Syllabus for College Now Precalculus, MAT172

Professor Sormani, Fall 2007

Mondays and Wednesday 4:05-5:55pm:
Text: R. Larson and R.P. Hostetler Precalculus, Houghton Mifflin Company 6th Edition (pick up at 189 Carmen Hall before Wed class)
Supplies: A spiral notebook of graph paper for notes. A cheap scientific calculator with buttons for sin, cos, tan, Ln, and Log.
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.
Homework: 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 Monday-Thursday, and in my office, Gillet 200B, Monday and Wednesday 2-4pm. 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.
Math Circle: Members of the Lehman CollegeMath Circle will attend the first hour of lectures marked with a *. You may invite your friends to these lectures, but please be sure they get permission from their parents. Lectures marked with a *** may be attended by senior members of the Lehman College Math Circle who have already completed precalculus on a college level. Friends of yours taking calculus may wish to attend such lectures.
Syllabus:

Lesson 1 (Mon 9/10): A.3, A.5 - Review Polynomials and Factoring
Homework was handed out on a sheet Weekend Review: A.2 and A.4, Check the answers to all your homework in the back of the book.
Read A.2 and A.4 on your own. Then do:
A.2/11, 13, 15, 21, 23, 27, 29, 31, 49, 69, 85, 89, 91
A.4/31, 33, 35, 37, 43, 49, 59, 73, 75,
Lesson 2 (Mon 9/17): A.1, A.6 - Review Intervals and Inequalities*
Do each problem and then check the answer in the back, if your answer is wrong, look at a similar example in the section and try again:
A.1/19, 25, 29, 31, 47, 49, 57, 75
A.6/1,3,5,7,9,11,21,25,37,49,53,99,101,151,159
Lesson 3 (Wed 9/19): 1.1- Graphs of Equations 1.2- Linear Equations in Two Variables
1.2/1, 3, 9, 21, 55, 67, 1.1/9, 11, 13, 23, 29
Lesson 4 (Mon 9/24): 1.3- Functions 1.4 Analyzing Graphs of Functions
Functions Project: 1.1/Read page 7, do 1.1/57, 59, 63, 67, 74 and 1.2/ Read page 19, do 1.2/39, 87, 91, 13, 17, 81 due 10/1
1.3/1,3,7,9,15,19,21,27,31,33,37,49,51, 59, 63, 87, 93, 95
1.4/ 1,3,9,11,13,15,17,21,31,33,35,37,53,61,63,65
Lesson 5 (Wed 9/26): 1.5 A Library of Functions
1.5/1,3,5,29, 31, 37, 41, 43, 45, 63
4.3/1,3,5,7,9,11,13,17,57,59
Lesson 6 (Mon 10/1): 1.6- Shifting, Reflecting, and Stretching Graphs*
1.6/1,5,9,11,13, 17,21, 25,27, 31, 33, 39, 43, 63
Lesson 7 (Wed 10/3): 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! (sormani at comet.lehman.cuny.edu). It may be an extra topic not on the exam. Next two hours: do the following examples as if they were problems on an exam (do not look at your notes). Then check your answers. Third 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!
A.2/ Examples 1, 6, 10, 13, 15
A.3/ Example 5, Example 6,
A.4/ Examples 2, 3, A.5/ Example 4,
A.6/ Examples 1, 2, 4, 5
1.1/ Example 3, Example 5, Example 7,
1.2/ Examples 4, 5, 7,
1.3/ Examples 1, 2, 3, 4, 5, 6
1.4/ Examples 2, 3, 4, 6, exercise 53, 61, 93,
1.5/ Examples 2, 3, exercise 37, 43, 49,
1.6/ Examples 1, 2, 3, 4,
If you like to work slowly ask your parents if you can stay late on the day of the exam.
Lesson 8 (Wed 10/10): Exam I on Functions and Graphing
Lesson 9 (Mon 10/15): 1.7 Composition of functions*, A.3, 2.1- Maximizing Quadratic Functions
A.5/ 83, 85, 87,
Read 1.7, Do 1.7/ 5, 9*, 27, 35, 37, 39, 43, 51, 53, 55, 59
Read 2.1/Examples 1-2 Do 2.1/1,3,5,7, 43, 45, 17, 19, 31
Lesson 10 (Wed 10/17): Max Min Problems
Read 2.1/ Example 2 Do 2.1/17, 19, 23, 25, 29, 31
On Monday there will be 30 a thirty minute quiz which will be very similar to Exam I. You will need to do the problems that you did incorrectly on Exam I in order to improve your score. To study for this quiz study the sections and examples corresponding to the problems you got wrong on Exam I: (1) A.2, A.3, A.4 (2) A.6 (3) A.6 (4) 1.3 and A.6 (5) 1.3 and A.6 (6) 1.4 and A.6, (7) 1.2, (8) 1.5 and 1.6, (9) 1.1, (10) 1.5-6
Lesson 11 (Mon 10/22): 30 Minute Quiz 1.8- Inverse Functions, emphasize graphing!
Read 1.8, do 1.8/1,3,13, 15, 17, 25, 27, 31, 39, 41, 63
Inverses Project (1.8/ 22, 44, 46, 50, 64, 82, 84, 92) due 10/29
Lesson 12 (Wed 10/24): 1.8- Square roots and restricted domains, 2.3- Polynomial and Synthetic Division
1.8/19, 21, 22, 43, 45, 46,
2.3/5, 7, 13, 37, 49, 73
Lesson 13 (Mon 10/29): 2.2 and 2.6- Graphing Polynomial and Rational Functions*
Emphasize graphing y=f(x) versus y=1/f(x) 4.2- Trigonometric Functions: The Unit Circle, Mention the pythagorean identity
Unit Circle Project will be started in class and due 11/5.
1.8/ 23, 49, 53
2.2/1,3,5,7,41,90, 2.6/5,7,9,21,31
Lesson 14 (Wed 10/31): Halloween No Meeting Study 4.1- Radian and Degree Measure
4.1/13,17, 19, 25, 27, 37, 39, 41, 47, 59, 87, 89
finish the unit circle project, 4.2/5, 13, 55
Lesson 15 (Mon 11/5): 4.3- Right Triangle Trigonometry, 4.4- Trigonometric Functions of Any Angle
Review for Right Triangle Trigonometry
4.2/1,3,5,7,9,11,13,15,21,27,43,45,49,51
4.3/1,3,5,7,9,13,17,49,51,57,(59), 61
4.4/1,3,11 3.3/25, 91 Extra Credit 4.1/67a, 71a
Lesson 16 (Wed 11/7): 4.5- Graphs of Sine and Cosine Functions (review 1.7)
4.6- Graphs of other trigonometric functions (review 2.6)
4.5/1,3,7,9,13,71; 4.6/1-6
Lesson 17 (Mon 11/12): 4.7- Inverse Trigonometric Functions *** pages 322-325 (review 1.8/ Ex 6-7)
4.7/1,3,11,37,41 and catch up on Monday HW
Review for the exam by doing the following examples from the text:
1.7/4,5, 1.8/6,7, 2.1/2,4, 2.2/4,5,6, 2.3/1,2, 2.6/3,6,
4.1/3,4,5, 4.2/ page 274 unit circles, 4.3/4,5, 4.4/5,chart on p 294
4.5/2,3, 4.6/1, 4,5, 4.7/pages 322-325

