Name: ________________________ Class: ___________________ Date: __________
ID: A
Algebra 2 - Spring Final 2013 Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Classify –2x4 – x3 + 8x2 + 12 by degree.
a. quartic
b. quintic
c.
d.
quadratic
cubic
What are the zeros of the function? What are their multiplicities?
____
4
3
2
2. f(x)  x  4x  3x
a.
b.
c.
d.
____
the numbers –1 and –3 are zeros of multiplicity 2; the number 0 is a zero of multiplicity 1
the number 0 is a zero of multiplicity 2; the numbers 1 and 3 are zeros of multiplicity 1
the numbers 0 and 1 are zeros of multiplicity 2; the number 3 is a zero of multiplicity 1
the number 0 is a zero of multiplicity 2; the numbers –1 and –3 are zeros of multiplicity 1
3. Use the Rational Root Theorem to list all possible rational roots of the polynomial equation
x 3  4x 2  7x  8  0 . Do not find the actual roots.
a. –8, –1, 1, 8
c. 1, 2, 4, 8
b. –8, –4, –2, –1, 1, 2, 4, 8
d. no possible roots
How many roots do the following equations have?
____
____
4. 2x 4  x 3  12x 2  25x  5  0
a. 2
b. 3
5. Find all the real square roots of 
a.
no real root
b.

c.
d.
4
5
9
.
16
c.
3
4
d.
3
3
 and
4
4
81
256
Find the real-number root.
____
6.
125
343
25
a.
49
3

b.

125
343
c.
1

125
1029
d.

5
7
Name: ________________________
ID: A
What is a simpler form of the radical expression?
____
7.
3
27x 15 y 24
a. 3x 5  y 8 
b.
9x 15  y 24 
c.
3x 5 y 8
c.
d.
x 7 x
 42x
c.
5x 4 y 6
d.
9 x 15 y 24
d.
3x 6
Multiply and simplify if possible.
____
8.


7x  x  7 7 


a. x 7  49 x
7x  49x
b.
49
What is the simplest form of the product?
____
50x 7 y 7 
9.
2x 4 y 6
a.
4
b.
10x y
3
270x 20
____ 10.
3
a.
6xy 4
75y
5
3y
4
12
5
d.
30x y
c.
3
c.
13 5
5 5
y
5x
2x 3 3x 6
b.
3x 6 3 2x
135x 19
What is the simplest form of the expression?
____ 11.
20  45 
a. 4 5
b. 6 5
5
d.
What is the product of the radical expression?


____ 12.  7  2   8 


a. 54  56 2
b.
54 
2

2 

c.
d.
2
13  15 2
58  56 2
135x
Name: ________________________
ID: A
How can you write the expression with rationalized denominator?
____ 13.
2
3
3
3
6
a.
2 3 6  9 3 18
6
c.
23 6  93 4
6
b.
2 3 36  3 3 2
6
d.
2 3 36  3 3 4
6
3
____ 14. Write the exponential expression 3x 8 in radical form.
3
a.
38 x 3
b.
8
3x 3
c.
33 x 8
d.
3 8 8 x3
d.
8x 15
____ 15.
Write the radical expression

a.
8x
7
7
15
8
in exponential form.
x 15
15
b.
8x

7
c.
8x
15
7
What is the simplest form of the number?


2  8 2 


____ 16.
a.
b.
1024
2
c.
5
8
____ 17. What is the solution of
a. x = 0
b. x = 16 and x = 0
5x  1 
1
10
d.
2
c.
d.
x = 16
x = 16 and x = 1
x  5?
____ 18. Let f(x)  3x  6 and g(x)  x  2 . Find
a.
b.
c.
d.
2
8
5
f
and its domain.
g
3; all real numbers
3; all real numbers except x  2
1; all real numbers
–3; all real numbers except x  3
3
7
Name: ________________________
ID: A
____ 19. The half-life of a certain radioactive material is 32 days. An initial amount of the material has a mass of 361
kg. Write an exponential function that models the decay of this material. Find how much radioactive material
remains after 5 days. Round your answer to the nearest thousandth.
1
a.
 1  32 x
y  361   ; 0 kg
2
b.
 1  32 x
y  361  
; 323.945 kg
 2
c.
 1  32 x

