want to play with them for yourself.  The first assignment is in the 2.1 section, page 2 #2,4-6,8,10,11,13 of the Chapter 2 Derivatives Workbook.  This assignment won't be due until Thursday, but I will be adding to it as we go.

1.4 and 1.6 TEST MONDAY MARCH 10

Friday Mar 7:  work/ask questions period for the 1.6 #1-5,8 in the Chapter 1: Limits and Rates of Changes booklet and the Limits to Infinity worksheet that I handed out today.  Test Monday.  If you are looking for extra practice, go to  page 24 #3-6.

Thursday Mar 6:  we did the examples on this handout together.  Then we had time to work on 1.6 #1-5,8 in the Chapter 1: Limits and Rates of Changes booklet.  I'll let you have time to work and ask questions tomorrow (but another worksheet is coming)  and then we test on Monday. 

Wednesday Mar 5: today's lesson is for Limits as x approaches infinity.  This covers pages 42-44 of the Unit A: Limits Notes Package.  We started with a little refresher on infinite geometric series and  then went into the examples.  We'l do a few more examples tomorrow.  The next assignment, it is 1.6 #1-5,8 in the Chapter 1: Limits and Rates of Changes booklet.

Tuesday Mar 4:  we did a lesson on pages 38-39 of Unit A: Limits Notes Package where we go from Formula 2 to a general equation for the slope of a tangent for any specific curve.    There is no new assignment for this lesson, so you have another night to work at the 1.4 assignment #1,2,6-11 in the Chapter 1: Limits and Rates of Changes booklet and, if you are looking for more practice, page 24 #3-6.  If you want to play with the Desmos files I used in class today, here it is: Examples 1.

Monday March 3:  work/ask questions period for the 1.4 Assignment in the Chapter 1: Limits and Rates of Changes booklet #1,2,6-11.   If you are already finished it and you are looking for more practice, go to Page 24 and work on #3-7

Friday Feb 27:  1.3 TEST.  We'll give you a work/get help class on Monday for the 1.4 Assignment in the Chapter 1: Limits and Rates of Changes booklet #1,2,6-11.  I'll give you Monday's class as work/ask questions time for that assignment and start the next new lesson on Tuesday.

Thursday Feb 26:  We looked at one more continuity example on page 40 of the Unit A: Limits Notes Package.  This one is named Example 3 and it is a piecewise function that you are expected to determine whether or not it is continuous without having a graph to look at.  Then, of course, we graphed it.  After that it was work and ask questions time for the 1.4 Assignment in the  Chapter 1: Limits and Rates of Changes booklet. The assignment is #1,2,6-11.  If you want to play with the Desmos file I used in class today, here it is:  Example 3.

Wednesday Feb 25:  work time to either finish up 1.3 #1-9 (or the extra practice on page 27 #1-8) or to work on  Exercise 1.4 #1,2, 6-11 in the Chapter 1: Limits and Rates of Changes booklet.

Tuesday Feb 24:  our warm up today is another Continuity Example (the file here has a key at the end) and today's lesson is part 2 of the Chapter 1.4 lesson, where we introduce "Formula 2" for finding the slope of a tangent line using limits. This covers pages 34-37 in the Unit A: Limits Notes Package.   Here is the video of the lesson.  Your homework for this part of the lesson is Exercise 1.4 #1a(ii), #2a(ii), #8-11 (use Formula 2 for all of these) in the  Chapter 1: Limits and Rates of Changes booklet.  Reminder:  1.3 Test on Friday. Tomorrow will be a work period to either finish up the 1.3 practice or to work on the new 1.4 assignment and the one from yesterday.

Monday Feb 24:  I checked in to see if anyone needs any help/explanation for any of the 1.3 questions, then we we started our two part lesson on the Equation of tangent lines with the lesson that derives and gives us examples of "Formula 1".  This took us through pages 30-33 of the  Unit A: Limits Notes Package. You'll be able to tackle all of the Exercise 1.4 assignment in the Chapter 1: Limits and Rates of Changes booklet after tomorrow's part 2 of the lesson.  I'll give you work time for this assignment (and the one I'll assign tomorrow) on Wednesday, but if you feel ready for Friday's 1.3 Quiz and you want to get started on the new homework early, you can do Exercise 1.4 #1a(i),b,c, #2a(i),b,c, #6-7.   Reminder that if you want more practice for Friday's 1.3 test, go to page 27 of the workbooklet and do #1-8 (the answer key is the "Section 3.3" part on page 32)

Friday Feb 21:  1.1 and 1.2 Test.  If you finish with time to spare, you can work on  Exercise 1.3 #1-9 in the  Chapter 1: Limits and Rates of Changes booklet.  If you want more practice, skip to page 27 of the workbooklet and do #1-8.  

Thursday Feb 20:  Today we did examples 3-4 in the lesson on Continuity.  We're still, technically in Lesson 1.3 of your workbook, covering page 29 of the Unit A: Limits Notes Package.   Now you should be able to finish all of Exercise 1.3 #1-9 in the  Chapter 1: Limits and Rates of Changes booklet.  We'll quiz 1.3 next week.  Reminder that we test 1.1 and 1.2 tomorrow. 

