Download Algebra II Honors Final Exam Review Name: Period: ______ Date

Algebra II Honors
Final Exam Review
Name: __________________________________________ Period: __________ Date: __________________
To prepare for the final exam review all notes, quizzes, and tests in chapter 7 & 8 and pre-calc chapters 4 & 5.
Chapter 7
Solve the equation. Check for extraneous solutions.
1.) 2 x 1  16 x  2
2.) e  x  4
3.) 3 2 x  5  13
6.) log 3 (2 x  5)  2
5.) 5 x  32
9.) 3 log( x  4)  6
7.) ln x  ln( x  2)  3
10.) log 4 x  log 4 ( x  6)  2
Graph the function. State the domain and range.
12.) y  3 x
13.) y  2  4 x2
1
16.) y  2 
 3
x2
Use change-of-base to evaluate the logarithm.
22.) log 5 50
23.) log 6 23
8.) 7 2 x  30
11.) log 3 (5 x  3)  5
14.) f ( x)  5  2 x 3  3
15.) y  40.25
x
x
2
17.) g ( x)     2
3
Evaluate the logarithm without using a calculator.
1
19.) log 5 25
20.) log 2
32
4.) 3 x 1  5  10
18.) y  log 2 x
21.) log 6 1
24.) log 9 45
25.) From 1996 to 2001, the number of households that purchased lawn and garden products at home gardening
centers increased by about 4.85% per year. In 1996, about 62 million households purchased lawn and garden
products. Write a function giving the number of households H (in millions) that purchased lawn and garden
products t years after 1996.
26.) You deposit $2,500 in an account that pays 3.5% annual interest compounded continuously. What is the
balance after 8 years?
27.) The model y  7.7e 0.14 x gives the number y (in thousands per cubic centimeter) of bacteria in a liquid
culture after x hours. After how many hours will there by 50,000 bacteria per cubic centimeters? Round your
answer to the nearest tenth of an hour.
Chapter 8
1.) The number n of photos your digital camera can store varies inversely with the average size s (in
megapixels)of the photos. Your digital camera can store 54 photos when the average photo size is 1.92
megapixels. Write a model that gives n as a function of s. How many photos can your camera store when the
average photo size is 3.87 megapixels?
Simplify the complex fraction.
x
6
3
2.)
4
10 
x
15 
3.)
2
x
16
x2
4.)
4
6

x 1 x
x
4
5
Perform the indicated operation and simplify.
x 2  3x  4 x  6
3x 2 y
6y2
5.)
6.)


4 x 3 y 5 2 xy3
x 2  3x  18 x  1
x 2  11x  28 2
8.)
 x  16
x 2  5x  4

11.)
3x
6

x  x  12 x  4
2

9.)
3x
4x  1

x5 x5
12.)
7.)
x 2  8 x  15
x4
 2
2
x  12 x  32 x  25
10.)
4
2

x3 x6
15.)
x2 x2

x 1 x  4
4
2x
 2
x  5 x  25
Solve the equation. Check for extraneous solutions.
3
x3
1
x 1
13



13.)
14.)
x  2 2x  4
x6
x
x6
Pre-Calculus Chapter 4
Convert the angle measure from degrees to radians (# 1 &2) or radians to degrees (# 3 & 4).
3
 7
1.) 115 
2.) 642 
3.)
4.)
2
12
Evaluate (if possible) the sine, cosine, and tangent of the real number.
7
11
5
5.) t  
6.) t 
7.) t 
4
6
3
Solve for the variable.
8.)
9.)
10.) A 30-meter line is used to tether a helium filled balloon. Because of a breeze, the line makes an angle of
approximately 75 with the ground. (a) Draw a right triangle to represent the problem. Shown the known
quantities on the triangle and use a variable to indicate the unknown height of the balloon. (b) Use a
trigonometric function to write an equation involving the unknown. (c) What is the height of the balloon?
11.) You are standing 75 meters from the base of the Jin Mao Building in Shanghai, China. You estimate that
the angle of elevation to the top of the building is 80  . What is the approximate height of the building? Suppose
one of your friends is at the top of the building. What is the distance between you and your friends?
Evaluate the expression.
12.) arccos
1
2
13.) arccos 0
Sketch the graphs. Include two full periods.
16.) f ( x)  2 sin x
17.) g ( x)  4 sin x
20.) y  3 cos6 x   
21.) y 
1
sin  x   
2

2

14.) arcsin  

2


15.) arctan


18.) y  sin  x  
4

19.) f ( x)  4  cos x
22.) y  8 cosx   


23.) y  6 cos x  
6

3
3
Pre-Calculus Chapter 5
Verify the identity.
1.) sin t csc t  1
2.) tan y cot y  1
csc 2 x
3.)
 csc x sec x
cot x
4.) cot 2 y(sec 2 y  1)  1
5.) cos 2   sin 2   1  2 sin 2 
6.) tan 2   6  sec 2   5
7.) 2  csc 2 z  1  cot 2 z
8.) cos x  sin x tan x  sec x
9.)
Solve the equation for 0  x  2 .
10.) 2 cos x  1  0
11.) 2 sin x  1  0
12.)
cot 3 x
 cos x(csc 2 x  1)
csc x
3 sec x  2  0
13.) cot x  1  0
Find the exact value of the trigonometric function given that sin u  5 13 , where 0  u   2 and
cos v   3 5 , where  2  v   .
14.) sin( u  v)
15.) cos(v  u )
16.) cos(u  v)
17.) sin( u  v)
Find the exact value of the trigonometric function given that sin u  7 25 , where  2  u   and
cos v  4 5 , where 3 2  v  2 .
18.) cos(u  v)
19.) sin( u  v)
20.) sin( v  u )
21.) cos(u  v)
Find all solutions of the equation in the interval [0,2 ).



 1




22.) sin  x    sin  x    1
23.) sin  x    sin  x   
3
3
6
6 2








24.) cos x    cos x    1
4
4






25.) cos x    cos x    1
6
6


Find the exact values of sin 2u , cos 2u , and tan 2u using the double-angle formulas.
3

2 
1
3
26.) sin u  ,0  u 
27.) cos u   ,  u  
28.) tan u  ,   u 
5
2
7 2
2
2