y  2 
; 0.797 kg

361


d.
1
y 
2
1
1
 1  32 x


; 0.199 kg
 361 


____ 20. Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you
have in the account after 4 years?
a. $800.26
b. $6,701.28
c. $10,138.07
d. $1,923.23
____ 21. You open a savings account and deposit $1,000. After 1 year of earning continuously compounded interest,
your balance is $1,018.16. After 2 years, the balance is $1,036.66. Assuming you make no deposits or
withdrawals, find the equation for the best-fitting exponential function to represent the balance of the account
after x years. How much money will be in the account after 10 years?
a.
b.
A  1000  e 1.8 , $6,049.65
A  1000  e 0.018t , $1,001.20
c.
d.
A  1000  e 0.018t , $1,197.22
A  1000  e 1.8 * t , $1,001.20
c.
d.
log 32  5
log 5 32  2
c.
d.
c 16  (a  b)
(a  b) c  16
c.
4
c.
log 3 11  3 log 3 p
d.
11 log 3 p 3
Write the equation in logarithmic form.
____ 22. 2 5  32
a. log 32  5  2
b. log 2 32  5
Write the equation in exponential form.
____ 23. log (a  b) c  16
a.
b.
(a  b) 16  c
16 (a  b)  c
Evaluate the logarithm.
____ 24. log 3 243
a. 5
b.
–5
Expand the logarithmic expression.
____ 25. log 3 11p 3
a. log 3 11  3 log 3 p
b.
log 3 11  3 log 3 p
4
d.
3
Name: ________________________
ID: A
____ 26. Use the Change of Base Formula to evaluate log 7 40 .
a. 0.527
c. 3.689
b. 1.602
d. 1.896
Write the expression as a single natural logarithm.
1
(ln b  ln c 2 )
2
3a
ln
b.
0.5bc 2
____ 27. 3 ln a 
a.
3
a
ln
2 bc 2
c.
ln
1
3e
c.
6e
c.
a3
bc
a3
d.
ln
3e
d.
1
3
e6
d.
ln 6
c
b
____ 28. Simplify ln e 3 .
a.
3
b.
____ 29. Solve ln x  ln 6  0 .
a. 6
b.
Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? If
it is a direct or inverse variation, write a function to model it.
____ 30.
a.
b.
c.
x
9
11
13
15
y
–17
–1
6
27
153
x
17
direct variation; y =  x
9
neither
inverse variation; y 
____ 31. Suppose that x and y vary inversely, and x = 10 when y = 8. Write the function that models the inverse
variation.
2
80
a. y 
c. y 
x
x
18
b. y 
d. y = 0.8x
x
____ 32. Suppose that y varies directly with x and inversely with z, and y = 28 when x = 32 and z = 8. Write the equation
that models the relationship. Then find y when x = 12 and z = 3.
8z
7z 7
a. y 
;2
c. y 
;
x
x 4
7x
8x
b. y 
; 28
d. y 
; 32
z
z
5
Name: ________________________
____ 33. This graph of a function is a translation of y 
a.
b.
4
4
x3
4
y
4
x3
y
ID: A
4
. What is an equation for the function?
x
c.
d.
4
3
x4
4
y
3
x4
y
Find any points of discontinuity for the rational function.
____ 34. What are the points of discontinuity? Are they all removable?
y 
a.
b.
(x  7)(x  3)
x 2  10x  21
x = 1, x = –8, x = –2; yes
x = 7, x = 3; yes
c.
d.
x = –7, x = –3; no
x = –1, x = 8, x = 2; no
____ 35. Describe the vertical asymptote(s) and hole(s) for the graph of y 
a.
b.
c.
d.
asymptote: x = 5 and hole: x = 1
asymptote: x = –5 and hole: x = –1
asymptote: x = –3 and hole: x = 5
asymptote: x = 5 and hole: x = –1
2x 3  3x  2
.
2x 3  6x  2
c. no horizontal asymptote
d. y = 0
____ 36. Find the horizontal asymptote of the graph of y 
a.
b.
(x  3)(x  1)
.
(x  1)(x  5)
y=1
y = 1
6
Name: ________________________
ID: A
Simplify the rational expression. State any restrictions on the variable.
____ 37.
n 4  10n 2  24
n 4  9n 2  18
n2  4
a.
;n  
n2  3
6, n  
3
n2  4
; n  6, n  3
n2  3
b.
c.
d.
n2  4
; n  6, n  3
n2  3
(n 2  4)
n2  3
;n  
6, n  
What is the product in simplest form? State any restrictions on the variable.
____ 38.
3g 5
10h
2

h5
10g 2
a.
3g 3 h 3
, g  0, h  0
100
c.
b.
100
, g  0, h  0
3g 3 h 3
d.
3g 7
, g  0, h  0
100h 7
3 7 7
g h , g  0, h  0
100
y2
y2  y  6
____ 39.

y3
y 2  1y
a.
y 2  2y
, y  3,  1
y1
c.
y2
, y  3, 0,  1
y1
b.
y 2  2y
, y  3, 0,  1
y1
d.
y2
, y  3,  1
y1
What is the quotient in simplified form? State any restrictions on the variable.
____ 40.
a2
a1

a  5 a 2  8a  15
(a  2)(a  3)
, a  5,  1, 3
a.
a1
(a  2)(a  1)
, a  5, 3,  1
b.
(a  5) 2 (a  3)
c.
d.
7
(a  2)(a  3)
, a  3,  1
a1
(a  2)(a  1)
, a  5, 3
(a  5) 2 (a  3)
3
Name: ________________________
ID: A
Simplify the difference.
____ 41.
z 2  11z  30 z 2  2z  24
 2
z 2  z  20
z  9z  18
a.
z  34
(z  4)(z  3)
c.
2z 2  2
(z  4)(z  3)
b.
17z  2
(z  4)(z  3)
d.
2z 2  8z  34
2z 2  34
c.
3x 2 (y  4)
7y
Simplify the complex fraction.
x
____ 42.
4x
y
7
3x
a.
15x 2
7y
b.
7x(y  4)
3xy
8
d.
3(y  4)
7y
Name: ________________________
ID: A
____ 43. Graph 4x 2  4y 2  64. What are the domain and range?
a.
c.
Domain: 16  x  16
Range: 16  y  16
Domain: 4  x  4
Range:4  y  4
b.
d.
Domain: all real numbers
Range: 16  y  16
Domain: all real numbers
Range: 4  y  4
9
Name: ________________________
ID: A
Identify the center and intercepts of the conic section. Then find the domain and range.
____ 44.
a.
b.
The center of the ellipse is (0, 0).
The x-intercepts are (0, 5) and (0, –5).
The y-intercepts are (–3, 0) and (3, 0).
The domain is {x | –3  x  3}.
The range is {y | –5  y  5}.
The center of the ellipse is (0, 0).
The x-intercepts are (–3, 0) and (3, 0).
The y-intercepts are (0, 5) and (0, –5).
The domain is {x | –3  x  3}.
The range is {y | –5  y  5}.
c.
d.
The center of the ellipse is (0, 0).
The x-intercepts are (0, 5) and (0, –5).
The y-intercepts are (–3, 0) and (3, 0).
The domain is {x | –5  y  5}.
The range is {y | –3  x  3}.
The center of the ellipse is (0, 0).
The x-intercepts are (–3, 0) and (3, 0).
The y-intercepts are (0, 5) and (0, –5).
The domain is {x | –5  y  5}.
The range is {y | –3  x  3}.
What are the vertex, focus, and directrix of the parabola with the given equation?
2
____ 45. 8y  x  8x  16
a. vertex (–4, –4); focus (4, –2); directrix y = –6
b. vertex (4, 4); focus (0, –2); directrix y = –2
c. vertex (4, –4); focus (4, –2); directrix y = –6
d. vertex (–4, 4); focus (0, 2); directrix y = 2
Write an equation of an ellipse in standard form with the center at the origin and with the given
characteristics.
____ 46. vertex at (3, 0) and co-vertex at (0, 5)
y2
x2

