Precalculus, MAT172, Fall 2005
Monday, Wednesday 10:00-11:50 am, Gillet Hall 333
Professor:
Christina Sormani,
Office Hours: Gillet Hall 200B, Mon Wed 12-1:30 pm,
Email: sormani at comet.lehman.cuny.edu
Webpage: http://comet.lehman.cuny.edu/sormani/teaching/172f05.html
Text: R. Larson and R.P. Hostetler
Precalculus, Houghton Mifflin Company 6th Edition
Prerequisite:
MAT104 or placement by the ACT math exam. Note that if your grade in
MAT104 is a C or below or you took the prerequisite over a year ago, it
is strongly recommend that you review the course material either by
sitting in the class again or by redoing your old homework assignments.
Homework: Approximately 2 hours of homework will be assigned
each meeting and additional review assignments will be given on weekends.
Since we only meet once the first and second weeks, four hours worth
of homework have been assigned. All answers are in the back of the
book so check each answer before proceeding to the next problem
and work together to figure out your mistakes. At the beginning
of each lesson the students will present *ed problems. To present a problem
you must arrive early and write it up on the board including the precise
statement of the problem and detailed work towards the solution.
Math Lab:
All students should plan on spending at least an hour a week at the Math Lab in
Gillet 222. Some faculty may require proof of attendance.
Grading:
Three exams and a final have been scheduled in this syllabus.
The final is only 30% of your grade. The other three exams are
20% of the grade each. 10% of the grade will be based on classwork
including posting *ed problems on the blackboard.
Students who are not prepared to take Calculus I at the end of the semester
will not be passed.
Syllabus: (the homework will be posted on the webpage)
Lesson 1:(Wed 8/31) A.3, A.5-Review Polynomials and Factoring
First HW: A.3/17,19,21,23,27,29,39*,41*,139*,141*,143*
Second HW: A.5/7*,21,31,37*,39*,55,57*,83*,89,93,111
Lesson 2:(Wed 9/7) A.1, A.6 -Review Intervals and Inequalities
Third Homework: A.1/19, 21, 25, 29, 43, 45*, 47 & 49*, 65, 67*, 69*,
A.6/7,9,11, 21*, 27*, 49, 53*, 69*, 93*, 95*
Weekend Review: Review A.2 and A.4
on your own and do the following
Review Homework:
A.2/13,31, 33, 37, 73, 87, A.4/1,5,7, 17, 23, 31, 33, 35, 47,
Lesson 3:(Mon 9/12) 1.1- Graphs of Equations
1.2- Linear Equations in Two Variables
1.1/5,9,13,15*, 21,23, 25*, 29, 31, 43*, 59*, 67, 75
1.2/1,3,5,7,9,21, 31*, 41, 45*, 47*, 51, 57*, 81*,
Lesson 4: (Wed 9/14) 1.3- Functions
1.4 Analyzing Graphs of Functions
1.3/1,3,7,9*,15,19,21,27*,31*,33*,37,49,51*,63*, 87*, 93*, 95*
1.4/1,3,9,11,13,15,17*,21*, 31, 33*, 35*, 37*, 53*, 61*, 63*, 65*
Weekend Review: Study everything as if for an exam and
redo all starred homework problems without looking at your notes.
Lesson 5: (Mon 9/19) 1.5 A Library of Functions,
1.6- Shifting, Reflecting, and Stretching Graphs
1.5/ 3,5,29,37*, 39*, 43, 57, 59*, 67*
1.6/1a, 2a*, 5a*, 8f*, 5cd, 1b*, 2b*,9*, 11*, 13*, 21* , 27*, 43*, 63*
Lesson 6: (Wed 9/21)
1.6 Continued and a One Hour Practice Exam
HW: 1.6/15*, 17* , 25*, 31*, 33*, 39*,
HW: Check your practice exam online here. Study and retake.
HW: Study 1.3-1.6 and redo all starred problems without looking at notes.
Lesson 7: (Mon 9/26) 1.7-Combinations of Functions
and Review for Exam I
Practice what you have trouble with and get rest.
Warning: there was a mistake in the solutions of the practice
exam problem 3c. The corrected version is now posted.
