Upload
trinhthien
View
216
Download
0
Embed Size (px)
Citation preview
[NAME OF PROGRAM: ACCESS ACADEMY]
[COURSE CODE – MATH0100: COURSE NAME – PRECALCULUS]
ACADEMIC YEAR 2018-2019[SEMESTER – Fall ]
COURSE SYLLABUS
1. COURSE INFORMATION
Classes held: 29 August, 2018 Credits : 4Prerequisite: Higher Secondary Mathematics
2. FACULTY INFORMATION
Faculty Name: Faiz AhmadEmail: [email protected] 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) during 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.
1
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)
2
[Fall Semester]
Learning Goals
Graphs
o Graphs of Equations in Two Variables
o Lines
Functions and their Graphs
o Functions
o The Graph of a Function
o Properties of Functions
o Transformations
Linear and Quadratic Functions
o Linear Functions and Their Properties
o Building Linear Functions from Data
o Quadratic Functions and Their Properties
o Building Quadratic Functions from Data
o Inequalities Involving Quadratic Functions
Polynomial and Rational Functions
o Polynomial Functions and Models
o Properties of Rational Functions
3
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.
4
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 5 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.
5
Fall Semester Pre-Calculus Lesson Plan
Week 1
1st class 2nd class 3rd class Objectives Mathematics
Placement Test Introducing the Fall Syllabus Familiar with rectangular coordinate system
Use the Distance Formula
Use the Midpoint Formula
Class Outline
N/ASome basics discussion, for instance, finding area of circle geometrically, proving Pythagorean theorem, defining undefined, zero and infinity, some puzzle problems
Proof of Mid-Point and Distance formula,Doing some examples on Midpoint and Distance formula,
Handouts N/ASyllabus
None
Homework N/A None Some problems from Exercise 1
Evaluation N/A N/A Get some problems done by students from exercise.
6
Pre-Calculus Lesson Plan
Week 2
1st class 2nd class 3rd class Objectives Graph Equation by
plotting points
Find intercept from graph
Find intercepts from equation
Understanding Symmetry concept
Test equation for symmetry w.r.t x-axis, y-axis and origin
To graph some important equations
Class Outline
Some problems shown on graphing by taking points.
Shown the symmetry concept practically by papers and markers
Shown to draw graph up to third order equations by implementing the concept of intercept and symmetry
Handouts N/AN/A
N/A
Homework Some problems from Exercise-1.2 based on that conceptions
Some problems from Exercise-1.2 based on that conceptions
Some problems from Exercise-1.2 based on that conceptions
Evaluation Students done some problems based on the conceptions.
Students done some problems based on the conceptions.
Started my Tutorial class on every Wednesday to evaluate the students
7
Pre-Calculus Lesson PlanWeek 3
1st class 2nd class 3rd class Objectives Calculate and interpret
the slope of a line,Graph lines given a point and the slope,Find the equation of a vertical line and horizontal line
To learn negative slope,
To find the line equation from intercept and slope,
To find the equation of parallel lines
Find equation of perpendicular lines
Class Outline Drawing graphs up to 3rd
order equation,Concept of slope,Some example problems on that concept,Derive the equation of a line given slope and one point,Shown how to find the slope of a vertical and horizontal line and work out some example problems
Recap of previous class on drawing graphs quickly by knowing the shapes up to 3 order equation.
Negative slope, Practically shown to form Negative slope,
Drawing graphs by knowing intercept and slope from equation,
Finding equations of parallel lines,
Difference between similar and congruent triangle,
Proof of parallel lines having same slope by similar triangle method
Recap of proof of parallel lines equation,
Recap of horizontal and vertical lines equation,
Concept of Perpendicular lines and its equation
Handouts None None Problem sheet on the concepts taught
Homework Some problems from Exercise-1.2 based on that conceptions
None Exercise 1.3 from Larson’s Precalculus book.
Evaluation Students done some problems based on the conceptions.
Students done some problems based on the conceptions.
Problems given to the students from Larson book, not been able to complete the pre-planned selected problems for evaluation because of lack of time.
8
Evaluation Some Students worked out problems based on the conceptions correctly, however they have some confusion specially on parallel and perpendicular line equation
Evaluation is done by (2nd class of the week Tutorial Class) where the students solved some selected problems from Exercise 1.3. Most of them responded well.