 1
a.
5
3
y2
x2

 1
b.
25
9
c.
d.
10
y2
x2

 1
9
25
y2
x2

 1
3
5
Name: ________________________
ID: A
____ 47. Write an equation of the ellipse with foci at (0, 11) and vertices at (0, 12).
y2
y2
x2
x2
a.

 1
c.

 1
265 144
144
23
b.
y2
x2

 1
265 144
____ 48. A hyperbola has vertices  5,0  and one focus
2
x2 y
a.

1
11 25
b.
y2 x2

1
25 11
d.
y2
x2

 1
23
144
 6,0  . What is the standard-form equation of the hyperbola?
 
y2 x2
c.

1
11 25
d.
2
x2 y

1
25 11
Identify the conic section. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If
it is an ellipse or a hyperbola, give the center and foci.
____ 49. y 2  4x  10y  33  0
a. parabola; vertex (–2, 5)
b. parabola; vertex (4, 5)
c.
d.
parabola; vertex (2, 4)
parabola; vertex (2, –5)
____ 50. x 2  y 2  8x  8y  17
a. circle; center (–4, –4); radius = 49
b. circle; center (–4, –4); radius = 7
c.
d.
circle; center (4, 4); radius = 49
circle; center (4, 4); radius = 7
Short Answer
51. Use synthetic division to find P(–2) for P(x)  x 4  6x 3  2x 2  7x  10 .
52. Find a third-degree polynomial equation with rational coefficients that has roots –4 and 2 + i.
Find all the zeros of the equation.
53. 2x 4  5x 3  53x 2  125x  75  0
What is a simpler form of the radical expression?
54.
36g 6
What is the simplest form of the radical expression?
55. 2 4 2x  6 4 2x
11
Name: ________________________
ID: A
How can you write the expression with rationalized denominator?
56.
3 
6
3 
6
What is the solution of the equation?
57. 2 5 (x  6) 3  3  19
4
58. 4(3  x) 3  5  59
What is the solution of the equation? Eliminate any extraneous solutions.
1
1
59. 2x  6 5  8  10x 5
60. Let f(x)  4x  5 and g(x)  6x  3 . Find f(x)  g(x).
61. Let f(x)  2x  7 and g(x)  4x  3 . Find (f  g)(5).
62. For the function f(x)  (8  2x) 2 , find f 1 . Determine whether f 1 is a function.
63. y  7 6
x2
1
Write the expression as a single logarithm.
64. 4 log x  6 log (x  2)
Solve the exponential equation.
65.
1
 64 4x  3
16
Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary.
66. Solve log(4x  10)  3 .
Use natural logarithms to solve the equation. Round to the nearest thousandth.
67. 8e 4x  8  15
12
Name: ________________________
ID: A
Solve the equation. Check the solution.
68.
4
1

