Pre - Calculus

MTH 30       D09 (51360)

Mondays, Wednesdays: 10:00 am - 11:50 am, at CP 309


 
 
12/16

Final Exam


The Final Exam has 30 questions, 121 points total. You need to get only 100 points to get 100% for the Final Exam!
Warning: each question will have a limited number of attempts, so pay attention to it!

I will be available at our regular Zoom meeting if you get any questions!

Visit the Midterm and Final Exams page to see all information related to the Final Exam.
Visit the Midterm and Final Exams page to see all information related to the Final Exam.

The opportunity to earn extra points:
I placed Sample Final Exam at the WeBWorK. It will be available until Tuesday, December 15th, 11:59pm.
It has 26 questions, but to get 100 points you need to do any 25 questions (each problem is worth 4 points).
* If you get 100 points on it, 10 points will be added either to your Final Exam score, your Midterm Exam score, your quizzes score or your homeworks score, whichever yields the highest course grade.
* If you get 90 points on it, 9 points will be added either to your Final Exam score, your Midterm Exam score, your quizzes score or your homeworks score, whichever yields the highest course grade.
* And so forth.

Given the circumstances we are in this semester, I believe that it would be fair to give you this opportunity.
 		 9 am - 11:50am
at WeBWorK

Week 16
 
12/09

Review of logarithmic and exponential functions

Review Problems

Meeting recording

For additional preparation go over the review on October 28th
 
12/07 Review of topics from the very beginning of the class until exponential and logarithmic functions

Review Problems

We didn't do the last four problems. Here are the solutions of problems 8-10. The solution and answer to problem 7 is coming.

Meeting recording

 

Week 15

You can find your grades here. Use last 4 digits of your shcool id. 
12/02

Review of topics from trigonometry

Meeting recording

We only covered some of the problems. You can find the solutions and answers to the rest of the problems below.

Review Problems
Solutions and asnwers to some of the problems: Problem 6, Problem 7 (item b only), Problem 8, Problem 9, Problem 10
 

Additional problems for review (only answers are given, see the second page).
 

11/30 Trigonometric Equations

We are experiencing technical issues. It might be on my side. I rebooted the router but it didn't help. So I cancel the meeting. I promised to record a lecture for us.

Here is the recording of the lecture

The recording of the lecture from another MTH30 section: Meeting recording

Lecture slides
 zyBooks:
review Section 7.5
or
Textbook:
review Sections 5.5

Week 14
 
11/26 - 28

no classes - Thanksgiving Recess
 

 
11/25


Wednesday, but follows Friday schedule
 

 
11/23 Verifying Trigonometric Identities
Sum and Difference Formulas

Lecture slides ("Verifying Trigonometric Identities)
Lecture slides ("Sum and Difference Formulas")

Meeting recording

Other videos (of topics and practice we didn't do during the meeting):
1) Sum and Difference Formulas recording (theory, ~ 15 mins)
2) Sum and Difference Formulas recording (examples, ~ 32 mins)

Quiz 18 - last quiz, based on Inverse Functions
 HW 19 - last HW assignment:

1)(due date: Monday, November 30th) HW 19 Verifying Identities - Sum and Difference Formulas

2)(due date: Monday, November 30th)
zyBooks:
review Sections 7.1 and 7.2
or
Textbook:
review Sections 5.1 and 5.2

Week 13
 
Note that on Friday - Sunday, November 26-29th, there are not classes at BCC - Thanksgiving

You can find your grades here. Use last 4 digits of your shcool id.
11/18

Inverse Trigonometric Functions

Lecture slides ("Inverse Trigonometric Functions)

Meeting recording

Quiz 17, based on graphs of sine and cosine functions

 HW 18:

1)(due date: Wednesday, November 25th) HW 18 Inverse Trigonometric Functions

2)(due date: Monday, November 23rd)
zyBooks:
review Section 6.3
or
Textbook:
review Section 4.7
11/16 Graphs of Sine and Cosine Functions

Lecture slides ("Graphs of Sine and Cosine Functions" - we will continue covering this section next time)

Meeting recording (part 1)
Meeting recording(part 2)