Wednesday Feb 19:  Today, we did a lesson on one sided limits, coving pages 23-25 in the Unit A: Limits Notes Package .  We also started the Continuity lesson on page 26-28 (it's all pretty much one lesson)  Your homework for this lesson is Exercise 1.3 #1-9 in the  Chapter 1: Limits and Rates of Changes booklet.

Tuesday Feb 18:  we went over the "you try" questions on page 22 of the  Unit A: Limits Notes Package.   Then we had time to work on (or ask questions about) Exercise 1.2 #1-9,12, and the Limit Practice handout that I handed out today (here is the answer key).  We'll do our first  test on 1.1 and 1.2 this Friday.

Friday Feb 14:  Happy Valentine's Day!  Today we go through more examples of using algebra methods to calculate limits, on page 21 of the Unit A: Limits Notes Package.  Your homework is to continue to finish the "you try" examples on page 22, then work on Exercise 1.2 #1-9,12 in the  Chapter 1: Limits and Rates of Changes booklet as well as the Limit Practice handout that I handed out today (here is the answer key).  We'll do our first  test on 1.1 and 1.2 next Friday.

Thursday Feb 13:  We moved on to pages 16-20 of the Unit A: Limits Notes Package and examples of "Limit Laws" as we moved on to more algebraic ways to calculate limits.  We didn't quite get through all of the examples for this lesson, so you can use tonight to finish the 1.1 assignment from yesterday.    The next assignment will be Exercise 1.2 #1-9,12 in the Chapter 1: Limits and Rates of Change Workbook.  You might not be ready for all of these problems until after tomorrow's examples.

Wednesday Feb 12:  We went through Examples 2 and  3 on pages 12-14 of the Unit A: Limits Notes Package together.   Here is the Desmos file I used for Example 2.  For homework, do the "Secant Example for you to Try" sheet on page 15 of the booklet.  You can also start work on the first work booklet assignment, which is Exercise 1.1 #1-5,7-10 in the Chapter 1: Limits and Rates of Change Workbook that I handed out yesterday. The answer key starts on page 16.  Here is the answer key for the "Secant Example for you to try" on page 15.

Tuesday Feb 11:  we continued through the lesson on pages 9-12 of the Unit A: Limits Notes Package together, making it  through example 1 of the lesson.  We'll pick it up there tomorrow.  We're still not quite ready for the first homework assignment just yet.  If you want to play with the files I used in class, here is the Desmos file and here is the Excel file.  Here is a video I made last year on how to make these graphs on Desmos for yourself.  I also made this video of how to use Excel to to do the same calculations repeatedly, as an alternative to Desmos.  

Monday Feb 10: today's lesson is on this handout: Limits: An Introduction.  We looked at two very important ideas in calculus:  1) you can say that if you are infinitely close to a value, you actually have that value and 2)  you can find the size of something finite by spliting into infinite pieces and then counting them.  There is no new assignment for today's lesson, so if you need to finish the  Grade 11 Skills Review (here is the answer key), or you want to do more of the  Dividing Polynomials practice sheet (here is the answer key), you have one more night.

Friday Feb 7:  I'm not in today, so students can use today's class to finish up and check your answers for the  Grade 11 Skills Review booklet (Here is the answer key).  If you have time to spare after that, work on the Dividing Polynomials practice sheet (here is the answer key).  Your only other homework this weekend is to  watch this Professor Dave video introducing the concept of what calculus actually is.

Thursday Feb 6:  we finished up Examples 4 and 5 on pages 6 and 7 of the Unit A: Limits Notes Package .  Then we reviewed working with rational and radical expressions - two KEY skills for the rest of this course - and introduced using function notation to find f(x) values and slopes of equations.   You can now do the rest of the Grade 11 Skills Review booklet.  I'll let you have a work class tomorrow to finish it up  (Here is the answer key).  Also, you can work on the  Dividing Polynomials practice sheet (here is the answer key).  

Wednesday Feb 5:  we started with a couple more examples of long division from the board, then we went through how to do the long division shortcut: synthetic division which covers pages 2 and 3 of the Unit A: Limits Notes Package .  Then we started looking at the factor theorem, using pages 4-6.  We'll finish up Examples 5 and 6 tomorrow.  Now you can do #7 in the Grade 11 Skills Review booklet and this Dividing Polynomials practice sheet (here is the answer key).  

Tuesday Feb 4:  today we reviewed factoring - a few examples on the board and the ones from page 8 of the  Unit A: Limits Notes Package.  I also handed out this Recap of Prior Skills page that focuses on reviewing dividing polynomials where the numerator contains the denominator as one of its factors.  This lead us to  consider how to handle a situation where the denominator ISN'T a factor of the numerator and we introduced algebraic long division.  You can now do #3-6, 8 in the  Grade 11 Skills Review booklet.  

Monday Feb 3:  Welcome to Introduction to Calculus!  Today we looked at the oft forgotten skills from grade 10 Linear Equations.  We did a few examples on the board, then I handed out the 1st 4 pages of this Grade 11 Skills Review.  You can do #1 and 2 tonight.  Please note there is a typo in the instructions on #2 - write the answer in STANDARD form, not point-slope (get used to that format - it's kind of the default format for lines in this course).  Here is the answer key

ESSENTIAL MATH GRADE 12 - Semester 2 FEB 2025

Friday Mar 28:  we went over  #4 and 5 on the Worksheet 2D in the  HF Workbook (here is the answer key).  Then we went into Lesson 5: Home Insurance on pages 18-21 in the  Home Finance Notes Booklet.   We didn't quite get through the whole lesson, so we will finish it next Monday.  If you missed today's class here is a video of the Lesson 5 part of the class (we made it up to the 29 minute mark in this video).  Have a great spring break, everyone!

