Precalculus Orientation and FAQ

Transcription

1 Precalculus Orientation and FAQ MATH 1011 (Precalculus) is a four hour 3 credit course that prepares a student for Calculus. Topics covered include linear, quadratic, polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric functions as well as conic sections. MATH 1021 and 1026 are a two-semester sequence of courses specifically designed for the student who requires more pre-algebra concepts and a slower pace. Essentially they contain MATH 1011 material spread out over two semesters. Each course is a four hour 2 credit course. Topics for MATH 1021 include linear, quadratic, polynomial, rational, exponential and logarithmic functions. Topics for MATH 1026 include trigonometric and inverse trigonometric functions and conic sections. It should be emphasized that together MATH 1021 (Precalculus A College Algebra) and MATH 1026 (Precalculus B Trigonometry and Conics) are equivalent to MATH 1011 (Precalculus). In other words MATH 1011 is a higher level course than MATH 1021 or 1026, despite the course numbers. Should I take MATH 1021 or the two-semester sequence MATH 1021 and 1026? It depends on your placement test scores and whether you feel comfortable enough with the material to enter the fast-paced MATH If you are returning to school after a break, working a part-time job, or have issues with mathematics, then the two-semester sequence MATH 1021 (Algebra) and MATH 1026 (Trigonometry & Conic Sections) is better for you. I am a non-traditional student returning for my second degree. What should I take? We recommend that you take Math This course covers what is considered College Algebra in other schools. Your instructor will build into the syllabus pre-algebra prerequisites like fraction arithmetic. Do I need a graphic calculator or will a scientific calculator be enough? It depends on your instructor. Technology will be used when it assists in the learning mathematics, not as a substitute for it. However, a standard scientific calculator is recommended. Note that department policy prohibits graphing calculators on all examinations. Is there a departmental final for MATH 1011, MATH 1021, and MATH 1026? Yes. There is a departmental final for MATH 1011 and also one for MATH 1021 and MATH This is to ensure consistency of learning objectives across all sections. 1

2 Do I have to attend class? Yes. Students who are frequently absent rarely succeed. Instructors may call or students who are absent. I m falling behind. What should I do? Seek advice from your instructor first. Consider visiting the Learning Center at 1300 Boylan Hall where you can get a free peer tutor to help you at a time convenient for you and your tutor. I ve heard the term instructional technology mentioned. How will it affect me? Instructional technology is the term used when the instructor uses technology in the classroom, usually with the goal of improving communication with students and explaining topics in different ways. Some instructors like to use SmartBoards and interactive PowerPoint slides in the classroom. Some use CUNY s online course management system called Blackboard which makes it easy to post copyrighted content and grades. Some communicate with students via and public blogs. Some like to hold office hours via chat. Some give links for appropriate YouTube videos for self-study. And so on communication methods have increased dramatically in the past few years and this is now reflected in the classroom. It is up to you to get in sync with your instructor s teaching style and communication preference. I ve heard conflicting opinions on the importance of using graphic calculators (TI-80, TI-89) and computer algebra systems (Maple, Mathematica, Matlab). Can you give me some information on this topic? You are expected to be able to draw graphs by hand. However, no one will stop you from using a graphic calculator to improve your visual intuition and speed up routine computation. As long as you can do-by-hands and show all steps, you can use whatever technology you find helpful. A year ago, the makers of Mathematica created a website called where you can enter your equation and have it solved, enter your graph and have it drawn, and essentially do, with a click of a button, just about anything. This is a great free tool and a forgiving tool. Graphic calculators and software expect you to type things exactly in order to work. This website allows you to type something carelessly and then it guesses what you meant to type. Hard not to like it! Your goal should be to make technology work for you, not the other way round -- don't become a slave to technology. 2