Lesson 8: (Wed 9/28) Exam I on Functions and Graphing
(students who fail should drop the course
and audit MAT104)
HW: 1.7/ Read 1.7/ 5, 9*, 27*, 35*, 37*, 39*, 43*, 51*, 53*, 55*, 59
Lesson 9: (Mon Oct 3) 1.8- Inverse Functions.
Read 1.9- Mathematical Modeling on your own.
1.8/1-4, 5, 7, 9*, 11, 18, 19*, 21*, 29-32*, 61*, 81
1.9/3*, 17*, 19*, 21, 23, 25, 33, 35, 41, 47*, 49*, 53*,
Extra Credit Assignment: The following assignment covers
the absolute essential knowledge students need to continue in this course.
It is important not only to be able to do these problems but to be able
to do them without consulting the textbook. But before you try to do
them on your own, reread the examples and check each answer in the back
as you proceed. Go to the math lab Thursday 10am-8pm and get assistance.
Then go home and do all the problems again without looking at the answers
you were given. Students who complete this assignment by October 11
along with the complete homework assignments from 1.7, 1.8 and 1.9
will be given the opportunity to take a test on this material
Wednesday October 12. Up to 20 points may be added to the first exam's
grade based on this assignment and the extra credit test. Students who do
not improve their score to a grade above 60% after this retest
should drop the course. If you do not want to put in this intense
effort to improve your situation and have failed the midterm you should
drop the course now and switch to MAT104 or learn the material on your
own before attempting to retake the class.
A.1/ 29, 57, A.2/ 29, 31, 33, 85, A.3/ 93, 117, 119, 121, 139,
A.4/ 11, 35, 43,
Learn to complete the square at
this interactive
Arkansas State University website, then do A.5/ 83, 85, 87,
A.6/ 19, 21, 25, 51, 53, 69, 71, 127, 129
Read 1.2 page 17 Point Slope formula, 1.2/21, 23, 29, 55, 57, 59, 61, 63
1.3/ 63, 65, 67, 1.4/15, 53, 55, 57
1.6/9, 11, 23, 27, 29, 33, 35, 37
The test problems will be similar to these problems and not
like the ones on the first exam and sample test.
There are no scheduled classes Wed Oct 5 Mon Oct 10 or Wed Oct 12:
we meet Tuesday Oct 11 and the extra credit test will be Wed Oct 12!
Lesson 10: (Tuesday Oct 11)
A.3, 2.1- Maximizing Quadratic Functions
2.1/1, 3, 5, 7, 17*, 23*, 37*, 41*, 45*, 71*, 77*, 79*,
The Max-Min Problem Sheet
is due to be handed in on Monday October 24.
Extra Credit Exam: (Wednesday October 12)
This exam is only for students who have completed the Extra Credit
Assignment and all homework from 1.7-1.9 by Tuesday October 11. Since
Lehman College is closed Wednesday October 11, the building may be locked.
In that case, we will meet in front of Gillet Hall and I will have
security open the building. Children are welcome as long as they bring some
reading or coloring to do.
Lesson 11: (Mon Oct 17)
2.2- Polynomial Functions of Higher Degree (we will pospone this section)
2.3- Polynomial and Synthetic Division (we will skip synthetic division)
A.2- Review exponents
2.1/ 19, 39, 73, 81, 83*, Online Max Min problem sheet 1-5.
2.3/5, 7, 9, 13, 15, 37, 39, 41,
A.2/37, 39, 85, 87, 115-120
Lesson 12: (Wed Oct 19) 3.1- Exponential Functions and Their Graphs
3.1/1,3,7-10, 43, 45, 47, 55, 63, due Mon Oct 24 along with Max Min set
Lesson 13: (Mon Oct 24) 3.2- Logarithmic Functions and Their Graphs
3.3- Properties of Logarithms 1 & 2 (see Example 3)
3.2/1, 3, 9, 11, 13, 17, 19, 21, 23, 25,
39, 47, 65, 67, 73 3.3/17, 39, 41,
Lesson 14: (Wed Oct 26) 3.3-Properties of Log (Examples 4-6)
3.4- Exponential and Logarithmic Equations
Warning: Extra Long Homework due Oct 31.
Plan to spend more than one day and work in groups.
