Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 1 Name: ______________________
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Algebra 2/Trigonometry Regents Bimodal Worksheets
1 If log x 2 − log 2a = log3a , then logx expressed in
terms of loga is equivalent to
8 The table below shows five numbers and their
frequency of occurrence.
2 How many negative solutions to the equation
2x 3 − 4x 2 + 3x − 1 = 0 exist?
3 A circle is drawn to represent a pizza with a 12
inch diameter. The circle is cut into eight
congruent pieces. What is the length of the outer
edge of any one piece of this circle?
The interquartile range for these data is
1

−
9 Which expression is equivalent to  9x 2 y 6  2 ?


4 A video-streaming service can choose from six
half-hour shows and four one-hour shows. Which
expression could be used to calculate the number of
different ways the service can choose four
half-hour shows and two one-hour shows?
5 Which expression is equivalent to (n  m  p)(x),
10 The expression
1 + cos 2A
is equivalent to
sin2A
11 The expression (2a) −4 is equivalent to
given m(x) = sinx , n(x) = 3x , and p(x) = x 2 ?
6 Expressed in simplest form,
3y
9
+
is
2y − 6 6 − 2y
3
12 If sin A = , what is the value of cos 2A?
8
equivalent to
7 What is the range of f(x) = |x − 3 | + 2?
1
13 What is a positive value of tan x , when
2
sin x = 0.8?
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 2 Name: ______________________
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14 How many distinct ways can the eleven letters in
the word "TALLAHASSEE" be arranged?
15 If log2 = a and log3 = b , the expression log
22 A spinner is divided into eight equal sections. Five
sections are red and three are green. If the spinner
is spun three times, what is the probability that it
lands on red exactly twice?
9
is
20
equivalent to
16 The expression (x + i) 2 − (x − i) 2 is equivalent to
23 If the amount of time students work in any given
week is normally distributed with a mean of 10
hours per week and a standard deviation of 2 hours,
what is the probability a student works between 8
and 11 hours per week?
x 2 + 9x − 22
÷ (2 − x) is equivalent
x 2 − 121
17 The sum of the first eight terms of the series
3 − 12 + 48 − 192 + . . . is
24 The expression
18 What is the common ratio of the sequence
1 5 3 3 3 4 9
a b ,− a b , ab 5 ,. . .?
32
16
64
25 When factored completely, the expression
x 3 − 2x 2 − 9x + 18 is equivalent to
19 How many different ways can teams of four
members be formed from a class of 20 students?
to
26 A study compared the number of years of education
a person received and that person's average yearly
salary. It was determined that the relationship
between these two quantities was linear and the
correlation coefficient was 0.91. Which conclusion
can be made based on the findings of this study?
20 The value of csc 138°23′ rounded to four decimal
places is
27 The terminal side of an angle measuring
21 Which transformation of y = f(x) moves the graph
7 units to the left and 3 units down?
radians lies in Quadrant
4π
5
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 3 Name: ______________________
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4
28 Which expression is equivalent to
∑ (a − n) ?
2
35 When x 2 + 3x − 4 is subtracted from x 3 + 3x 2 − 2x ,
the difference is
n=1
9
29 Which equation has roots with the sum equal to
4
3
and the product equal to ?
4
30 The expression x 2 (x + 2) − (x + 2) is equivalent to
 2
3 
31 What is the product of  x − y 2  and
4 
5

 2
 x + 3 y 2  ?
 5
4 

b
c
is equivalent to
32 The expression
b
d−
c
a+
36 A school math team consists of three juniors and
five seniors. How many different groups can be
formed that consist of one junior and two seniors?
37 A math club has 30 boys and 20 girls. Which
expression represents the total number of different
5-member teams, consisting of 3 boys and 2 girls,
that can be formed?
38 In the interval 0° ≤ x < 360°, tanx is undefined
when x equals
39 What is the total number of different nine-letter
arrangements that can be formed using the letters in
the word “TENNESSEE”?
40 Which ordered pair is a solution of the system of
equations shown below? x + y = 5
(x + 3) 2 + (y − 3) 2 = 53
1
2
33 What is the value of 4x + x 0 + x
1
−
4
when x = 16?
41 What is the conjugate of
34 If 2x 3 = y, then logy equals
1 3
+ i?
2 2
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 4 Name: ______________________
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42 When factored completely, x 3 + 3x 2 − 4x − 12
equals
49 The domain of f(x) = −
3
is the set of all real
2−x
numbers