Thursday Mar 27:  we went over the last example in Lesson #4 on page 16 of the  Home Finance Notes Booklet.  Then we had time to work on Worksheet 2D in the  HF Workbook (here is the answer key).  We ended class by going over #1-3 together.  We'll go over #4 tomorrow.

Wednesday Mar 26: We started by continuing into Lesson 4 on page 15 of the  Home Finance Notes Booklet while we waited for our guest speaker, Ms Locheed to arrive.  Then we listened to her talk about financial planning from her years of experience in the industry..  If you missed the class here is a video of the notes part of lesson.- our class today starts at the 44 minute mark and continues to the end.  Then the rest of the lesson starts at the 16:48 mark of this video (the examples are a little different, but you will get the gist of it) . The assignment for this lesson is Worksheet 2D in the  HF Workbook,  Here is the answer key.  You will have time to work on it tomorrow.

Tuesday Mar 25:  We went over the questions from Worksheet 2C in the  HF Workbook (here is the answer key).   After that, we started going  through Lesson #4 on pages 14-15 of the  Home Finance Notes Booklet.  If you missed the class here is a video of the lesson.- our class today made it up to the 44 minute mark.   No new assignment yet, so if you have some time tonight, you can catch up on older assignments if you need to.

Monday Mar 24:  We started by going over a few of the questions from the Mortgages Lesson 1 and 2 Review Assignment (here is the answer key).  Then we went through the second part of the Lesson 3 on pages 13-14 of the in the Home Finance Notes Booklet.  If you missed class today, watch this video  starting at the 17:00 minute mark.  The only new question for this part of the lesson is #5 from Worksheet 2C in the  HF Workbook, so I added that to the homework from Friday.  Here is the answer key. 

Friday Mar 21:  reminder that for Monday you should be done the Mortgages Lesson 1 and 2 Review Assignment (here is the answer key).  For class today,  we looked at people's responses on the  anonymous questionaire from last week.  Then went through the first part of lesson 3, pages 10-11 in the Home Finance Notes Booklet.  Here is a video of the lesson if you missed the class (today's lesson went up to the 17:00 mark).  The assignment or this lesson is Worksheet 2C #1-4 in the  HF Workbook,  Here is the answer key.  

Thursday Mar 20:  after I went over the 2B worksheet in the HF Workbook (here is answer key - if you missed class, you should go over it yourself), students worked on the Mortgages Lesson 1 and 2 Review Assignment.  It should be done for Monday, here is the answer key if you want to check your answers as you go.  As I was going over the 2B worksheet, I took a few minutes to show the class how to do these questions using an Excel Spreadsheet.  Here is a video of that part of today's lesson.

Wednesday Mar 19: we went over another example of making a mortgage amorization schedule.  If you missed the class, here is a video of that example.  Then we had some time to finish worksheet 2B in the HF Workbook,  Here is the answer key for the 2B worksheet. If anyone is finished that, they can start on this Mortgage Payments Assignment that I handed out.

Tuesday March 18:  we started by going over the Mortgage Practice page (here is the answer key).  Then we went into Lesson 2: Mortgage Amortization Schedules, pages 7-9 in the  Home Finance Notes Booklet.  If you missed class, here is a video of that part of the class.  worksheet 2B in the HF Workbook and  I handed out some Blank Amortization Charts that we can use on future questions.

Monday Mar 17:  after a few more minutes of work time, we went through Assignment 2A, of the HF Workbook together. If you missed class, here is a video of that part of the class and here is the answer key.  Then we had the rest of class to work on this Mortgage Practice page (here is the answer key).  

Thursday Mar 13:  we went through Examples 1 and 2 at the end of Lesson 1 (up to the end of page 6) in the Home Finance Notes Booklet.  If you missed today's class, watch this lesson starting at the 34:30 mark.  Then I handed out a Mortgage Amortization Table that you will need for the first assignment.  That assignment is in your Home Finance Workbook - it is the 2A Worksheet on pages 1-3.  You can have the rest of the class to work on it.  NOTE THAT THERE IS A TYPO IN QUESTION #1 - see if you can find it.  Here is the answer key to the 2A Worksheet.  You have to use the formulas given to find the answers yourself, but if, just for fun you want to use the On-line Mortgage calculator I used in the lesson, here is a link to it.  If you finish the 2A Worksheet, I'll give you this Mortgage Practice page (here is the answer key).  It is just meant as more practice, it is not a hand in.  

Wednesday Mar 12:  we started our new unit today.  We got started by thinking about how much it costs to buy a house using this online mortgage calculator and watching this video.  We used the video to fill in the blanks on this handout.   I handed out a Home Finance Notes Booklet and we went through the first two pages of lesson 1.  We'll start the examples and calculations tomorrow.  No new assignment yet.   If you missed class today, here is a video of the lesson (our class today made it to the 34:30 mark of this video).