Quiz 16, based on Reference Angles and Graphs of Sine and Cosine functions (up to variations of graphs, excluding)
 no HW assignment

Week 12
 
Note that on Friday - Sunday, November 26-29th, there are not classes at BCC - Thanksgiving

You can find your grades here. Use last 4 digits of your shcool id.
11/11

Trigonometric Functions of Any Angle
Graphs of Sine and Cosine Functions

Lecture slides (for "Trigonometric Functions of Any Angle", we will do examples 3 and 4, and continue to reference angles)
Lecture slides ("Graphs of Sine and Cosine Functions") - we stoped at variation of graphs (we will continue covering this section next time)

Quiz 15, based on Trigonometric Identities and Right Angle Trigonometry

Meeting recording

Additional Resouces:
0) https://www.mathsisfun.com/algebra/trig-sin-cos-tan-graphs.html
1) Graph of sin function (9:21 mins, video)
2) Features of sinusoidal functions (4:57 mins video, discussing amplitude, period and midline, the last one we didn't cover and I will not ask about it, but it is an easy feature of the graph)
3) Practice: amplitude of sinusoidal functions from graph (guided practice)
4) Practice: period of sinusoidal functions from graph (guided practice)
5) Amplitude and period of sinusoidal functions from equation (8:20 mins, video)
    Note that from that page, in the menu on the left you will see link to two more videos:
      Transforming sinusoidal graphs: vertical stretch & horizontal reflection (12:51 mins) and
      Transforming sinusoidal graphs: vertical & horizontal stretches (10:42 mins), and
    three practices:
      Amplitude of sinusoidal functions from equation
      Midline of sinusoidal functions from equation (you can skip this one since we are not doing midlines)
      Period of sinusoidal functions from equation
6) Practice: graph sinusoidal functions (guided practice)
7) Practice: Graph sinusoidal functions: phase shift (guided practice)

 HW 17:

1)(due date: Wednesday, November 18th) HW 17 Referece Angles Graphs

2)(due date: Monday, November 16th)
zyBooks:
review Section 6.1 and 6.2
or
Textbook:
review Sections 4.5 and 4.6
11/09 Right Triangle Trigonometry
Trigonometric Functions of Any Angle

Lecture slides (starting from "Right Angle Trigonometry", the slides are from Nov. 3rd meeting).
Lecture slides (for "Trigonometric Functions of Any Angle")

Meeting recording

We stopped at Example 2. Next time we will cover examples 3 and 4, and proceed with reference angles.

We won't have quiz today
Quiz 15, based on Trigonometric Identities only
 HW 16:

1)(due date: Monday, November 16th) HW 16 Right Angle Trig Any Angle Trig

2)(due date: Wednesday, November 11th)
zyBooks:
review Section 5.4 and 5.2 (reference angles)
or
Textbook:
review Section 4.4

Week 11
 
11/04

Trigonometric Identities
Right Triangle Trigonometry

Lecture slides (we will only cover the slides up to the"Right Angle Trigonometry"). We will continue covering the slides in the next class.

Meeting recording

Quiz 14, based on Angles, Radian Measure and Trigonometric Function on Unit Circle

 We finished the lecture slides from the previous meeting and proceed with the today's topics. We didn't finish all the slides in today's meeting and will continue covering them in the next class

 HW 15:

1)(due date: Wednesday, November 11th) HW 15 Fundamental Identities

2)(due date: Monday, November 9th)
zyBooks:
review Sections 5.3 (skip the Using
reference angles to evaluate tangent, secant, cosecant, and cotangent) and 5.4
or
Textbook:
review Sections 4.2 and 4.3
11/02 Angles and Radian Measure
Trigonometric Functions: Unit Circle

Lecture slides
Table of values of trigonometric functions

Meeting recording

We didn't do all the slides. We will continue covering them in the next class.

