Division of Science






Department of Mathematics
The City College of New York
160 Convent Avenue
New York, NY 10031

Phone: (212) 650-5346
Fax: (212) 650-6294

Math 19500: Precalculus

Supervisor: Matthew Auth

Intervals, inequalities, operations on functions, inverse functions, graphing polynomial functions, exponential and logarithmic functions, trigonometric functions and formulas. Prereq.: A grade of C or above in MATH 19000 or placement. 4 hr./wk.; 3 cr. 195 CLO


Syllabus and Schedule

Individual instructors may alter the schedule slightly due to holidays or in order to spend more (or less) time on a given topic.

Lesson Summaries with Video Links for Flipped Classroom

Topic Summaries and Video Links

We will be using a flipped classroom model this course. Watch the videos for the day's lesson before coming to class. You can even try some of the optional linked Khan Academy exercises. You will get more out of class by first watching a couple videos beforehand. After watching the videos you will then have more time to work on problems during class. Doing problems is most important. It is impossible to learn math by only watching videos.

The summaries can be helpful to consult for a quick overview of each section covered in the syllabus. While reading you will learn what concepts and techniques are most important in each section, and what topics can be skipped or deemphasized. Ultimately, working through the assigned webassign hw problems on your own or in groups of students is most important. The only way to learn the material in this course is to do many problem on your own.

Webassign Quizzes

We will use webassign for homework and in-class quizzes in this class. Webassign quizzes can only be taken in-person during class. There are no make-up webassign quizzes. You may take the quizzes with your phone or with a laptop. If you plan to use your phone, please practice beforehand. Some students complain that they have difficulties entering webassign answers on their phones. One solution is to change your phone web browser. If that does not work, you may borrow an iPad or laptop from the ccny iMedia office on the first floor of the NAC building. You will get two attempts for each webassign quiz question.

Webassign HW

Here is the best advice: Consistently do lots of problems. Between WebAssign, textbook examples and exercises, and Khan Academy practice sets linked above, there are more problems than any one student (or instructor) can complete. The webassign hw sets are most important. All exam questions will be chosen similar to the problems on your assigned webassign hw sets and webassign quizzes. It is better to consistently to spend two hours every day doing an assortment of math problems than to spend the weekend before an exam cramming. Consider the final exam like running a marathon and the problems as your training sessions. Ultimately this is a tesIf you consistently do problems (train) then you will be well-prepared for the final exam but if you take long gaps between working on problems you will always have difficulty getting back into the math mindset necessary to complete the problems. The first day of training is always the most painful.

Your score on the webassign hw sets does not count toward your final course grade. The assigned webassign hw sets are for practice only. Nevertheless your course instructor will assign due dates for your webassign hw sets---usually four or five days after the topic was covered in class, in order to force you to keep up with the course. After the assignment due date you will see the answer to each question. You can (and should) use the "Ask Another Version" button on past due hw assignments to continue to practice different versions of the hw questions.

Finally use the "Ask Your Teacher" button to ask questions while doing a webassign assignment. Each problem on your webassign assignments will have an "Ask Your Teacher" button. By clicking the button and describing what you are thinking on a given problem is a great way to get help. It also helps your instructor to know what topics must be reviewed.

Read the Book

Here is some good advice: Read the textbook. Learning how to read a math textbook will be helpful in all your future math courses. Start practicing reading your math textbook now. You get a free e-copy of our textbook with your webassign access key. There are good videos, formula lists, and worked examples in each section of our book. You can find topics, advice reading textbook, examples in the section to know, examples in the section to avoid, end of section exercises to try (odd answers in back), as well as relevant Khan Academy videos, practice problem sets, and overviews in the course topics link above.

Getting Help:

Working alone on your math exercises sets and getting stuck is frustrating, but it is a best way to learn math. Really focusing and trying to sort out your ideas while stuck on a problem is an essential way to learn a math concept. Do not panic. We all learn math this way. However do not remain stuck for too long, for more than a couple days. There are many ways to get help. Experiment with different ways to get support and find a method that works for you.

(1) CCNY FREE TUTORING: Take advantage of ccny free tutoring schedule.

(2) WORKING IN GROUPS: There is evidence that students who form study groups in math courses perform better. Meeting with a group of classmates before or after class to work on exercises is a great way to learn the material and avoid getting stuck.

(3) OFFICE HOUR: There will be an office hour each week. Your instructor can help you work through an exercise when you are stuck.

(4) WEBASSIGN ASK MY TEACHER: Use the Webassign "Ask My Teacher" feature when you get stuck while doing an exercise.

Suggested Grading Factors

Quiz Average: 20% of course grade.

Midterm Exam 1: 20% of course grade.

