Precalculus, MAT172

Professor Sormani, Fall 2015

Mondays and Wednesdays 3:00-4:40 pm

MAT172 Precalculus: 4 hours, 4 credits. Polynomial, rational, logarithmic, and trigonometric functions, with applications to problems in mathematics and the sciences.

Prerequisite: A grade of C (or better) in MAT 104 or placement by the Dept of Mathematics and Computer Science. Students should thoroughly review all material from this subject.

Notes: (1.) Students may not receive credit for both MAT 171 and MAT 172.

(2.) MAT 172 is a prerequisite for MAT 175.

We have 28 lessons to prepare you for calculus. Be ready for a fast fun course that will challenge you like never before. If you've never seen the movie "Stand and Deliver", rent it now and watch it with your family so they know what you're up to.

Course Webpage: https://sites.google.com/site/professorsormani/teaching/precalculus-f15

Professor's Webpage: https://sites.google.com/site/professorsormani

Professor's Email: sormanic at gmail Professor's Office: 200A Gillet Hall Office Hours: Mon/Wed 2:00-3:00 pm & 5:30-6:00 pm

Homework: Homework will be assigned on the webpage beneath the lesson where the material is taught and due in the next meeting.. Odd problems have answers in the back of the text so you can check your work before proceeding to the next problem. On random days the professor will verify that the homework has been worked on. Working with study partners can make homework easier and more fun. Help is available at the Math Lab Gillet Hall 222 and in my office hours. You may also email me questions. Special graded homework projects are part of the final grade.

Grading for our section: Exam I-III are 15% each totalling 45%.

Functions Project, Inverses Project, Unit Circle Project, Credit Card Project and Trigonometry Project are 5% each totalling 25%,

The final is 30% of the grade. Departmental policy: Must pass the final exam to pass the course.

Departmental Policy

Expectations: Students are expected to learn both the mathematics covered in class and the mathematics in the textbook and other assigned reading. Completing homework is part of the learning experience. Students should review topics from prior courses as needed using old notes and books.

Students should go to their instructor’s office hours, to the Math Lab or to problem sessions regularly.

Homework: Approximately two hours of homework will be assigned in each lesson as well as additional review assignments.

Grades: Students who do not pass the departmental final will not pass the course. The precise grading policy for your section will be distributed by your instructor.

Materials, Resources and Accommodating Disabilities

Textbook: R. Larson and R.P. Hostetler Precalculus, Houghton Muffin Company 9th Edition

Available in bookstore, or to order here, or as a more expensive ebook here. Note old Edition 7 is also alright.

Supplies: A spiral notebook of graph paper for notes.

Technology: Students should purchase a basic scientific calculator able to compute trigonometric and exponential functions like cos, sin, and Ln. No graphing calculators are permitted.

Tutoring: Departmental tutoring is available in the Math Lab on the 2nd floor of Gillet Hall.

Reliable Web Resources: See http://comet.lehman.cuny.edu/calculus

Reserve: Selected books have been placed on reserve in the library.

Accommodating Disabilities: Lehman College is committed to providing access to all programs and curricula to all students. Students with disabilities who may need classroom accommodations are encouraged to register with the Office of Student Disability Services. For more info, contact the Office of Student Disability Services, Shuster Hall, Room 238, 718-960-8441.

Course Objectives:

1. Graph linear, polynomial, trigonometric, exponential, and logarithmic equations (a,b)

2. Identify equations for given graphs (a,b, & e)

4. Work with functions: inverting, composing, multiplying and dividing functions (a,b,e)

5. Represent and solve real-world problems requiring optimization of quadratic functions (a,b,c)

7. Use the unit circle to determine the values of trigonometric functions (b,e)

8. State and apply trigonometric identities (b,e)

9. Represent and solve real-world problems involving exponential growth and decay (b,c)

These objectives will be assessed on the final exam along with other important techniques.

Course Calendar

• • Lesson 1 (Mon 8/31): A.3, A.5 - Review Polynomials and Factoring

  • No homework except to email the professor with your name in the subject line containing the following information: what majors you are considering, what math courses you have taken in high school and in college, your career goals (just a list of possible professions), and a schedule of 6-8 hours per week that you will spend on studying and doing homework for this course. Be sure to schedule 2 hours between Monday class and Wednesday class. Mark onto your calendar that you will need to schedule extra studying time before exams as scheduled and described below.

