Download Read and answer all questions accordingly

Algebra II Honors Spring 2009 Semester Review
1
Name ________________________________________ Date ________
Read and answer all questions accordingly. All work and problems must be
done on your own paper and work must be shown. No work = No Exemption
= NO EXCEPTIONS.
Chapter 8 - Polynomials
Solve each polynomial by any method of factoring. State all
multiplicity roots.
1.  x( x 2  6 x  5)  0
2. x 4  6 x 2  27  0
3. List ALL POSSIBLE rational zeros for f ( x)  2 x3  4 x 2  10 x  9 .
4. The volume of a rectangular solid is 675 cubic centimeters. The width is
4 centimeters less than the height, and the length is 6 centimeters more than
the height. V = lwh
Write in the alternative form.
1. 161/ 4  2
2. 160.5 
1
4
3. a b  x
1
1
4. log81  
3
4
Condense and Simplify.
5. log 4 128  log 4 8
Solve.
6. log 2 12.8  log 2 5
7.
4e x
e4 x
8. 3x 1  729 x /2 9. ln
x 1
 6 10. log 2.5 3.125  log 2.5 x  log 2.5 15.625
2
11. e7 x  6.9
12. log x  log( x  9)  1
13. ln e  2
5. Write the polynomial with the roots of 1, 4, and –5.
Tell whether the function shows growth or decay. Then graph.
6. f ( x)  0.4
x
6
7. f ( x)  1.2  
5
14. Use the formula A  Pe rt . If $5300 is deposited in an account at the
bank and earns 7% annual interest, compounded continuously, what is the
amount in the account, rounded to the nearest dollar, after 9 years?
x
Chapter 8 - Rational Expressions
1. If y varies directly as x, and y=15 when x=10, find y when x=14.
2. If y is directly proportional to the square of x, and y=12 when x=14, find
y when x=6.
3. If c is inversely proportional to d, and c=2 when d=3.6, find c when
d=4.5.
Chapter 5 - Logarithms
4. Suppose r varies jointly as t and n and inversely as the square of v.
When t=3, n=18, and v=5, then r=3.78. Find r when t=4, n=12, and v=4.
Algebra II Honors Spring 2009 Semester Review
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x2  x  6
5. Simplify f ( x)  2
. Identify any x-values for which the
x  4x  3
expression is undefined.
6. Sketch the graph of f ( x) 
x 1
and label all
x2
asymptotes.
of f ( x ) 
8. Label all asymptotes, f ( x) 
x2  1
.
x2
Multiply or divide. Assume that all expressions are defined.
3x  3
. Then graph.
x2
Solve each equation.
15. 2 
7. Label all asymptotes and holes of
x2
f ( x)  2
.
x 4
x 9
x 5
 2
9.
2 x  10 x  81
14. Identify the zeros and asymptotes
3
 10
x 1
16.
x
x
5
 
x 1 3 x 1
Chapter 9 – Compositions of Functions
If f(x) = x3 and g(x) = 2x2 + 7, solve the following:
1. f(x) – g(x)
2. g(x) • f(x)
3. f(g(x))
4. g(f(x))
Chapter 11-Conics
1. The transmission of a radio signal can be received at the locations (1, 10) and (–11, 6) . Write an equation for the range of the signal if a line
between the locations represents a diameter of the range.
3x3  9 x 2
2x  6
10.
 2
2
x  16
x  8 x  16
2. Find the center, vertices, co-vertices, and foci of the ellipse with
equation, 49( x  4)2  16( y  2) 2 =784 . Then graph.
Add or subtract. Identify any x-values which the expression is defined.
11.
5
x

x  5 2 x  10
12.
5x 9 x  6

x7 x3
13. Lorraine averaged 62 words per minute when typing the first 3
pages of a 6-page report. Her average typing speed for the last 3
pages was 45 words per minute. To the nearest word per minute,
what was Lorraine’s average typing speed for the entire report?
3. A shelter for a patch of young strawberry plants is constructed in the
form of an ellipse. If the shelter is 4.5 feet high at its highest point and the
patch is 19 feet wide, write an equation for the ellipse.
4. Find the center, vertices, co-vertices, foci, and asymptotes of the
x2 y 2

