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1
FINAL EXAM TOPIC ASSIGNMENT
There are 50 questions altogether.
32 questions on the non-calculator section &
18 questions on the calculator section.
TOPIC With
Calculator
Non-
Calculator
Trigonometry
Transformations
Parametric Equations
Summation Notation
Binomial Expansion/Specific Term
Sequence/Series
Exponential Graphs
Exponential/ Banking Applications
Solving Exponential Equations
Properties of Logs
Log Graphing
Solving Log Equations
Polynomial Function and Graphs
Zeros of Polynomials
Rational Functions and Graphs
The above chart is subject to slight modification.
A calculator may be used for questions indicated with an “*”;
do all other questions by hand – no calculator!.
2
Review for Spring Exam 2014
For questions 1 and 2, consider the pair of parametric equations: 4
2 3
x t
y t
______1. Find the rectangular form of the parametric equations above.
(A) 22 5y x
(B) 22 11y x
(C) 5
2
yx
______2. Find the restrictions placed on t, x, and y.
(A) 4, 0, 5t x y
(B) 4, 0, 5t x y
(C) 4, 0, 5t x y
______3. Identify the curve for the pair of parametric equations: cosθ
cos2θ
x
y
(A) parabola opening up
(B) a portion of a parabola opening up
(C) vertically-oriented hyperbola
(D) a portion of a vertically-oriented hyperbola
______4. Which graph best illustrates the parametric equations 2sinθ 1
3cosθ 1
x
y
(A) (B) (C)
x
y
x
y
x
y
3
______5. Identify the curve for the parametric equations: 2 23 , 1 2x t y t
(A) (B) (C) (D)
______6. Evaluate 77
8
3n
(A) 207
(B) 210
(C) 231
______7. Evaluate 5
0
!
2n
n
(A) 77
(B) 77.5
(C) 154
______8. Find the sum: 6
2
1 2k
k
k
(A) 40
(B) -4
(C) 6
(D) 8
x
y
x
y
x
y
x
y
4
______9*. 400!
398! 2!=
(A) impossible
(B) 79,800
(C) 159,600
______10. ( 1)!
( 1)!
n n
n
=
(A) 2n n
(B) 2
1
n n
(C) 1
1n
______11. 2 !
(2 3)!
n
n=
(A) 2
2 3
n
n
(B)
2
1 2n n
(C) 2 1 2n n n
(D) 2 2 1 2 2n n n
______12. Which of the following is the definition of e?
(A) 1
2
!n
n
n
(B) 1
1
!n n
(C) 0
1
!n n
5
______13*. Evaluate: 16
14
(A) 8/7
(B) 120
(C) 224
______14. Which of the following is not equal to 1 if x is any whole number?
(A) x xC
(B) 0xC
(C) 1xC
______15. Find a value of x (other than 50) for which the following is true: 500 500
50 x
(A) 450
(B) 250
(C) 10
______16. Expand 4
5 2i without a calculator.
(A) –41–840i
(B) 41 +840i
(C) 41–840i
______17*. Find the middle term in the expansion of
10
2
4
xy
.
(A)
510263
256
x y
(B) 5 5252x y
(C) 5 1063
256
x y
6
______18. Find the term containing x6 in the expansion of
83x y .
(A) 6 228x y
(B) 5 628x y
(C) 6 628x y
(D) 6 256x y
______19. Use the Binomial Theorem to expand 3
2 .x y
(A) 3 2 2 32 6 6x x y xy y
(B) 3 2 2 38 4 2x x y xy y
(C) 3 2 2 32 3 3x x y xy y
(D) 3 2 2 38 12 6x x y xy y
______20*. Given the explicit definition, find the 30th
term: ( 1) 2
4 5
n
n
na
n
.