I finally posted the recording of the review problems 7-10 (we were working on them on October 28th).		 HW 14:

1)(due date:Monday, November 9th) HW 14 Angles,Radial Measures, Trig Functions

2)(due date: Wednesday, November 4th)
zyBooks:
review Sections 5.1 (up to Finding the area of a sector of a circle, excluding), 5.2 (up to Reference Angle, excluding) , and 5.3
or
Textbook:
review Sections 4.1 and 4.2

Week 10
 
10/28 Review

Quiz 13, based on Exponential and Logarithmic Equations

Lecture slides

Meeting recording (we only covered examples 1-6)

The rest of the examples (7-10) video recording

We are given the date and time of our Final Exam: Wednesday, December 16th, 9 am - 11:50am.
10/26 Exponential and Logarithmic Equations

Quiz 12, based on Properties of Logarithms

Lecture slides

Meeting recording

We didn't finish our in-class practice, therefore I'm posting the video recording of me working on them.

Things we discussed today:
1) Our last quiz will be on November 23rd
2) last HW assignment will be also given on November 23rd
Therefore, make sure you are submitting the homeworks on time and participate in the quizzes. 		HW 13:

1)(due date: Monday, November 2nd) HW 13 Exponential and Logarithmic Equations

2)(due date: Wednesday, October 28th)
zyBooks:
review Section 4.6
or
Textbook:
review Section 3.4

Week 9
10/21

Properties of Logarithms

Lecture slides

Quiz 11, based on Exponential and Logarithmic Functions

Common and Natural Logarithms recording
Properties of Logarithms recording

We didn't do practice problems condensing the logarithms. There is the recording: practice problems, part 2

 HW 12:

1)(due date: Wednesday, October 28th) HW 12 Properties of Logarithms

2)(due date: Monday, October 26th)
zyBooks:
review Section 4.5
or
Textbook:
review Section 3.3
10/19 Exponential Functions
Logarithmic Functions

Lecture slides

Meeting recording

Midterm Exam grade will be composed of HWs 1-10 (30%) , quizes 1-10 (30%) and Midterm Exam grade (40%).
All grades will be posted in the Google spreadsheet (don't forget to check the tabs at the bottom). So far I posted HWs 1-7 scores, Quizzes 1-10 scores, except for Quiz 8 and Midterm Exam scores with some statistics.

We discussed during the meeting:
1) I reminded that the DRF from the end of the Pearson's book is extremely handy and that you should print it out and keep it nearby (see September 9th meeting)
2) I'm looking at your quiz 8 and replying to your emails with the score during this week.
 HW 11:

1)(due date: Thursday, October 22nd) HW11 Exponential and Logarithmic Functions

2)(due date: Tuesday, October 20th)
zyBooks:
review Sections 4.1 - 4.4
or
Textbook:
review Sections 3.1 - 3.2

Week 8

You can find your grades here. Use last 4 digits of your shcool id.
10/14


Wednesday, but follows Monday schedule

Midterm Exam

Exam date: Wednesday, October 14th, 9:30 am - 12pm at WeBWorK
The exam has 26 questions.
Warning: some questions have limited number of attempts (you can see it at the bottom of the screen: how many attempts you already made and how many are left).

If you have any questions, I will be at our Zoom meeting. Feel free to connect and ask your questions!

the midterm exam covers Chapters 1-2 from the Peason textbook and Chapters 1-3 from zyBooks

Here is a review list of exercises for the Midterm Exam (updated on October 11th, 1:30pm). The answers are on the last pages.
The solutions: problems 1-5, problem 6, problems 7-8, problem 10, problem 11, problems 12, problems 13 and 15, problems 14 and 16, problem 17, problems 18-20, problems 21-23, problems 41-25, problems 26-27, problems 28-30, problems 31-32, problems 33-34, problem 35, problem 36, problems 37-38.  

  
10/12 BCC is closed - Columbus Day

Week 7

Note that on Monday, October 12th, BCC is closed - Columbus Day
10/07

Preparation for the Midterm Exam

Quiz 10, based on Polynomial and Rational Inequalities

Preparation to Midterm Exam slides

Meeting recording

The review problems will be posted tonight.

The Midterm Exam will be at WeBWorK.
It will open on Wednesday, October 14th, at 9:30am and will close at 12pm that day.
It will have 32 to 34 questions.

If you have any questions during the exam, I will be available at our zoom meeting so feel free to connect.

