Algebra 2
Review for MP 3 Quarterly
Name ________________________
Block_________________________
PART 1 – POLYNOMIALS
Questions 1 – 10 are multiple choice. Show all work on separate paper.
1)
Jim is simplifying the expression (3x4 + 4x2)(x3 – 2x2 – 1). Which of the following shows
the correct product?
A.
3x12 – 6x8 + 4x6 – 11x4 – 4x2
B. 3x7 + 6x6 – 4x5 + 11x4 + 4x2
C.
3x7 – 6x6 + 4x5 – 11x4 – 4x2
D. 3x12 – 6x8 – 4x6 + 11x4 + 4x2
2) Simplify (x2 + 2x – 5) – (3x2 – 4x + 7)
A.
2x2 – 2x – 12
B.
-2x2 + 6x – 12
C.
4x2 – 2x – 2
D.
4x2 + 6x + 2
3)
A.
C.
Which describes the number and type of roots of the equation x4 – 64 = 0.
4 imaginary roots
B.
4 real roots
3 real roots, 1 imaginary root
D.
2 real roots, 2 imaginary roots
4)
A.
C.
Find p(-4) if p(x) = 3x3 – 2x2 + 6x – 4.
-252
B.
132
D.
-140
180
5)
A.
C.
If r(x) = 4x2 – 3x + 7, find r(3a2)
36a4 – 9a2 + 7
36a4 + 9a2 + 7
B.
D.
144a4 – 9a2 + 7
12a4 – 9a2 + 7
6)
A.
C.
Find p(x + 1) if p(x) = x2 – 3x – 1
x2 – 3x
x2 – 3x – 3
B.
D.
x2 – 3x + 3
x2 – x – 3
7)
A.
C.
Solve x4 – 13x2 + 36 = 0
-3, -2, 2, 3
2, 3, 2i, 3i
B.
D.
-9, -4, 4, 9
-3, -2, 2i, 3i
8) As x  - ∞, f(x)  __?__ describes the end behavior of f(x) = -4x3 – 2x – 2
A.
C.
9)
A.
C.
-∞
0
Factor 27x3 – 1 completely.
(3x – 1)3
(3x – 1)(9x2 + 3x + 1)
B.
D.
+∞
x
B.
D.
(3x – 1)(9x2 – 3x – 1)
(3x – 1)(9x2 – 3x + 1)
10) Factor completely: x3 + 5x2 – 4x – 20
A. (x + 5)(x2 – 2)
B.
(x + 5)(x2 – 4)
C. (x + 5)(x – 2)(x + 2)
D.
(x2 + 5)(x2 – 4)
Open-Ended
1. A rectangular prism is shown at the right. The
length is 1 centimeter less than the height, and the
width is 9 centimeters less than the height.
Note that V = l∙w∙h
a) Write a polynomial equation in standard form for V(h)
that can be used to solve for the height of the prism h.
b) How many possible roots are there for h in the polynomial equation you wrote? Explain.
c) The volume of the prism is 90 cubic centimeters. Use this information to solve the equation
from part a for all real roots h. What are the dimensions of the prism? Show all work.
2. Given the equation f(x) = 2x3 - 8x + 10x2 - 40
a. Algebraically find the zeros of f(x).
b. Identify its degree and lead coefficient.
a________________
Degree = ________________________
Lead Coefficient = _________________
c. Accurately graph f(x) on the grid provided. Identify the coordinates of any relative maximums or
minimums to the right of the grid. Round coordinates to the nearest tenth if necessary.
Relative Maximum(s)
__________________________
Relative Minimum(s)
__________________________
c. What is the domain and range for the graph you drew in part d above?
Domain_______________________________________________________
Range_______________________________________________________
d. Complete the following statements regarding end behavior of this graph.
As x → + ∞, f(x) →__________________
e. Name all intervals that are increasing.
f. Name all intervals that are negative.
As x → - ∞, f(x) →_________________
PART 2 – PROBABILITY
1) A bag contains 10 red marbles, 6 yellow marbles, 2 black marbles.
Two marbles are randomly drawn from the bag without replacement.
a) What is the probability of drawing a black marble followed by another black marble?
b) What is the probability of drawing a red marble and then a yellow marble?
c) What is the probability of drawing two marbles of the same color?
2) How many different ways can the letters of the word “probabilities” be arranged?
3) A card is randomly selected from an ordinary deck of cards.
a) Find the probability that it is a picture card or a red card.
b) Find the probability that it is not a red, even numbered card.
4) If the probability that it will be cloudy during the graduation ceremony is 79% and that it will
rain during the graduation ceremony is 62%, what is the probability that it will not rain during
the ceremony?
For Questions 5-8, refer to the table below representing the population of a college dormitory
housing 300 students from which a student representative must be selected to serve on the
President’s Advisory Council.
Freshman
Sophomore
Junior
Senior
Male
4
8
50
100
Female
7
11
60
60
5. If a student is selected at random, what is the probability that the student will be a female
given that the student selected is a senior?
a. 60/160
b. 60/300
c. 60/138
d. 160/300
6. If a student is selected at random, what is the probability that the individual is not a female?
a. 60/300
b. 138/300
c. 162/300
d. 138/162
7. If a student is selected at random, what is the probability that the student is a male who is a
sophomore?
a. 8/162
b. 8/300
c. 154/300
d. 8/19
8. If a student is selected at random, what is the probability that the student will be a junior
given that the student selected is a female?
a. 60/110
9.
b. 60/300
c. 50/60
d. 60/138
The student council advisor needs to appoint four council members to be officers, one
president and one vice-president, one secretary and one treasurer. The student council
consists of twelve members. How many possible ways are there for the advisor to fill the
offices?
10. Let R = {1, 2, 5, 7, 9, 10} and S = {2, 6, 7, 9}
A) Find R U S
B) Find R ∩ S

C) If T = {Multiples of 3}, find T ∩ 𝑆
D) If W = {prime numbers less than 20}, find R ∩ W
E) If P = {Multiples of 5}, find P ∩ 𝑆
11. For the diagram shown, find the probability that a dart that hits the target will land in the
shaded region.
12. Renee is going on vacation and has to pack her suitcase. She can fit 2 shorts, 3 shirts and 2
shoes. Her shorts are khaki, and white. Her shirts are 2 solid colors and one striped shirt. Her
shoes are sneakers and sandals.
a) List the sample space of all possible outfits using a tree diagram. Be certain to label
your diagram clearly.
b) Using your diagram, find the probability that she either wears a solid shirt or sneakers.
c) What is the probability that she picks an outfit with the striped shirt or white shorts?
d) What is the probability that she picks an outfit with the striped shirt and the white shorts?
e) What is the probability that she wears the khaki shorts, a solid shirt and the sandals?