Tuesday Mar 11:  Geometry Test.  If you finish with time to spare, you can work on answering this anonymous questionaire to get us ready for our Home Finance unit.

Monday Mar 10:  we went over the the  Polygon Problems from Old Exams.   Then we had time to work on the  Polygon Review Assignment (here is the key for that).   It's a good idea to use some time today to make your study sheet for tomorrow's test.

Friday Mar 7:  we went over Lesson 8 Practice Assignment, pages 17-18 of the Geo+Trig Workbook.  Then we had more time to work on the  Polygon Problems from Old Exams.  If you don't finish that, it is homework for Monday.  If you are finished it and you are ready to move on, I gave out a Polygon Review Assignment (here is the key for that).  We'll use Monday as a review day and test on Tuesday.

Thursday Mar 6:  we had time to work on the Lesson 8 Practice Assignment, pages 17-18 of the Geo+Trig Workbook.  That one is homework if you can't finish it in class.  If you finished that, you could start on this handout of  Polygon Problems from Old Exams.  After that we had time to work on the Polygon Review Assignment. 

Wednesday Mar 5:  we went through some of the questions in Practice Lessons 6 and 7 in the Geo+Trig Workbook.  Then we did the second part of Lesson 8:  Regular Polygons and Formulas, pages 21-23 of the Geometry and Trigonometry Notebook,  For the rest of the period, I gave the class time to work on the Lesson 8 Practice Assignment, pages 17-18 of the Geo+Trig Workbook.   If you missed the class or want to see the examples again, here is a video of the lesson.  At the end of class, I handed out the formula sheet for this unit.  I will hand it out again on test day, and don't forget, you still get to bring in a piece of paper to the test with any notes you might want written on it - front and back.

Tuesday Mar 4:  we started with an interesting drawing activity, then we had more work time to finish Assignments 6 (page 13) and 7 (pages 14-17 in the  Geo+Trig Workbook.  Then we went through the first part of Lesson 8:  Regular Polygons and Formulas, pages 19-20 of the Geometry and Trigonometry Notebook,  Then we watched this video.  If you missed today's class, here is a link to a video of the lesson.  

Monday March 3 :  We started by looking at a video that answers the question, "what is the centre of a triangle?"  If you missed class you can watch the video here.   Then we went through Lesson 7 (pages 17-18) in the Geometry and Trigonometry Notebook, which looked at more properties of Quadrilaterals.  Then we had time to work on Assignments 6 (page 13) and 7 (pages 14-17 in the  Geo+Trig Workbook.   You'll get a little more work time tomorrow.  If you missed today's class, here is the lesson video.

Friday Feb 28:  SIN and COSINE LAW TEST.  If you finish with time to spare, you can work on the assignment from yesterday:  Assignment 6 (page 13) in the  Geo+Trig Workbook. 

Thursday Feb 27:  we finished going over the Trig Problems from Old Provincial Exams (the file link here has answers) that I handed out on Tuesday. Then we made out study sheets for tomorrow's test.   After that, we started the 2nd part of Unit 1 and switched from Trigonometry to Polygons.   Then we went through lesson 6 (pages 14-16) in our Geometry and Trigonometry Notebook, which looked at Quadrilaterals.  You can now work on Assignment 6 (page 13) in the  Geo+Trig Workbook.  You might have some work time to finish working on it tomorrow after you finish the test.  If you missed today's class, here is the lesson video. 

Wednesday Feb 26:  we only had time to go over a couple of the Trig Problems from Old Provincial Exams (the file link here has answers) that I handed out yesterday.  After that, we had a grad meeting that I forgot about, so we'll finish going over this worksheet tomorrow and I have moved the test to Friday.

Tuesday Feb 25:  After we went over a couple of questions from each of the  Sine Law Assignment (here is the answer key) and the Cosine Law Assignment (the file link has an answer key at the end of the file),  I handed out one last set of Trig Problems from Old Provincial Exams (the file link here has answers) and we worked on it until the end of the class.  It makes for a nice review as we get ready for Thursday's test.

Monday Feb 24:  we started with more questions from an old provincial exam (the file line has a key if you missed it and want to try them on your own).  Then we had more time to work on the Sine Law Assignment (here is the answer key) and the Cosine Law Assignment (the file link has an answer key at the end of the file). 

Friday Feb 21: we went over #4 from Practice Lesson 5, page 12 in the  Geo+Trig Workbook together.  If you are still working on this assignment, see yesterday's post if you need the solutions.  After that I gave the class time to work on the Sine Law Assignment (here is the answer key) and the Cosine Law Assignment (the file link has an answer key at the end of the file). 

Thursday Feb 20:  We started with these questions from an old provincial exam (the file link has a key if you missed class and want to try them).  Then we went through #1-3 in  Practice Lesson 5 (pages 11-12) in the Geo+Trig Workbook.  We will go over #4  in that assignment tomorrow, so if you didn't finish it in class, do it for homework.  The booklet has an answer key at the back, but here are full solutions if you are stuck.   Also, you can keep working on the Sine Law Assignment (here is the answer key).  If you are finished both of those things, you can start on this Cosine Law Assignment (the file link has an answer key at the end of the file).  I'll give you time tomorrow to work on those.