Midterm Exam 2: 20% of course grade.

Final exam 40% of course grade

However at then end of the course if your final exam average is superior to your midterm 1 grade or your midterm 2 grade, then you can use your final exam grade to replace all lower midterm average(s). For instance if your midterm 1 grade 70, your midterm 2 grade 87, and your final exam grade 81 then your course grade will be computed as 20% * (quiz average) + 20% * 87 + 60% * 81 = course grade. You can even replace both midterm exam scores if your final is superior to both. One way to think of these grading factors is that your performance on midterms cannot hurt your final grade, as compared to your final exam grade. Your performance on the midterms can only help your grade in comparison to your final exam score. If you miss a midterm exam for any reason, your final exam grade will be used to make-up your missed midterm.

Your quiz average CANNOT be replaced by your final exam grade. There will be a quiz every class period. There will be no make-up quizzes. Instead your lowest four quiz grades will be dropped before computing your quiz average.

With these grading factors you will be less stressed taking the midterms knowing that you can replace a bad score with your final exam score. Moreover if you feel ill, test positive for covid, you can skip either midterm, or both midterms. However, you must take the final. If you are sick for the final, do not come to campus. There will be a make-up final exam.

Sample Midterm and Final Exams

NO ELECTRONICS OR CALCULATORS ON MIDTERM AND FINAL EXAMS. Midterm and final exams will be given in-person. All sample exam questions modeled on the assigned webassign homework problems. If you've worked through the assigned webassign homework and classwork problems there should be no surprises on the written exams. Your grade in this course depends on your performance on the written midterm and final exams. It is you against the questions on the webassign questions on these tests. The best way to prepare to take these written exams is by continuously practicing webassign hw, classwork, and quiz questions. The sample exams below have been included to give you an idea of the exam format. During any semester exam problems will be shuffled between the assigned webassign problems from those sections, however the exam format will be similar to the format of the exams below.

Sample Exam 1. Questions from exam 1 are picked from sections between (and including) 1.1-2.8 on our syllabus.

Sample Exam 1A. Questions from exam 1 are picked from sections between (and including) 1.1-2.4 on our syllabus.

Sample Exam 2. Questions from exam 2 are picked from sections between (and including) 3.1--5.2 on our syllabus.

Sample Exam 2A. Questions from exam 2 are picked from sections between (and including) 2.6-2.8, ch3, ch4, 6.1, 6.2.

Sample Final Exam. Questions from the final exam are picked from all sections on our syllabus.

Sample Final Exam 2. Questions from the final exam are picked from all sections on our syllabus.

Discounted Webassign Access Code ($44)

If you have not already purchased a 195 Webassign Access code, you can purchase one for $44 by following each step until you reach step 5A in the Strong Start Student Guide. If you already purchased a 195 Webassign Access code in a previous semester, do NOT purchase another code. Your old code will work this semester. The access code remains valid even if you need to take math 195 multiple times. Before you purchase an access code, you should take advantage of the free trial before purchasing in case you need to drop the course. A 190 Webassign Access Code will NOT work in math 195. If you have not already purchased a 195 access code, you must purchase one.

(If you are taking multiple courses outside the math dept. that also require a webassign access code, then Cengage Unlimited may save you money? You should then compute what is the best value for your semester. If this is the only class with Webassign you are taking this semester, the cheapest option (step 5A) to purchase an access code that I know is the $44 option in the above link.)


For Spring 2023, the following sections are being offered:

LetterInstructorTime & Place
ABSiobhan O'ConnorMoWe 8:00AM-9:40AM in NAC 4/113
BCJohn AdamskiMoWe 10:00AM-11:40AM in NAC 6/113
CDTsz Chung LoMoWe 12:00PM-1:40PM in NAC 6/111
EFSahar TariqMoWe 2:00PM-3:40PM in NAC 6/114
FGLavinia CiunguMoWe 4:00PM-5:40PM in NAC 5/102
FG2Jania BegumMoWe 4:00PM-5:40PM in NAC 4/209
GHRavi RampersadMoWe 6:00PM-7:40PM in NAC 4/115
KLDavid JohnTuTh 8:00AM-9:40AM in NAC 6/111
LMTsz Chung LoTuTh 10:00AM-11:40AM in NAC 5/108
LM2Tek BamTuTh 10:00AM-11:40AM in NAC 4/113
PRAnthony PaolilloTuTh 2:00PM-3:40PM in NAC 4/156
RSPatrick OkpoTuTh 4:00PM-5:40PM in NAC 6/114
RS2Ghasan YousefTuTh 4:00PM-5:40PM in NAC 5/102
STDavid ScheimanTuTh 6:00PM-7:40PM in NAC 4/130

Historical offerings