[NAME OF PROGRAM: ACCESS ACADEMY]

[COURSE CODE – MATH0100: COURSE NAME – PRECALCULUS]

ACADEMIC YEAR 2018-2019[SEMESTER – SPRING]

COURSE SYLLABUS

1. COURSE INFORMATION

Classes held: 6th January, 2019 Credits : 4Prerequisite: Higher Secondary Mathematics

2. FACULTY INFORMATION

Faculty Name: Faiz AhmadEmail: faiz.ahmad@auw.edu.bdOffice Location: H 518Office Hours: 4 Hours

Qualifications: M.Sc. in Physics, University of Chittagong, Bangladesh B.Sc. in Physics, University of Chittagong, Bangladesh

Areas of Expertise: Pre-calculus, Calculus, Newtonian Mechanics, Nuclear Physics, and Astrophysics.

Profile:

Faiz served as a Senior Instructor in Mathematics, Pathways for Promise at AUW from Summer II 2016 to Fall 2017 and then in AA as Instructor (Pre-Calculus) from 2018 Spring Semester. He graduated from the University of Chittagong (Bangladesh), in Physics with both first class results. Before joining AUW, he worked for Presidency International School (Cambridge affiliated) and Bangladesh Elementary School (NC English medium) for 5 years. He actively participated in numerous training sessions conducted by local and international experts on teaching methods, lesson planning, class room management, student psychology etc. He is also one of the 29 listed junior researchers from South Asia selected by NABIC & BCAS (Dhaka) and NERSC (Bergen, Norway). In 2017 he successfully completed AuthorAID (based in Oxford, UK) grant proposal and research writing online course and obtained Merit grade.

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3. TEXT AND OTHER COURSE MATERIALS

Required Text: Michael Sullivan Pre-calculus.Other necessary course materials will be providing in the class room.

4. COURSE OBJECTIVES AND DESCRIPTION

Course Description: Pre-calculus is a one year course of mathematics. Pre-calculus exposes

students to a rigorous level of mathematics, essential to the study of UG level courses under Liberal

arts and Sciences. The pace of the class and depth of the material may be different than those

encountered in previous education. The focus of this course is primarily on various types of

functions: polynomial, rational, exponential, logarithmic and trigonometric. The student will also

learn about the behavior of functions through graphs and transformations; they will gain insight into

the properties of these functions and their inverse forms. At the end of the course, students will be

able to apply a variety of techniques to abstract and real-life problems alike. They will also use

"Khan Academy Videos/ Resources" in this course in a blended learning and assessing approach.

Course Objectives:

1. Gaining factual knowledge (Essential)

2. Learning fundamental principles, generalizations or theories (Important)

3. Learning to apply course material (to improve thinking, problem solving, and decisions) (Important)

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Spring Semester

Learning Goals:

Exponential and Logarithmic Functions

o One-to-One Functionso Inverse Functionso Exponential Equation/Function and its properties.o Logarithmic Equation/Function and its properties.o Applications of Exponential and Logarithmic Functions

Trigonometric Functions

o Types of Trigonometric Functionso Properties of the Trigonometric Functions

Analytic Trigonometry

o Trigonometric Identities o Sum and Difference Formulaso Double-angle and Half-angle Formulas o Product to Sum and Sum to Product Formulas

Systems of Equations

o Matrix Algebra.

Describing Data Sets

o Characterizing Data.

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5. LEARNING OUTCOMES

Student Learning Outcomes Method of Assessment1) Demonstrate the fundamental concept of a mathematical function and all of its properties.

Quiz based upon class lecturer, Assigned homework exercises, and exam.

2) Solve equations and inequalities both algebraically and graphically.

Quiz based upon class lecturer, Assigned homework exercises, and exam.

3) Find zeros of polynomials and the zero product property.

Quiz based upon class lecturer, Assigned homework exercises, and exam.

4) Graph polynomial, absolute value, square root, rational function and polynomial functions.

Quiz based upon class lecturer, Assigned homework exercises, and exam.