Wednesday Feb 19:  we went over a  couple of Cosine Law questions from Practice Lesson 4 (pages 9-10) in the Geo+Trig Workbook and a couple of questions from the Sine Law Assignment.  Practice Lesson 4 has an answer key at the back of the booklet, but here is the full solutions, if you are stuck.  Then we did the notes and examples for Lesson 5: Cosine Law Angles (page 13) of the Geometry and Trigonometry Notebook .   You can now work on Practice Lesson 5 (pages 11-12) in the Geo+Trig Workbook.  Here is a video of the lesson if you missed class or need a refresher.  If you aren't finished it, you should also keep working on the Sine Law Assignment (here is the answer key). 

Tuesday Feb 18:  we went over a couple of Sine Law questions from the last two assignments together, then we did the notes and examples for Lesson 4: Cosine Law sides (pages 11- 12) of the Geometry and Trigonometry Notebook .   You can now work on Practice Lesson 4 (pages 9-10) in the Geo+Trig Workbook.  Here is a video of the lesson if you missed class or need a refresher.

Friday Feb 14:  Happy Valentine's Day.  We did a little quiz on the material from Lesson 1 of the Geometry and Trigonometry Notebook.  Once people were done, they could finish up yesterday's Practice Lesson 3 (pages 7-8) in the Geo+Trig Workbook (if the answer key at the back is not enough explanation for you, here are the solutions).  When people finish that, I handed out some extra practice on this Sine Law Assignment (here is the answer key).  As long as you are finished the Practice Lesson 3 quesitons, you have no homework this weekend.  I'll give you more time next week for the  Sine Law Assignment.

Thursday Feb 13: We finished example 4 in Lesson 3 in the  Geometry and Trigonometry Notebook.   I handed back yesterday's practice quiz and we went over it for a few minutes.  The real quiz for marks will be tomorrow.  Then we had time to work on Practice Lesson 3 (pages 7-8) in the Geo+Trig Workbook.  There is an answer key at the back of the booklet, but if you want to see full solutions, here they are.

Wednesday Feb 12:  we started with a little practice quiz to help get ready for Friday's first quiz for marks.  Then we went through the answers for Practice Lesson 2 (pages 4-6).  Here is the answer key if you missed the class and need to correct it yourself.  Lesson 3, pages 9 and 10 from the Geometry and Trigonometry Notebook.  Then we had time to work on  Practice Lesson 3 on pages 7 and 8 of the Geo+Trig Workbook 

Tuesday Feb 11:  we finished up the last two Lesson 2 examples on pages 7-8 in the Geometry and Trigonometry Notebook .  Then we had time to work on Practice Lesson 2 (pages 4-6).  Here is the answer key.

Monday Feb 10:  I went over a few problems from the Pythagoras Practice Sheet and the SOHCAHTOA (Right Angle Trigonometry) worksheet (here is the answer key).  Then  we did most of lesson 2 (pages 7-8) in the Geometry and Trigonometry Notebook .  If you missed the class or get home and want to see the examples explained again, here is a video of Lesson 2.  The assignment for this lesson is  Practice Lesson 2, which I handed out today.  I will give you work time for this assignment in class tomorrow, but if you want to try starting it tonight, you can give some of it a try.

Friday Feb 7: I had my guest teacher read out the answers to the rest of the Geo+Trig Workbook - Practice Lesson 1 (pages 2 and 3).  If you missed class and still need to correct your work, here is that answer key. After that my guest teacher handed out this Pythagoras Practice Sheet and this SOHCAHTOA (Right Angle Trigonometry) worksheet (here is the answer key) to work on for the rest of class.  The Pythagoras page has an answer key on the back, but if you want to see full solutions, look here.

Thursday Feb 6:  we started with another SET game.  Then we had some time to work on  Geo+Trig Workbook - Practice Lesson 1 and we corrected the first page together.  Then we did a quick summary of all of the things from lesson 1 that you need to know.  If you are still working on pages 2 and 3, try to finish them tonight.

Wednesday Feb 5: we finished up Example 11 on page 5 of the Geometry and Trigonometry Notebook and I did an "example 12" on the board that wasn't in your notes.  Then I handed out the first four pages of the  Geo+Trig Workbook - Practice Lesson 1 and people got started working on it.  The answer key is at the back of the booklet (Question #1 has a mistake in the answer key - it should be 9 not 3!).  We lost quite a bit of our class time to a fire drill, so we'll have some time to finish it tomorrow.  You NEED a scientific calculator for class from now on. 

Tuesday Feb 4: we started with another round of the SET game.  Then we picked up back at Example 3 on page 3 of the Geometry and Trigonometry Notebook .   We finished to the end of Example 10 on page 5, we will pick it up from there tomorrow.  If you want to try Example 11 yourself, go for it!  Our first official assignment will be tomorrow.

Monday Feb 3:  Welcome to Grade 12 Essential Math!   Today we went over a course outline and got ourselves thinking about shapes and geometry by playing the SET game.  We are going to start this course with a unit on Trigonometry, which hopefully you remember a little bit from grades 10 and 11. I handed out the first four pages from our first unit note booklet:  Geometry and Trigonometry Notebook . We went through page 2 and Examples 1 and 2 on page 3.  We started Example 3, see if you can finish it for tomorrow.

