Syllabus for College Now Precalculus, MAT172

Professor Sormani, Spring 2006

Mondays and Wednesday 4:05-5:55pm: We do not meet Mon Feb 20, Wed Feb 22, Apr 17, Wed Apr 12, Apr 19.
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. 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: sormani@comet.lehman.cuny.edu Special graded homework projects are part of the final grade.
Exam I is 15%, Exam II is 20%, Classwork is 5%,
Max/Min Project, Inverses Project, Trig Project, Credit Card Project Inverses of Functions with Exponenetials Project are 5% each totalling 30%,
The final is 30% of the grade.
Syllabus:

Lesson 1 (1/30): A.3, A.5 - Review Polynomials and Factoring
Homework was handed out on a sheet
Lesson 2 (2/1): 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
Weekend Review: A.2 and A.4, Check the answers to all your homework in the back of the book.
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 3 (2/6): 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 (2/8): 1.3- Functions 1.4 Analyzing Graphs of Functions
1.1/Read page 7, do 1.1/57, 59, 63, 67, 74
1.2/ Read page 19, do 1.2/39, 87, 91, 13, 17, 81
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
No meeting 2/13 Lehman is closed.
Lesson 5 (2/15): 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
No meeting during winter recess
Lesson 6 (2/27): 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 (2/29): 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 (3/6): Exam I on Functions and Graphing
Lesson 9 (3/8): 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 (3/13): Max Min Problems
Read 2.1/ Example 2 Do 2.1/17, 19, 23, 25, 29, 31
Max-Min Problem Project due 3/20
Lesson 11 (3/15): 1.8- Inverse Functions, emphasize graphing!
Read 1.8, do 1.8/1,3,13, 15, 17, 25, 27, 31, 39, 41, 63
Note that from here on the syllabus has been changed because half the class will be gone 3/27 and 3/29, since those students were confident about their trig I've put trig before exponentials and moved Exam II back to 4/10. This made Exam II cover more material so it is now 20% of the final grade. There is also no natural place for a third exam so I have increased the amount of graded homework projects so that homework will now be 30% of the course. We end the course on 5/24 as planned.
Lesson 12 (3/20): 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 (3/22): 2.2 and 2.6- Graphing Polynomial and Rational Functions
Emphasize graphing y=f(x) versus y=1/f(x)
1.8/ 23, 49, 53
2.2/1,3,5,7,41,90, 2.6/5,7,9,21,31
Inverses Project (1.8/ 22, 44, 46, 50, 64, 82, 84, 92) due 4/3
Lesson 14 (3/27): 4.1- Radian and Degree Measure 4.2- Trigonometric Functions: The Unit Circle, Mention the pythagorean identity
Online Unit Circle Project will be started in class and due 4/3.
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 (3/29): 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 (4/3): 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 (4/5): 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 (4/10): Exam II on Inverses, Rationals and Trigonometry
1.7, 1.8, 2.1, 2.2, 2.6, 4.1-4.7
No meetings during Spring Break: this is the opportunity to catch up on everything that you needed to learn before the last exam. Focus on studying and redoing homework on material you didn't understand on the last exam. Redo the homework assigned on 4.7
Lesson 19 (4/24): 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 20 (4/26): 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
Trigonometry Project (4.7/50, 54, 58, 100, 102, 108, 4.8/ 26, 39, 40, 42, page 406/7) due 5/8
Lesson 21 (5/1): 6.1 Law of Sines 6.3 Vectors in a Plane (427-431)
6.1/1,7,25*,29,43, 6.3/1,3,7,13,15,19,67,87
Lesson 22 (5/3): 6.2 Law of Cosines 6.4 Dot Products
6.2/1,3,43,45, 6.3/63, 6.4/1,5,9,15,25,31
Review A.2, do A.2/5,9,11,31,33
Lesson 23 (5/8): 3.1- Exponential Functions and Their Graphs
Credit Card and Student Loans Project due 5/15.
4.6/78, 3.1/1,3,7-10, 43, 45, 47, 55, 63
Lesson 24 (5/10): 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 25 (5/15): 3.4- Exponential and Logarithmic Equations
Inverses of Functions with Exponentials due 5/22.
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 26 (5/17): Review for the Final
Schedule three 2 hour study sessions before Monday:
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 the Max-Min project particularly problems 1,2,7,8.
Study Session II: Then go over 4.7 pages 326-327 carefully. Then memorize the addition formulas, learn how to rederive the double angle formulas from them, 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. Bring questions to Monday's review class.
Lesson 27 (5/22): Review for Final
Check out a Practice Final. There will be more exponentials on your final. Get plenty of sleep the night before the exam.
Lesson 28 (5/24): Final Exam Emphasizing Exponentials