5)Identify some connection between the mathematics at this level and the real world

Quiz based upon class lecturer, Assigned homework exercises, and exam.

6. ATTENDANCE REQUIREMENT & GRADING POLICY

An “A” designates truly excellent and outstanding work and an “F” represents complete lack of effort resulting in unacceptable work.

A+ 4.3 (96.68-100) A 4.0 (93.33-96.67) A- 3.7 (90.00-93.32)

B+ 3.3 (86.68-89.99) B 3.0 (83.33-86.67) B- 2.7 (80.00-83.32)

C+ 2.3 (76.68-79.99) C 2.0 (73.33-76.67) C- 1.7 (70.00-73.32) *

D+ 1.3 (66.68-69.99) D 1.0 (63.33-66.67) D- 0.7 (60.00-63.32)

F 0 (59 .99 or below)

* Any grade below C- (70%) requires remedial work. A course of action will be decided in agreement between the student, teacher, and an academic administrator.

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7. CONTACT WITH YOUR PROFESSOR

If you face any problem you can contact me during my office hours or by appointment.Students are expected to check their email at least twice daily, preferably in the morning and evening. Students are advised that a majority of faculty answer email within a 24 hour period during the week and a 48 hour period during weekends. Please be aware that students who do not check email regularly may miss important class announcements.

8. COURSE SCHEDULE

*Please see Khan Academy Video links provided at last 4 pages of this plan booklet. Also, note that you can watch much more that fits our lesson objectives and we may update (include/exclude) the list as Khan Academy also uploads new videos time to time and to make the links more useful for

our students and lesson. I may send you all the links in your email as well so that you can click and go to the link directly.  

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Spring Semester Pre-Calculus Lesson Plan

Week 1

1st Class 2nd class 3rd class Objectives

Introducing the Spring SyllabusDetermine whether the function is one-to-one.

Draw the graph of inverse function, Check the inverse function algebraically and state domain and range.

Class Outline An hour long discussion on

Spring Syllabus and course plan

I will show how to work with problems 10,12,16,18,20,22,26,30,32,36 38 and 40 from exercise 5.2 (Sullivan Book) then Ss will have to solve few problems individually and answer will be given on the board.

I will show how to work with problems 48, 58 and 66 from exercise 5.2 (Sullivan Book) then Ss solve most of the problems individually and answer will be written on the board.

HandoutsSpring Syllabus

Ex;5.2 N/A

Homework None Some problems from Exercise-5.2 based on those conceptions.

All odd number exercises from (47-58) and (59-70).

Evaluation N/A Students will solve some problems based on the conceptions. Some students might straggle with problems 36 and 40.

Students will solve some problems based on the conceptions.

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Week 2

1stclass 2nd class 3rd class

Objectives Study two Transcendental functions: the Exponential function and Logarithmic function.

Determine whether the given data represent exponential functions or not. Use the transformation to draw exponential graphs and then find out domain and range.

Change exponential expressions to logarithmic expression, evaluate logarithmic functions.

Quiz test 1

Class Outline Evaluate exponential functions,

Graph exponential functions; laws of exponents and define the number ‘e’.  

I will show some problems from Ex: 5.3 (Sullivan Book). Most of the problems will complete by the students.

Review of the Chapter(Use of Khan Academy videos/Resources)

Handouts Some Vocabulary to familiar with.

Ex:5.3(Sullivan Book) Ex:5.4 (Sullivan Book)

Homework Some problems from Larson’s Precalculus Book

All Odd numbers exercises from ex: 5.3. N/A

Evaluation Some Students may work out problems based on the conceptions correctly, however they might have some confusion especially on exponential graphs.

Most of the students are expected to respond well. Students will be asked

to solve random problems by themselves.

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Week 3 & 4

1st and 2nd class 3rd and 4th class 5th and 6th classObjectives SWBAT determine the domain

of logarithmic function and graph logarithmic function.Discussing the Quiz-1 mistakes.

SWBAT learn how to solve logarithmic equations

SWBAT Identify the logarithmic expression as a single logarithm and evaluate logarithm whose base is neither 10 nor e.

