Semester 2 Review 2015-2016 Name ______________________________________________________

Algebra 2/Trig Honors Date _____________________ Hour ___________

Chapter 5

Analyze and graph each function. Show algebraically how you found each of the following: domain, x

intercepts, y intercept, holes, vertical asymptotes, and horizontal/oblique asymptotes. Also, split the

domain into intervals (use the x values when the numerator or denominator equal zero to define the

intervals), and test a point within each interval to determine whether the function is positive or negative.

1.) a.)

3

2

3

2 1

x

x x b.)

2

2

4

2

x

x x

Chapter 7

2.) Convert each angle to radians: a.) 135° b.) 15°

3.) Convert each angle to degrees: a.) 2p

3 b.)

-3p

2

4.) Find the exact value of each expression (do not use a calculator):

a.) tanp

4- sin

p

6 b.) cos

p

3+ sin

p

2

c.) 3sin45° - 4 tanp

6

5.) Find the exact value of each of the 5 remaining trig functions:

a.) sinq =4

5, q is acute b.) tanq =

1

4, q is acute

6.) Graph one period of each function. Show the 5 key points of one complete cycle.

a.) y = 2sin4(q)

b.) y = -3cos2(q)

c.) y = -2cos q +p

2

æ

èçö

ø÷

d.) y = 3sin q -p( )

7.) Determine the amplitude and period of each function without graphing:

a.) y = 4cosq b.) sin 2y

c.) 8sin2

y x

d.) 2cos 3y x

e.) 1

2cos3

y

8.) Write the equation of the following graph: ___________________________

9.) Write the equation of the following graph: ___________________________

10.) Find the value of each of the six trigonometric functions of the angle q in the illustration.

11.) Use a calculator to approximate sec10° . Round to two decimal places.

12.) Find the reference angle of -4p

5.

13.) Find the length of segment AC:

B C

A

50 ft.

13

12

Chapter 8

14.) Find the exact value of each expression:

a.) 1sin 1 b.) 1cos 0 c.) 1tan 1

d.) 1 1sin

2

e.) 1 3cos

2

f.) 1tan 3

g.) 1sec 2 h.) 1cot 1

15.) Find the exact value:

a.) 1 3sin sin

8

b.) 1 3cos cos

4

c.) 1 2tan tan

3

d.) 1sin sin8

e.) 1 15cos cos

7

f.) 1 8sin sin

9

g.) 1cos cos 0.3 h.) 1tan tan 5

i.) 1cos cos ( 1.6) j.) 1sin sin (1.6)

16.) Prove each identity:

a.) 2 2tan cot sin cos b.) 2 2sin csc sin cos

c.) 2 2sin (1 cot ) 1 d.) 2 2(1 sin )(1 tan ) 1

e.) 2 2 25cos 3sin 3 2cos f.) 2 2 24sin 2cos 4 2cos

17.) Find the exact value of each expression (no decimal answer):

a.) sin165 b.) tan105

18.) Given: 4

sin5

; 02

AND

5sin

13 ;

2

Find the exact value of:

a.) sin( ) b.) cos( )

c.) sin( ) d.) sin(2 )

e.) cos(2 ) f.) sin2

g.) cos2

19.) Solve each equation on the interval 0 2 .

a.) 1

cos2

b.) 3

sin2

c.) 2cos 2 0 d.) sin(2 ) 1 0

e.) cos(2 ) 0 f.) tan(2 ) 0

g.) sin(3 ) 1

Chapter 6

20.) Given ( ) 3 5f x x and 2( ) 1 2g x x

a.) Find b.) Find

c.) Find

21.) Given ( ) 2f x x and ( ) 3 1g x x , find each:

( )( )f g x ( )( )g f x

( )( )f f x ( )( )g g x

22.) Find the inverse of each function:

a.) ( ) 9 3f x x b.) 1

( )1

f xx

23.) Given: ( ) 3xf x and 3( ) logg x x Find each of the following:

a.) (4)f b.) (9)g

c.) ( 2)f d.) 1

27g

24.) Evaluate without a calculator:

a.) log2

1

8

æ

èçö

ø÷ b.) log3 81 c.) lne 2

25.) Write as a sum or difference of logarithms:

log3

uv2

w

æ

èçö

ø÷

26.) Write as a single logarithm:

-2log3

1

x

æ

èçö

ø÷+

1

3log3 x

27.) Solve each equation. Round any decimals to the nearest hundredth.

a.) 86+3x = 4 b.) logx 64 = -3

c.) 5x = 3x+2 d.) 92x = 273x-4

e.) log6(x + 3)+ log6(x + 4) =1 f.) log(7x -12) = 2log x

g.) 1 2 4xe

28.) A child’s grandparents wish to purchase a bond to be used for her college education. The bond pays

4% interest compounded semiannually.

a.) How long will it take the bond to double in value under these terms?

b.) If the bond matures in 18 years, how much should they pay now so that the bond will be worth

$85,000 at maturity?

30.) The bones of a prehistoric man found in the desert of New Mexico contain approximately 22% of the

original amount of carbon 14. If the half-life of carbon 14 is 5600 years, approximately how long ago

did the man die?

Statistics

31.) For each scenario, identify whether the correlation also implies causation. Explain.

a.) A recent study found that dog ownership is positively correlated with overall health.

b.) The number of days this winter with a temperature below 32°F is positively correlated with

the percentage of Lake Mendota that was frozen.

32.) The number of nails of a given length is normally distributed with a mean length of 5.00 inches and

a standard deviation of 0.03 inches.

a.) Find the number of nails in a bag of 120 that are less than 4.94 inches long.

b.) Find the number of nails in a bag of 120 that are between 4.97 and 5.03 inches long.

c.) Find the number of nails in a bag of 120 that are more than 5.09 inches long.