Algebra II - Final Exam Review Part 1

Algebra II - Final Exam Review Part 1

Chapters 8 and 10

(most recent material)

Before each set of problems, you will see a short video.

Please watch and take notes to study from.

Multiple Choice

 What are the vertical and horizontal asymptotes of the rational function shown?

 $f\left(x\right)=-\frac{2}{x}-1$  

• VA: x = -2; HA: y = -1

• VA: x = -2; HA: y = 1

• VA: x = -1; HA: y = 0

• VA: x = 0; HA: y = -1

Multiple Choice

What is the domain and range of the rational function shown?

 $g\left(x\right)=\frac{3}{x-1}$  

• Domain: All reals except -3; Range: All reals except 0

• Domain and Range are all real numbers

• Domain: All reals except 1; Range: All reals except 0

• Domain: All reals except 0; Range: All reals except 1

Multiple Select

Which points (x, y) are on the graph of this rational function? (Select all that apply)
 $y=\frac{2}{x+2}-3$   

• (-2, 0)

• (-4, -4)

• (0, -2)

• (-3, -5)

• (2, 2)

Multiple Choice

What error was made in graphing this rational function?

• They did not make an error.

• Their vertical asymptote is incorrect.

• Their horizontal asymptote is incorrect.

• They plotted the branches in the incorrect sides of the each asymptote.

Multiple Choice

Simplify the expression:   $\frac{m^2-6m-27}{m-9}\cdot\frac{1}{3m^2}$  

•  $\frac{m+3}{3m^2}$  

•  $\frac{m+7}{m-5}$  

•  $8m$  

•  $\frac{m-6}{10\left(m-3\right)}$  

Multiple Choice

What is the GCF of the first denominator?
 $\frac{4m}{12m^2-40m}\div\frac{5}{27m-90}$  

• 3

• 4

• 4m

• 3m

Multiple Select

How do you divide rational expressions?  (Select all correct responses)

Example: $\frac{a}{b}\div\frac{c}{d}$  

• Keep-Change-Flip

• Multiply the first by the reciprocal of the 2nd fraction

• Multiply straight across

• Make a common denominator

Multiple Choice

Simplify the expression:   $\frac{1}{n+4}\div\frac{n-2}{n^2+6n-16}$  

•  $\frac{n+9}{n-9}$  

•  $\frac{\left(n-10\right)\left(n+4\right)}{7n^2}$  

•  $\frac{n+8}{n+4}$  

•  $\frac{7n}{4\left(n-4\right)}$  

Multiple Choice

Read carefully: What was the technique that Mrs. Karcher taught you to add fractions without a common denominator?

• Cross multiplication

• Keep-Change-Flip

• Cross-over, Cross-over, All-Under

Multiple Choice

Simplify this expression:   $\frac{6n}{n+5}-\frac{6}{2n-1}$  

•  $\frac{6n-5}{6}$  

•  $\frac{6n^2-5n-1}{6\left(n+5\right)}$  

•  $\frac{12n^2-12n-30}{\left(2n-1\right)\left(n+5\right)}$  

•  $\frac{36n+6}{\left(2n-1\right)\left(n+5\right)}$  

Chapter 10 Review

Counting Principle, Permutations & Combinations, and Probability

Multiple Choice

Find the number of possible outcomes in the sample space:

A jewelry store sells gold and platinum rings. Each ring is available in nine styles and is fitted with one of nine gemstones.

• 86

• 162

• 233

• 235

Multiple Choice

Find the number of possible outcomes in the sample space:

You flip a coin and roll a six-sided die.

• 11

• 10

• 1

• 12

Multiple Choice

State if this scenario is a permutation or a combination:

A team of 17 soccer players needs to choose a captain and co-captain.

• Permutation

• Combination

Multiple Choice

State if this scenario involves a permutation or a combination:

Selecting which 7 players will be in a batting order on a 9 person team.

• Permutation

• Combination

Multiple Choice

State if each scenario involves a permutation or a combination. Then find the number of possibilities.

The student body of 195 students wants to

elect a president and vice president.

• Permutation; 37,830

• Combination; 47,305

• Permutation; 48,800

• Combination; 32,120

Multiple Choice

State if each scenario involves a permutation or a combination. Then find the number of possibilities.

A group of 20 people are going to run a

race. The top 10 finishers advance to the

finals.

• Permutation; 0

• Combination; 369,512

• Combination; 121,063

• Combination; 184,756

Multiple Choice

Are these events independent or dependent events?

You flip a coin four times and then roll a

fair six-sided die five times.

• Independent

• Dependent

Multiple Choice

Are these events independent or dependent?

A bag contains four red marbles, five blue

marbles, and three yellow marbles. You

randomly pick three marbles without

replacement.

• Independent

• Dependent

Multiple Choice

Determine whether the scenario involves independent or dependent events. Then find the probability.

A cooler contains ten bottles of sports

drink: five lemon-lime flavored and five

orange flavored. You randomly grab a

bottle and give it to your friend. Then,

you randomly grab a bottle for yourself.

Your friend gets a lemon-lime and you get

an orange.

• Independent; $\frac{1}{8}=0.125$

• Independent; $\frac{1}{36}\approx0.028$

• Dependent; $\frac{35}{132}\approx0.265$

• Dependent; $\frac{5}{18}\approx0.278$

Multiple Choice

Determine whether the scenario involves independent or dependent events. Then find the probability.

You select a card from a standard shuffled deck of 52 cards. You return the card, shuffle, and then select another card. Both times the card is a diamond. (Note that 13 of the 52 cards are diamonds.)

• Independent;  $\frac{2}{9}\approx0.222$ 

• Independent;  $\frac{1}{16}\approx0.063$ 

• Dependent;  $\frac{1}{20}=0.05$ 

• Independent;  $\frac{1}{9}\approx0.111$ 

Here's a little more probability...

Let's see what you got!

Multiple Choice

Find the probability.

A litter of kittens consists of two gray

kittens, two black kittens, and three

mixed-color kittens. You randomly pick

one kitten. The kitten is gray or

mixed-color.

• $\frac{5}{7}$

• $\frac{6}{11}$

• $\frac{13}{14}$

• $\frac{7}{10}$

Multiple Choice

Find the probability.

A bag contains five yellow jerseys

numbered one to five. The bag also

contains four purple jerseys numbered one

to four. You randomly pick a jersey. It is

yellow or has a number less than two.

• $\frac{8}{11}$

• $\frac{5}{7}$

• $\frac{2}{3}$

• $\frac{9}{11}$

Multiple Choice

Find the probability.

A politician is about to give a campaign

speech and is holding a stack of seven cue

cards, of which the first 3 are the most

important. Just before the speech, she

drops all of the cards and picks them up in

a random order. What is the probability

that cards #1, #2, and #3 are still in order

on the top of the stack?

• $\frac{1}{210}$

• $\frac{1}{20}$

• $\frac{1}{330}$

• $\frac{1}{1287}$