Applied Math Grade 11 - Semester 2 Feb 2025

CHAPTER 3: SINE and COSINE LAW for ACUTE TRIANGLES TEST THURSDAY MARCH 27

Friday March 28:  we went over the last question from Wednesday's Congruent Triangle Activity.   Then we went through most of lesson 4.1 in our Chapter 4: Trig Ratios of Obtuse Triangles Notes booklet.  If you missed the class - here is the key for the lesson notes.  I  left some of the examples on the last page of the lesson for you to try over the break.  We'll go over them on the Monday when we get back.  If you want to try the homework for this section, it is textbook page163 #1-3.  I'll assign it officially on the Monday.  If you want to play with the interactive unit circle for yourself, here is the link.  Have a great spring break everyone!

Thursday March 27:  Chapter 3 Test - if you finish with some time to spare, you can try the last diagram in yesterday's  Congruent Triangle Activity.  If you still need something to do you can try filling out the chart on the second page of the Chapter 4: Trig Ratios of Obtuse Triangles Notes booklet that I handed out once people were finished.  

Wednesday March 26:  we did  the Congruent Triangle Activity.  If you missed class and want to try it for yourself, you can work your way through this power point that goes step by step on drawing the triangles.  No new homework for this activity besides the question I left you with at the end of the activity (the last diagram in the booklet and the question of AAA or AAS). 

Tuesday Mar 25:  we went over the Page 147 #3-5, 8-10 assignment questions.  Then we had time to work on review questions from textbook page 152 #1-8 and if you want more practice than that, try 154 #2-12.  Don't forget to make yourself a study sheet - I am NOT giving you a formula sheet for Thursday's test! 

Monday March 24:   we started by asking if anyone is stuck on any of the page 124 or 136 assignment questions.  Then we had work time to do Page 147 #3-5, 8-10.  If anyone is already finished these questions, work on some review from textbook pages 152 and 154 and get started on making the study sheet that you will be bringing into Thursday's test.

Friday Mar 21: we continued with a 3.3 ACC (Cosine Law) ( the file has a key).  Once again, if you can't do these questions, you are not keeping up with the pace of the course and you can't expect to pass the next test if you don't turn things around.  After that, we did pages 9-11, Lesson 3.4 in the  Chapter 3: Using Trigonometry to Solve Acute Triangles Notes Booklet.   Today's homework is textbook page 147 #3-5,8-10.  You will get some work time for it on Monday.

Thursday Mar 20:  we started with a few more minutes to work on textbook page 136 #1-7,9-11,13,15.  Then we did this 3.2 ACC ( Acute Sine Law) ( the file has a key ).  If you couldn't do these questions, you need to go back and catch up on homework or you will almost certainly fail the next test.  We'll do a mini-practice-quiz like this for 3.3 tomorrow.  We ended class by going over a few of the page 136 questions together.  

Wednesday Mar 19:  we started by going over some of the questions in the textbook page 124 #2-17 assignment.  Then we finished up the examples in Lesson 3.3 of the   Chapter 3: Using Trigonometry to Solve Acute Triangles Notes Booklet and then had time to work on textbook page 136 #1-7,9-11,13,15.

Tuesday Mar 18:  we started with some more work time for textbook page 124 #2-17.  Then we went back to the   Chapter 3: Using Trigonometry to Solve Acute Triangles Notes Booklet and we started Lesson 3.3 where we derived and did the first couple of examples of the Cosine Law.  We'll finish up that lesson tomorrow, but if you are finished all of the page 124 assignment, you can get started on page 136 #1-7,9-11,13,15.

Monday Mar 17:  we went over the examples on the last two pages of lesson 3.2 of the  Chapter 3: Using Trigonometry to Solve Acute Triangles Notes Booklet.  We also did Example 3 from page 122 and #9 from page 126 of your textbook together.   The assignment for lesson 3.2 is:  textbook page 124 #2-17.  The rest of the class was work time.

Thursday Mar 13:  we corrected the rest of the examples that we didn't finish on Tuesday in the  Chapter 3 Introduction - Right Angle Trig Review Notes.  You should now be able to finish the Right Angle Trig Practice sheet.  (here is the answer key).  Then I handed out the  Chapter 3: Using Trigonometry to Solve Acute Triangles Notes Booklet.  On the first page we derived the formula for the SINE LAW and learned how to use it as we worked through lesson 3.2.   Your homework for this part of the lesson is to finish the examples on the last two pages of lesson 3.2.  We'll go over them on Monday.

Wednesday Mar 12:  Chapter 2 Test.  Anyone who finished with time to spare can work on this Right Angle Trig Practice sheet.   Here is the answer key.  

Tuesday Mar 11:  After a quick go-over of the two Chapter 2 reviews, I handed out this Chapter 3 Introduction - Right Angle Trig Review Notes.  We went through the notes and the first few examples together.  

Monday Mar 10:  we went over the page 99 questions together, then had time to work on the 2.1-2.3 Review (here is the key for that) or the 2.4 Review (here is the key for that one).  That work time would also be a good time to get your study sheet ready for Wednesday's test.