  • Lesson 2 (Wed 9/2): A.1, A.2, A.4, A.6 - Review Intervals and Inequalities, Absolute Values,

  • HW: Read A.1-A.6 and do the following exercises checking your answers in the back of the book after each exercise is completed. Work quickly. Do all the problems you know how to do first, then come back and work on the more difficult problems:

  • Edition 9 Homework:

  • A.1/17,19,21,23,25,27,33,35,37,39,51,53; A.2/11,13,15,19,23,25,69,73; A.3/27,29,33,41,49,83,95,101,106;

  • A.4/17,19,21,23,27,35,43,75,79; A.5/25,43,51,100; A.6/13,15,19,23,31,45,47,51,53,97,109,111;

  • Edition 7 Homework:

  • A.1/31, 33, 35, 37, 55, 67,69; A.2/13, 15, 25,27,29,33,53,55,95,97; A.3/29,31, 51,95,103,107,205;

  • A.4/11,21,33,41,55,69,77,79; A.5/55,61,175,189; A.6/1,3,5,7,9,11,19,21,25,29,45,49,56,83,87,97,103,105;

  • Lehman Closed Mon 9/7 Labor Day

  • Lesson 3 (Wed 9/9): 1.2- Graphs of Equations 1.3- Linear Equations in Two Variables

  • HW Read 1.1-1.3. Do the following problems before next week:

  • 1) Write equation for a circle about (2,7) of radius 3. Graph and check by plotting points.

  • 2) Find the symmetries of x=y^2 +2. Graph and check by plotting points.

  • 3) Graph |x|+|y|=3. What are the symmetries? Verify them by substitution.

  • 4) Graph 2y+3x=12. Then graph 2|y|+3|x|=12. Compare.

  • 5) Think about the graph of xy=1. Does it have any points in Quadrant I, Quad II, Quad III, Quad IV? Any symmetries? Do not just plot points. State mathematical facts and explain why.

  • 6) Find the point where 2x+3y=7 and 1x+2y=8 meet. What is the slope of these lines? Do they meet perpendicularly?

  • 7) Find the formula for the line perpendicular to y=5x+2 passing through (1,4). Graph both.

  • 8) Find the formula for the line parallel to y=-2x+3 passing though (5,5). Graph both.

  • 9-15) Do 6 odd numbered word problems from the textbook section 1.3

  • Lesson 4 (Th 9/10): Graphs in 1.6

  • HW: memorize these graphs and complete previous assignment

  • Lehman Closed Mon 9/14

  • Lesson 5 (Wed 9/16): 1.4-1.6 Functions

  • Functions Project: (Edition 9) 1.5/8,10,18,32,36,56,60,72,84,88a due 9/21

  • Lesson 6 (Mon 9/21): 1.7- Shifting, Reflecting, and Stretching Graphs 1.8 Composition of functions,

  • HW: 1.7/1,3,5,7,9,11,13,15,17,19; 1.8/1-23 odd; review A.5

  • Lehman Closed Wed 9/23

  • Lesson 7 (Mon 9/28): 1.9- Inverse Functions, emphasizing graphing!

  • HW 1.8/25-54 odd; 1.9/7,9,11,13,15,17,35,45,47,53,55,57,

  • Inverses Project: 1.9/18,20,38,40,46.48.54,58,60 due 10/7.

• Lesson 8 (Wed 9/30): Review for Exam I

  • Preparing for a college exam (4 study sessions): First 1-2 hours: quickly look through your old notes and homework. Mark down anything that confuses you and email me! (sormanic at gmail). It may be an extra topic not on the exam. Next 2 hours: do the following examples [1.3/3,4; 1.4/3,4,7,8,; 1.5/ 2,3,4,8,; 1.6/1,2,3; 1.7/1,2,3,4,5 and functions project] as if they were problems on an exam (do not look at your notes). Then check your answers. 3rd study session: study everything you got wrong when you tested yourself and again you can email me with questions. This study session could be long or short depending on how you did on the practice. The night before the exam: look over this list of review problems again focussing on 1.1-1.6 and get plenty of sleep. When you are asleep you are processing knowledge. Without sleep, you will forget what you learned and also have a higher chance of making stupid mistakes. Aim for a perfect score.

  • If you like to work slowly ask your parents if you can stay late on the day of the exam.

  • Lesson 9 (Mon 10/5): Exam I on Functions and Graphing

  • Lesson 10 (Wed 10/7): REVIEW EXAM I (this time prepare for the exam as described above)

  • Lesson 11 (Wed 10/14): EXAM I RETAKE

  • Study this topic on your own: 2.1 Max Min Problems. Max-Min homework (but not a project)

  • Lesson 12 (Mon 10/19): 3.1- Exponential Functions and Their Graphs

  • start Credit Card and Student Loans Project due 10/26

  • Some students have been recommended to withdraw based on very low performance on both the first exam and its retake (see your exam). The withdrawal deadline is Nov 9. Students who withdraw may continue to attend class, do homework and take exams, and should do so in order to learn exponentials and trigonometry. They should also start seeing tutors to improve their understanding of the material from the first quarter of the course (usually they need help with algebra). The reason to withdraw is to avoid an F on your transcript which can damage your GPA. If you do get an F and need to retake precalc for your major, then the F will no longer count towards the GPA when you pass precalc.

  • All students:

  • it is very serious that you do the homework and check the answers in the back for every lesson!!!!!