Class Outline

First 30 minutes I will discuss the mistakes which Ss did on the Quiz-1.Then I will show how to find out the domain of the logarithmic function and how to graph. I will solve 44, 48 and 68 and will ask Ss to solve 38, 40, 42, 46, 50, 54, 56, 64, 66, and 70. Ss will go through the problems individually and I will roam to see Ss work.

I will give an example and then I asked to solve 88,90,92,94,96,98,100,102,104,106,108 and 110. (Ex: 54 from Sullivan Book) Ss start to solve individually and answer will be given on the board.

Students will see Khan Academy videos/Resources for more clear concepts.

Handouts N/A N/A N/A

Homework 37,39,41,43,47,51,53,55,61,63,65,67,69 ( Ex:5.4 Sullivan)

Solve Worksheet. N/A

Evaluation Ss can easily understand my solution and easily solve problems.

Ss can easily understand and solve application problems.

Students will have to solve some random problems.

                                             

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Week 5 & 6

1st and 2nd class 3rd and 4th class 5th and 6th class

Objectives SWBAT use the properties of logarithm to find the exact value, express as a sum and/or difference and each expression as a single logarithm.

One more lesson on logarithm. To make students familiar with Application based problems,

To model a problem from data.

Class Outline

I will solve few problems from Ex: 5.5 then will ask the Ss to solve 8, 12, 16, 20, 22, 26, 28.30,36, 38, 44, 48, and 50. Answer will be given on the board.

I will show problems no. 56, 64 and 70.Will ask to solve problems No 52,54,58,60,62,66,68 and 72. Answer will be given on the board.

I will discuss some problems based on Economics & some problems based on Life Science.

Handouts Sullivan  Ex:5.5 N/A Application problems handouts

Homework Revise Ex: 5.2-5.4. Revise : Ex:5.5 From handouts.Evaluation Most of the students might

struggle with problems: 22, 48 and 50.

Ss can easily understand and will solve problems.

At first few students struggle then they will get fun.

Week 7 & 8

1st and 2nd class 3rd and 4th class 5th and 6th classObjectives To find the exact values of

the trigonometric functions using a point on the unit circle.

SWBAT learn properties of the trigonometric functions.

Review of the trigonometric functions.

Class Outline

Will show some numerical problems on finding trig. Values graphically and numerically.

Determine the domain and range of trigonometric functions and period of trigonometric function and work with first six fundamental identities.

After the discussion Ss will see Khan Academy videos/Resources for more clear concepts.

Handouts Ex:6.2 Ex:6.3 N/A

Homework Exercise 6.2 (29-48) and (67-82) Sullivan Book.

Exercise 6.3 (27– 34, 59 - 76)Sullivan book.

N/A

Evaluation Get few problems done by students, students may be confused on some problems related to Phi.

Students will solve few problems from Exercise and will rectify the previous difficulties.

Random questions will be asked to judge the level of understanding.

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Week 9

1st class 2nd class 3rd classObjectives Revision for Midterm. Midterm Review of Mid-Term

questions.

Class Outline

Revise all concepts in Midterms.

Students will participate in the midterm exam.

N/A

Handouts A work sheet Question paper. N/A

Homework Preparation for Midterm. N/A N/A

Evaluation Hope class will finish well.

N/A N/A

Week 10

1st class 2nd class 3rd class

Objectives SWBT will use algebra to simplify trigonometric expression and establish identities.

Second lesson on using algebra to simplify trigonometric expression and establish identities.

Third lesson on using algebra to simplify trigonometric expression and establish identities.

Class Outline

Demonstrate algebraic techniques to simplify trigonometric expression .Then I ask to solve 10, 12 18,30,31,32 and 34. Ss will work with the problem. I will be checked each students answer when they will work.

Ss will work with the problems 40 42, 44,46,48,50, 52,54,56,58,60,62,64,66,68,70 72and74. I will be checked each students answer when they will work.

Ss will have to solve problems 76,78,80,82,84,86,88,90,92,94,96,98,100 and 102. I will be checked each students answer when they will work.