3 
3

 =
43 If tan  Arc cos
, then k is

k 
3


50 In the right triangle shown below, what is the
measure of angle S, to the nearest minute?
44 The exact value of csc 120° is
45 Which expression is equivalent to
2x −2 y −2
4y −5
?
46 A customer will select three different toppings for a
supreme pizza. If there are nine different toppings
to choose from, how many different supreme pizzas
can be made?
47 Susie invests $500 in an account that is
compounded continuously at an annual interest rate
of 5%, according to the formula A = Pe rt , where A
is the amount accrued, P is the principal, r is the
rate of interest, and t is the time, in years.
Approximately how many years will it take for
Susie’s money to double?
48 Which expression is equivalent to
x −1 y 2
x 2 y −4
7
and ∠A terminates in Quadrant IV,
25
tan A equals
51 If sin A = −
52 What is the solution set of the equation
− 2 sec x = 2 when 0° ≤ x < 360°?
53 A population, p(x) , of wild turkeys in a certain area
is represented by the function p(x) = 17(1.15) 2x ,
where x is the number of years since 2010. How
many more turkeys will be in the population for the
year 2015 than 2010?
54 How many full cycles of the function y = 3 sin2x
appear in  radians?
?
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 5 Name: ______________________
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55 The expression
−180x 16 is equivalent to
56 Which equation could be used to solve
2
5
− = 1?
x−3 x
57 Which value of k satisfies the equation
8 3k + 4 = 4 2k − 1 ?
58 The expression
5
4−
11
is equivalent to
59 What is the solution set for 2cos θ − 1 = 0 in the
interval 0° ≤ θ < 360°?
60 In the diagram below, the length of which line
segment is equal to the exact value of sin θ ?
61 Which graph represents the solution set of
| 4x − 5 |
|
| > 1?
| 3 |
62 Approximately how many degrees does five
radians equal?
63 The area of triangle ABC is 42. If AB = 8 and
m∠B = 61, the length of BC is approximately
64 What is the fourth term in the binomial expansion
(x − 2) 8 ?
65 What is the solution set of |x − 2| =3x + 10?
66 If f(x) =
9 − x 2 , what are its domain and range?
67 When −3 − 2i is multiplied by its conjugate, the
result is
68 The expression log4m2 is equivalent to
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 6 Name: ______________________
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69 The expression sin(θ + 90)° is equivalent to
75 A circle with center O and passing through the
origin is graphed below.
70 The formula to determine continuously
compounded interest is A = Pe rt , where A is the
amount of money in the account, P is the initial
investment, r is the interest rate, and t is the time,
in years. Which equation could be used to
determine the value of an account with an $18,000
initial investment, at an interest rate of 1.25% for
24 months?
71 Liz has applied to a college that requires students
to score in the top 6.7% on the mathematics portion
of an aptitude test. The scores on the test are
approximately normally distributed with a mean
score of 576 and a standard deviation of 104. What
is the minimum score Liz must earn to meet this
requirement?
What is the equation of circle O?
1−
76 The simplest form of
1−
4
x
2
8
− 2
x x
is
72 Which expression is equivalent to (5 −2 a 3 b −4 ) −1 ?
77 What is the solution of the inequality 9 − x 2 < 0?
73 For y =
3
, what are the domain and range?
x−4
74 A theater has 35 seats in the first row. Each row
has four more seats than the row before it. Which
expression represents the number of seats in the nth
row?
78 An arithmetic sequence has a first term of 10 and a
sixth term of 40. What is the 20th term of this
sequence?
79 What is the product of
3
4a 2 b 4 and
3
16a 3 b 2 ?
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 7 Name: ______________________
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80 The graph below shows the average price of
gasoline, in dollars, for the years 1997 to 2007.
86 If cos θ =
3
, then what is cos 2θ ?
4
87 There are eight people in a tennis club. Which
expression can be used to find the number of
different ways they can place first, second, and
third in a tournament?
What is the approximate range of this graph?
88 The expression
 3

 
2
 x + 1   3 x − 1  −  3 x − 1  is
 2
  2
  2



 

equivalent to
81 If f(x) = 4x − x 2 and g(x) =
 1 
1
, then (f  g)   is
x
2
equal to
89 The table of values below can be modeled by
which equation?
82 What is the common difference in the sequence
2a + 1, 4a + 4, 6a + 7, 8a + 10, . . .?
83 What is the period of the graph y =
1
sin6x ?
2
84 In DEF , d = 5, e = 8, and m∠D = 32. How
many distinct triangles can be drawn given these
measurements?
90 What are the sum and product of the roots of the
equation 6x 2 − 4x − 12 = 0?