Friday Mar 7:  we started with a mini-quiz (ACC) for 2.3.   Then we had time to work on the 2.4 assignment: page 99 #1-3,6,7, or you could also work on the 2.1-2.3 Review (here is the key for that) or the 2.4 Review (here is the key for that one).

Thursday Mar 6:  I handed back the chapter 1 test and we went over a few of the questions.  At the end of the semester, I will drop the lowest test score from your average.  BUT keep in mind that the material from all of the Chapter tests will be on the final exam in June.  After that, we started class by going over a few homework questions from the textbook page 90 assignment, then we watched this video.  Then we went through the 2.4 lesson on pages 19-20 of the Chapter 2: Properties of Angles and Triangles Notes Package.   No new homework tonight, but now that you have seen how we should be doing the "prove" questions, you may want to re-try some of the page 90 homework from yesterday.  If you want to start on the 2.4 assignment it is page 99 #1-3,6,7 - I'll give you some work time for it tomorrow.  We'll use Monday as a review day and test Chapter 2 on Tuesday.

Wednesday Mar 5: we started with a mini-quiz (ACC) for 2.1-2.2.  The file link has an answer key at the end if you missed class and want to try it for yourself.   After that we had a little more time to finish the assignment from yesterday:  textbook page 90 #2-5,7,10,13,14,15.  If anyone is finished that, I will give them a 2.1-2.3 Review (here is the key for that)  to work on. 

Tuesday Mar 4:  we went over some of the page 72 and 78 questions,  Then we went back to the notes for Chapter 2.3 on pages 17-18 of the Chapter 2: Properties of Angles and Triangles Notes Package.   Then we had some time to work on the assignment for this lesson, textbook page 90 #2-5,7,10,13,14,15.   If anyone is interested in watching the rest of the cartoon I showed you a clip from today, here is the link.

Monday March 3: as promised, we had some work time for Textbook Page 72 #2,5,6 and page 78 #1,2,4,17,20.  Then we discussed what "classical" geometry used to look like and watched at a video that answers the question, "what is the centre of a triangle?"  If you missed class you can watch the video here. Then we started the started the notes for Chapter 2.3 on pages 16-17 of the Chapter 2: Properties of Angles and Triangles Notes Package.  We'll finish the notes and examples on Tuesday,

Friday Feb 28:  CHAPTER 1 TEST.  If you finish with time to spare you can work on Textbook Page 72 #2,5,6 and page 78 #1,2,4,17,20.  I'll give you more work time tomorrow if you finish the test early, and again on Monday, so you don't have to do any homework this weekend.  Huzzah!

Thursday Feb 27:  one more check in to see if the class has any Chapter 1 questions before tomorrow's test.  Then one more SET game then we finished up the notes for lesson 2.2 in our new  Chapter 2: Properties of Angles and Triangles Notes Package.  If you missed today's lesson, the filled in version of the notes package is here.   The assignment for this section is Textbook Page 72 #2,5,6 and page 78 #1,2,4,17,20.  

Wednesday Feb 26:  after another check in to see if anyone had any Chapter 1 questions (and another SET game) ,  we started notes for lessons 2.1 and 2.2, on page 10 in our new  Chapter 2: Properties of Angles and Triangles Notes Package.  If you missed today's lesson, the filled in version of the notes package is here.   

Tuesday Feb 25:  we spent a few minutes going through questions from the Chapter 1 review booklet.  Then we started Chapter 2.  We did some examples in the introductory section, pages 2-8 in the Chapter 2: Properties of Angles and Triangles Notes Package together.  You can finish the rest of the examples that we didn't get to for homework.  

Monday Feb 24:  today was the last day I'll give you class time to work on the Chapter 1 Review Booklet.   The 1.1 section has answers on page 6.  To see the answers to the 1.2 to 1.6 sections, click on this answer key.

Friday Feb 21:  we started with another SET game,  then we went through some of the questions from the page 49 assignment.  Then I handed out this Chapter 1 Review Booklet.   We will work on this for a couple of classes and then do our Chapter 1 test on Wednesday of next week.  I have an answer key for the 1.2 to 1.6 sections of the review here.  We'll correct the 1.1 section together on Monday.  Also, on Monday and Tuesday, we'll go over some of the puzzles I handed out on Wednesday.

Thursday Feb 20: After another  SET game,  we went through the questions from the page 42 assignment from Tuesday's homework.   Then we had some time to work on the last three pages of the   Chapter 1 Notes Package, then textbook page 49 #2-4,6-11,14.  These should be done for tomorrow.  If you want a break from the textbook questions, there's the puzzles I handed out yesterday. 

Wednesday Feb 20:  After another  SET game, we figured out what is going on in this  YouTube video (which is how to think about #4 from yesterday's homework).  After that, we did the 1.6 notes in our  Chapter 1 Notes Package and I handed out this Introduction to Sudoku puzzle and we went over it.   The textbook assignment for this section is to finish the last couple of examples on the last three pages of the notes booklet, then do textbook page 49 #2-4,6-11,14.  If you need a little break from the textbook questions, I handed out a 5-Triangle Puzzle, or the Logic Problem (here is the key), or  the Tax Collector problem (here is the solution)  and this practice Sudoku, (here is the key)..  I'll give you some more work time tomorrow.

