Show all work to receive full credit!
ADVANCED FUNCTIONS
aa
Mid-Term EXAM Review 2012-2013
NAME __________________________
DATE ______________ PER _______
In order to earn full credit, you must:
5 pts - completion
 draw and label diagrams
 show all work for each

20 pts - accuracy
The exam review will be graded on completion (5 points) and randomly selected
problems answered correctly (20 points). You will lose one completion point for
every problem not completed.
The exam review is due no later than 3:48pm on:
 Wednesday Jan. 2, 2013 for a max of 10 points out of 5 completion points.
 Friday January 4, 2013 for a max of 8 points out of 5 completion points.
 Monday January 7, 2013 for a max of 6 points out of 5 completion points.
DUE DATE – Due in class
 A Day – Tuesday January 8, 2013
B Day – Wednesday January 9, 2013
for a maximum of 5 points out of 5 completion points.
 There will be no exceptions made!
This exam review covers the basics for Chapters P, 1, 2, and 3.
Be sure to study your old quizzes and tests.
1) Simplify 64
3) Simplify
2
3

2) Simplify 3x 2 y 4
completely.
12  18 completely.


5) Simplify 2 x  5 3x 2  x  7 .
 2
2
4) Multiply and simplify:
1
x0 y


3
completely.
3  5


3  7 .
#6-10 Factor completely.
7) 48x 2  3
6) 27m3n  9mn
8) x 2  3x  54
9) x 3  27
11) Factor by grouping to find all solutions of
10) 2 x 2  3x  12
x 3  2x 2  x  2  0 .
x 2  7 x  12
x 2  6x  8
 3
12) (Section P.5) Simplify
completely. State the Domain!!
x3  1
x  x2  x
13) (Section P.5) Simplify
3x
6
 2
completely. State the LCD and the Domain!!
x  4
x 4
2
#14-17 Solve the following equations.
14) Solve for a.
2
a – 12 = 3(a + 7)
5
16) Solve for x.
7x 6x  7 3


4
8
2
15)
Solve for x.
17) Solve for x.
2( x  3)2  7  31
2 4x  6  8   4
#18) Solve each quadratic by graphing. (You must show at least 5 point including the vertex.)
y
x 2  2 x  24  0
x
19) Solve the quadratic 81x 2  49  0 by factoring.
20) Find the discriminant of 2 x 2  x  1  0 . Describe the nature of the root(s).
21) Solve the quadratic 3x 2  2 x  5  0 using the quadratic formula.
22) Solve the quadratic x 2  16 x  46  0 by completing the square. Simplify completely.
23) Graph the relation and determine whether the relation is a function and/or one-to-one. Explain your
answer.
y
y 4 x  6
x
24) Evaluate
 3.1.
26) Find the slope of the line passing through
25) Given f ( x)  x 3  7 , find f (2) .
 2, 6
and
 3, 9 .
27) State the domain of f ( x) 
x  6.
28) Find the y-intercept for
f ( x)  2 x 3  3x 2  12 x
29) Find the slope and the y-intercept of the line passing through
 8, 11
and
 4, 11 .
y
30) Write the equation shown by the graph.
x
_______________________
31) Write the slope-intercept form of the equation of the line passing through 4,  4 and 5,  10 .
32. Look at the graphs. Determine if it is a function and/or one-to-one, or neither AND EXPLAIN
WHY YOU DECIDED THIS. Circle all that applies.
a.
b.
Function / One-to-One / Neither
Function / One-to-One / Neither
REASON ____________________
REASON ____________________
33) Graph the piecewise function:
 x  1, x  0
f ( x)  
.
2 x  1, x  0
y
x
**********************UNIT 3***********************
34)