2
91 The expression  2 − 3 x  is equivalent to


85 The ninth term of the expansion of (3x + 2y) 15 is
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 8 Name: ______________________
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92 As shown in the table below, a person’s target heart
rate during exercise changes as the person gets
older.
97 The solution set of the equation
2x − 4 = x − 2 is
98 If $5000 is invested at a rate of 3% interest
compounded quarterly, what is the value of the
investment in 5 years? (Use the formula
nt

r 


A = P  1 +  , where A is the amount accrued, P
n

is the principal, r is the interest rate, n is the
number of times per year the money is
compounded, and t is the length of time, in years.)
Which value represents the linear correlation
coefficient, rounded to the nearest thousandth,
between a person’s age, in years, and that person’s
target heart rate, in beats per minute?
1
93 If sin A = , what is the value of cos 2A?
3
94 What is the sum of the first 19 terms of the
sequence 3,10,17,24,31,. . .?
99 Circle O has a radius of 2 units. An angle with a
measure of
π
radians is in standard position. If
6
the terminal side of the angle intersects the circle at
point B, what are the coordinates of B?
100 How many different six-letter arrangements can be
made using the letters of the word “TATTOO”?
101 Given y varies inversely as x, when y is multiplied
1
by , then x is multiplied by
2
95 Which equation represents a graph that has a period
of 4π ?
96 Expressed in simplest form,
−18 −
−32 is
102 Two sides of a triangular-shaped sandbox measure
22 feet and 13 feet. If the angle between these two
sides measures 55°, what is the area of the sandbox,
to the nearest square foot?
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 9 Name: ______________________
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103 Which equation is represented by the graph below?
109 If order does not matter, which selection of
students would produce the most possible
committees?
110 What is the domain of the function shown below?
104 Max solves a quadratic equation by completing the
square. He shows a correct step:
(x + 2) 2 = −9
What are the solutions to his equation?
105 Which ordered pair is in the solution set of the
system of equations shown below?
y 2 − x 2 + 32 = 0
3y − x = 0
106 If sin θ < 0 and cot θ > 0, in which quadrant does
the terminal side of angle θ lie?


1
111 If log b x = 3log b p −  2 log b t + log b r  , then the


2
value of x is
2
112 What is the value of
∑ (3 − 2a) ?
x
x=0
107 What is the domain of the function g x  = 3 x -1?
113 The first four terms of the sequence defined by
1
a 1 = and a n + 1 = 1 − a n are
2
108 What is the inverse of the function f(x) = log 4 x?
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 10 Name: ______________________
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114 Which expression is equivalent to
x −1 y 4
−5
3x y
−1
?
115 Yusef deposits $50 into a savings account that pays
3.25% interest compounded quarterly. The
amount, A, in his account can be determined by the
nt