x1
x5
69.
6
1

 1
x3
x2  9
70. Write an equation of a parabola with a vertex at the origin and a directrix at y = 5.
71. Write an equation for the translation of x 2  y 2  49 by 3 units left and 4 units up.
Write an equation in standard form for the circle.
72.
73. Divide 4x 3  2x 2  3x  4 by x + 4.
74. Write –2x2(–5x2 + 4x3) in standard form.
Find the roots of the polynomial equation.
75. x 3  2x 2  10x  136  0
76. A polynomial equation with rational coefficients has the roots 3 
What is the simplest form of the expression?
77.
3
128a 13 b 6
Multiply and simplify if possible.
78.
4
11 
4
3
13
6, 2 
5 . Find two additional roots.
Name: ________________________
ID: A
Simplify.
79. 3
1
1
3
 93
80. For the function f(x)  x  9 , find (f  f 1 )(5).
14
ID: A
Algebra 2 - Spring Final 2013 Review
Answer Section
MULTIPLE CHOICE
1. ANS: A
PTS: 1
DIF: L2
REF: 5-1 Polynomial Functions
OBJ: 5-1.1 To classify polynomials
NAT: CC A.SSE.1.a| CC F.IF.4| CC F.IF.7| CC F.IF.7.c
TOP: 5-1 Problem 1 Classifying Polynomials
KEY: degree of a polynomial | polynomial function | standard form of a polynomial function
2. ANS: B
PTS: 1
DIF: L3
REF: 5-2 Polynomials, Linear Factors, and Zeros
OBJ: 5-2.2 To write a polynomial function from its zeros
NAT: CC A.SSE.1| CC A.APR.3| CC F.IF.7| CC F.IF.7.c| CC F.BF.1
TOP: 5-2 Problem 4 Finding the Multiplicity of a Zero
KEY: multiple zero | multiplicity
3. ANS: B
PTS: 1
DIF: L2
REF: 5-5 Theorems About Roots of Polynomial Equations
OBJ: 5-5.1 To solve equations using the Rational Root Theorem
NAT: CC N.CN.7| CC N.CN.8
TOP: 5-5 Problem 1 Finding a Rational Root
KEY: Rational Root Theorem
4. ANS: C
PTS: 1
DIF: L3
REF: 5-6 The Fundamental Theorem of Algebra
OBJ: 5-6.1 To use the Fundamental Theorem of Algebra to solve polynomial equations with complex
solutions
NAT: CC N.CN.7| CC N.CN.8| CC N.CN.9| CC A.APR.3
TOP: 5-6 Problem 1 Finding All the Roots of a Polynomial Function
KEY: Fundamental Theorem of Algebra | roots
5. ANS: A
PTS: 1
DIF: L2
REF: 6-1 Roots and Radical Expressions
OBJ: 6-1.1 To find nth roots
NAT: CC A.SSE.2| A.3.e
TOP: 6-1 Problem 1 Finding All Real Roots
KEY: nth root
6. ANS: D
PTS: 1
DIF: L3
REF: 6-1 Roots and Radical Expressions
OBJ: 6-1.1 To find nth roots
NAT: CC A.SSE.2| A.3.e
TOP: 6-1 Problem 2 Finding Roots
KEY: radicand | index | nth root
7. ANS: C
PTS: 1
DIF: L3
REF: 6-1 Roots and Radical Expressions
OBJ: 6-1.1 To find nth roots
NAT: CC A.SSE.2| A.3.e
TOP: 6-1 Problem 3 Simplifying Radical Expressions
KEY: radicand | index | nth root
8. ANS: A
PTS: 1
DIF: L4
REF: 6-2 Multiplying and Dividing Radical Expressions
OBJ: 6-2.1 To multiply and divide radical expressions
NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.e
TOP: 6-2 Problem 1 Multiplying Radical Expressions
9. ANS: B
PTS: 1
DIF: L3
REF: 6-2 Multiplying and Dividing Radical Expressions
OBJ: 6-2.1 To multiply and divide radical expressions
NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.e
TOP: 6-2 Problem 3 Simplifying a Product
KEY: simplest form of a radical
10. ANS: B
PTS: 1
DIF: L3
REF: 6-2 Multiplying and Dividing Radical Expressions
OBJ: 6-2.1 To multiply and divide radical expressions
NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.e
TOP: 6-2 Problem 4 Dividing Radical Expressions KEY:
simplest form of a radical
1
ID: A
11. ANS: A
PTS: 1
DIF: L3
REF: 6-3 Binomial Radical Expressions
OBJ: 6-3.1 To add and subtract radical expressions
NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.e
TOP: 6-3 Problem 3 Simplifying Before Adding or Subtracting KEY: like radicals
12. ANS: B
PTS: 1
DIF: L2
REF: 6-3 Binomial Radical Expressions
OBJ: 6-3.1 To add and subtract radical expressions
NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.e
TOP: 6-3 Problem 4 Multiplying Binomial Radical Expressions
KEY: like radicals
13. ANS: D
PTS: 1
DIF: L2
REF: 6-3 Binomial Radical Expressions
OBJ: 6-3.1 To add and subtract radical expressions
NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.e
TOP: 6-3 Problem 6 Rationalizing the Denominator
KEY: like radicals
14. ANS: A
PTS: 1
DIF: L2
REF: 6-4 Rational Exponents
OBJ: 6-4.1 To simplify expressions with rational exponents
NAT: CC N.RN.1| CC N.RN.2
TOP: 6-4 Problem 2 Converting Between Exponential and Radical Form
KEY: rational exponents
15. ANS: C
PTS: 1
DIF: L4
REF: 6-4 Rational Exponents
OBJ: 6-4.1 To simplify expressions with rational exponents
NAT: CC N.RN.1| CC N.RN.2
TOP: 6-4 Problem 2 Converting Between Exponential and Radical Form
