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