(A) 12
25
(B) 12
23
(C) 12
23
______21. Find the tenth term of the sequence whose nth term is defined as
2 1
5 3 1n
na
n
(A) 21
32
(B) 21
72
(C) 22
32
(D) 19
29
7
______22. Which of the following is the recursive definition for the sequence shown below?
1
120, 40, 13 ,...3
nd
(A)
11
1203
n
nd
(B) 1 1
1120,
3n nd d d
(C) 1
1
3n nd d
(D) 1 1120, 3n nd d d
______23. Which of the following is an arithmetic sequence?
(A) 2, 4, 8, 16, 32,... (B) 2, 4, 8, 16, 32,...
(C) 3, 6, 9, 12, 15,... (D) 2, 4, 6, 10, 16,...
______24. In an arithmetic sequence, 5 38a and 9 21a . Which is the 25th
term in the sequence?
(A) –47
(B) 165.5
(C) –17.75
______25. Which of the following is a geometric sequence?
(A) 1 1 1 1
2, , , , ,...2 4 6 8
(B) 2, 4, 8, 16, 32,...
(C) 2, 0, 2, 4, 6,... (D) 2, 7, 3, 8, 4,...
______26*. In a geometric sequence, 2 80000g and 6 32768g . Which is the 7th
term in the sequence?
(A) 100000
(B) 26214.4
(C) 20971.52
(D) 16777.216
______27. Rewrite the following definition explicitly: 1 n n-1A 9, A 4 A
(A) n 1nA 9(4) (B) nA 9 4n (C)
n 1
n
1A 9
4
(D) nA 5 4n
8
______28*. Find the sum of the finite arithmetic sequence: 5,9.5,14,...,68}
(A) 543
(B) 547.5
(C) 552
(D) 556.5
______29*. Find the sum: 500
1
3 5n
n
(A) 756, 500
(B) 376,250
(C) 752,500
(D) 378,250
______30*. Find the sum of the finite geometric sequence: 1,3,9,...,6561
(A) 9841
(B) 11327
(C) 18336
(D) 29524
______31*. Find the sum of the expression: 10
0
32
5
n
n
to four decimal places.
(A) 4.9698
(B) 5.0000
(C) 4.9819
(D) 55.0000
______32*. Determine whether the infinite geometric series converges and if so, find the sum:
500 100 20 4 ...
(A) diverges (B) converges; 624
(C) converges; 625 (D) converges; 626
9
______33*. Evaluate: 0
25
3
n
n
(A) 6
(B) 3
(C) 1
(D) 0
______34. Solve for x:
2 1
5127
9
x
x
(A) x = 4/3
(B) x = –17
(C) x = 13/7
_____35*. The population of Bedrock is 14,500. If it decreases at a rate of 2½ % per year, what will the
population be in 10 years?
(A) 816.55
(B) 1462.31
(C) 11256.78
(D) 18561.22
_____36*. The population of Smallville is 50,000. It increases at a rate of 3.12% per year. In how many
years will it reach 60,500?
(A) 0.16 years
(B) 0.7 years
(C) 4.5 years
(D) 6.2 years
10
_____37*. A substance weighing 10 grams has a half-life of 36 days. After how many days will the
substance weigh only 2 grams?
(A) 63.14 days
(B) 75.68 days
(C) 83.59 days
(D) 92.34 days
_____38. Which of the following is the graph of 24 3xy ?
(A) (B) (C)
For questions 39-42, match each function with the correct graph.
______39. 14 3xy (A) (B) (C)
______40. 34 3xy
______41. 22 4 3xy (D) (E)
______42. 24 1xy
______43. Which of the following is the graph of 1 1xy e ?
(A) (B) (C)
(3, -2)
(-1, -4)
(2, 0)
(-2, -1)
(1, -4)
x
y
(2, -2)
x
y
(-2, -2)
x
y
(-2, -2)
x
y
(1, 2)
x
y
(-1, 2)
x
y
(-1, -2)
11
______44. The domain of 3 xy e is:
(A) 3, (B) 0, (C) , (D) ,3
______45. The range of 3 xy e is:
(A) ,3 (B) ,3 (C) 3, (D) ,
_____46. Determine the x-intercept: 22 3 5xy
(A) 3log 2.5 2
(B) ln2.5 2ln3
ln3
(C) 2.5log 3 2
(D) 2log3 log2.5
log3
_____47. Which of the following is not equivalent to 21(2) 2
2
xy ?