KEY: rational exponents
16. ANS: B
PTS: 1
DIF: L3
REF: 6-4 Rational Exponents
OBJ: 6-4.1 To simplify expressions with rational exponents
NAT: CC N.RN.1| CC N.RN.2
TOP: 6-4 Problem 4 Combining Radical Expressions
KEY: rational exponent
17. ANS: C
PTS: 1
DIF: L3
REF: 6-5 Solving Square Root and Other Radical Equations
OBJ: 6-5.1 To solve square root and other radical equations
NAT: CC A.CED.4| CC A.REI.2| A.2.a
TOP: 6-5 Problem 5 Solving an Equation With Two Radicals
KEY: radical equation | extraneous solution
18. ANS: B
PTS: 1
DIF: L3
REF: 6-6 Function Operations
OBJ: 6-6.1 To add, subtract, multiply, and divide functions
NAT: CC F.BF.1| CC F.BF.1.b| A.3.f
TOP: 6-6 Problem 2 Multiplying and Dividing Functions
19. ANS: B
PTS: 1
DIF: L3
REF: 7-2 Properties of Exponential Functions
OBJ: 7-2.1 To explore the properties of functions of the form y = ab^x
NAT: CC A.SSE.1.b| CC A.CED.2| CC F.IF.7| CC F.IF.7.e| CC F.IF.8| CC F.BF.1| CC F.BF.1.b| N.3.f|
G.2.c| A.1.b| A.2.d| A.2.h
TOP:
7-2 Problem 3 Using an Exponential Model
KEY: exponential function
20. ANS: D
PTS: 1
DIF: L2
REF: 7-2 Properties of Exponential Functions
OBJ: 7-2.2 To graph exponential functions that have base e
NAT: CC A.SSE.1.b| CC A.CED.2| CC F.IF.7| CC F.IF.7.e| CC F.IF.8| CC F.BF.1| CC F.BF.1.b| N.3.f|
G.2.c| A.1.b| A.2.d| A.2.h
TOP:
7-2 Problem 5 Continuously Compounded Interest
KEY: continuously compounded interest
21. ANS: C
PTS: 1
DIF: L4
REF: 7-2 Properties of Exponential Functions
OBJ: 7-2.2 To graph exponential functions that have base e
NAT: CC A.SSE.1.b| CC A.CED.2| CC F.IF.7| CC F.IF.7.e| CC F.IF.8| CC F.BF.1| CC F.BF.1.b| N.3.f|
G.2.c| A.1.b| A.2.d| A.2.h
TOP:
7-2 Problem 5 Continuously Compounded Interest
KEY: compare properties of two functions | continuously compounded interest
2
ID: A
22. ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
23. ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
24. ANS:
REF:
OBJ:
NAT:
TOP:
25. ANS:
OBJ:
TOP:
26. ANS:
OBJ:
TOP:
27. ANS:
OBJ:
NAT:
TOP:
KEY:
28. ANS:
OBJ:
NAT:
TOP:
KEY:
29. ANS:
OBJ:
TOP:
30. ANS:
OBJ:
TOP:
31. ANS:
OBJ:
TOP:
32. ANS:
OBJ:
TOP:
KEY:
B
PTS: 1
DIF: L2
7-3 Logarithmic Functions as Inverses
7-3.1 To write and evaluate logarithmic expressions
CC A.SSE.1.b| CC F.IF.7.e| CC F.IF.8| CC F.IF.9| CC F.BF.4.a| G.2.c| A.2.h| A.3.h
7-3 Problem 1 Writing Exponential Equations in Logarithmic Form
write a function in different but equivalent forms
A
PTS: 1
DIF: L4
7-3 Logarithmic Functions as Inverses
7-3.1 To write and evaluate logarithmic expressions
CC A.SSE.1.b| CC F.IF.7.e| CC F.IF.8| CC F.IF.9| CC F.BF.4.a| G.2.c| A.2.h| A.3.h
7-3 Problem 1 Writing Exponential Equations in Logarithmic Form
write a function in different but equivalent forms
A
PTS: 1
DIF: L2
7-3 Logarithmic Functions as Inverses
7-3.1 To write and evaluate logarithmic expressions
CC A.SSE.1.b| CC F.IF.7.e| CC F.IF.8| CC F.IF.9| CC F.BF.4.a| G.2.c| A.2.h| A.3.h
7-3 Problem 2 Evaluating a Logarithm
KEY: logarithm
C
PTS: 1
DIF: L3
REF: 7-4 Properties of Logarithms
7-4.1 To use the properties of logarithms
NAT: CC F.LE.4| N.1.d| A.3.h
7-4 Problem 2 Expanding Logarithms
D
PTS: 1
DIF: L3
REF: 7-4 Properties of Logarithms
7-4.1 To use the properties of logarithms
NAT: CC F.LE.4| N.1.d| A.3.h
7-4 Problem 3 Using the Change of Base Formula
KEY: Change of Base Formula
D
PTS: 1
DIF: L4
REF: 7-6 Natural Logarithms
7-6.1 To evaluate and simplify natural logarithmic expressions
CC F.LE.4| A.3.h
7-6 Problem 1 Simplifying a Natural Logarithmic Expression
natural logarithmic function
A
PTS: 1
DIF: L2
REF: 7-6 Natural Logarithms
7-6.1 To evaluate and simplify natural logarithmic expressions
CC F.LE.4| A.3.h
7-6 Problem 1 Simplifying a Natural Logarithmic Expression
natural logarithmic function
A
PTS: 1
DIF: L4
REF: 7-6 Natural Logarithms
7-6.2 To solve equations using natural logarithms
NAT: CC F.LE.4| A.3.h
7-6 Problem 2 Solving a Natural Logarithmic Equation
KEY: natural logarithmic function
C
PTS: 1
DIF: L3
REF: 8-1 Inverse Variation
8-1.1 To recognize and use inverse variation NAT:
CC A.CED.2| CC A.CED.4
8-1 Problem 1 Identifying Direct and Inverse Variations
KEY: inverse variation
C
PTS: 1
DIF: L2
REF: 8-1 Inverse Variation
8-1.1 To recognize and use inverse variation NAT:
CC A.CED.2| CC A.CED.4
8-1 Problem 2 Determining an Inverse Variation
KEY: inverse variation
B
PTS: 1
DIF: L3
REF: 8-1 Inverse Variation
8-1.2 To use joint and other variations
NAT: CC A.CED.2| CC A.CED.4
8-1 Problem 4 Using Combined Variation