r 
formula A = P  1 +  , where P is the initial
n

amount invested, r is the interest rate, n is the
number of times per year the money is
compounded, and t is the number of years for
which the money is invested. What will his
investment be worth in 12 years if he makes no
other deposits or withdrawals?
120 In a certain high school, a survey revealed the mean
amount of bottled water consumed by students each
day was 153 bottles with a standard deviation of 22
bottles. Assuming the survey represented a normal
distribution, what is the range of the number of
bottled waters that approximately 68.2% of the
students drink?
121 A population of rabbits doubles every 60 days
t
60
according to the formula P = 10(2) , where P is
the population of rabbits on day t. What is the
value of t when the population is 320?
1
7 2 3
5
x − x is subtracted from x 2 − x + 2,
4
4
8
8
the difference is
122 When
116 If f x  = 4x 2 − x + 1, then f(a + 1) equals
117 Which values of x in the interval 0° ≤ x < 360°
satisfy the equation 2sin 2 x + sin x − 1 = 0?
118 In parallelogram BFLO, OL = 3.8, LF = 7.4, and
m∠O = 126. If diagonal BL is drawn, what is the
area of BLF ?
119 The quantities p and q vary inversely. If p = 20
when q = −2, and p = x when q = −2x + 2, then x
equals
123 The conjugate of the complex expression −5x + 4i
is
124 What is the product of the roots of the quadratic
equation 2x 2 − 7x = 5?
125 A wheel has a radius of 18 inches. Which distance,
to the nearest inch, does the wheel travel when it
2π
radians?
rotates through an angle of
5
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 11 Name: ______________________
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126 What are the zeros of the polynomial function
graphed below?
131 Which equation is represented by the graph below?
127 A scholarship committee rewards the school's top
math students. The amount of money each winner
receives is inversely proportional to the number of
scholarship recipients. If there are three winners,
they each receive $400. If there are eight winners,
how much money will each winner receive?
132 If logx = 2log a + log b , then x equals
133 The expression
128 Which expression represents the third term in the
expansion of (2x 4 − y) 3 ?
129 The expression
3
27a 3 ⋅
4
16b 8 is equivalent to
130 If f(x) = 2x 2 − 3x + 1 and g(x) = x + 5, what is
f(g(x))?
3
64a 16 is equivalent to
134 What is the solution set for the equation
5x + 29 = x + 3?
135 By law, a wheelchair service ramp may be inclined
no more than 4.76°. If the base of a ramp begins 15
feet from the base of a public building, which
equation could be used to determine the maximum
height, h, of the ramp where it reaches the
building’s entrance?
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 12 Name: ______________________
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136 What is the period of the graph of the equation
1
y = sin2x ?
3
141 Given angle A in Quadrant I with sin A =
12
and
13
3
angle B in Quadrant II with cos B = − , what is the
5
value of cos(A − B)?
137 Which equation is graphed in the diagram below?
142 Which equation represents the graph below?
138 A sequence has the following terms: a 1 = 4,
a 2 = 10, a 3 = 25, a 4 = 62.5. Which formula
represents the nth term in the sequence?
139 A cliff diver on a Caribbean island jumps from a
height of 105 feet, with an initial upward velocity
of 5 feet per second. An equation that models the
height, h(t) , above the water, in feet, of the diver in
time elapsed, t, in seconds, is
h(t) = −16t 2 + 5t + 105. How many seconds, to the
nearest hundredth, does it take the diver to fall 45
feet below his starting point?
140 Angle θ is in standard position and (−4,0) is a
point on the terminal side of θ . What is the value
of sec θ ?
143 What is the range of the function shown below?
144 If sin x = siny = a and cos x = cos y = b , then
cos(x − y) is
145 What is the product of the roots of 4x 2 − 5x = 3?
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 13 Name: ______________________
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146 What is the area of a parallelogram that has sides
measuring 8 cm and 12 cm and includes an angle of
120°?
1
1
x + 8 and h(x) = x − 2, what is the
2
2
value of g(h( − 8))?
153 If g(x) =
147 If x = 3i , y = 2i , and z = m + i, the expression xy 2 z
equals
154 The expression
148 What is the fourth term of the sequence defined by
a 1 = 3xy 5
155 What is the graph of the solution set of
|2x − 1| > 5?
1
7−
11
is equivalent to
 2x 
a n =   a n − 1 ?
 y 
149 In FGH , f = 6, g = 9 , and m∠H = 57. Which
statement can be used to determine the numerical
value of h?
150 If f(x) = 2x 2 + 1 and g(x) = 3x − 2, what is the value
of f(g( − 2))?
 x 1 
 x 1 
151 What is the product of  −  and  +  ?
 4 3
 4 3
152 Which graph represents the solution set of
x + 16
≤ 7?
x−2
 3 
156 The points (2,3),  4,  , and (6,d) lie on the graph
 4
of a function. If y is inversely proportional to the
square of x, what is the value of d?
1 3 9
157 The common ratio of the sequence − , ,− is
2 4 8
3
158 If p varies inversely as q, and p = 10 when q = ,
2
3
what is the value of p when q = ?
5
159 What is the solution set of the equation
3x 5 − 48x = 0?
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160 What is the common difference of the arithmetic
sequence below?
−7x,−4x,−x,2x,5x,. . .
161 If d varies inversely as t, and d = 20 when t = 2,
what is the value of t when d = −5?
162 What is the common ratio of the geometric
sequence shown below?
−2,4,−8,16,. . .
3
163 The sum of 6a 4 b 2 and
simplest radical form, is
3
162a 4 b 2 , expressed in
164 What is the number of degrees in an angle whose
8π
?
radian measure is
5
165 The table below displays the number of siblings of
each of the 20 students in a class.
166 When factored completely, the expression
3x 3 − 5x 2 − 48x + 80 is equivalent to
167 What is the number of degrees in an angle whose
measure is 2 radians?
168 What is the product of the roots of x 2 − 4x + k = 0
if one of the roots is 7?
169 When x −1 + 1 is divided by x + 1, the quotient
equals
 3
  3

