Algebra 2 Final Study Guide 2016/2017

ALGEBRA 2 FINAL EXAM STUDY GUIDE

Unit: Polynomials

1. (2x4 – 7x3 + 4x – 7) + (2x2 – 4x + 8)

2. (-4x3 + 7x – 6) – (7x4 + 3x3 – 2x – 4)

3. (3x3 + 2x + 7)(x2 – 4)

4. x4 − 4x3 − 3x2 + 14x − 8 ÷ (x − 3) (Long AND synthetic division)

Write answer as quotient + remainder/divisor

5. Simplify this expression to find an equivalent polynomial in standard form:

(3m+9p)2

6. Consider the polynomial g(x) = x3 + 5x2 – 9x + 1. For how many values of a will g(a) = 0?

7. At what values of x does

f(x)= x4 +5x2 – 36 cross the x axis?

8. f(x)= x3 + 9x2 + 6x – 56

Is (x + 7) a factor of f(x)? Explain how you know. (Tip: there’s a quick way to check!)

Algebra 2 Final Study Guide 2016/2017

9. Write an equation for the graph: 10. Write an equation for the graph:

11. For each equation, list the letters of the graphs that have the same end behavior.

f(x) = −x5 + 2x − 1 _________________________ g(x) = x6 + 5x4 − 3x2 + 7 ______________________

Explain: Explain:

p(x) = −3x2 + 2x − 5 _______________________ h(x) = 2𝑥3 + 9x2 − 1 _______________________ Explain: Explain:

D

C

B

A

F

E

G

H

Algebra 2 Final Study Guide 2016/2017

Unit: Probability and Statistics

1. a. Find the mean, median, mode, and range of the following data: 21, 27, 20, 29, 23, 21, 21, 27, 26, 25 b. If the number 48 was added to the dataset, what would change the most – mean, median, mode, or range? (Re-calculate them all)

2. This data shows the daily mileage (miles ran) for two different cross country teams over 3 weeks (21 days).

a. Which team has a greater median mileage? Why?

b. Would either have a mean different from their median? Why?

c. Which team varied more in their daily mileage? Why?

Use the box plot to answer questions 3 – 6.

3.In which year were the gas prices the highest?

4.In which year were gas prices the lowest?

5. In which year were gas prices least stable? Explain.

6. Compare each of the following features for all three graphs:

a. Medians

b. Ranges

c. Interquartile Ranges

d. Upper quartiles

e. Lower quartiles

Algebra 2 Final Study Guide 2016/2017 7. These graphs show the heights of 20 year old men and women in the United States.

a. Which graph is symmetrical? Which graph is skewed? Which direction? b. Which one has a different mean from its median? Why? c. Estimate the median for each graph. Which is higher? d. Estimate the mean for each graph. Which is higher? e. What is the range for each graph? f. What is the mode for each graph? g. Which has a higher standard deviation?

58 60 62 64 66 68 70 72 74 76 78 80 82 84 Height (inches)

58 60 62 64 66 68 70 72 74 76 78 80 82 84 Height (inches)

Algebra 2 Final Study Guide 2016/2017

8. Use the obstacle course information provided to choose an appropriate histogram.

Team R Obstacle Course Times

5:32 6:48 4:25 8:05 7:23 5:37 5:12 6:26 5:31 4:43 6:08 7:16 5:52 5:21 6:53 4:49 5:02 6:33 5:54 6:20

9. A family has four children, ages 17, 19, 13 and 21. a. Calculate the median, mean, and range of ages for these kids. b. If the family adopts a 2 year old toddler, calculate the new median, mean, and range. c. Which value changed the most?

10. A group of friends took a test. Their scores are listed below:

a. Calculate the mean, median, and range of their scores. b. The student who earned a 54 retakes the test and earns a 71. Calculate the new mean, median, and range. c. Which values are changed? Which are not changed? Why?

97 61 92 88 80 54 78 75

Algebra 2 Final Study Guide 2016/2017

Use the information provided to answer questions 11-15. Give all probabilities in both fraction and percent form.

The two-way table shows the classification of students in a mathematics class by gender and dominant

hand. A student who is ambidextrous uses both hands equally well.