inverse variation | combined variation
3
ID: A
33. ANS: D
PTS: 1
DIF: L3
REF: 8-2 The Reciprocal Function Family
OBJ: 8-2.2 To graph translations of reciprocal functions
NAT: CC A.CED.2| CC F.BF.1| CC F.BF.3| G.2.c
TOP: 8-2 Problem 4 Writing the Equation of a Transformation KEY: reciprocal function
34. ANS: B
PTS: 1
DIF: L2
REF: 8-3 Rational Functions and Their Graphs
OBJ: 8-3.1 To identify properties of rational functions
NAT: CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h
TOP: 8-3 Problem 1 Finding Points of Discontinuity
KEY: rational function | point of discontinuity | removable discontinuity | non-removable points of
discontinuity
35. ANS: A
PTS: 1
DIF: L3
REF: 8-3 Rational Functions and Their Graphs
OBJ: 8-3.1 To identify properties of rational functions
NAT: CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h
TOP: 8-3 Problem 2 Finding Vertical Asymptotes
KEY: rational function
36. ANS: B
PTS: 1
DIF: L3
REF: 8-3 Rational Functions and Their Graphs
OBJ: 8-3.1 To identify properties of rational functions
NAT: CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h
TOP: 8-3 Problem 3 Finding Horizontal Asymptotes
KEY: rational function
37. ANS: A
PTS: 1
DIF: L3
REF: 8-4 Rational Expressions
OBJ: 8-4.1 To simplify rational expressions
NAT: CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e
TOP: 8-4 Problem 1 Simplifying a Rational Expression
KEY: rational expression | simplest form
38. ANS: A
PTS: 1
DIF: L2
REF: 8-4 Rational Expressions
OBJ: 8-4.2 To multiply and divide rational expressions
NAT: CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e
TOP: 8-4 Problem 2 Multiplying Rational Expressions
KEY: rational expression | simplest form
39. ANS: B
PTS: 1
DIF: L3
REF: 8-4 Rational Expressions
OBJ: 8-4.2 To multiply and divide rational expressions
NAT: CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e
TOP: 8-4 Problem 2 Multiplying Rational Expressions
KEY: rational expression | simplest form
40. ANS: A
PTS: 1
DIF: L3
REF: 8-4 Rational Expressions
OBJ: 8-4.2 To multiply and divide rational expressions
NAT: CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e
TOP: 8-4 Problem 3 Dividing Rational Expressions
KEY: rational expression | simplest form
41. ANS: B
PTS: 1
DIF: L4
REF: 8-5 Adding and Subtracting Rational Expressions
OBJ: 8-5.1 To add and subtract rational expressions
NAT: CC A.APR.7| N.5.e| A.3.c| A.3.e
TOP: 8-5 Problem 3 Subtracting Rational Expressions
42. ANS: C
PTS: 1
DIF: L3
REF: 8-5 Adding and Subtracting Rational Expressions
OBJ: 8-5.1 To add and subtract rational expressions
NAT: CC A.APR.7| N.5.e| A.3.c| A.3.e
TOP: 8-5 Problem 4 Simplifying a Complex Fraction
KEY: complex fraction
4
ID: A
43. ANS: A
PTS: 1
DIF: L4
REF: 10-1 Exploring Conic Sections
OBJ: 10-1.1 To graph and identify conic sections
NAT: CC G.GPE.1| CC G.GPE.2| CC G.GPE.3| G.4.c
TOP: 10-1 Problem 1 Graphing a Circle
KEY: conic sections
44. ANS: B
PTS: 1
DIF: L2
REF: 10-1 Exploring Conic Sections
OBJ: 10-1.1 To graph and identify conic sections
NAT: CC G.GPE.1| CC G.GPE.2| CC G.GPE.3| G.4.c
TOP: 10-1 Problem 4 Identifying Graphs of Conic Sections
KEY: conic sections
45. ANS: C
PTS: 1
DIF: L3
REF: 10-2 Parabolas
OBJ: 10-2.1 To write the equation of a parabola and to graph parabolas
NAT: CC G.GPE.2 TOP: 10-2 Problem 4 Analyzing a Parabola
KEY: directrix | focus of a parabola
46. ANS: C
PTS: 1
DIF: L3
REF: 10-4 Ellipses
OBJ: 10-4.1 To write the equation of an ellipse
NAT: CC G.GPE.3| G.4.g
TOP: 10-4 Problem 1 Writing an Equation of an Ellipse
KEY: ellipse | vertices of an ellipse | co-vertices of an ellipse | center of an ellipse
47. ANS: D
PTS: 1
DIF: L2
REF: 10-4 Ellipses
OBJ: 10-4.1 To write the equation of an ellipse
NAT: CC G.GPE.3| G.4.g
TOP: 10-4 Problem 4 Using the Foci of an Ellipse
KEY: ellipse | focus of an ellipse | major axis | center of an ellipse | minor axis | vertices of an ellipse |
co-vertices of an ellipse
48. ANS: D
PTS: 1
DIF: L3
REF: 10-5 Hyperbolas
OBJ: 10-5.1 To graph hyperbolas
NAT: CC G.GPE.3| G.4.g
TOP: 10-5 Problem 1 Writing and Graphing the Equation of a Hyperbola
KEY: hyperbola | focus of the hyperbola | vertex | transverse axis | axis of symmetry | conjugate axis
49. ANS: D
PTS: 1
DIF: L2
REF: 10-6 Translating Conic Sections
OBJ: 10-6.2 To identify a translated conic section from an equation
NAT: CC G.GPE.1| CC G.GPE.2| G.2.c TOP: 10-6 Problem 3 Identifying a translated conic section
50. ANS: B
PTS: 1
DIF: L3
REF: 10-6 Translating Conic Sections
OBJ: 10-6.2 To identify a translated conic section from an equation