Divide x 3  4 x 2  12 x  9 by x  2 using SYNTHETIC division.
35) Divide 3x  2 6 x3  16 x 2  23x  5 using LONG division.
36) Find f (2) if f ( x)  3x3  6 x 2  7 x  10 using the Remainder Theorem.
37) What is happening with this graph?
y
As x    , f (x)  _________.
f (x)
As x   , f (x)  _________.
How many turning points does this graph have? _____
What is the lowest degree of this polynomial? _____
What is the sign of the leading coefficient? _______________
38) What happens at x  4 if y  ( x  3)3 ( x  4)4 .
39) Use the Zero Location Theorem to determine if P( x)  3x3  11x 2  6 x  8 has a real zero
between x = -2 and x = -3.
EXPLAIN WHY OR WHY NOT.
40) Find the zeros of P (x ) and state the multiplicity of each zero.
x
P ( x)   x  3  x  2 
3
 x  2x
3
 1
2
_____ occurs as a zero of multiplicity _____ .
_____ occurs as a zero of multiplicity _____ .
_____ occurs as a zero of multiplicity _____ .
_____ occurs as a zero of multiplicity _____ .
41) Find all the zeros of P( x)  3x3  11x 2  6 x  8 . Determine the number of zeros and also
include the use of the Rational Root Theorem and Descartes’ Rule of Signs. Be able to do this without
the use of a calculator.
42) Write the polynomial of least degree for the roots of 3i , 3i , and 2 .
_____ 43) Determine the far-left and the far-right end behavior of the graph of
P( x)   0.02 x6  4 x3  0.01x 2  200 . Create a sketch of the graph.
a) As x  , f ( x)    ; x  , f ( x)   
b) As x  , f ( x)    ; x  , f ( x)   
c) As x  , f ( x)    ; x  , f ( x)   
d) As x  , f ( x)    ; x  , f ( x)   
3x  6
.
2 x  5x  2
Hole in graph:
__________
44) Graph f ( x) 
2
V.A.
__________
H.A.
__________
Quick Sketch:
y
x
x-intercept
__________
y-intercept
__________
slant asymptote
__________
Domain
__________
Range
__________
x
y
x
y
45) Sketch the graph of f ( x)   x3  6 x 2  9 x . Label x- and y-intercepts, maximum and
minimum points, and the graph. USE CALC TO FIND MAX/MIN.
y
HINT: You need to factor first.
x
y
Relative maximum: __________
Relative minimum: __________
ZEROS ______________
x
46) Explain why this polynomial has a slant asymptote and find it. F ( x) 
x 2  3x  1
.
x 1
47) At most, how many roots could the polynomial f ( x)  4 x9  3x6  10 x3  8 x  2 have?
EXPLAIN WHY.
**************************UNIT
3.14************************
Simplifying radicals review. No decimal answers!! Use Sections P1/P2 in your book for
help if you are going to turn this in early.
48)
225a 2 b3 using rational exponents.
Express
49) Express
x
x
50) How would you write 493/5 in radical notation?
51) How would you write

3
64

5
5
4a8b14c5
 2 x 2 y 
54) 
3 
 3 xy 
2
5
using radicals.
____________________________________
in exponential notation? _______________________________
Simplify the following expressions.
52.
3
5
53.
2
55)
3
16w2 x 4 y14
3
2
*****************LABS/REGRESSION PROBLEM******************
Automotive Engineering: The fuel efficiency, in miles per gallon, for a certain midsize car at various
speeds, in miles per hour, is given in the table below.
mph
mpg
25
29
30
32
35
33
___________________________
___________________________
____________________
____________________
40
35
45
34
50
33
55
31
60
28
65
24
70
19
75
17
1a. Find a linear model for these data.
Round to the nearest hundredth.
1b. Find a quadratic model for these data.
Round to the nearest hundredth.
2a. What is the coefficient of determination(r2) for the linear model?
Round to the nearest hundredth.
2b. What is the coefficient of determination(r2) for the quadratic model?
Round to the nearest hundredth.
____________________
2c. Which model (linear or quadratic) is a better predictor of the data? WHY?
____________________
3a. Use your model from #1 to predict the fuel efficiency of this car when it is
traveling at a speed of 27 mph. Show work. Round to the nearest tenth. Give
proper units.
____________________
3b. Use your model from #1 to predict the fuel efficiency of this
car when it is traveling at a speed of 5 mph. Show work. Round to the
nearest tenth. Give proper units.
_____________________ 4. Use the quadratic formula to find the possible speeds that a midsize car can
go to average 20 miles per gallon. Round your solutions to the nearest tenth. Do not round until your final
solutions.
3.1 – The Remainder and Factor Theorem
5. Selection of Cards The number of ways you can select three cards from a stack of n cards, in which
the order of selection is important, is given by P(n)  n3  3n2  2n, n  3
a.
Use the Remainder Theorem to determine the number of ways you can select three cards
from a stack of n = 8 cards.
b.
Evaluate P(n) for n = 8 by substituting 8 for n. How does the result compare with the result
obtained in part a.?
6. Profit A software company produces a computer game. The company has determined that is profit P,
in dollars, from the manufacture and sale of x games is given by
P( x)  0.000001x3  96 x  98, 000 where 0  x  9000 .
(Hint: Use your calculator to graph the function, use ZoomFit, and then CALC the MAXIMUM)
a. What is the maximum profit, to the nearest thousand dollars, the company can expect from the
sale of its games?
b. How many games, to the nearest unit, does the company need to produce and sell to obtain the
maximum profit?
Modeling Launched Objects The function h  16t 2  h0 was used to model the height of a
dropped object. For an object that is launched or thrown, an extra term v0t must be added
to the model to account for the object’s initial vertical velocity v0 (in feet per second).
Recall that h is the height (in feet), t is the time in motion (in seconds), and h0 is the initial
height (in feet).
7. Juggling: A juggler tosses a ball into the air. The ball leaves the juggler’s hand 4 feet
above the ground and has an initial vertical velocity of 40 feet per second. The juggler
catches the ball when it falls back to a height of 3 feet.
How long is the ball in the air? Round to the nearest hundredth ____________
8. Football: In a football game, a defensive player jumps up to block a pass by the
opposing team’s quarterback. The player bats the ball downward with his hand at an
initial vertical velocity of -50 feet per second when the ball is 7 feet above the ground.
______________ How long do the defensive players’ teammates have to
intercept the ball before it hits the ground? Round to the nearest hundredth.