Here is a review list of exercises for the Midterm Exam (updated on October 11th, 1:30pm). The answers are on the last pages.
The solutions will be posted later.  
 
10/05 Polynomial and Rational Inequalities

Lecture slides

Video recording of our meeting

Quiz 9, based on Rational Functions and Their Graphs

Additional Materials:
1) Polynomial Inequalities (a set of examples with solutions)
2) Quadratic inequality (video example fromKhan Academy, ~ 8 mins)
3) Quadratic inequality, example 2 (video example fromKhan Academy, ~ 8mins)
4) Rational Inequalities (a set of examples with solutions)
5) Solving a rational inequality (video example from Khan Academy, ~ 12 mins)
6) Solving a rational inequality, right side is not zero (video example from Khan Academy, ~ 13 mins)		 HW 10:

1)(due date: Monday, October 12th) HW10 Polynomial and Rational Inequalities

2)(due date: Wednesday, October 7th)
zyBooks:
review Lecture slides, look through the additional materials if you feel that you need extra practice
or
Textbook:
review Sections 2.7 Polynomial and Rational Inequalities

Week 6

You can find your grades here. Use last 4 digits of your shcool id.
09/30

Rational Functions and Their Graphs

Asynchronous: we will not be meeting in a Zoom. Everybody will be working on their own.

Things to do:
1. Please view this video: a "full" analysis of a polynomial function: everything we can do so far! (30 minutes long)
You can use this video to help you with Quiz 8
2. Please view the videos on Rational Functions and Their Graphs:
    (1) Rational Functions and their graphs (~21 mins)
    (2) Example 1 (~11 mins)
    (3) Example 2 (~10 mins)
3. Take Quiz 8, which is based on everything we learned about the polynomial functions so far.
I am asking you to make a full analysis of the polynomial function. All the details are in this file: MTH30Quiz8Polynomial Functions.
You MUST send me your work by Monday, October 5th, 11:59pm Tuesday, October 6th 11:59pm to this email: natna20@gmail.com

 HW 9:

1)(due date: Saturday, October 10th) HW9 Rational Functions

2)(due date: Monday, October 5th)
zyBooks:
review Section 3.7 Rational functions
or
Textbook:
review Sections 2.6 Rational Functions
09/29
Tuesday, but follows Monday schedule

Zeros of Polynomial Functions

Quiz 7, based on Dividing Polynomials, Remainder and Factor Theorems

Lecture slides

Videos:
1) Video recording of the meeting
2) Descartes's rule of signs (we didn't have time to cover it during our meeting. Make sure to watch it and be prepared for the next quiz) 
HW 8:

1)(due date: Wednesday, October 7th) HW8 Zeros of Polynomial Functions

2)(due date: Monday, October 5th)
zyBooks:
review Section 3.6 Zeros of polynomial functions
or
Textbook:
review Sections 2.5 Zeros of Polynomial Functions
09/28

no classes at BCC - Yom Kippur

  

Week 5

Note that on Monday, September 28th, there are no classes scheduled at BCC - Yom Kippur

You can find your grades here. Use last 4 digits of your shcool id.
 
09/23

Dividing Polynomials, Remainder and Factor Theorems

Lecture slides

Quiz 6, based on Quadratic and Polynomial Functions

Video recording of our meeting

 HW 7:

1)(due date: Wednesday, September 30th) HW7 Dividing Polynomials

2)(due date: Tuesday, September 29th)
zyBooks:
review Sections 3.5 Dividing polynomials, and 3.6 Zeros of polynomial functions (everything until Using the rational zero theorem to find rational zeros)
or
Textbook:
review Sections 2.4 Dividing Polynomials, Remainder and Factor Theorems.
09/21

Quadratic Functions
Polynomial Functions and Their Graphs

Lecture slides

Videos:
our meeting video

Additional Materials and Practice (Khan Academy):
1) completing the square (worked example, ~3 mins)
2) Here you can find everything about quadratic functions and graphing them (Khan Academy unit)
3) Polynomials functions: graphing (end behavior, zeros, multiplicity of zeros, etc)