 1 . Then graph.
hyperbola with equation:
25 144
Algebra II Honors Spring 2009 Semester Review
5. Find the center, vertices, co-vertices, foci, and asymptotes of the
hyperbola with equation:
 x  2
4
2

 y  5
12
2
 1 . Then graph.
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Chapter 15 - Probability
1. A mall employee is dressing a mannequin. There are 6 pairs of shoes, 4
types of jeans, and 8 sweaters. Using 1 of each, how many ways can the
mannequin be dressed?
6. Write the equation of the hyperbola with vertices (0, 7) and (0, -7) and
conjugate axis length is 28.
2. How many ways can you award first, second, and third place to 8
contestants?
7. Find the vertex, value of p, axis of symmetry, focus, and directrix of the
3. How many ways can a group of 3 students be chosen from a class of 30?
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parabola with equation: y + 4 =
(x – 2)2. Then graph.
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4. The table shows the results of tossing 2 coins. Find the HH HT TH TT
experimental probability of tossing 2 tails.
8. Find the equation of the parabola with vertex at (-3,1), and focus (-1,1).
9. Find an equation of the ellipse with vertices at (-2,2) and (4,2), and covertices at (1,4) and (1,0).
Each letter of the alphabet is written on a card. The cards are placed into
a bag. Determine the indicated probability.
10. Write the equation of the circle in standard form. Identify the center
and radius. x 2  y 2  4 x  6 y  9  0
11. Find the equation of the hyperbola with vertices (2,2) and (2,8), and
foci (2,0) and (2,10).
12. Find the equation whose center is (1, –3), length of transverse axis is 7
units long on the x-axis. Length of the conjugate axis is 4 units.
5. The letter D is drawn, replaced in the bag, and then the letter J is drawn.
6. Three vowels are drawn without replacement.
A card is drawn from a bag containing the 9 cards shown. Find each
probability.
13. Find the equation whose vertices are (6, –6) and (0, –6) and focus at
3 
13, 6

14. What is the discriminant and type of conic section of x2 + 4y2 − 6x −
7y = 0?
7. Selecting a C or even number
3
8. Selecting odd number or multiple of
Algebra II Honors Spring 2009 Semester Review
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9. The probability distribution for the number of absent students on any
given day for a certain class is given. Find the expected number of absent
students.
Solve.
10. 8 P3
11. 8 P8
12. 8 C6
Evaluate each inverse trigonometric function. Give your answer in both
radians and degrees.
 2

 2 
Chapter 13-Trigonometry
Find the values of the six trigonometric functions for θ.
1.
Use the unit circle to find the exact value of each trigonometric function.
12. cos 210°
13. tan 11π/6
14. csc 315
15. cos 1 

2.

16. sin 1  


3

2 
17. A limestone cave is 6.2 mi south and 1.4 mi east of the entrance of a
national park. To the nearest degree, in what direction should a group at the
entrance head in order to reach the cave?
3. Katy is flying on 150 ft of string. The string makes an angle of 62° with
the horizontal. If Katy holds the end of the string 5 feet above the ground,
how height is the kite? Round to the nearest foot.
Use figure on the right to solve the question below
18. Use the given measurements to solve # DEF. Round to
the nearest tenth.
Draw an angle with the given measure in standard position.
4. 100°
5. –210°
P is a point on the terminal side of θ in standard position. Find the exact
value of the six trigonometric functions of θ.
6. P (–32, 24)
7. P (-3, -7)
Convert each measure from degrees to radians or from radians to
degrees.
8. 310°
9. –36°
10. 2π/9
11. –5π/6
19. An artist is designing a wallpaper pattern based on triangles. Solve all
measurements if a = 28, b = 13, and m  A = 102°. Round to the nearest
tenth.
20. Solve LMN for its missing sides
and angles. Round to the nearest tenth.
21. List 3 ways you will do to help you study for the final exam.