(A) 21(2) 2
2
xy
(B) ( 2)1(2) 2
2
xy
(C)
21 1
22 2
x
y
(D)
21 1
22 2
x
y
(E) ( 2)1
2 22
xy
_____48*. Determine how much money must be deposited at 9% interest compounded monthly in order to
have a balance of $35,000 after 20 years.
(A) $5824.45
(B) $6914.23
(C) $9470.02
(D) $12500.00
12
_____49*. If $9200 is invested at 9.5% interest compounded continuously, find the balance in the account
after 10 years.
(A) $17940.00
(B) $22628.35
(C) $23788.53
(D) $25040.56
For questions 50-53, match each function with one of the graphs shown on the right.
_________50. 1
2 3x
y
(A) (B)
_________51.
11
32
x
y
_________52. 212 3
xy
(C) (D)
_________53.
211
2 32
x
y
__________54. Identify the CP’ for
21
5 42
x
y
(A) (-2, 4)
(B) (-2, -1)
(C) (-2, 9)
__________55. Which functions have a point that is a “cusp” at the CP’?
(A) x
y b (B) 2xy b
__________56. Which functions have a smooth, rounded shape at the CP’?
(A) x
y b (B) 2xy b
x
y
xy
x
y
x
y
13
_____57. Evaluate: 7ln 7
(A) 1 (B) 0 (C) 2 (D) 49
_____58. Evaluate: 1ln xe
(A) 1 xe
(B) e
(C) 1 x
(D) ln 1 x
_____59. 4log 20 is equivalent to
(A) log 5 (B) 20 log 4 (C) log20
log4 (D)
log4
log20
______60. Write in logarithmic form: 34 64
(A) 4log3 64 (B) 3log 64 4 (C) 3log 4 64 (D) 4log 64 3
______61. Which of the following represents the condensed form of the log expression given below?
1
log 3log log2
x y z
(A) 3
logx z
y
(B)
3log
x
y z (C)
3
log
log
x
y z (D)
2
3log
x z
y
______62.Which of the following represents the expanded form of the log expression shown?
22 3
log10
a b
(A) 2log 3log 2a b (B) 1
4log log 13
a b
(C) 1
2log log 13
a b (D) 2
4log log 23
a b
14
_____63. Solve for x: 82log ( ) 5 1x
(A) 6561 (B) 1
64 (C) 262144 (D) 512
_____64*. Determine the y-intercept: 4log 3 1y x
(A) –0.21 (B) –1.79 (C) –0.88 (D) –1.12 (E) none
_____65. Determine the x-intercept: 1
2
log 5 2y x
(A) 4.75
(B) 5.25
(C) 1
(D) 1.25
(E) none
______66. Solve for x: 14 9x x
(A) log9
log4 log9
(B) log9
log9 log4
(C) log4
log4 log9
______67. Solve for x: 2 1ln 9xe
(A) 1 ln9
2
(B)9 1
2ln 2e
(C) 23
(D) 4
15
______68. Solve for x: 2
6010
4 xe
(A) 2
ln2 (B)
ln 20
2
(C) ln1 (D) ln2
2
______69*. Solve for x: ln 2 ln 5 2ln2x x [Do NOT solve graphically]
(A) 2.53, -5.53
(B) 2.53
(C) 5.53
(D) { }
70. Matching: Write the letter of the graph which best illustrates each function.
_______i. log 1 2y x A. E.
_______ii. 22 1
xy
_______iii. log 1 2y x
_______iv. ln 1 2y x B. F.
_______v. 15 2 2x
y
_______vi. 20.5 1
xy
_______vii. 22 1
xy
C. G.
_______viii. 10.5 2x
y
D. H.
(-1, 3)
(-2, 0)
16
______71. Which of the following best illustrates the graph of lny x ?
(A) (B) (C)
______72. Which of the following best illustrates the graph of 7
4
log ( ) 1y x ?
