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

Overview

Much of the material in this course will be a review of high school algebra, trigonometry, and precalculus. Yet the expectations for CCNY math students is much different than the expectations for most high school math students. Each CCNY math student is required to do a wide variety of problems (with pen and paper only) on the course final exam. Most high school students take shorter math tests. When only a few topics are covered in an exam, the exam is simple. Each problem-solving technique introduced in this course is simple on its own. However, when all the techniques from the course are mixed into a large exam, it is often difficult to decide which problem-solving technique is to be used in a given problem. Deciding which technique to use when faced with a test problem is the most challenging part of this course.

Making the transition to doing well on long written exams is difficult for many students coming from high school, especially considering remote learning. Fortunately doing well on high-stakes written exams is a skill that can be practiced. You will be given many low-stakes written quizzes in this course so that you can practice taking tests without much pressure. We will also offer tutoring and study sessions to practice taking the sample exams below. Most students find that after practicing the sample exams on their own the real tests become doable. Most students who practice doing written problems with pen and paper consistently throughout the semester improve their test taking skills remarkably.

Syllabus

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

The videos are grouped by textbook section. It will be helpful if you 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 after watching the videos because you will then have more time to work out problems. Doing problems is most important. It is impossible to learn math by only watching videos. You must pause each math video frequently to work out the given problem for yourself on scrap paper.

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 problems on your own.

In-Class Quizzes

There will be an in-class quiz each class (except for on midterm days) covering material from the previous lesson or two. Gradescope will help grade the in-class quizzes. The quizzes are designed for you to practice the material without much pressure, since your quiz average only counts 10% of your course grade. There will be no make-up quizzes. Instead, we will drop each student's four lowest quiz grades before computing the course quiz average at the end of the semester, so it is ok to miss a few.

Webassign HW

Here is the best advice: Consistently do lots of problems. Between WebAssign, workbook problems, practice problems, and the sample exams linked below there are more problems than any one student (or instructor) can complete. All quiz and exam questions will be chosen similar to these problems. It is better to consistently to spend an hour 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. If you consistently do many problems (train) then you will be well-prepared for the final exam. However, if you take days off 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.

Do your assigned webassign problems consistently throughout the week. Since our major exams will be written (and without electronics) work out each webassign problem with scrap paper before typing your final answer on the computer.

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.

DO Problems using Scrap Paper Only. NO technology.

Webassign is great to practice solving problems, but it is essential that you work each problem with scrap paper by your side. You cannot learn math by typing guessed answers into webassign on your phone. There will be no technology used on exams. You must work out all exam problems with scrap paper only. Practice your hw problems using scrap paper only. You will be better prepared for the exams that way.

Chapters 1-3 Practice Problems. Two questions from each secion, P2-P7.

Chapters 4-7 Practice Problems. Two questions from each secion, P2-P7.

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. Everyone gets stuck sometimes. 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. Do your assigned webassign problems consistently throughout the week. Since our major exams will be written (and without electronics) work out each webassign problem with scrap paper before typing your final answer on the computer.

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

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

Grading Factors

Webassign HW: 5% of course grade.

In-Class Quizzes / Classwork: 10% of course grade.

Midterm Exam 1: 15% of course grade.

Midterm Exam 2: 15% of course grade.

Midterm Exam 3: 15% of course grade.

Final exam 40% of course grade

However at then end of the course if your final exam average is superior to any of your midterm grades, 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, your midterm 3 grade was 79 and your final exam grade 75 then your grade will be computed as

5% * hw grade + 10% * (quiz average) + 15% * 87 + + 15% * 79 + 55% * 75 = 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 and webassign hw average CANNOT be replaced by your final exam grade. Your final exam grade will count between 40% and 85% of your course grade.

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 all midterms--and use your final exam grade as your make-up. 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 workbook and quiz problems, there should be no surprises on the written exams. Your grade in this course depends most on your performance on the written midterms and the final exam. It is you against the questions on these tests. We want every student to be successful. The best way to prepare to take these important written exams is by continuously practicing solving problems. 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.

You should practice taking the sample exams, especially the sample final exams, before you take the exam. When practicing use scrap paper only. No electronics. Your exam grades are the most important factor in determining your course grade. Most high school math students are not used to taking high-stakes math exams that cover so much (14 weeks) material. The quizzes are easy in comparison. Quizzes only cover one or two days of material. As you go through the course, you'll find that each individual topic is relatively simple, so the quizzes and webassign problem sets will mostly be simple. They are neatly divided by topic. However, when the topics are mixed together on a midterm or a final exam, the questions become more difficult. Even though each problem-solving technique is, more or less, simple by itself, it is indeed difficult to decide which problem-solving technique to use on which problem when all the problems are mixed together on a final exam.

Luckily this challenge is not so difficult if you practice the sample exams. After you practice the sample exams, you realize that the exams are repetitive. After some practice you begin to recognize which technique to use for different problems.

After I give an exam in this course, there are inevitably a couple students who approach me and say, "I wish I had practiced more of the sample exams beforehand. I would have done better on this exam if I had." Don't be that student. Prepare consistently for each exam. You will get better.

Sample Exam 1. Questions from sections 1.1-2.4.

Sample Exam 1B. Another sample using questions from sections 1.1-2.4.

Sample Exam 2. Questions from sections 2.6-4.4.

Sample Exam 2B. Questions from sections 2.6-4.4.

Sample Exam 3. Questions from exam 3 sections 4.5, 4.6, chapters 5, 6.

Sample Exam 3B. Questions from exam 3 sections 4.5, 4.6, chapters 5, 6.

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.

Sample Final Exam 3. Questions from the final exam are picked from all sections on our syllabus.

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

Old Sample Midterm 2. Questions from exam 2 are picked from sections between (and including) 2.7--6.2 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.)

Sections

For Spring 2024, the following sections are being offered:

Historical offerings