Right-handed Left-handed Ambidextrous

Male 11 4 1

Female 12 2 0

11. If a student is chosen at random from the class, what is the probability they are left handed? (in both

fraction and percent form)

12. What is the probability that a randomly selected student in the class is male or left-handed?

13. If a female student is chosen at random, what is the probability she is right-handed?

14. If a right-handed student is chosen, what are the chances they are male?

15. What is the probability that a randomly selected student in the class is ambidextrous?

16. a. If you roll a 6-sided die, what are the chances of rolling a 4?

b. What are the chances of rolling a 4 twice in a row? three times in a row? four times?

c. What are the chances of rolling a 4 and then a 6?

Unit: Trigonometry Final Exam Review (NC = no calculator)

1. Convert the following angles to degrees:

a. 𝟑𝝅

𝟓 b.

𝝅

18 c. −

25𝝅

12

2. Convert the following angles to radians:

a. 5100 b. 3450 c. −9300

3. If Sin 𝜃 = −5

11 and 𝜃 𝑖𝑠 𝑖𝑛 𝑞𝑢𝑎𝑑𝑟𝑎𝑛𝑡 𝐼𝐼𝐼, what is tan𝜃?

4. If tan 𝜃 = −7

8 and the sine of the angle is positive, find cos𝜃.

5. For each equation, determine amplitude, period, and midline:

a. f(x) = 7sin (2𝑥) b. f(x) = 2cos (𝜋𝑥) − 4 c. f(x) = 5cos (1

2𝑥)+3

6. If a tree casts a 72 foot shadow when the sun is at a 41o angle of elevation, what expression could be used to find

the height of a tree? (Hint: draw a diagram, then consider SOH CAH TOA)

Algebra 2 Final Study Guide 2016/2017

7. Write an equation for the function shown below by following these steps:

a. What is the amplitude?

b. What is the period?

c. What is the value of b? (Tip: use the period)

d. What is the midline?

e. Is it sine or cosine?

8. Write an equation for this graph: 9. Write an equation for this graph:

10. Find the coordinates of points A, B, C and D on the unit circle below

A

B

C[Type a quote

D

Algebra 2 Final Study Guide 2016/2017

Unit: Sequences and series

1. Find the missing term or terms of the following sequences: a) 14,___,54,____,74 b) 10,40,___,_____,130 c) 1,-3,____,_____,81

2. Find the 8th term of each of the following sequences:

a) 66,50,34,18,…… b) 1,4,9,16,……

UNIT : EXPONENTIAL and Logarithmic FUNCTIONS

1. Graph 𝑓(𝑥) = 2𝑥 and g(x)= log2 𝑥 on the same xy- plane. How are those functions related?

2. Which of the following functions would be exponential functions? Give a rationale for OR against for each

problem.

a) The total amount paid for gas over x number of weeks if Sara puts $25 of gas in her car each week.

b) The value of a computer after x years if it depreciates 12% each year.

c) The total cost of a wedding for x people if you pay $50/person.

d) The population of Jonesville after x years if the population decreases by 20 people each year.

3. Write an exponential model for the following situation: Hussein bought a house for $115,000. The value of

the house appreciates by 3% each year. Write a model for the value of the house after x years.

Algebra 2 Final Study Guide 2016/2017

4. Write an exponential model for the following situation: Laurie bought some office furniture. For tax

purposes, the value of the furniture depreciates by 13% each year. Write a model for the value of the

furniture after x years.

5. Joe took a job for $30,000 and gets an $800 raise each year. Nora took a job for $28,000 and gets a 3% raise

each year. If this is a career choice and they are planning on staying in this job for the long term, who took

the better deal? Explain.

6. The population of Berkeley can be modeled by the function P(t) = 115,000(1.013)t where t is the number of

years after 2015.

a) What is the population of Berkeley in 2015?

b) Is Berkeley getting bigger or smaller? Explain.

c) What is the rate of increase/decrease each year?

d) When will the population of Berkeley reach 121,000?

7. Convert between exponential and log

a) 3x = y

b) log x y = 2

c) log21

8= −3

d) log5 50 = 𝑘

8. Solve the equations for t using logarithm.

a) 3 = 9t

b) 100 = 50(1.2)t

c) 3500 = 700(1.05)t