(A) (B) (C) (D)
______73. The domain of ln 3 1y x is:
(A) 1
,3
(B) , (C)
1 1, ,
3 3
(D) 0,
______74. The range of 3 xy e is:
(A) , 3 (B) ,3 (C) 3, (D) ,0
______75. Which function(s) will have a “double hockey stick?”
I. logy x II. logy x III. 2
logy x
(A) I only (B) II only (C) III only (D) none
(E) all (F) I and II (G) II and III
______76. Find the translation (not the T.P.) for: log 10 50 2y x .
(A) right 5, up 2
(B) left 50, up 2
(C) right 50, up 3
(D) right 5, up 3
x
y
x
y
x
y
x
y
x
y
x
y
x
y
17
______77. Find all the real zeros of the polynomial function: 4 25 36f x x x
(A) 3, 2
(B) 3
(C) 3, 2
(D) 2
______78. Find a polynomial function with the given zeros: –2, –2, 1, 3
(A) 1 3 2f x x x x
(B) 2
1 3 2f x x x x
(C) 2
1 3 2f x x x x
(D) 1 3 2f x x x x
______79. Determine the correct function for the given graph.
(A) 3 22 3f x x x
(B) 4 33 2f x x x
(C) 3 22 3f x x x
(D) 2 33 2f x x x
______80. Find a fourth degree polynomial with real coefficients that has zeros: 2, 3, 2i
(A) 4 3 25 8 10 12f x x x x x
(B) 4 25 6f x x x
(C) 4 3 25 6f x x x x
(D) 4 3 25 8 10 12f x x x x x
x
y
18
______81. Find a quadratic polynomial with real coefficients that has zeros: 2 5 3
4
i
(A) 216 16 79f x x x
(B) 216 16 29f x x x
(C) 24 16 79f x x x
(D) 216 16 79f x x x
______82. Determine the correct function for the given graph.
[assume least multiplicity]
(A) 2 33
2 1 34
f x x x x
(B) 2 31
2 1 34
f x x x x
(C) 2 31
2 1 34
f x x x x
(D) 2 31
2 1 34
f x x x x
______83. Which of the following is the graph of 2 23 2 4 2f x x x x
(A) (B) (C) (D)
______84. Use synthetic division to divide: 3 8x by 2x
(A) 2 2 4x x
(B) 2 4x
(C) 2 2 4x x
(D) 2 2 4x x
x
y
x
y
x
y
x
y
x
y
19
______85. Divide: 4 3
2
3 2 3 1
1
x x x
x
(A) 2
2
5 23 2 3
1
xx x
x
(B) 2
2
5 43 2 3
1
xx x
x
(C) 3 2
2
53 4
1x x x
x
(D) 2
2
4 53 1
1
xx x
x
______86. Which of the following is not a possible rational zero of 2 33 5 2f x x x
(A) 2
3
(B) 2 (C)
2
5 (D)
1
5
______87. Find all the real zeros of the function 3 22 14 24f x x x x
(A) 0, 3, 4
(B) 3, 4
(C) 4, 3, 0
(D) 0, 1, 6
______88. Find all the real zeros of the function 3 2 3 1f x x x x
(A) 1, 2
(B) 1, 1 2
(C) 1, 2
(D) 1, 1 2
______89. Simplify: 3
25
(A) 125
(B) 125i
(C) 125i
(D) 125
20
______90. Divide, then write the result in standard form: 4
1 4
i
i
(A) 8
17i
(B) i
(C) i
(D) 8
17i
______91. Simplify: 37 726 4i i
(A) 6 4i
(B) 4 6i
(C) 6 4i
(D) 4 6i
______92. Solve for x: 23 4 2x x
(A) 2 2 2
3
i
(B) 2 2 10
3
(C) 2 2
3
i
(D) 2 10
3
______93. Use the fact that 2 3i is a zero of f to find the remaining zeros:
4 3 26 12 2 21f x x x x x
(A) 2, 2, 2 3i
(B) 1, 3, 2 3i
(C) 1, 3, 2 3i