Lesson 18 (Wed 11/14): Exam II on Inverses, Rationals and Trigonometry
on sections 1.7, 1.8, 2.1, 2.2, 2.6, 4.1-4.6
Lesson 19 (Mon 11/19): 5.1,5.2 -Using Fundamental Identities 5.4- Sum and Difference Formulas and their proofs ***
5.1/1,31,99 5.2/1,3,5, 5.4/1,3,7,37,51
Lesson 20 (Wed 11/21): No class but read 4.7 Difficulties with Inverse Trig Functions pp 326-327
Read 4.7 focussing on 326-327, Do 1.7/41, 1.8/49,63, 4.7/43,47,49,53,61,99
Lesson 21 (Mon 11/26): 3.1- Exponential Functions and Their Graphs*
Credit Card and Student Loans Project due 12/3.
4.6/78, 3.1/1,3,7-10, 43, 45, 47, 55, 63
Lesson 22 (Wed 11/28): 3.2- Logarithmic Functions and Their Graphs 3.3 Properties of Logarithms
3.2/1, 3, 9, 11, 13, 17, 19, 21, 23, 25, 39, 47, 65, 67, 73
3.3/19, 21, 23, 29, 37, 45, 47, 51, 61, 63, 65, 69, 71, 89, 97
Lesson 23 (Mon 12/3): 3.4- Exponential and Logarithmic Equations
Inverses of Functions with Exponentials due 12/10.
3.1/ 49. 57, 65, 67, 3.2/5, 7, 3.4/7, 11, 19, 23, 27, 29, 31, 35, 37, 87, 91, 109, 111, 127
Lesson 24 (Wed 12/5): 6.1 Law of Sines, 6.2 Law of Cosines ***
6.1/1,7,25*,29,43, 6.2/1,3,43,45, 6.3/63,
Lesson 25 (Mon 12/10): 6.3 Vectors in a Plane * (427-431) 6.4 Dot Products ***
6.3/1,3,7,13,15,19,67,87, 6.4/1,5,9,15,25,31
Review A.2, do A.2/5,9,11,31,33,
Lesson 26 (Wed 12/12): Review for the Final ***
Schedule three 2 hour study sessions before 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:
5.1/2,5,8, 5.2/4,5, 5.3/1,2, 5.4/1,4,6a, 5.5/1,4, 6.1/1,4,5, 6.2/1
Study Session III: Next memorize the laws for exponentials and logs and then practice the following examples:
3.1/2,3,7,8, 3.2/4,7,9 3.3/3,4,5,6 3.4/3,7,8,9,10
Credit Card Project/Example 1,
Inverses of Exponentials and Logs Project/Example
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 12/17): Review Sample Final Study key points you had difficulty with. Get plenty of sleep before the final.
Lesson 278(Wed 12/19): Final Exam Emphasizing Exponentials Wed Dec 19 4-6 pm GI 205.