 HW 6:

1)(due date: Tuesday, September 29th) HW6 Quadratic and Polynomial Functions

2)(due date: Wednesday, September 23rd)
zyBooks:
review Section 3.2 Quadratic Functions, 3.3 Power functions and polynomial functions (skip the power function), and 3.4 Graphs of Polynomial Functions
or
Textbook:
review Sections 2.2 Quadratic Functions and 2.3 Polynomial Functions and Their Graphs

Week 4

Note that on Friday - Sunday, September 18-20th, there are no classes scheduled at BCC - Rosh Hashanah

You can find your grades here. Use last 4 digits of your shcool id.
09/16

Chapter 1 Review

Quiz 5, based on Inverse Functions

meeting video recording
We only went over the second part of the review (except for exercises 6 and 7)

Here is a recording of the review of the first part (from another MTH 30 section)

Chapter 1 review, part 1
Chapter 1 review, part 2
Answers only: Chapter1review_answers.pdf

 no HW assignment
09/14

Section 1.8 Inverse Functions

Lecture slides

Videos from the meeting:
1) Domain of composite functions
2) Inverse functions

Quiz 4, based on Transformations of Functions

 HW 5:

1)(due date: Monday, September 21st) HW5 Inverse Functions

2)(due date: Wednesday, September 16th)
zyBooks:
review Section 1.6 Inverse Functions
or
Textbook:
review Section 1.8 Inverse Functions.

Week 3

You can find your grades here. Use last 4 digits of your shcool id.

 
09/09

Transormations of Functions

Lecture slides
Definitions, Rules and Formulas (from the back of the book)

Quiz 3, based on Combinations and Compositions of Functions

Videos from the meeting:
1) meeting video (the link is updated!)

Additional Materials and Practice (Khan Academy):
1) completing the square (worked example, ~3 mins)
2) page with a list of transformations that has video examples as well as guided practices. Check the sections Shifting Functions, Reflecting Functions, Scaling Functions (it is the same as stretching/shrinking) and Putting it all Together.

 HW 4:

1)(due date: Wednesday, September 16th) HW4 Transformations of Functions

2)(due date: Monday, September 14th)
zyBooks:
review Section 1.5 Transformation of Functions
read Section 1.6 Inverse Functions
or
Textbook:
review Section 1.6 Transformations of Functions
read Section 1.8 Inverse Functions.
09/07 Labor Day. BCC is closed.  

Week 2

Note that on Monday, September 7th, College Closed - Labor Day
 
09/02

Section 1.7 Combinations and Compositions of Functions

Quiz 2, based on Section 1.3

Lecture slides

WebWorK cheat sheet (will help you with entering your answers at WeBWorK)

Videos:
1) Meeting video (combinations of functions)
The topics we didn't cover in class:
2) Introduction to Compositions of Functions (Khan Academy Video, 6:14 mins)
3) Composing Functions (walk through examples, explanations, and practice problems to learn how to find and evaluate composite functions; Khan Academy)
4) Evaluating Composite Functions (Khan Academy Video, 4:09 mins)
5) Guided practice on evaluation of composite Functions (Khan Academy)
6) Evaluating composite functions: using tables (Khan Academy Video,  4:09 mins)
7) Evaluating composite functions: using graphs (Khan Academy Video, 3:01 mins)
8) Practice: Evaluate composite functions: graphs & tables (Khan Academy)
9) Finding composite functions (Khan Academy Video, 2:55 mins)
10) Practice: Find composite functions (Khan Academy)
11) Evaluating composite functions (advanced) (Khan Academy video, 4:10 mins)

 HW 3:

1)(due date: Wednesday, September 9th - extended to Sunday, Sept. 13th) HW3 Combinations and Compositions of Functions

2)(due date: Wednesday, September 9th)
zyBooks:
review Section 1.4 Composition of Functions
read Section 1.5 Transformation of Functions
or
Textbook:
review Section 1.7 Combinations of Functions, Compositions of Functions
read Section 1.6 Transformations of Functions.
08/31

Section 1.3 More on Functions and Their Graphs

Lecture slides (all errors corrected)

1) Lecture video
2) in-class practice video, problems 1-2 (we did three problems only, Zoom was glitching)
3) Practice problem 3
4) in-class practice, problems 4-6 (we didn't do them during the meeting)

Quiz 1, based on Section 1.2
At our next meeting we will have quiz 2. It will be based on both section 1.3


We will be skipping two sections: Section 1.4 Linear Functions and Slope and Section 1.5 More on slope.
I would recommend skimming through these two sections and we are assumed to know this material already.