Tuesday Feb 18:  We started with today's SET game.  Then we finished up the discussion and examples and notes for Lesson 1.5 in the  Chapter 1 Notes Package.  The assignment for this section is textbook page 42 #3-5,7,9,10.  We watched this little video and then, in addition to the textbook assignment, I want you to try to figure out what is going on here  (if that link does not work for you, here it is on YouTube).  The solution will be discussed tomorrow.

Friday Feb 14:  Happy Valentine's Day!  We started by going through the linear relations section of the grade 10 (and earlier) skill review package together.   Then we went over the textbook page 23 and 31 questions from yesterday.  Finally, we went back to the Chapter 1 Notes Package and went through the examples and notes for Lesson 1.5.  We didn't quite finish the lesson discussion, so we'll finish it on Tuesday and your only homework for the weekend is to try to find the mistake or reasoning error in the last example we did (or did we really just prove that 2=0 !?)

Thursday Feb 13:  we went over the trigonometry questions in the grade 10 (and earlier) skill review package together.  Then we had more time to work on textbook page 23 #10-12, 15-17 and page 31 #1-5, 7,8,10,11,15.  They should be done for tomorrow.

Wednesday Feb 12: We went through the factoring section of the grade 10 (and earlier) skill review package together, including how to use Desmos when you are stuck on a factoring question.  Then we went back to the Chapter 1 Notes Package and went through the examples and notes for Lesson 1.4.  The assignment for this section is textbook page 23 #10-12, 15-17 and page 31 #1-5, 7,8,10,11,15.  You can have the rest of class to work on this today and I'll give you some more time tomorrow.

Tuesday Feb 10:  we discussed the a,b,c,d,e questions in the last example of Lesson 1.3 in the Chapter 1 Notes Package.  Then we had some time to work on the grade 10 (and earlier) skill review package.  We'll start going over it tomorrow as we keep working through Chapter 1.

Monday Feb 8:  since there was a mix up with the class coverage on Friday, I handed out this grade 10 (and earlier) skill review package today for the people who missed it.   I'll give you some time to work on it tomorrow.  Then we went over textbook page 17 #2 and page 22 #1,3,4.  After that, I handed out a couple more pages of the Chapter 1 Notes Package and we did some notes.  If you didn't finish a,b,c,d,e of the last example in Lesson 1.3, do them for homework.  We will discuss them tomorrow.

Friday Feb 7:  work time to finish page 17 #2 and page 22 #1,3,4.   After that, my guest teacher handed out this  grade 10 (and earlier) skill review package.  Try as much of it as you can.  Don't panic if there are parts of it that you can't remember how to do - we'll spend a little bit of time in each of the following week or so of classes reviewing these skills while we finish up chapter 1.

Thursday Feb 6:  we looked at the conjecture that you made for the relationship between the number of points on a circle and the number of regions formed by its cords.  We had a little more discussion about conjectures and proofs of their validity.  We watched this video and this video.  We figured out this webpage is "reading your mind".   Then we had time to work on textbook questions:   page 17 #2 and page 22 #1,3,4.  They should be done for Monday.

Wednesday Feb 5:  we started doing some notes from our  Chapter 1 Notes Package.  Today we did some definitions and examples (for homework, come up with a conjecture about the last example with the cords of a circle).  For our first textbook work, I assigned the following textbook questions:   page 17 #2 and page 22 #1,3,4. I'll give you time to work on them tomorrow. See if you can figure out how this webpage is "reading your mind"

Tuesday Feb 4:  we started with a problem:  is 8^x always going to be larger than 9^(x-1)?  We found out  the answer (thanks to an excel spreadsheet!).  Then we looked at the climb to a prime game, which leads to more conjectures. Will my favourite (non-prime) two digit number climb to a prime?  Will ALL numbers eventually climb to a prime?  Here is a direct link to the prime number checker to help you play.  The "climb to a prime" game explains why 13 532 385 396 179 is Mr K's favourite number.  Just to show us that math isn't just about numbers we looked for patterns in shapes with The SET game.

Monday Feb 3:  Welcome to Grade 11 Applied Math!  Here is the course outline.  We played a couple of  games with 2 digit numbers (and learned about Kaprekar's constatnt and the Collatz Conjecture) while I assigned textbooks and tried get to know you a little bit.  No homework yet!  If anyone wants to use the HOTPO online calculator that I was using in class, here is the link.  If anyone who is also taking computer science wants to have a try at coding a program to calculate it yourself, let me know! 

TEXTBOOK:   Chapter 3 Getting Started, Chapter 3.1, Chapter 3.2, Chapter 3.3, Chapter 3.4, Chapter 3 Review, Chapter 3 Self-Test, Chapter 2.1, Chapter 2.2, Chapter 2.3, Chapter 2.4, Chapter 1.1, Chapter 1.2, Chapter 1.3, Chapter 1.4, Chapter 1.5, Chapter 1.6, Chapter 1.7,  ANSWER KEYS

CHAPTER 3 & 4 VIDEO LESSONS:  Deriving the Sine Law,  Using the Sine Law (examples), Deriving the Cosine Law, Using the Cosine Law (examples), Lesson 3.4-word Problems, 4.1 - 4.2 Trig of Obtuse Angles, 4.3 Part 1, 4.3 Part 2,