Pre-Calculus Lesson Plan
Week 4
1st class 2nd class 3rd class Objectives To test the concept of the whole
chapter (Slope, straight line equation)To make students familiar with Application based problems,
To model a problem from data
Class postponed due to Strike
Class Outline Various problems on slope, vertical
line, horizontal line, slope-intercept form, slope- point form, parallel and perpendicular line and graphing them.
Some problems on straight lines based on Application.Some problems on linear curve fitting from given data
Handouts Some Vocabulary to familiar with none
Homework Some problems from Larson’s Precalculus Book
Some problems on application based problems
Evaluation Some Students worked out problems based on the conceptions correctly, however they have some confusion specially on parallel and perpendicular line equation
Evaluation is done by Wednesday Tutorial Class where the students solved some selected problems from Exercise 1.3. Most of them responded well.
9
Pre-Calculus Lesson PlanWeek 5
1st class 2nd class 3rd class
Objectives SWBAT form the sum, difference, product, and quotient of two functions.Discussing the Quiz-1 mistakes.
SWBAT understand what difference quotient of a function is and how it is related to calculus. SWBAT learn how apply the function’s problem in real life.
SWBAT identify the graph of a function.
Class Outline
First 25 minutes I discussed the mistakes which Ss did on the Quiz-1.Then I showed the formula Sum ,difference, product, and quotient for function and I taught how to solve The problems 62, and 70 ( Ex2.1 , Sullivan). Then I asked Ss to solve 64, 66, 68, 69, 71 and 72. Ss went through the problem individually and I was roaming to see Ss work.
.
Introduction –key vocabulary (difference quotient). I give an example and showed that graphically then I asked to solve 74, 76,78,80( Ex:2.1 Sullivan)……..Ss start to solve individually and answer was written on the board .Ss took 20 minutes to solve , then I taught Application problem from Blitzer book ( page 162 problem 99-102)
Introduction –key vocabulary (Graph of a function, Vertical-line test) and I taught how to work with the problem 10, 12 (Ex: 2.2 Sullivan). Then I asked to solve 11, 13, 14, 16, 18, 20 and 22. Ss solved individually and answer was written on the board.
Handouts Sullivan Ex:2.1 Work sheet -3 Ex: 2.2 ( Sullivan)
Homework 61,63,65,67,69 ( Ex:2.1 Sullivan) Solve worksheet -3. 9,15,17,19,21 ( Ex:2.2 Sullivan )
Evaluation Ss can easily understood formula and easily solve problems.
Ss can easily understood vocabulary and solve application problems.
Ss got fun when they were solving graph related problems.
10
Pre-Calculus Lesson PlanWeek 6
1st class 2nd class 3rd class
Objectives SWBAT determine where a Function is increasing and or decreasing and able to locate local Maximum and minimum.
SWBAT learn how apply the graph of the function.SWBAT learn how to find out Even Odd or neither even nor odd functions from graph .
One more lesson on Local Maximum and Minimum.
Class Outline
Introduction –key vocabulary (Increasing, decreasing, Local Max. and Local Min. ). Then I give an example to show how to find out Increasing , decreasing , Local Max and Local Min from a graph of a function . I asked to solve problems 11-20 ( Ex:2.3 Sullivan )
First 25 minutes I spend on Application problems from Blitzer book (Page 176, problem 83-90). Then Introduction –key vocabulary (Even and Odd functions).I showed problem no. 24. Asked to solve problem No. 22, 26, 28. Answer was written on the board.
Introduction –key vocabulary again (Local Maximum and Local Minimum) and I taught how to work with the problem 30 (Ex: 2.3 Sullivan). And few examples from me. Taught how to Locate the location of Max and Min and what is the difference of Max and Min values of a function s and their location .Then I asked to solve 29 and 32 ( Ex:2.3 )Ss solved individually and answer was written on the board.
Handouts Sullivan Ex:2.3 N/A N/A
Homework Revise 11-20 at home Ex: 2.3 ( problems 21, 23, 25, 27 from Sullivan Book )
Revise Ex:2.3
Evaluation Most of the student struggle with 15 and 16.
Ss can easily understood vocabulary and solve problems.
At first few students struggle then they got fun and said Max and Min is not difficult.
Pre-Calculus Lesson Plan
11
Week 7
1st class 2nd class 3rd class Objectives To find the average rate of change
of function,
TO find the equation of a secant line.