3.1/ 49. 57, 65, 67, 3.2/5, 7,
3.3/19, 21, 23, 29, 37, 45, 47, 51, 61, 63, 65, 69, 71, 89, 97
3.4/7, 11, 19, 23, 27, 29, 31, 35, 37, 87, 91, 109, 111, 127
Lesson 15: (Mon Oct 31) 3.5- Exponential and Logarithmic Models
3.5/1-6, 7, 9, 11, 13, 15, 25, 31, 39, 51, 53, 77, 81, 83
Online Growth and Decay Problem Sheet
Lesson 16: (Wed Nov 2) Review for Exam II
Practice Homework for the Exam (Problems similar to these will
be on the exam. Extra problems are given in parenthesis if you
need more practice with a particular problem. Try to do these problems
after studying in an exam setting)
1.7/ 35 (37), 51, (53), 1.8/17, 19, (21), 45 (43),
2.1/1,3, (5,7), 21 (25, 27), 71 (73) 77 (79)
2.3/ 5, (7,9), 37, (39), 3.1/ 7, (9), 43 (45, 51), 55
3.2/39, 47, 65, 71 3.3/9, (11), 17, 19, 21, 39, 7 (9), 19, 21, 23
Also be able to find the domain and range of exponential functions,
log functions, square roots, functions with denominators, and be able to
use this to find an inverse. For example: Find the inverse of
a) f(x)= e^{(5x-2)} including the domain and range
The domain of f is everything and the range is positive reals.
The inverse is f^{ -1}(x)=(Ln(x)+2)/5 and its domain is the
positive reals and its range is everything.
b) f(x)= Ln (x-3)
The domain is is greater than 3 and the range is everything.
The inverse is f^{ -1}(x)= e^{x} +3 and its domain
is everything and it's range is greater than 3.
c) f(x)= (2x +8)^{(1/2)}
Since this is a square root, the domain of f has 2x+8 greater than or
equal to 0, so the domain is x greater than or equal to -4, and the range is
greater than or equal to 0.
The inverse is f^{ -1}(x)=(x^{2}-8)/2 with the
domain x greater than or equal to 0 and the range greater than or equal to -4.
Also a problem like the publisher problem or the landlord
problem from the maxmin worksheet will be on the exam.
Lesson 17: (Mon Nov 7) Extra Review for Exam II
emphasizing domains and ranges
Lesson 18: (Wed Nov 9) Exam II on Polynomials and Exponentials
This exam will include Combinations of Functions and their Inverses.
Review Homework for Nov 13:
Read Parallel and Perpendicular Lines on page 19, Do 1.2/87, 89, 91, 93, 95
What is the formula for a circle of radius 1 about the origin?
Lesson 19: (Mon Nov 13) 4.1- Radian and Degree Measure
4.2- Trigonometric Functions: The Unit Circle,
Online Unit Circle Project
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 20: (Wed Nov 16)
4.3- Right Triangle Trigonometry
4.4- Trigonometric Functions of Any Angle
(see this webpage for help).
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 21: (Mon Nov 21) 4.5- Graphs of Sine and Cosine Functions
4.6- Graphs of other trigonometric functions
finish in class worksheet, 4.4/5, 7, 11, 15, 17, 21, 29, 35,
4.5/ 1,3,5, 7, 27, 29,
Lesson 22: (Wed Nov 23) 4.7- Inverse Trigonometric Functions
4.8- Applications and Models (Thanksgiving Weekend)
4.5/1,3,5,9, 15, 17, 19,23, 25, 69, 4.6/ 1,3,5, 7, 11, 73
4.7/33, 37, 39, 41, 43, 45, 61, 65, 4.8/1, 5, 11, 15, 31, 43, 45
Lesson 23: (Mon Nov 28) 6.1-6.2 Law of Sines and Law of Cosines
6.1/1,3,29,31,35,37, 6.2/1,3,31,39,43,45
Lesson 24: (Wed Nov 30) Review for Exam III
This review assignment is selected from the examples.
Read the example question, then try to do it without looking at the text,
then check your solution against the textbook's.
