Name: __________________________
Date: _____________
ALGEBRA 2 – SEMESTER FINAL 2 – Q4
I. Multiple Choice
1. What is the inverse of y  2 x
a) y  log 2 x
2. Solve for x:
4
a)
3
1
c) y   
2
b) y  log x 2
x
d) y  x 2
3x  4 .
b) log3 4
d) log  43 
c) log 4 3
3. Which is the solution to the equation log 6 x  5 ?
(A) 7776
(B) 30
(C) 15,625
(D) 1
4. The product of a 2x3 matrix and a 3x2 matrix is
a 3x3 matrix
b 2x2 matrix
c 2x3 matrix
(E) 11
d. Can not be done
Solve the matrix equation:
5.
6. The identity matrix for a 2x2 matrix is:
0 1 
A. 

1 0 
1 1
B. 

1 1
7. Evaluate the determinant:
1 0 
C. 

0 1 
3
7
4
9
=
(A) 23
1 1 
D. 

0 0
(B) -1
Find the product:
8.
[12]
(C) 1
(D) 55
3 x  8 y  13
9. Which of the following could be used to find x in this system? 
5 x  3 y  11
3
A.
3
8
5 3
13 8
11 3
B.
8
3 13
5 3
3 13
5 11
C.
13
5 11
3 8
5 3
D.
8
11 3
3 8
5 3
10. If the probability of rain tomorrow is 65%, what is the probability that it will not rain tomorrow?
a. 0.65
c. 0.45
b. 0.55
d. 0.35
a)
11. What is the probability of getting a sum of 7 on rolling a pair of dice?
b)
c)
d)
12. What is the probability of randomly selecting either a club or a non-face card from a standard
deck of cards?
a)
b)
c)
d)
II. Free Response SHOW ALL WORK!
1. Multiply the following matrices together.
 4 2   2 3 1
0 1  2 1 0 



2. Solve the exponential equation: 3 x1  5 .
3. Determine the inverse matrix of:
6 5
 4 3


Hint:
4. Use Cramer’s rule to solve the following system of equations for x, y, and z.
4x + 2y + z = 7
x – y + 6z = -1
2x + 3y – 5z = 5
5. The population of a bacterial culture doubles every 6 hours. If the present population is 4000
bacteria, how long will it take for the population to reach 75 000. (round answer to nearest
hour) y= a b^x / P = Po * e^rt
6. Which one of the equations below would correctly model the number of zombies turned each
day if you start with 5 zombies?
a. Explain in detail the model of your choice.
b. What does the unknown variable, x, represent in the equation you chose from #6? Explain
c. According to your experience in the project, if you were given the choice of between more initial
zombies, but a slower growth rate or fewer initial zombies, but a greater growth rate, which
would you pick and why?
7. You have four $1 bills, five $5 bills, and three $10 bills in your wallet. You select a bill at
random. Without replacing the bill, you choose a second bill at random. Find P($5 then $1).
8. The probability that Jacqueline will be elected to the students’ council is 0.6, and the probability
that she will be selected to represent her school in a public-speaking contest is 0.75. The
probability of Jacqueline achieving both of these goals is 0.5.
a. Are these two goals mutually exclusive?
b. What is the probability that Jacqueline is either elected to the students’ council or picked for
the public-speaking contest?
9. Thomas, Jenna, and Maria are playing a game. They have a bag that contains 48 white tiles and 2
red tiles. Each player takes turns picking a tile at random and does not return the tiles to the bag.
The player who draws a red tile first is the winner. In the first round, Thomas goes first, then
Jenna, and then Maria, and none of them draws a red tile. What is the probability that Thomas
will win the game on his second turn?
10. Refer to the spinner below.
Find P(even and shaded).
Find the odds of the spinner landing on a number divisible by 2.
Extra Credit:
Len just wrote a multiple-choice test with 15 questions, each having four choices. Len is sure that he got
exactly 9 of the first 12 questions correct, but he guessed randomly on the last 3 questions. What is the
probability that he will get at least 80% on the test?
3.
You have the numbers 1–36 written on slips of paper. If you choose one slip at random, what is
the probability that you will not select a number which is divisible by 4?
4.
Suppose you choose a marble from a bag containing 3 red marbles, 2 white marbles, and
4 blue marbles. You return the first marble to the bag and then choose again. Find P(red and white).
10.
You roll a standard number cube. Find P(number greater than 2)
11.
In a word game, you choose a tile from a bag, replace it, and then choose another. If there are 28
vowels and 16 consonants, what is the probability you will choose a consonant and then a vowel?
15.
You toss a coin and roll a number cube. Find P(heads and 3).
21. A cell phone company orders 1200 new phones from a manufacturer. If the probability of a phone being
defective is 1.5%, predict how many phones are likely to be defective.
The probability that Jacqueline will be elected to the students’ council is 0.6, and the probability that she
will be selected to represent her school in a public-speaking contest is 0.75. The probability of
Jacqueline achieving both of these goals is 0.5.
a) Are these two goals mutually exclusive? Explain your answer.
b) What is the probability that Jacqueline is either elected to the students’ council or picked for the
public-speaking contest?
ANS:
a) The two goals cannot be mutually exclusive since the probability of achieving both is 0.5.
b) 0.85
Len just wrote a multiple-choice test with 15 questions, each having four choices. Len is sure that he got exactly 9 of the first
12 questions correct, but he guessed randomly on the last 3 questions. What is the probability that he will get at least 80% on
the test?
ANS:
A score of 80% requires getting 12 out of the 15 questions right. If Len answered 9 out of the first 12 questions correctly, he
can score 80% only if he guessed all 3 of the remaining questions correctly.
Therefore Len has only about a 1.6% chance of getting 80% on the test.