Review of the Last class To graph the Functions listed in the Library of Functions;
Class Outline
Recap of even and odd functions and to relate them with symmetry,
Shown some numerical problems on finding even and odd function graphically and algebraically,
Secant line concept,
How to guess function from secant line,
Worked out a problem on Secant line.
Relation between even odd and symmetry and shown some problems on that.Shown some problems on average rate of change of Function and Slope of Secant Line
Shown how to draw square root function,Cube root function, Absolute value function, square function, Cube function, Reciprocal Function ,By using some of the properties such as even or odd property, intercept, increasing or decreasing or constant etc
Handouts NONE None None.
Homework Exercise 2.2 (11-27) Exercise 2.3 (11 – 44, 53 - 62)
Drawing the Parents Functions mentioned above with property.
Evaluation Get few problems done by students, students got confused on the y-intercept of secant line and y-intercept of function, i.e. they mixed up these two.
Students solved few problems from Exercise and rectified the previous difficulties.
Discussed on the Questions given in the CT on Wednesday Tutorial Class
Pre-Calculus Lesson Plan
12
Week 8
1st class 2nd class 3rd class Objectives Revision for
Midterm. Midterm SWBAT derivative as a function.
Class Outline
Revised all concepts in Midterms .
Students took Midterm
I give the definition of derivative of the function W.R.T variable. Then I taught how work with this definition. Student worked with the problems 2,4,6,8,10,12 and match Answer with me .
Handouts A work sheet Question paper .
Ex:3.2 ( Thoman Calculus)
Homework Preparation for Midterm.
N/A Ex: 3.2 (1,3,5,7,9,11)
Evaluation Class went well. N/A Ss could easily understand and solve the problems.
Pre-Calculus Lesson PlanWeek 9
1st class 2nd class 3rd class Objectives We could
not take Class for Strike
SWBAT understand The derivative as a function.
SWBAT understand One-sided Derivatives and Differentiability.
Class Outline
N/A I gave an example And solve problem 8 ( Ex 3.2 Thomas Book ) . Then I asked to solve from Ex:3.2 (10,12,14,16,18,20,25,26 Thomas Book)I was roaming the class and see their solution.
I taught how to solve problems 37 and 38 ( Ex:3.2 Thomas ) then student worked with the problems 39 and 40. Then solved 46 .I was observing Ss work.
Handouts N/A Ex:3.2 N/A
Homework N/A Ex:3.2(7,9,11,13,15,17,19,21,22,23,24) Ex: 3.2(39,40,43,44,45,47,48)
Evaluation N/A. Most of the students fells that problems are so calculation depended.
Ss could not easily understand “Differentiability”.
13
Pre-Calculus Lesson PlanWeek 10
1st class 2nd class 3rd class
Objectives 2nd lesson on Graph different functions which is related to Piecewise functions.
SWBT Linear functions and their properties.
SWBT understand the application related to the Ex: 2.5 and Ex: 3.1 .
Class Outline
Class was start with the problem no.29 ( Ex:2.4 Sullivan). Then I asked to solve 30,31,32 and 33. Ss worked with the problem. I checked each students answer when they were working.
I start the class with Concepts and Vocabulary. Then for skill building I solved 14 and 18 from Ex: 3.1 (Sullivan Book). Ss Worked with 16,20 , 22,24,28,32,33 from Ex: 3.1.Answer was written on the board.
In the class I solved one problem from Sullivan book ( Ex: 3.1 ,40 ) . Then I solved two problems from Blitzer book, Page 217 and 218.
Handouts N/A Ex: 3.1 Blitzer Page 217 , 218 and Work sheet -5
Homework Ex:2.4 (34,35,36,37,38) Ex:(21,23,25,27,29,31 ) Work Sheet-5
Evaluation Some of the students were struggling with graphing.
Ss easily solved the problems. Ss easily could understand the application problems and got fun.
14
Pre-Calculus Lesson Plan
Week 11
1st class 2nd class 3rd class
Objectives 2nd lesson on (SWBT Understand) the application related to the Ex:2.5 and Ex: 3.1 .
SWBT draw and interpret scatter diagrams and Distinguish between linear and non linear relations .
SWBT understand the graphing utility to find the line of best fit and second lesson on previous lesson.
Class Outline
Class was start with the self created problems Then I asked to solve39 and 40 (Sullivan Book ). Ss worked with the problem. I checked each students answer when they were working.
I start the class with a example of scatter diagrams. Then for skill building I asked to solve 3,4,5,6,7,8. from Ex: 3.2 (Sullivan Book ). Ss Worked with 10 and 15 from Ex: 3.2.I checked each students answer and working process.