4.1/examples 3,4,5; 4.2/ ex 1-2, 4.3/ex 1-4, ex 7, ex 8;
4.4/ex 2, ex 4; 4.5/ ex 1-5; (4.6/ ex 1, ex 4-5);
4.7/ ex 1-7; 4.8/ ex 1-3, ex 6;
Read p 468-9, 6.1/ ex 1, ex 2, ex 6; 6.2/ex 2, ex 3
(height of tree exercise was confusing)
Lesson 25: (Mon Dec 5) Exam III on Trigonometry
Please bring your Exam I and II to class Monday so I can
design a personalized homework assignment to prepare you for the final.
Homework: Look at your Exam II. If you have trouble with problem 1,
study 2.3, p 134-6 and A.5/ Examples 8-9, then do old HW from these sections.
If you had trouble with 2) then study 3.1-3.2 and do all homework.
I will give a handout about problem 3 on Wednesday. If you had trouble
with Part II, see 3.1/Examples 7 and 8 and do the handout of logs and
exponenets. If you had trouble with Part III, 2.1/ Examples 1-4 and do
the handout on Max and Min.
Lesson 26: (Wed Dec 7) 5.1- Using Fundamental Identities
5.2- Verifying Trigonometric Identities
5.4- Sum and Difference Formulas and their proofs
Hand in starred problems on Monday for up to 10 more points
on Exam III.
Read 5.1/examples 2, 5, 6, 7 Do 5.1/15, 27, 43, 65
Read 5.2/example 3,4 and 7, Do 5.2/ 1, 3*, 5,
Read all of 5.4, Do 5.4/ 1, 5*, 37, 39*, 55*, 77,79, 97*,99,101*,103
Read page 404 proof of double angle formula (read 403-405
if you plan to take calc) Do 5.5/ 3*, 117, Do 4.7/ 37*, 49*, 4.5/ 9, 11*
Lesson 27: (Mon Dec 12)
2.6 and 2.2 Polynomial and Rational Functions
Read 2.2 focussing on Examples 4, 5 and 6, Do 2.2/ 67, 71, 73
Review 2.3/ Example 2. Do 2.3/1, 5
Read 2.6 do not worry about horizontal and slant asymptotes
but do understand vertical asymptotes (Examples 2-6)
Do 2.6/17, 19, 25, 27, 29, 37, 71
Lesson 28: (Wed Dec 14) Review for the Final
A practice final complete with solutions but no graphs.
I will go over it on Friday.
To study for the final go over the key practice problems
for Exam I, the Extra Credit Exam, Exam II, Exam III, the review
assignment from last week based on your Exam II, the extra credit
assignments, the last two homeworks, memorize the key formulas for
exponentials and logs, memorize the unit circles and know how to
use the trig formulas, memorize the quadratic equation, the formula
for a line, the formulas for interest, how to complete a square
and how to find a vertex, and study the practice final.
Review Classes for other sections of precalc:
Mon Dec 12 and Wed Dec 14 12 am - 2pm Gillet 127
Thursday Dec 15, Gillet 333, 9am -10:50 am Gillet 333
Extra Review Class: (Friday Dec 16) usual time and place.
Final Exam (Mon Dec 19 8:30-10:30 am):
The final will be given during Finals Week covering
the entire course especially topics needed in Calculus.
The final exam will not be waived for students who are already
acing the course. This is your opportunity to reinforce your
knowledge and prepare yourselves to ace calculus.
Recommended for students going on in business over break:
Read 7.1 Do 7.1/ 5,7,9,15,17,29,67,69,71
Read 7.2, Do 7.2/1,3,5,7,11,13,15,43,45,51,53
Read 7.3 Do 7.3/1,3,5,7,13,25,27,33,37,39,53,55,67,69,71
Recommended for students going into calc over break:
1.7/51, 53, 55, 57, 67, 69, 71, 73
2.6/ 29, 31, 33, 35, 37, 39, 45, 47, 49
4.6/1,3,5,9,17,55,57
Review everything you didn't understand well yourself.
Recommended for Math Majors and Future teachers
Learn everything in the entire book and study all the proofs
Students are welcome to visit me and ask questions
whenever they wish in the future.
The official syllabi for Lehman College courses are available at:
http://comet.lehman.cuny.edu/calculus/ .