170 The expression  27x 2   16x 4  is equivalent



to
171 The table below displays the results of a survey
regarding the number of pets each student in a class
has. The average number of pets per student in this
class is 2.
What is the value of k for this table?
What is the population standard deviation, to the
nearest hundredth, for this group?
172 How many distinct triangles can be constructed if
m∠A = 30, side a = 34 , and side b = 12?
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173 Which value of k will make x 2 −
1
x + k a perfect
4
5
180 The expression 4 +
∑ 3(k − x) is equal to
k=2
square trinomial?

 −1
174 Which expression is equivalent to  3x 2  ?


181 The expression
175 The value of sin(180 + x) is equivalent to
182 What is the equation of the graph shown
cot x
is equivalent to
csc x
below?
176 What is the middle term in the expansion of
6
 x

 − 2y  ?
2



177 How many different 11-letter arrangements are
possible using the letters in the word
“ARRANGEMENT”?
178 What is the solution set of the equation
5
30
?
+1=
2
x−3
x −9
179 The scores on a standardized exam have a mean of
82 and a standard deviation of 3.6. Assuming a
normal distribution, a student's score of 91 would
rank
183 What is the third term in the expansion of
(2x − 3) 5 ?

15 
184 What is the value of tan  Arc cos  ?

17 
185 The expression
3−
8
3
is equivalent to
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 16 Name: ______________________
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Algebra 2/Trigonometry Regents Bimodal Worksheets
186 If f x  =
x
, what is the value of f(−10)?
x − 16
2
192 A dartboard is shown in the diagram below. The
two lines intersect at the center of the circle, and
2π
.
the central angle in sector 2 measures
3
187 In the diagram below of right triangle KTW,
KW = 6, KT = 5, and m∠KTW = 90.
What is the measure of ∠K , to the nearest minute?
If darts thrown at this board are equally likely to
land anywhere on the board, what is the probability
that a dart that hits the board will land in either
sector 1 or sector 3?
188 The solutions of the equation y 2 − 3y = 9 are
193 The conjugate of 7 − 5i is
189 What is the value of x in the equation
9 3x + 1 = 27 x + 2 ?
5
194 The value of the expression
∑ (−r
2
+ r) is
r =3
190 The expression 2logx − (3log y + log z) is equivalent
to
195 What is the fourth term in the expansion of
(3x − 2) 5 ?
191 The expression (x − 1)
2
−
2
3
is equivalent to
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196 Which equation is sketched in the diagram below?
202 If a = 3 and b = −2, what is the value of the
a −2
expression −3 ?
b
203 What is a formula for the nth term of sequence B
shown below?
B = 10,12,14,16,. . .
204 If r =
3
A2 B
, then log r can be represented by
C
197 If f(x) = x 2 − 5 and g(x) = 6x, then g(f(x)) is equal
to
205 The expression
198 The value of tan126°43′ to the nearest
ten-thousandth is
199 An amateur bowler calculated his bowling average
for the season. If the data are normally distributed,
about how many of his 50 games were within one
standard deviation of the mean?
a 2 b −3
is equivalent to
a −4 b 2
206 Brian correctly used a method of completing the
square to solve the equation x 2 + 7x − 11 = 0.
Brian’s first step was to rewrite the equation as
x 2 + 7x = 11 . He then added a number to both
sides of the equation. Which number did he add?
1
x − 3 and g(x) = 2x + 5, what is the value
2
of (g  f)(4)?
207 If f(x) =
200 In simplest form,
201 In
−300 is equivalent to
ABC , a = 3, b = 5, and c = 7. What is m∠C ?
208 What is the conjugate of −2 + 3i?
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 18 Name: ______________________
www.jmap.org
209 Three marbles are to be drawn at random, without
replacement, from a bag containing 15 red marbles,
10 blue marbles, and 5 white marbles. Which
expression can be used to calculate the probability
of drawing 2 red marbles and 1 white marble from
the bag?
215 What is the radian measure of an angle whose
measure is −420°?
216 The expression
210 The principal would like to assemble a committee
of 8 students from the 15-member student council.
How many different committees can be chosen?
211 A circle has a radius of 4 inches. In inches, what is
the length of the arc intercepted by a central angle
of 2 radians?
212 Which formula can be used to determine the total
number of different eight-letter arrangements that
can be formed using the letters in the word
DEADLINE?
x 1
−
4 x
213 Written in simplest form, the expression
is
1 1
+
2x 4
equivalent to
214 When x −1 − 1 is divided by x − 1, the quotient is
4
5−
13
is equivalent to
217 The number of minutes students took to complete a
quiz is summarized in the table below.
If the mean number of minutes was 17, which
equation could be used to calculate the value of x?
218 A four-digit serial number is to be created from the
digits 0 through 9. How many of these serial
numbers can be created if 0 can not be the first
digit, no digit may be repeated, and the last digit
must be 5?
219 The solution set of 4 x
2
+ 4x
= 2 −6 is
220 Which values of x are in the solution set of the
following system of equations?
y = 3x − 6
y = x2 − x − 6
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 19 Name: ______________________
www.jmap.org
221 In the diagram below of a unit circle, the ordered