In the class I solved 18 (which was H.W.). Then I asked to solve 21 and 22.
Handouts N/A Ex: 3.2 N/A
Homework N/A Ex:3.2(16 18,) Preparation for 2nd Quiz.
Evaluation Ss easily could understand. Ss easily solved the problems. Ss easily could understand the application problems and got fun.
Pre-Calculus Class Lesson Plan
15
Week 121st class 2nd class 3rd class
Objectives 2nd Quiz SWBT Building linear function from data and IDEA evaluation.
SWBT understand quadratic functions and their properties.
Class Outline
N/A At first I solved and explain problem no. 15 Ex:3.2 from Sullivan book .Then I asked to solve 16 . I checked each and every one answer. then student went to IDEA evaluation .
I introduced all key VocabularyFrom this concept (like Parabola , opens up , opens down , vertex , axis of symmetry etc )
Handouts N/A Ex: 3.2 Summary for quadratic functions.
Homework N/A Ex:3.2(18,) N/A
Evaluation Iron group did better than copper group.
Ss easily solved the problems. Ss easily could understand the vocabulary.
Pre-Calculus Class Lesson PlanWeek 13
1st class 2nd class 3rd class
Objectives Discuss with Quiz-2 problems and 2nd lesson on Quadratic functions.
SWBT Inequalities Involving Quadratic functions.
Second lesson on the Inequalities.
Class Outline
Class started with the Quiz-2 problems and then I solved problem no. 44 from Sullivan Ex. 3.3 . Then I asked Ss to solve 38,40,42,46,48,52 .Answer was written on the board .
I introduced key Vocabulary and give some example from Sullivan book. Then I made some problem and asked to solve. Then I select few problems from Ex 3.5 (Sullivan book), Ss solved the problems and Match answers.
I solved 32 for the students and asked to solve 26,28,30 from Ex:3.5 (Sullivan Book)
Handouts N/A Ex: 3.5 N/A
Homework Ex 3.3 ( 35,37,39,41,43,45,47,51,)
Ex:3.5(7,9,11,13,15,17,19,21,) Ex: 3.5 (25,27,29,31)
Evaluation Some of the student struggled with few problems.
Ss easily solved the problems. Some Ss struggled with the problem No. 30.
16
Pre-Calculus Lesson Plan
Week 14
1st class 2nd class 3rd class
Objectives I’m going to start a new chapter. We will look at two general classes of function. One is polynomial another is rational function.
SWBT determine which functions are polynomial functions and graph few polynomial functions.
Third lesson on polynomial.
Class Outline
Introduced Key vocab. (What is polynomial function, degree of polynomial, power function, properties of power function , real zeros , multiplicity, turning points and end behavior, etc.)
I select few problems from Ex 4.1( Sullivan book ), Ss solved the problems and Match answer s.
I solved 38 and 50 for the students and asked to solve 40,42 and 44 , 46 ,48,52 and 56 from Ex:4.1 (Sullivan Book).
Handouts N/A Ex: 4.1 N/A
Homework
N/A Ex:4.1(,11,13,15,17,19,21,23,25,27,29,31 and 35)
Ex: 4.1(37,39,41,43,45,47,49,51,53 and 56)
Evaluation Some of the student struggled with few vocab.
Ss easily solved the problems. Some Ss struggled with the problem No. 52.
17
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 Fall – 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 before Mid-Term date as provided with this syllabus.
Final Exam (30%) The Final Exam will test all of the content covered by the end of Fall semester.
10. KEY DATES & DEADLINES
Mid-Term Exam: Between 15th to 18th October.Final Exam: Between 9th to 13th December.
18
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.
12. STRATEGIES TO PREVENT PLAGIARIM& VIOLATIONS OF ACADEMIC INTEGRITY
19
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.
