Syllabus for College Now Precalculus, MAT172

Professor Sormani, Fall 2014

Mondays and Wednesday 4:10-5:50pm:

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-s14

Professor's Webpage: http://comet.lehman.cuny.edu/sormani

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, Gillet 200A, Monday and Wednesday 5:50-6:30pm. You may also email me questions: sormanic at member.ams.org Special graded homework projects are part of the final grade.

Grading: Exam I is 20%, Exam II is 20%, Classwork is 5%, Homework is 5%,

Functions Project, Inverses Project, Unit Circle Project, Credit Card Project are 5% each totalling 20%,

The final is 30% of the grade.

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

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 2/3): 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: when you will graduate high school, your high school name, which NYS Mathematics Regents Exams you have taken, your favorite subjects in math and science, 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 2/5): 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;

  • Lesson 3 (Mon 2/10): 1.2- Graphs of Equations 1.3- Linear Equations in Two Variables

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

  • 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

  • No class Wed 2/12 or Mon 2/17

  • Lesson 4 (Wed 2/19): 1.4- Functions 1.5 Analyzing Graphs of Functions

  • HW from 1.4 and 1.5, Functions Project: 1.5/8,10,18,32,36,56,60,72,84,88a due 2/24

  • Lesson 5 (Thursday 2/20): 1.6 A Library of Functions

  • Lesson 6 (Mon 2/24): 1.7- Shifting, Reflecting, and Stretching Graphs

  • HW: 1.7/1,3,5,7,9,11,13,15,17,19

  • Lesson 7 (Wed 2/26): 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 8 (Mon 3/3): Exam I on Functions and Graphing

  • Lesson 9 (Wed 3/5): 1.8 Composition of functions, Review A.5, HW: 1.8/1-54 odd

  • Lesson 10 (Mon 3/10): 1.9- Inverse Functions, emphasize graphing!

  • HW 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 3/17.

  • Lesson 11 (Wed 3/12): 1.9- Square roots and restricted domains, 2.3- Polynomial and Synthetic Division HW: 1.9/63,73,75,77,79,81,93,97,99; 2.3/7,11,13,15,17

  • Lesson 12 (Mon 3/17): 2.2 and 2.6- Graphing Polynomial and Rational Functions, Emphasize graphing y=f(x) versus y=1/f(x). 2.2/9,67,69,71,73,75,77,89,91, 2.6/27,29,31,33,35,37,45,

  • Lesson 14 (Wed 3/19): 2.1 Max Min Problems. Homework (but not a project)

  • Lesson 13 (Mon 3/24): 4.1- 4.4 Radians, Trigonometric Functions: The Unit Circle, Mention the Pythagorean Identity. Unit Circle Project will be started in class and due 3/26. Read 4.2 carefully, Do 4.2/1,3,5,7,9,11,29,31,33,35 4.3/1,3,9,11,17,23,59,6165,67,69

  • Lesson 15 (Wed 3/26): 4.5- Graphs of Sine and Cosine Functions (review 1.7) 4.6- Graphs of other trigonometric functions (Review 2.6) 4.2/37,39; 4.3/ 11,13,15,,19,21,25,27,29,31; 4.4/45,49,51,65,67,69,73,75,4.5/1,3,5,7,9,11; 4.6/1-6.

  • Lesson 16 (Mon 3/31): 4.7- Inverse Trigonometric Functions up to page 323 (review 1.8/ Ex 6-7) 4.5/15,17,19,21,,27,29,31,33,35,37,73,79,80,4.6/7,9,75,79,; 4.7/1,3,5,7,9,11,13,15,35,,37,39,41,

  • Lesson 17 (Wed 4/2): 4.7 Difficulties with Inverse Trig Functions; 4.7/43,45,47,49,51,53,57,59,61,89,91,,95,96,; 4.8/15,17,19,21

  • Lesson 18 (Mon 4/7): 5.1,5.2 -Using Fundamental Identities 5.4- Sum and Difference Formulas and their proofs

  • Lesson 19 (Wed 4/9): Review for Exam II on Inverses, Rationals and Trigonometry on Sections 1.8, 1.9, 2.1, 2.2, 2.6, 4.1-4.6

• Review for the exam only after catching up on homework. Then go over the following examples from the text broken into different study sessions as described before: Examples from 1.8, 1.9, 2.1, 2.2, 2.6, 4.1-4.6 particularly those which involve graphing.

  • Spring Break

  • Lesson 20 (Wed 4/23): Exam II

  • Lesson 21 (Mon 4/28): 3.1- Exponential Functions and Their Graphs Credit Card and Student Loans Project due 5/5.

  • Lesson 22 (Wed 4/30): 3.2- Logarithmic Functions and Their Graphs 3.3- Properties of Logarithms (credit cards project due 5/5)

  • Lesson 23 (Mon 5/5): 3.4-3.5 Applications of Exponential and Logarithmic Equations

  • 3.2/15,17,19,57,59,65,67,69,77; 3.3/41,45,51,57,71,75,83; 3.4/3,5,7,9,11,51,55,59,85; 3.5/19,29,33,35,37,4547,57,59 also Inverses of Functions with Exponentials due 5/12.

  • Lesson 24 (Wed 5/7): 6.1 Law of Sines, 6.2 Law of Cosines

  • 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 (also inverses with exponentials is due 5/12).

  • Lesson 25 (Mon 5/12): 6.3 Vectors in a Plane 6.4 Dot Products

  • Lesson 26 (Wed 5/14): Review for the Final

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

  • Study Session I: Go over Exams I and II 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 adding vectors and finding their magnitudes and unit vectors.

  • Study Session II: Memorize the addition formulas and memorize the law of sines and cosines. Practice the following examples: Examples will be posted on the webpage

  • Study Session III: Next memorize the laws for exponentials and logs and then practice the following examples: Examples will be posted on the webpage

  • 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 Practice Final as a two hour exam.

  • Lesson 27 (Mon 5/19): Review Sample Final Study key points you had difficulty with. Get plenty of sleep before the final.

  • Lesson 28 (Wed 5/21): Final Exam 3:45-5:45pm. If you cannot arrive before 4:10pm you will still be given 2 hours but may need to move to my office at 5:45 pm.