  • Lesson 13 (Wed 10/21): 3.2- Logarithmic Functions and Their Graphs 3.3- Properties of Logarithms

  • HW: 3.2/15,17,19,57,59,65,67,69,77; 3.3/41,45,51,57,71,75,83;

  • Lesson 14 (Mon 10/26): 3.4 Exponential and Logarithm Equations

  • 3.4/3,5,7,9,11,51,55,59,85; Inverses of Functions with Exponentials homework (not a project)

  • Lesson 15 (Wed 10/28): Review for Exam II on Inverses, Exponentials, Logs and Applications

  • Prepare for the exam like last time choosing examples from 1.9, 2.1, 2.3, 3.1-3.4 and the Max-Min and Credit Card Problem sets.

  • Lesson 16 (Mon 11/2 sub): Exam II on Inverses, Exponentials, Logs and Applications

    • Study this topic on your own: 2.3- Polynomial Division 1.9-Square roots and Restricted domains

    • HW: 2.3/7/11/13/15/17; 1.9/63,73,75,77,79,81,93,97,99;

  • Lesson 17 (Wed 11/4 sub): 3.5 Applications of Exponential and Logarithmic Equations

  • HW: 3.5/19,29,33,35,37,4547,57,59

  • Lesson 18 (Mon 11/9): 4.1- 4.4 Radians, Trigonometric Functions: The Unit Circle, Mention the Pythagorean Identity.

  • HW: Read 4.2 carefully, Do 4.2/1,3,5,7,9,11,29,31,33,35; 4.3/1,3,9,11,17,23,59,61; 4.4/45,49,51,65,67,

  • Unit Circle Project will be started in class and due 11/16.

  • Lesson 19 (Wed 11/11): 4.5- Graphs of Sine and Cosine Functions (review 1.7) 4.6- Graphs of other trigonometric functions (Review 2.6)

  • HW 4.2/37,39; 4.3/ 13,15,19,21,25; 4.5/1,3,5,7,9,11; 4.6/1-6.

  • Lesson 20 (Mon 11/16): 4.7- Inverse Trigonometric Functions up to page 323 (review 1.8/ Ex 6-7)

  • HW: 4.5/15,17,19,21; 4.6/7,9,75,79,; 4.7/1,3,5,7,9,11,13,15,35,37,39,41,

  • Lesson 21 (Wed 11/18): 4.7 Restricted domains and 4.8 Applications;

  • HW 4.7/43,45,47,49,51,53,57,59,61,89,91,,95,96; 4.8/15,17,19,21

  • Lesson 22 (Mon 11/23): Review for Exam III on Trigonometry 4.1-4.8 be sure to memorize the values of cosine and sine for key angles

  • Lesson 23 (Wed 11/25): Exam III on Trigonometry 4.1-4.8 (Material from Trig Quiz plus y=5cos(3x) and Arcsin/Arccos/Arctan and Applications)

  • Lesson 24 (Mon 11/30): Retake of Exam I plus Max/Min 2.1 and Polynomial Division 2.3

  • HW: 4.3/ 27,29,31,65,67,69; 4.4/69,73,75; 4.5/27,29,31,33,35,37,73,79,80

  • If you have not yet done the Max/Min assignment, then you still must learn this topic before the final!

  • Lesson 25 (Wed 12/2): 6.1 Law of Sines, 6.2 Law of Cosines

  • Trigonometry Project: 6.1/5,7,9,11,39,47,49,51; 6.2/5,7,9,13,15,25,31,37,45,47,51,55,59 due 12/7 (check your answers in the back of the text)

  • Lesson 26 (Mon 12/7): 5.1 Using Fundamental Identitites 5.2 Trigonometric Identities 5.4 Sum/Difference Formulas

  • HW Practice using the sum and difference formula

  • Lesson 27 (Wed 12/9): 2.2 and 2.6- Graphing Polynomial and Rational Functions, Emphasize graphing y=f(x) versus y=1/f(x).

  • HW: 2.2/9,67,69,71,73,75,77,89,91; 2.6/27,29,31,33,35,37,45,

  • Schedule three 2 hour study sessions plus 2 hours for taking the practice final:

  • Study Session I: Go over Exams I, II and III and study the problems you got wrong. Then try similar problems from the homework and examples in the textbook. Review the examples recommended above each exam. Make sure you have memorized how to compute sine and cosine functions using the unit circle and know sin(30), sin(45), sin(60) etc.

  • Study Session II: Memorize the addition formulas and memorize the law of sines and cosines. and practice Max/Min problems.

  • Study Session III: Next memorize the laws for exponentials and logs

  • Credit Card Project/Example 1, Inverses of Exponentials and Logs Project/Example 1

  • If there is a formula you have difficulty memorizing, practice rederiving it.

  • Then take the department's sample final as a two hour exam with no help and go over it with someone.

  • Lesson 28 (Mon 12/14): Review for Final

  • Final Exam during finals week: Mon 12/21 3:45-5:45 pm in Gillet 205