20
Useful links from Khan Academy
Graphs: Graphs of equations in two variables
1) Two-variable linear equations intro
https://www.khanacademy.org/math/algebra/two-var-linear-equations/solutions-to-two-var-linear-equations/v/2-variable-linear-equations-graphs
Duration: 8 min 20 sec
2) Solutions to 2-variable equations
https://www.khanacademy.org/math/algebra/two-var-linear-equations/solutions-to-two-var-linear-equations/v/checking-ordered-pair-solutions-to-equations-1
Duration: 2 min 34 sec
3) Practice: Solutions to 2-variable equations
https://www.khanacademy.org/math/algebra/two-var-linear-equations/solutions-to-two-var-linear-equations/e/plugging_in_values
4) Completing solutions to 2-variable equations
https://www.khanacademy.org/math/algebra/two-var-linear-equations/solutions-to-two-var-linear-equations/v/graphing-solutions-to-2-variable-linear-equations-1
Duration: 7 min 10 sec
5) Lines, line segments, & rays
https://www.khanacademy.org/math/basic-geo/basic-geo-lines/lines-rays/v/lines-line-segments-and-rays
Duration: 3 min 34 sec
21
6) Practice: Draw rays, lines, & line segments
https://www.khanacademy.org/math/basic-geo/basic-geo-lines/lines-rays/e/drawing-lines
Functions and their Graphs
1) What is a function?
https://www.khanacademy.org/math/algebra/algebra-functions/evaluating-functions/v/what-is-a-function
Duration: 7 min 54 sec
2) Recognizing functions from graph
https://www.khanacademy.org/math/algebra/algebra-functions/recognizing-functions-ddp/v/graphical-relations-and-functions
Duration: 4 min 06 sec
3) Testing if a relationship is a function
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/cc-8th-function-intro/v/testing-if-a-relationship-is-a-function
Duration: 2 min 22 sec
4) Practice: Recognize functions from graphs
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/cc-8th-function-intro/e/recog-func-2
5) Shifting & reflecting functions
22
https://www.khanacademy.org/math/algebra2/manipulating-functions/stretching-functions/v/shifting-and-reflecting-functions
Duration 6 min 39 sec
6) Intro to parabola transformations
https://www.khanacademy.org/math/algebra/quadratics/transforming-quadratic-functions/v/shifting-and-scaling-parabolas
Duration: 8 min 01 sec
7) Compressing functions
https://www.khanacademy.org/math/algebra2/manipulating-functions/stretching-functions/v/compressing-functions-example
Duration: 3 min 15 sec
8) Practice: Transforming functions
https://www.khanacademy.org/math/algebra2/manipulating-functions/stretching-functions/e/shifting_and_reflecting_functions
Linear and Quadratic Functions
1) Recognizing linear functions
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/linear-nonlinear-functions-tut/v/recognizing-linear-functions
Duration: 4 min 01 sec
2) Interpreting linear functions — Basic example
https://www.khanacademy.org/test-prep/sat/sat-math-practice/new-sat-heart-of-algebra/v/sat-math-h8-easier
Duration: 2 min 16 sec
23
3) Linear function word problems — Harder example
https://www.khanacademy.org/test-prep/sat/sat-math-practice/new-sat-heart-of-algebra/v/sat-math-h3-harder
Duration: 4 min 37 sec
4) Graphing linear equations — Basic example
https://www.khanacademy.org/test-prep/sat/sat-math-practice/new-sat-heart-of-algebra/v/sat-math-h9-easier
Duration: 2 min 24 sec
5) Graphing quadratics: standard form
https://www.khanacademy.org/math/algebra/quadratics/quad-standard-form-alg1/v/graphing-a-parabola-using-roots-and-vertex
Duration: 4 min 41 sec
6) Finding features of quadratic functions
https://www.khanacademy.org/math/algebra/quadratics/features-of-quadratic-functions/v/finding-features-of-quadratic-functions
Duration: 8 min 22 sec
7) Comparing features of quadratic functions
https://www.khanacademy.org/math/algebra/quadratics/features-of-quadratic-functions/v/comparing-features-of-quadratic-functions
Duration: 4 min 10 sec
8) Practice: Compare quadratic functions
https://www.khanacademy.org/math/algebra/quadratics/features-of-quadratic-functions/e/compare-properties-quadratic-functions
24
Polynomial and Rational Functions
1) Intro to function symmetry
https://www.khanacademy.org/math/algebra2/polynomial-functions/introduction-to-symmetry-of-functions/v/recognizing-odd-and-even-functions
Duration of the video (minutes. seconds): 12.25
2) Intro to end behavior of polynomials
https://www.khanacademy.org/math/algebra2/polynomial-functions/polynomial-end-behavior/v/polynomial-end-behavior
Duration of the video (minutes. seconds): 8.10
3) Graphing rational functions according to asymptotes
https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/graphs-of-rational-functions/v/finding-asymptotes-example
Duration of the video (minutes. seconds): 11.21
25