NAT: CC G.GPE.1| CC G.GPE.2| G.2.c TOP: 10-6 Problem 3 Identifying a translated conic section
SHORT ANSWER
51. ANS:
52
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L3
REF: 5-4 Dividing Polynomials
5-4.2 To divide polynomials using synthetic division
CC A.APR.1| CC A.APR.2| CC A.APR.6| N.1.d| A.3.c| A.3.e
5-4 Problem 5 Evaluating a Polynomial
synthetic division | remainder theorem
5
ID: A
52. ANS:
x 3  11x  20  0
PTS: 1
DIF: L3
REF: 5-5 Theorems About Roots of Polynomial Equations
OBJ: 5-5.2 To use the Conjugate Root Theorem
NAT: CC N.CN.7| CC N.CN.8
TOP: 5-5 Problem 4 Using Conjugates to Construct a Polynomial
KEY: Conjugate Root Theorem
53. ANS:
3
1, ,  5i
2
PTS: 1
DIF: L3
REF: 5-6 The Fundamental Theorem of Algebra
OBJ: 5-6.1 To use the Fundamental Theorem of Algebra to solve polynomial equations with complex
solutions
NAT: CC N.CN.7| CC N.CN.8| CC N.CN.9| CC A.APR.3
TOP: 5-6 Problem 2 Finding All the Zeros of a Polynomial Function
KEY: Fundamental Theorem of Algebra
54. ANS:
6 g 3 
PTS: 1
DIF: L2
REF: 6-1 Roots and Radical Expressions
OBJ: 6-1.1 To find nth roots
NAT: CC A.SSE.2| A.3.e
TOP: 6-1 Problem 3 Simplifying Radical Expressions
KEY: radicand | index | nth root
55. ANS:
8 4 2x
PTS: 1
DIF: L2
REF: 6-3 Binomial Radical Expressions
OBJ: 6-3.1 To add and subtract radical expressions
NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.e
TOP: 6-3 Problem 1 Adding and Subtracting Radical Expressions
KEY: like radicals
56. ANS:
3  2 2
PTS: 1
DIF: L3
REF: 6-3 Binomial Radical Expressions
OBJ: 6-3.1 To add and subtract radical expressions
NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.e
TOP: 6-3 Problem 6 Rationalizing the Denominator
KEY: like radicals
57. ANS:
26
PTS: 1
DIF: L3
REF: 6-5 Solving Square Root and Other Radical Equations
OBJ: 6-5.1 To solve square root and other radical equations
NAT: CC A.CED.4| CC A.REI.2| A.2.a
TOP: 6-5 Problem 2 Solving Other Radical Equations
KEY: radical equation
58. ANS:
–5, 11
PTS: 1
DIF: L4
REF: 6-5 Solving Square Root and Other Radical Equations
OBJ: 6-5.1 To solve square root and other radical equations
NAT: CC A.CED.4| CC A.REI.2| A.2.a
TOP: 6-5 Problem 2 Solving Other Radical Equations
KEY: radical equation
6
ID: A
59. ANS:
7
6
PTS: 1
DIF: L4
REF: 6-5 Solving Square Root and Other Radical Equations
OBJ: 6-5.1 To solve square root and other radical equations
NAT: CC A.CED.4| CC A.REI.2| A.2.a
TOP: 6-5 Problem 4 Checking for Extraneous Solutions
KEY: radical equation | extraneous solution
60. ANS:
–2x – 2
PTS: 1
DIF: L3
REF: 6-6 Function Operations
OBJ: 6-6.1 To add, subtract, multiply, and divide functions
NAT: CC F.BF.1| CC F.BF.1.b| A.3.f
TOP: 6-6 Problem 1 Adding and Subtracting Functions
61. ANS:
–53
PTS: 1
DIF: L3
REF: 6-6 Function Operations
OBJ: 6-6.2 To find the composite of two functions NAT:
CC F.BF.1| CC F.BF.1.b| A.3.f
TOP: 6-6 Problem 3 Composing Functions
KEY: composite function
62. ANS:
f 1 (x) 
8
x
2
; f 1 is not a function.
PTS: 1
DIF: L3
REF: 6-7 Inverse Relations and Functions
OBJ: 6-7.1 To find the inverse of a relation or function
NAT: CC F.BF.4.a| CC F.BF.4.c| A.1.j
TOP: 6-7 Problem 4 Finding an Inverse Function
KEY: inverse function
63. ANS:
PTS: 1
DIF: L4
REF: 7-2 Properties of Exponential Functions
OBJ: 7-2.1 To explore the properties of functions of the form y = ab^x
NAT: CC A.SSE.1.b| CC A.CED.2| CC F.IF.7| CC F.IF.7.e| CC F.IF.8| CC F.BF.1| CC F.BF.1.b| N.3.f|
G.2.c| A.1.b| A.2.d| A.2.h
TOP:
7-2 Problem 2 Translating y = ab^x
KEY: exponential function
7
ID: A
64. ANS:
none of these
PTS: 1
DIF: L4
REF: 7-4 Properties of Logarithms
OBJ: 7-4.1 To use the properties of logarithms
NAT: CC F.LE.4| N.1.d| A.3.h
TOP: 7-4 Problem 1 Simplifying Logarithms
65. ANS:
7
12
PTS:
OBJ:
NAT:
TOP:
KEY:
66. ANS:
495
2
1
DIF: L4
REF: 7-5 Exponential and Logarithmic Equations
7-5.1 To solve exponential and logarithmic equations
CC A.REI.11| CC F.LE.4| A.3.h| A.4.c
7-5 Problem 1 Solving an Exponential Equation-Common Base
exponential equation
PTS: 1
DIF: L3
REF: 7-5 Exponential and Logarithmic Equations
OBJ: 7-5.1 To solve exponential and logarithmic equations
NAT: CC A.REI.11| CC F.LE.4| A.3.h| A.4.c
TOP: 7-5 Problem 5 Solving a Logarithmic Equation
KEY: logarithmic equation
67. ANS:
–1.843
PTS: 1
DIF: L3
REF: 7-6 Natural Logarithms
OBJ: 7-6.2 To solve equations using natural logarithms
NAT: CC F.LE.4| A.3.h
TOP: 7-6 Problem 3 Solving an Exponential Equation
KEY: natural logarithmic function
68. ANS:
19