(D) 1, 3, 2 3i
______94. Find the domain: 2
2
3 2
xf x
x x
(A) all reals (B) all reals except 2, 1, 2x
(C) all reals except 2x (D) all reals except 1, 2x
21
______95. Find the equation of any horizontal asymptote(s): 5 3
2 5
xf x
x
(A) 5
2y
(B)
3
2y
(C)
3
5y
(D)
3
2y (E) none (Egyptian)
______96. Find the equation of any vertical asymptote(s) and whether each has a ‘jump’ or ‘stay’:
3 2
1
1 3
xf x
x x
(A) 1 , 3J Sx x (B) 1 , 3J Sx x (C) 1 , 3S Jx x (D) 1 , 3S Jx x
______97. Find the location of any crossing(s):
2
2 1 6
3
x xf x
x
(A) no crossings (B) 24
, 223
(C)24
, 123
(D) 24
, 223
______98. Find the location of any crossing(s):
3 2
2
3 3
4
x x xf x
x
(A) 3, 0 (B) 3, 6 (C) 3, 6 (D) 5, 5 (E) no crossings
______99. Determine the end behavior of the rational function:
2 3
2
2 1 2 4
4
x x xf x
x
(A) even-positive (B) odd-positive (C) even-negative (D) odd-negative
______100. Determine the location of any hole(s):
2
2
1 2 3
1 2 3
x x xf x
x x x
(A) no holes (B) 1, 2 (C) 3, 0
(D) 1, 2 and 3, 0 (E) 4
1, and 3, 03
22
______101. Which of the following function describes the graph shown:
(A)
2
2 4
3
xy
x
(B) 2 4
3
xy
x
(C) 3 6
3
xy
x
(D) 2 4
3
xy
x
______102. Which of the following function describes the graph shown:
(A) 2
10
4y
x
(B) 2
8
4y
x
(C)
2
10
2y
x
(D) 2
10
4y
x
______103. Which of the following function describes the graph shown:
(A) 2
2
4
9
xy
x
(B) 2 2
2
4
9
x xy
x
(C) 2
2
4
9
x xy
x
(D) 2
2
4
9
x xy
x
x
y
x
y
x
y
23
______104. Which of the following function describes the graph shown:
(A)
22
2
2 2
1
x x xy
x
(B)
22
2
2 2
1
x x xy
x
(C)
22 2 2
1
x x xy
x
(D)
22
2
2 2
1
x x xy
x
______105. Which of the following function describes the graph shown:
(A) 2
1
x xy
x
(B) 2
1
x xy
x
(C) 2
1
x xy
x
(D) 3 2
1
x xy
x
x
y
x
y
24
106. Find tan if sec = 13
5 and sin 0.
a. 12
5 b.
5
12 c.
12
5 d.
5
12 e.
13
12
107. Which of the following best represents one cycle of the graph of 3
2cos 3 14
y x
?
a. b. c.
d. e.
y
x
y
x
y
x
4
7
12
11
12
y
x
12
5
12
3
4
12
5
12
3
4
12
4
5
12
y
x
12
5
12
3
4
25
108. Which equation is best represented by the graph shown?
a. 2cot 28
y x
b. 2tan 28
y x
c. 2tan 28
y x
d. 2cot 28
y x
e. 5
2tan 28
y x
109. Find the radian solutions for x over the interval [0, 2).
24sin 1 0x
a. π 5π
,6 6
b. π 3π 5π 7π
, , ,4 4 4 4
c. π 3π
,4 4
d. π 2π 4π 5π
, , ,3 3 3 3
e. π 5π 7π 11π
, , ,6 6 6 6
110. Simplify the trigonometric expression: 2 2 2cot csc sinx x x
a. -1 b. csc2 x c.
2cot 1x d. 1 e. sin(2x)
111. Evaluate: arcsec 2 =
a. 5π
6 b.
11π
6 c.
π
6 d.
π
3 e.
2π
3
112. * Which of the following is not coterminal with an angle of 45o .
a. 9π
4 b.
7π
4
c. 2565 d.