Handouts Ex:7.3( Sullivan Book) N/A N/A

Homework Ex:7.3 (20,22,24,26,30,32,34,35,36,37,38)

Ex:7.3(41,43,45,47,49,51,53,55,57,73)

Ex: 7.3 All odd number exercises from 75-101.

Evaluation Some of the students might struggle with applying techniques.

Ss will easily solve the problems.

Ss will easily solve problems.

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Week 11

1st class 2nd class 3rd class

Objectives Proof the sum and difference formulas and use sum and difference formulas to find the exact values.

SWBAT use sum and difference formulas and use sum and difference formulas to establish identities (Double angle and half angle formulas; Product to sum and sum to product formulas)

SWBAT understand the graphing utility to find the line of best fit and second lesson on previous lesson.

Class Outline

Class will start with the some basic of Euclidian geometry then I will prove the sum and difference formulas. Ss will work with the problems. I will be checked each students answer when they will work.

I will show few examples then ask to solve 46,48,50,52,56,58,60,62,64,68 and 70 from Ex: 7.4 (Sullivan Book) .I will be checked each students answer when they will work.

In the class I will solve 18 (which was H.W) Then I will ask to solve 21 and 22.

Handouts Ex:7.4 Ex: 7.4 N/A

Homework Ex:7.4 (All odd numbers from 9-38)

Ex:7.4 ( all odd numbers from 45-69) Preparation for 2nd Quiz.

Evaluation Ss might confuse with geometry problems.

Ss easily will solve the problems. Ss easily could understand the application problems and will get fun.

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Week 12

1st class 2nd class 3rd class

Objectives 2nd Quiz Proof the sum and difference formulas and use those to establish identities.

Proof the product to sum and sum to product formulas and use those to establish identities.

Class Outline

N/A Class will start with formulas proof then I will solve and explain problem no. 64 Ex: 7.5 from Sullivan book .Then I will ask to solve all even numbers from 48-68. I will check each and every one answers.

Class will start with formulas proof then I will solve and explain problem no. 28 Ex: 7.6 from Sullivan book .Then I will ask to solve all even numbers from 20-36. I will check each and every one answers.

Handouts N/A Ex: 7.5 Ex:7.6

Homework N/A Ex:7.5 ( all odd numbers) Ex:7.6 ( all odd numbers)

Evaluation Hope most of the student will do better.

Ss will easily solve the problems. Ss will easily understand the problems.

Week 13

1st class 2nd class 3rd class

Objectives Basic concept on matrix with definition and Types of matrix.

Will learn how to find the sum and difference of two matrices and scalar multiples of a matrix.

Will learn how to find the product of two matrices.

Class Outline

N/A Class will start with formulas proof then I will solve and explain problem no. 7, 8, and 9 Ex: 11.4 from Sullivan book .Then I will ask to solve all even numbers from 10-22. I will check each and every one answers.

Class will start with formulas proof then I will solve and explain then I solved and explain problem no. 23 Ex: 11.4 from Sullivan book .Then I will ask to solve all even numbers from 24-28. I will check each and every one answers.

Handouts EX:11.4 N/A N/A

Homework Examples:1,2 Examples: 3,4,5 Examples: 6,7,8,9,10

Evaluation Hope most of the students will do better.

Ss will easily solve the problems. Ss easily could understand the problems.

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Week 14

1st class 2nd class 3rd class

Objectives Will learn how to find the inverse of a matrix.

Solve a system of linear equations using an inverse matrix.

Application of Matrices.

Class Outline

Class will start with the Quiz-2 problems and then some basic discussion on inverse matrix. Will show few examples. Then will ask to solve skill building problems from Ex: 11.4 (29, 36).Answer will be written on the board.

Ex: 11.4 (39, 40) Ss will solve the problems and Match answers.

I will solve 73 for the students and will ask the students to solve  74,75 from Ex:11.4 ( Sullivan Book )(Also see Khan Academy videos /Resources for more clear concepts)

Handouts N/A N/A N/AHomework Ex: 11.4 ( 30-38) Ex:11.4(41-58) Ex: 11.4 (76,77)Evaluation Some of the students might struggle with

some problems.Some of the students might struggle.

