Algebra 2 Trig Honors

SEMESTER 2 REVIEW PACKET Name ______________________________

Trigonometry: 6.1, 6.3, 6.4, 6.5, 7.5

Problems #1 – 12: Calculator OK

1. State the exact measure of the reference angle (in degrees) to the given angle in standard position.

a. 671 b. 1123

2. State the exact measure of the reference angle (in radians) to the given angle in standard position.

a. 5

7

π b. 3

3. State a coterminal angle to 671 in the interval 0 ,360 :

4. Convert 5

7

π to degrees. 5. Convert 671 to radians.

6. Given the terminal point, find a rotation angle in the interval 0 ,360 . Round the angle to the nearest degree.

a. 4 3

,5 5

b. 5,0

7. Given the rotation angle and the radius (r) of the circle, determine the terminal point. Round your

answer to the nearest hundredth.

a. 7 325r θ b. 9

28

πr θ

8. Find x to the nearest hundredth.

a. cot 3x b. sec54 x

9. Solve the given triangles (find all the missing sides and angles):

10. Suppose β is an angle in standard position whose terminal side is in the given quadrant. For each

function, find the exact values of the required trig ratios.

a. 8

cos cot 0, csc17

β and β find β b. 4

tan cos 0, csc3

β and β find β

11. Lucy and Charlie are riding on a Ferris wheel. Lucy decides to start timing their rotation. They hit the

first high point of 80 feet 8 minutes after she starts timing and it takes 12 minutes to complete a revolution.

She later finds out that the lowest point of the wheel is 5 feet off the ground and decides to write a function of

how high she was off the ground in relation to time in minutes.

a. Write the equation of the function.

b. Graph the function:

c. At what time(s) do they hit 35 feet off the ground in one revolution.

5.6

A

C B

8.3

A

C B

8.3

12. Mary Jane noticed Spiderman on top of a building. The angle of elevation she has with Spiderman is 53 .

Spiderman climbs to a lower location on the building and Mary Jane’s new angle of elevation is 41 . If Mary

Jane is 60 feet from the base of the building, how far did Spiderman move down the building from the first

sighting to the second sighting?

Problems #13 – 16: No Calculator

13. Graph two periods of each function. Please label your axes clearly, and be sure to plot a point every

quarter of a period. When given x use radians, θ use degrees.

a. 3 cos4

πy πx

b. tan 2y πx

c. 1 4sin 0.5 90y θ

14. Find the exact value of the following:

a. 5

cos3

π

b. 6csc 240

c. 2 2sin 135 cos 135 d. tan 390

e. 3

sec2

π f.

11cot

4

π

15. Write the equation of all the asymptotes over the entire domain of secy θ .

16. Solve each equation in the indicated domain. Given x use radians, and given θ use degrees.

a. 24cos 3 0 2 ,0x π b. 22sin 2 5sin 0 ,360θ θ

x

y

c. 2sec 1 #x all real s d. 2cos cos #θ θ all real s

Chapter 5 – Logs R2, 5.1 – 5.5

Simplify the following: (no calculator)

1. 22 9x y xy 2.

12 3 3

4 3

64

27

x y

x y

3. 3 35 16 81

4. 2

364 5. 6

5 2 6.

4 84 16x n

7. 4log 16 8. 64log 4 9. 2log 5

8

10. Graph and then state the domain and range: 2log 1x

(no calculator)

Expand each of the logarithms using your log properties: (no calculator)

11. log3

x 12.

2

2 3log

x y

z

Use the properties of logarithms to write as a single log. (no calculator)

13. log 2 5 logx x 14. 1

7log log2

x y

Solve the following equations. (calculator okay)

15. 10 3.91x 16. 4log 5 3x 17. 3 3log 5 log 3 2x x

18. log5 log( 2) log11 log( 3) x x 19. 5 5 5 5

1 1 2log 27 log 49 log 32 log

3 2 5 x

21. Solve for x: 2 5 13 5 x x

20. log(2 3) 1 log( 2) x x

22. 9e2x – 7 = 47

23. ln x + ln 9 = 2 24. Solve for x: ln 1 ln 1x x (exact answer)

(round to the nearest tenth)

Simplify:

25. 272

3

26. ( ) ( )2 33 5 3 2x x y 27. 15

5

2 3 5

2

x y z

y z

( )

28. 9 53 54x y 29. 3 320 40 5 30. 6

2 5

31. Jenna is a freshman in college and working with a substance that has a

half-life of 12 years. She drops 60mg into a petri dish. How much is left

when she retrieves it exactly 3 years later for an experiment her senior year?

32. The value of Kris’s Jeep is depreciating at a rate of 13% per year.

He bought the Jeep used in 2004 and estimates that it is now (2014) worth

$9,624.00. How much did the motorcycle cost when he bought it?

