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IMSA MI-4 Prob. Set 1 DUE: Friday, August 28th Fall 15 General Directions for the Problem Sets: The purpose of these problem sets is threefold: a. To review, enhance and make connections with your past knowledge b. To work with current concepts being discussed in class in both familiar and new contexts. c. To preview ideas and techniques that will become important in the near future. In addition, some ideas will be introduced/explained in the problem sets. Usually the first time such an explanation is presented it will appear in a box. You should be sure to pay special attention to such boxed directions as you will be expected to be able to use that information from then on. Detailed - Correct - Neat & Legible Solutions are to be written on the answer sheets provided and turned in by the due date. You are permitted to obtain help from books, your teacher, other students, or the math department instructional aides in order to clarify anything that you don't understand, but the work must be your own. You are expected to solve problems marked with NC without your calculator. Be sure to review anything that you needed help with, in order to be sure that you can do it by yourself. You are ultimately held accountable for being able to perform any tasks related to the problems. The Problem Sets are to be completed along with your regular math class homework, which will be shorter and with a different emphasis than the Problem Sets. Budget your time to allow for you to get help when needed, before the due date. It does you no good to rush through these problems the night before they are due, because some of the concepts will be needed during the class lessons that meet before the due date. EACH Problem Set is due the following D-Day; early on C-Day. In addition to the written problem sets, you will also have problems on webwork (https://webwork.imsa.edu/webwork2) . Same rules apply for those problems as well. Instructions for webwork problems are provided for you (on moodle, student server or by your MI4 teacher). PS 1.1 Rev. F15 IMSA MI-4 Prob. Set 1 DUE: Friday, August 28th PS 1.2 Fall 15 Rev. F15 IMSA MI-4 Prob. Set 1 DUE: Friday, August 28th Fall 15 NOTE: While some answers may be "obvious", in most situations it is necessary to write down how you arrived at your answer in such a way that anyone who did not understand the problem could follow your directions and arrive at your answer. (In other words, show your work unless stated otherwise.) Note: NC designated the problem is to be done with no calculator or computer. NC NC (1) 2) A large wooden cube is formed by gluing together 343 small, congruent cubes and then it is painted red. After the paint is dry, the large cube is taken apart into the small cubes. How many of these cubes: (a) have 3 faces painted red? (b) have 2 faces painted red? (c) have 1 face painted red? (d) have no faces painted red? p ( x) . Complete: q ( x) a) f(x) has a bounce point at x = –3 Therefore, _______ has a factor of ______. Consider the rational function f ( x) b) The graph of f(x) has a hole at x = 4. Therefore ______. c) f(x) has a slant asymptote. What can you say about p(x) and q(x)? NC (3) For the unit circle at the right: A C (a) Find the coordinates of point A. 1 (b) Find sin . 3 4 (c) Find sin . D (d) Find cos . B 3 . (e) Find cos 2 NC (4) Find values of a and b such that the sequence 870, 580, a, b is: (a) arithmetic (b) geometric PS 1.3 (c) harmonic Rev. F15 IMSA (5) NC (6) (7) 8) Prob. Set 1 DUE: Friday, August 28th Find the equation of a cubic polynomial with roots (3,10). 3 4 Fall 15 and 2+3i containing the point Let f (x) be a function whose set of zeroes is 4, 0,1,5 . Find the set of zeroes of: (a) NC MI-4 f(x+3) (b) f ( -2x ) (c) f ( |x| ) (d) f ( -x2 – 1 ) æ pö Find all solutions to the equation 3cot 2 ç 2x + ÷ -1 = 0 . 6ø è a) If loga 4 = logb 8 solve for a and b. b) If loga (n) = logb (2n) (n > 0) what is the ratio of a to b 9) Prove (using mathematical induction) that for any positive integer n n 3 + 2n is divisible by 3. 10) Consider the rational function f ( x) p ( x) . Complete: q ( x) a) f(x) has a bounce point at x = –3 Therefore, _______ has a factor of ______. b) The graph of f(x) has a hole at x = 4. Therefore ______. c) f(x) has a slant asymptote. What can you say about p(x) and q(x)? 11. a) How many 10 digit numbers can be formed using 3 and 7 only? b) How many 5 digit numbers can be formed which are divisible by 3 using the numerals 0,1,2,3,4,5 (without repitition) c) Everyone shakes hands with everyone else in a room. Total number of handshakes is 66. Number of persons=? d) The number of parallelograms that can be formed from a set of four parallel straight line intersecting a set of three parallel straight lines? PS 1.4 Rev. F15