Ss will easily understand the problems.

Week 15

1st class 2nd class 3rd class

Objectives Will discuss on the Characterizing Data.

Will solve application problems from the provided worksheet.

Revision Class

Class Outline

I will discuss some problems based on Characterizing Data.

I will discuss some problems based on Economics & some problems based on Life Science.

Revision Class

Handouts One worksheet will handout. N/A N/A

Homework Will solve problems from the provided worksheet.

N/A N/A

Evaluation Students will do some problems based on the conceptions.

Ss will easily solve the problems. Hope everything will go smoothly.

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9. ASSESSMENT METHODS

There will be a number of different ways that your learning will be assessed this year:

Participation (25%)

The participation mark is divided into three areas:

1. Attendance – 5% If you have no or one unexcused absence/late then you will receive the full 10% attendance mark. However, for two late attendances will be counted as one day absence. Three days of absence will result in the lose 60% of your marks. For example a student with 3 unexcused absences will receive an attendance mark of 2.

2. Lesson Contribution/Class Participation – 10%

The lesson contribution mark can be achieved by speaking at the board (50%), answering questions and other contributions (50%).

3. Assignments/ Homework – 10%

Quizzes (20%) There will be three or four quizzes in Spring – one for each Chapter that is covered in Sullivan Pre-calculus. Each quiz will be equal in weighting.

Mid-Term Exam (25%) The Mid-Term exam will test all of the content covered by the end of February.

Final Exam (30%) The Final Exam will test all of the content covered by the end of Spring semester (April).

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10. KEY DATES & DEADLINES

Mid-Term Exam: Between 24th to 28th February.Final Exam: Between 22nd to 25th April.

11. PLAGIARISM & ACADEMIC INTEGRITY

All members of the AUW Community are bound by the Academic Honor Code published in the Academic Bulletin (http://www.auw.edu.bd/academics/course-bulletin/).

The integrity of students’ academic work is very important to AUW faculty. Universities are based upon the fundamental principle that the work presented truly belongs to the author, because the academic community revolves around ideas and creativity. Each person’s ideas are his or her contribution to the academic community. Therefore, taking another person’s ideas and representing them as one’s own is a serious form of dishonesty. Similarly, cheating (copying someone else’s work, asking for answers, sharing answers, etc.) and other forms of dishonesty (falsifying data, making up references, etc.) are also serious breaches of this honor code.

Plagiarism is intentionally or unintentionally taking credit for another’s words or ideas. You may not plagiarize in your academic work, and you must adhere to the following:

• When you use someone else’s words (whether they are from a distinguished author or a classmate’s paper), place the words you have copied in quotation marks and provide the appropriate citation of author and source. A good guideline to use to avoid plagiarism is to make sure quotes of three or more sequential words from someone else are put into quotation marks.

• If you paraphrase (reword) another person’s ideas, then you must also cite the source. Paraphrasing must involve changing the words and sentence structure of the original source.

• Cite materials you copy or paraphrase from the Internet, even if the author is not identified.

The various academic disciplines (humanities, social sciences, sciences) use slightly different formats for footnotes, endnotes, and bibliographies. Your professor for a particular class will tell you which format he or she wants you to use in that class.

Copying, asking for answers, sharing answers, and any other form of cheating (misrepresenting your own work and knowledge) on exams or quizzes are all forms of academic dishonesty.

Other Forms of Academic Dishonesty

1. Making up references, quoting wrong sources, etc. 2. Falsifying data. 3. Misrepresenting your situation to be excused from academic work. 4. Submitting the same paper in more than one class. 5. Informing a student in a later class about questions on tests or quizzes. 6. Misrepresenting your academic work or qualifications in any way.

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12. STRATEGIES TO PREVENT PLAGIARIM& VIOLATIONS OF ACADEMIC INTEGRITY

Students will not plagiarise –please see the Student Handbook.