3
PTS:
OBJ:
NAT:
TOP:
69. ANS:
4
1
DIF: L2
REF: 8-6 Solving Rational Equations
8-6.1 To solve rational equations
CC A.APR.6| CC A.APR.7| CC A.CED.1| CC A.REI.2| CC A.REI.11
8-6 Problem 1 Solving a Rational Equation
KEY: rational equation
PTS:
OBJ:
NAT:
TOP:
1
DIF: L3
REF: 8-6 Solving Rational Equations
8-6.1 To solve rational equations
CC A.APR.6| CC A.APR.7| CC A.CED.1| CC A.REI.2| CC A.REI.11
8-6 Problem 1 Solving a Rational Equation
KEY: rational equation
8
ID: A
70. ANS:
y  
PTS:
OBJ:
NAT:
KEY:
71. ANS:
1 2
x
20
1
DIF: L3
REF: 10-2 Parabolas
10-2.1 To write the equation of a parabola and to graph parabolas
CC G.GPE.2 TOP: 10-2 Problem 1 Parabolas with Equation y = ax^2
directrix
2
2
x  3    y  4   49
PTS:
OBJ:
TOP:
KEY:
72. ANS:
1
DIF: L2
REF: 10-3 Circles
10-3.1 To write and graph the equation of a circle
NAT: CC G.GPE.1| G.2.c| G.4.f
10-3 Problem 2 Using Translations to Write an Equation
circle | center of a circle | radius | standard form of the equation of a circle
2
2
x  3    y  6   16
PTS:
OBJ:
TOP:
KEY:
73. ANS:
4x 2 
1
DIF: L3
REF: 10-3 Circles
10-3.1 To write and graph the equation of a circle
NAT: CC G.GPE.1| G.2.c| G.4.f
10-3 Problem 3 Using a Graph to Write an Equation
circle | center of a circle | radius | standard form of the equation of a circle
14x  59, R –232
PTS: 1
DIF: L2
REF: 5-4 Dividing Polynomials
OBJ: 5-4.1 To divide polynomials using long division
NAT: CC A.APR.1| CC A.APR.2| CC A.APR.6| N.1.d| A.3.c| A.3.e
TOP: 5-4 Problem 1 Using Polynomial Long Division
74. ANS:
–8x5 + 10x4
PTS: 1
DIF: L3
REF: 5-1 Polynomial Functions
OBJ: 5-1.1 To classify polynomials
NAT: CC A.SSE.1.a| CC F.IF.4| CC F.IF.7| CC F.IF.7.c
TOP: 5-1 Problem 1 Classifying Polynomials
KEY: degree of a polynomial | polynomial function | standard form of a polynomial
75. ANS:
3 ± 5i, –4
PTS:
OBJ:
NAT:
KEY:
1
DIF: L2
REF: 5-5 Theorems About Roots of Polynomial Equations
5-5.1 To solve equations using the Rational Root Theorem
CC N.CN.7| CC N.CN.8
TOP: 5-5 Problem 2 Using the Rational Root Theorem
Rational Root Theorem
9
ID: A
76. ANS:
3
6, 2 
5
PTS: 1
DIF: L2
REF: 5-5 Theorems About Roots of Polynomial Equations
OBJ: 5-5.2 To use the Conjugate Root Theorem
NAT: CC N.CN.7| CC N.CN.8
TOP: 5-5 Problem 3 Using the Conjugate Root Theorem to Identify Roots
KEY: Conjugate Root Theorem
77. ANS:
4a 4 b 2 3 2a
PTS: 1
DIF: L3
REF: 6-2 Multiplying and Dividing Radical Expressions
OBJ: 6-2.1 To multiply and divide radical expressions
NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.e
TOP: 6-2 Problem 2 Simplifying a Radical Expression
KEY: simplest form of a radical
78. ANS:
4
33
PTS: 1
DIF: L2
REF: 6-2 Multiplying and Dividing Radical Expressions
OBJ: 6-2.1 To multiply and divide radical expressions
NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.e
TOP: 6-2 Problem 1 Multiplying Radical Expressions
79. ANS:
3
PTS:
OBJ:
TOP:
KEY:
80. ANS:
5
PTS:
OBJ:
TOP:
KEY:
1
DIF: L3
REF: 6-4 Rational Exponents
6-4.1 To simplify expressions with rational exponents
NAT: CC N.RN.1| CC N.RN.2
6-4 Problem 1 Simplifying Expressions with Rational Exponents
rational exponents
1
DIF: L2
REF: 6-7 Inverse Relations and Functions
6-7.1 To find the inverse of a relation or function
NAT: CC F.BF.4.a| CC F.BF.4.c| A.1.j
6-7 Problem 6 Composing Inverse Functions
rearrange formulas to highlight a quantity | composition of functions | inverse relations and functions
10