IMSA
MI-3
Problem Set 1
DUE: Tues. Jan 24
Spring ‘12
Note: NC designated the problem is to be done with no calculator or computer.
All answers should be exact whenever possible. Approximated answers should be rounded to four significant digits
unless otherwise stated in the problem.
Note: Items in boxes
future.
1.
contain significant information that you will be responsible to use in the
NC Solve for x:
b) 82 x 1   0.254 x 3 
a) 53 x  4  25x
c) 34 x 3  273 x 5
A perfect square trinomial is any trinomial of the form u 2  2uv  v 2 . For example
4 x 2  12 x  9 is a perfect square trinomial because it equals (2 x  3) 2 . Here u  2x and v  3 .
Similarly x 2  14 xy  49 y 2 is a perfect square trinomial because it equals ( x  7 y)2 . Here u  x
and v = 7y.
2. On each of the following, fill in the boxes and the blanks so that each expression is a perfect
square trinomial:
a) x 2  12bx 
 ( x _____)2
b) x 2  10 xy 
 ( x  _____)2
c) 36 x 4  60 x 2 y 2 
 (____  ____)2
3.
 3a 3b 2   ab 2 
NC Simplify: a)  2 4    4 5 
 2c d   c d 
4.
If f  x  
5.
3
b)
2n 5  4  2n 1 
8  2n  2 
x 1
, find f 1  x  and state its domain.
x
Make a sketch of each function and give its domain and range. Your sketch should clearly show
significant points. Give your answer in interval notation.
1
a) f ( x )   
3
x
b) g ( x)  25  x 2
PS 1.1
Rev. S12
IMSA
MI-3
Problem Set 1
DUE: Tues. Jan 24
Spring ‘12
6. Is there a relationship between Math SAT scores and the number of hours spent studying for the test?
A study was conducted involving 20 students as they prepared for and took the Math section of the
SAT Examination.
Hours spent
studying
4
9
10
14
4
7
12
22
1
3
10
13
16
13
5
6
10
8
11
11
7.
Math SAT
Scores
390
580
650
730
410
530
600
790
350
400
640
700
770
730
450
520
690
590
690
640
a) Graph the data and determine a linear regression
model equation to represent this data. Round your
answer to the nearest tenth. (You can use a calculator
or MS Excel to plot the graph and attach it to the
answer sheet)
b) Decide whether the new equation is a "good fit" to
represent this data. Explain your response clearly.
c) Interpolate data: If a student studied for 15 hours,
based upon this study, what would be the expected
Math SAT score?
d) Extrapolate data: If a student spent 100 hours
studying, what would be the expected Math SAT
score? Discuss this answer.
The distance between a point P  h, k  and the line
ax  by  c  0 can be found by evaluating the
expression:
d
ah  bk  c
a 2  b2
a. Find the distance from the point (2, 1) to the line
7 x  5 y  2  0 . Give exact answer.
b. Find the distance between the parallel lines
12 x  5 y  4  0 and 12 x  5 y  2  0 . Give
exact answer.
PS 1.2
Rev. S12
IMSA
MI-3
Problem Set 1
DUE: Tues. Jan 24
Spring ‘12
8) If the real roots of y  f ( x) are {5,3,10} (i.e. f (5)  0 , f (3)  0 and f (10)  0 ), find the real
roots of: (state exactly)
9)
a.
y  f ( x  5)
b.
y  f (3x)
c.
y  f ( x2 )
d.
y  f (2 x  3)
Find the set of all integers, n, for which the fraction
12
is a positive integer.
24  n
10) a) How many 5-letter code symbols can be formed with the letters A, B, C, and D if we allow a
letter to occur more than once?
b) In how many distinguishable ways can the letter of the word CINCINNATI be arranged?
11)
By pumping, the air pressure in a tank is reduced by 18% each second. So the percentage of air
pressure remaining is given by p = 100(0.82)t. Plot p against t for 0  t  20 sec.
a) Using the technique you used on page 1.3 of your MI 3 notebook, find an equation that models
the air pressure as a function of time t. Show your steps including a table, logarithmic
equation, and the final equation. Use three decimal places throughout this problem.
Note: You will learn how to do this using other technology, but for now, use your calculator
and enter your results on your answer sheet by hand.
b) Use your model to predict the time it will take the air pressure in the tank to get as close to
zero as possible. Can the air pressure ever become zero? Does your model agree with your
prediction? Explain.
12) If 0.6% of a radioactive substance decays every year,
a.
what percent will be left after 30 years?
b.
how many years will it take until half of the substance decays?
[Round your answer to the nearest year.]
a
13) Let L be a function such that L(a)  L(b)  L(a  b) and let L(a)  L(b)  L  
b
Find single term simplifications for:
a.
L(48) – L(8) + L(9)
PS 1.3
Rev. S12
IMSA
b.
MI-3
Problem Set 1
DUE: Tues. Jan 24
Spring ‘12
L(12) + L(6) – L(4) – L(9)
PS 1.4
Rev. S12