13. CLASS BEHAVIOUR

o You are expected to be in class on time.o You should participate in class discussions and contribute to the class goal of learning Pre-

calculus.o Read your class notes over within 24 hours (or at least once before the next class).o Students will complete all home works and assignments given by the required deadlines. o Mobile phones and similar electronic devices such as MP3 players, laptops, and so on should

be switched off and put away at the beginning of class.o You will treat others in this class with respect.o Students are expected to check their email at least twice daily, preferably in the morning and

evening. Students are advised that a majority of faculty answer email within a 24 hour period during the week and a 48 hour period during weekends. Please be aware that students who do not check email regularly may miss important class announcements.

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Useful links from Khan Academy

Exponential and Logarithmic Functions

1) Graphing basic logarithmic functions

https://www.khanacademy.org/math/algebra2/exponential-and-logarithmic-functions/

graphs-of-logarithmic-functions/v/graphing-logarithmic-functions

Duration of the video (minutes. seconds): 9.09

2) Graphs of logarithms & exponentials

https://www.khanacademy.org/math/algebra2/exponential-and-logarithmic-functions/

graphs-of-logarithmic-functions/v/comparing-exponential-logarithmic-functions

Duration of the video (minutes. seconds): 5.42

3) Surjective (onto) and injective (one-to-one) functions

https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-

transformations/v/surjective-onto-and-injective-one-to-one-functions

Duration of the video (minutes. seconds): 9.31

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4) Intro to inverse functions

https://www.khanacademy.org/math/algebra2/manipulating-functions/introduction-

to-inverses-of-functions/v/introduction-to-function-inverses

Duration of the video (minutes. seconds): 9.05

Trigonometric Functions

1) Graph of y=sin(x)

https://www.khanacademy.org/math/algebra2/trig-functions/graphs-of-sine-cosine-

tangent-alg2/v/we-graph-domain-and-range-of-sine-function

Duration of the video (minutes. seconds): 9.21

2) Limits of trigonometric functions

https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-continuity/ab-trig-and-

squeeze/v/limits-of-trigonometric-functions

Duration of the video (minutes. seconds): 6.05

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Analytic Trigonometry

1) Sine & cosine identities: symmetry

https://www.khanacademy.org/math/algebra2/trig-functions/trig-identities-alg2/v/

trigonometry-unit-circle-symmetry

Duration of the video (minutes. seconds): 7.57

2) Using trig angle addition identities: manipulating expressions

https://www.khanacademy.org/math/precalculus/trig-equations-and-identities-precalc/

using-trig-identities-precalc/v/cosine-angle-addition

Duration of the video (minutes. seconds): 6.11

3) Proof of the Pythagorean trig identity

https://www.khanacademy.org/math/algebra2/trig-functions/pythagorean-identity-alg2/

v/pythagorean-trig-identity-from-unit-circle

Duration of the video (minutes. seconds): 6.11

4) Trig word problem: modeling annual temperature

https://www.khanacademy.org/math/algebra2/trig-functions/constructing-sinusoids-

alg2/v/modeling-temperature-fluxtuations

Duration of the video (minutes. seconds): 7.08

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● Systems of Equations

1) Adding & subtracting matrices

https://www.khanacademy.org/math/precalculus/precalc-matrices/adding-and-

subtracting-matrices/v/matrix-addition-and-subtraction-1

Duration of the video (minutes. seconds): 5.34

2) Matrix product examples

https://www.khanacademy.org/math/linear-algebra/matrix-transformations/modal/v/

linear-algebra-matrix-product-examples

Duration of the video (minutes. seconds): 18.13

Describing Data Sets

1) Statistics intro: Mean, median, & mode

https://www.khanacademy.org/math/probability/data-distributions-a1/summarizing-

center-distributions/v/statistics-intro-mean-median-and-mode

Duration of the video (minutes. seconds): 8.32

2) Impact on median & mean: removing an outlier

https://www.khanacademy.org/math/probability/data-distributions-a1/summarizing-

center-distributions/v/impact-on-median-and-mean-when-removing-lowest-value-

example

Duration of the video (minutes. seconds): 5.36

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