 HW 2:

1)(due date: Wednesday, September 9th) HW 2 More on Functions and Their Graphs at WeBWorK

2)(due date: Wednesday, September 2nd)
zyBooks:
review Sections 1.1, 1.2, 1.3
read Section 1.4 Composition of Functions
or
Textbook:
review Sections 1.2 and 1.3
read Section 1.7 Combinations of Functions, Compositions of Functions.

3)(due date: Wednesday, September 2nd) double check that you have the Kahoot! app on your cell phone. We will have Quiz 2 based on todays topics in the beginning of our next meeting.

4)(due date: Wednesday, September 9th) Optional:
Week 1
 
08/26 Section 1.2 Basics of Functions and Their Graphs

Links to the videos of our meeting on YouTube:
1) Class structure (part 1): https://youtu.be/geaH90HC-5I
2) Class structure (part 2): https://youtu.be/dmEz4Hn2P2U
3) Lecture (part 1): https://youtu.be/psmdbYy11pg
4) Lecture 1 (part 2): https://youtu.be/2xlS8mFwYmA
5) Lecture 1 (part 3, including the Kahoot training quiz and other comments about course structure): https://youtu.be/d4mXp0seq5U
Not covered in class:
6) Graphs and functions: https://youtu.be/wUxNwfRpMfk
7) Practice: https://youtu.be/nzPU0d1paYM

Lecture slides

We didn't finish the slides. So I will record a series of video-lectures and post the links to them tonight.

We had a Training Quiz at Kahoot!

At our next meeting we will have Quiz 1. It will be based only on topics we covered from Section 1.2

Resources while you are getting the textbook:

Sections 1.2 and 1.3 of the book are available through e-reserves:
http://bcc-libweb.bcc.cuny.edu/electronic-course-reserves/
- choose MTH 30 from the drop-down menu
 HW1:

1)(due date: Wednesday, September 2nd) HW 1 at WeBWorK

2)(due date: Monday, August 31st)
  • zyBooks: Sections 1.1, 1.2, and 1.3 (note that we didn't cover one-to-one functions and horizontal line test)

    • or

  • Textbook: Sections 1.2 and 1.3
    Note that you will be seeing topics we covered today and new topics.

3)(due date: Monday, August 31st) Install Kahoot! app on your cell phone.
Be ready to use it in the beginning of our next meeting (Quiz 1).

4)(due date: Wednesday, September 2nd) Optional
  Self-Review:
Section 1.1 Graphs and Graphing Utilities


Khan Academy resources:
Intro to the Coordinate plane (video, 11:21 mins)
Coordinate plane : a section with video lectures and guided practice
Graphing two linear equations (5x+2y=20 and y=2x+7) and practice (including vertical and horizontal lines) - a section with videos and practice
Introduction to parabolas: a video (8:43 mins) and two practices
Review of graphing quadratic functions - a section with text (with links to videos) and practice
Forms and features of quadratic functions : videos and practice
Graphs of absolute value functions: videos and practice

Resources while you are getting the textbook:

Section 1.1: Ch1_Section1.pdf

Sections 1.2 and 1.3 of the book are available through e-reserves:
https://bcc-cuny.libguides.com/er.php?course_id=50863
- choose MTH 30 from the drop-down menu

 For practice from the Textbook:
Section 1.1 Practice Exercises: 18, 20, 22, 24, 25, 28, 41-46

Solutions: Section1_1ex_18_20.pdf, Section1_1ex_22_24.pdf, Section1_1ex_25.pdf, Section1_1ex_28.pdf, Section1_1ex_41-46.pdf

Section 1.1 from the textbook: Ch1_Section1.pdf