7π
4 e. 1755o
y
x
4
26
113. * Which of the following is the reference angle for -147
114. * An observer is 250ft from a flagpole. The angle of depression from the top of the flag pole
to the observer is 47o. Find the height of the flagpole.
a. 233.12 b. 268.09 c. 318.31 d. 172.65 e. 293.01
115. * Find two values of over the interval [0, 360): sinθ = -0.258
a. 14.951, 110.916 b. 14.951, 249.084
c. 194.951, 345.049 c. 165.049, 345.049
116. Find the values of 2
cos(2 )2
x , over the interval 0 360ox
a. 45o, 315
o b. 22.5
o, 157.5
o c. 22.5
o, 157.5
o, 202.5
o, 337.5
o
d. 45o, 135
o, 225
o, 315
o
117. * In ABC, a = 6, b = 12, and c = 7. Find the measure of the largest angle to the nearest
tenth of a degree.
a. 43.5 b. 100.3 c. 36.2 d. 134.6
a. 213 b. -213 c. 0.26 d. 33 e. 0.56
27
118. * Determine the period of the function: 1
cot2 6
xy
.
a. 1
6 b. c. 6 d. 12 e. 2
119. The equations of 3 consecutive asymptotes of 1
csc(4 4π)2
y x are:
a. 0 and and 2
b. and
4 2
c. and and
4 4 2
d. 5 3
and and 4 2
e. 0 and and 2
For the following questions, find the area of ABC and match it with the answers provided.
120. * a = 19, b = 8, c = 15
a. 60.00
b. 31.44
121. * C = 109, a = 7, b = 9.
c. 27.16
d. 6468
e. 57.24
122. What is the equation of the following graph?
a. 2
12
( 1)y
x
b. 1
2( 1)
yx
c. 2
12
( 1)y
x
d. 1
2( 1)
yx
e. 2
12
( 1)y
x
x
y
28
The following three questions are based on the formula: 39 6
5 310 7
y x , compared to a graph of
3y x
123. The 9/10 on the outside produces a:
a. Horizontal compression by a factor of 9/10 b. Horizontal stretch by a factor of 10/9
c. Vertical compression by a factor of 9/10 d. Vertical stretch by a factor of 10/9
124. The 6/7 on the inside produces a:
a. Horizontal compression by a factor of 6/7 b. Horizontal stretch by a factor of 7/6
c. Vertical compression by a factor of 6/7 d. Vertical stretch by a factor of 7/6
125. This graph exhibits:
a. A Vertical reflection only
b. No reflection
c. A Horizontal reflection only
d. Both a Horizontal and Vertical reflection
29
ANSWERS TO PRECALCULUS
HONORS EXAM REVIEW
1. A 31. C 61. B 84. A 114. B
2. C 32. C 62. D 85. B 115. C
3. B 33. B 63. D 86. A 116. C
4. A 34. B 64. B 87. C 117. D
5. A 35. C 65. C 88. D 118. C
6. B 36. D 66. A 89. C 119. D
7. A 37. C 67. D 90. B 120. E
8. D 38. B 68. D 91. D 121. B
9. B 39. E 69. B 92. C 122. C
10. C 40. A 70i. F 93. D 123. C
11. D 41. D ii. D 94. D 124. B
12. C 42. C iii. A 95. D 125. D
13. B 43. B iv. H 96. B
14. C 44. C v. B 97. D
15. A 45. B vi. E 98. A
16. C 46. A vii. G 99. C
17. A 47. C viii. C 100. D
18. C 48. A 71. B 101. B
19. D 49. C 72. C 102. D
20. C 50. C 73. A 103. C
21. A 51. B 74. B 104. A
22. B 52. D 75. G 105. B
23. C 53. A 76. D 106. C
24. A 54. B 77. B 107. A
25. B 55. A 78. C 108. B
26. B 56. B 79. D 109. E
27. D 57. A 80. D 110. B
28. B 58. C 81. D 111. E
29. D 59. C 82. D 112. D
30. A 60. D 83. C 113. D
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