33. At age 18, you inherit $15,000 from your grandma and decide to place the

money into a CD account earning 1.2% annual interest compounded monthly.

a. How much money is in the bank account after 6 years when you graduate

from college with your Master’s degrees and have to start paying off your student loans?

b. How long will you have to keep your money in the CD to earn $30,000?

34. If you put $8800 into a bank account compounding continuously at an annual

interest rate of 1.23%, how long would it take for your money to appreciate to

$12,900?

Probability – Not in the Book

All problems – Calc okay. Assume no replacement, unless told otherwise.

1. Find the probability that if a dart is thrown inside the square that it lands on the unshaded area.

2. a) If the spinner is spun one time, what is the probability of spining a...

b) Create a probability distribution for the possible spinner outcomes.

3. One card is chosen from a standard deck of cards. Find the probability of each situation occurring.

a. P(black or Jack) b. P(the 4 of hearts)

c. P(spade or Queen) d. P(at most a 9 of any suit with Ace low)

Outcome Probability

1 2 3

Total

4. Two cards are chosen from the standard deck of cards. Find the probability of...

a. P(club, then diamond), replacement b. P(heart, then heart)

c. P(2, then Queen) d. P(club and diamond)

5. You throw a pair of dice – one red, the other black

a. P(the sum is at least four) b. P(the sum is between three and ten, inclusive)

c. (the red die is a five or the black die is a two)

6. There are 2 red pens and 6 black pens on the desk. If 4 are selected at random, what is the probability...

a. you have exactly 1 red pen b. all of the pens are black

7. An ordinary deck of playing cards is used to play a game in which you are dealt a 4 card hand. Find the

probability that:

a. you have exactly two red cards and two

black cards

b. you have the ace of hearts

c. you have all spades

`

d. you have at least one spade

8. The table below holds information about students’ weather preferences.

Likes the cold No preference Does not like the cold Girls 45 70 50

Boys 60 30 35

A student is chosen at random. Find each probability. a. P(boy) b. P(someone who does not like cold) c. P(were a boy who did not like the cold) d. P(likes the cold, given that it’s a boy) e. P(a person with no preference, is a girl) f. P(were a girl who had no preference.)

9. Make a tree diagram based on the survey results to help you answer questions about probability.

Of all the respondents, 17% are male.

Of all the male respondents, 33% are left handed.

Of all the female respondents, 90% are right handed.

a. Find P(a female respondent is left handed).

b. Find P(a respondent is both male and right handed).

c. Find the probability that given you are right-handed, you are female?

Sequences and Series 11.1, 11.3

1. Write a general term (an) for the sequence:

a. 4 5 6, , ...

5 6 7 b. 4, 20,100, 500,...

2. Write each series using summation notation with the summing index k starting at k = 1.

a. 27 64 125 216 b. 2 3 4 5 6

1 1 1 1 1

3 3 3 3 3

3. Given the following sequences, write both the EXPLICIT and RECURSIVE formulas.

a. 10, 6, 2,2,6,.... b. 52, 13, 3.25, 0.8125,...

4. Find the 47th term in an arithmetic sequence with 1 5a and d = -3.

5. Find the 9th term in a geometric sequence with 2 6a and r = 2.

6. Find the 13th term of:

a) a geometric sequence with: 3 80a and 6 5,120a

b) an arithmetic sequence with: 6 33a and 12 81a

7. First determine if the series is arithmetic or geometric, or neither. Then, find the indicated sum.

a. 7

1

16

3

k

k

b. 4

1

1

1 (5 2)k

k

k

c.

23

k 1

6 2k d.

k 1

k 1

1

4

8. Find: 32

3

4 3( 1)k

k

9. Determine the summation of the following series: 18 + 12 + 6 + 0+ . . . + -30

10. In a geometric series with r = 7 and a2 = 28, which term (n) would have the value an = 3,294,172?

11. In a stadium the number of seats in each row often reduces as you go from the bottom to the top. For

example, in one section of a stadium the first row has 100 seats, the second row has 97 seats, the third row has

94 seats and so on following this pattern. How many rows are in this section of the stadium and how many

seats are in the last row?

12. Susie has been studying really hard in Spanish this semester and she has noticed a trend in her test grades.

Each test she takes is 1.4% better than the previous test. She got a 72% on the first test of the semester and

there are 8 total tests.

a. Write an explicit formula describing Susie’s percentage on the nth test.

b. What percent did she earn on the 8th test?

13. A bouncy ball is dropped from the top of Hinsdale Central, 30 feet above the ground. It hits the ground and

bounces 80% of its original height on each subsequent bounce.

a. What is the total distance that the ball travels when it hits the ground for the 4th time?

b. What is the total distance that the ball travels before it stops?