3 Can you tell me more about the Learning Center? What services do they offer? At the beginning of the semester, it is worth going over to the Learning Center (1300 Boylan Hall) to make yourself familiar with their procedures and get the most current tutoring schedule. It is also available online at but if you go over there, you ll get a paper copy of the most current schedule and you ll get to meet the staff and tutors. There are precalculus tutors available for several hours a day. Some hours draw more students than others. It is a good idea to see for yourself which hours are more or less crowded and plan accordingly. What topics will we cover in Precalculus Math 1011? All the topics below will be covered. COLLEGE ALGEBRA (THIS IS COVERED IN MATH 1021) Properties of real numbers Variables and algebraic expressions Solving linear equations Solving inequalities Absolute value equations & inequalities Factoring Solving quadratic equations Complex numbers Solving radical equations Graphing straight lines Finding equation of a line Graphing parabolas and circles What is a function? Graphs of functions Graphing techniques for functions Algebra of functions & inverse functions Polynomial Arithmetic Solving polynomial equations Graphing polynomial functions Rational root test Graphing rational functions Solving rational equations Solving polynomial and rational inequalities Exponential functions and their graphs Logarithmic functions and their graphs Properties of logarithms, e and ln Exponential and Log equations Systems of linear equations TRIGONOMETRY AND CONICS (THIS IS COVERED IN MATH 1026) Angles and their measure Right triangle trigonometry Trigonometric ratios for any angle Trigonometric functions Graphs of trigonometric functions Trigonometric identities Sum and difference formulas Double and half-angle formulas Trigonometric equations Inverse trigonometric functions Law of Sines and Cosines Conic Sections Circles Parabolas Elipses Hyperbolas Shifted Conics 3

4 As you can see the syllabus of MATH 1011 is extensive. You should have seen many of these topics before. Indeed 11 of the topics in the first column are very basic prerequisites for Algebra (highlighted in bold). Seeing all of them listed like this should give you a sense of how difficult it will be to succeed in Math 1011, if you don t already know the basic topics. You may decide that it is better to do the two-semester sequence Math 1021 and Math 1026 Not included in this list are some even more basic topics pre-algebra topics like the following which you are expected to know: INTEGERS Integers and absolute value Adding and subtracting integers Multiplying and dividing integers PRIME NUMBERS Prime factorization Greatest Common Factor Least Common Multiple FRACTIONS What are fractions? Adding and subtracting fractions Multiplying and dividing fractions DECIMALS Understanding decimals and irrational numbers Writing decimals as fractions and vice versa Ratios, proportions, percentages EXPONENTS AND RADICALS Exponents and their properties Radicals and their properties Rationalizing the denominator ARITHMETIC OF POLYNOMIAL & RATIONAL EXPRESSIONS Adding and Subtracting polynomials Multiplying and dividing polynomials Adding and subtracting rational expressions Multiplying and dividing rational expressions How much time per week should I budget for Precalculus? Now that you understand the difficult situation we are all grappling with, please take a moment to fill out a weekly schedule and budget 12 hours a week for Math Note that although it is a 3-credit course, you will meet with your instructor 4 hours a week. The general rule of thumb for math courses is to spend two hours at home for every hour in class. This means you must allocate 12 hours a week for Math 1011 to succeed in it. Students taking Math 1021 and Math 1026, will also be meeting with the instructor for 4 hours a week. Expect to spend at least 5 or 6 hours on homework for a total of 9 or 10 hours a week. Note that the amount of time spent when taking Math 1021 and 1026 is not that much less than Math The key to success is to free up your schedule for 10 to 12 hours per week and devote that time to Precalculus. Please fill out the weekly schedule below to determine where you can set aside 12 hours. 4

5 SUN MON TUE WED THUR FRI SAT 5:00 6:00 AM 6:00 7:00 AM 7:00 8:00 AM 8:00 9:00 AM 9:00 10:00 AM 10:00 11:00 AM 11:00 12:00 12:00 1:00 PM 1:00 2:00 PM 2:00 3:00 PM 3:00 4:00 PM 4:00 5:00 PM 5:00 6:00 PM 6:00 7:00 PM 7:00 8:00 PM 8:00 9:00 PM 9:00 10:00 PM Thanks for reading this document. We look forward to seeing you in our courses. 5