2
2 

 represents the point where the
,−
pair  −
2 
 2


terminal side of θ intersects the unit circle.
226 The expression 4ab
is equivalent to
2b − 3a
18b 3 + 7ab
6b
227 Which values of x are solutions of the equation
x 3 + x 2 − 2x = 0?
228 A survey completed at a large university asked
2,000 students to estimate the average number of
hours they spend studying each week. Every tenth
student entering the library was surveyed. The data
showed that the mean number of hours that
students spend studying was 15.7 per week. Which
characteristic of the survey could create a bias in
the results?
What is m∠θ ?
222 The product of (3 +
5) and (3 −


3 

?
229 What is the principal value of cos −1  −
 2 


5) is
230 What is the period of the function f(θ) = −2cos 3θ ?
223 Which two functions are inverse functions of each
other?
231 The solution set of the inequality x 2 − 3x > 10 is
224 What is the common difference of the arithmetic
sequence 5,8,11,14?
225 What is the solution of the equation 2 log 4 (5x) = 3?
232 In ABC , m∠A = 74, a = 59.2, and c = 60.3.
What are the two possible values for m∠C , to the
nearest tenth?
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 20 Name: ______________________
www.jmap.org
233 The graph of y = x 3 − 4x 2 + x + 6 is shown below.
237 The table below shows the first-quarter averages
for Mr. Harper’s statistics class.
What is the product of the roots of the equation
x 3 − 4x 2 + x + 6 = 0?
What is the population variance for this set of data?
234 The minimum point on the graph of the equation
y = f(x) is (−1,−3). What is the minimum point on
the graph of the equation y = f(x) + 5 ?
235 What is the number of degrees in an angle whose
11π
?
radian measure is
12
236 What is the domain of the function
f(x) = x − 2 + 3?
238 Which graph represents one complete cycle of the
equation y = sin3π x ?
239 Four points on the graph of the function f(x) are
shown below.
{(0,1),(1,2),(2,4),(3,8)}
Which equation represents f(x)?
240 What is the coefficient of the fourth term in the
expansion of (a − 4b) 9 ?
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 21 Name: ______________________
www.jmap.org
241 What are the domain and the range of the function
shown in the graph below?
247 The expression (3 − 7i) 2 is equivalent to
248 In ABC , m∠A = 120 , b = 10, and c = 18. What
is the area of ABC to the nearest square inch?
249 Ms. Bell's mathematics class consists of 4
sophomores, 10 juniors, and 5 seniors. How many
different ways can Ms. Bell create a four-member
committee of juniors if each junior has an equal
chance of being selected?
250 Which equation is represented by the graph below?
242 What is the range of f(x) = (x + 4) 2 + 7?
243 The product of i 7 and i 5 is equivalent to
244 What is the solution set of the equation
|4a + 6| − 4a = −10?
245 Factored completely, the expression 6x − x 3 − x 2 is
equivalent to
246 Which graph represents the solution set of
|6x − 7| ≤ 5?
251 What is the common ratio of the geometric
sequence whose first term is 27 and fourth term is
64?
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 22 Name: ______________________
www.jmap.org
252 In the diagram below of right triangle JTM,
JT = 12, JM = 6, and m∠JMT = 90.
2
255 The value of the expression 2
∑ (n
2
+ 2 n ) is
n =0
256 What is the value of x in the equation log 5 x = 4?
257 The expression cos 2 θ − cos 2θ is equivalent to
What is the value of cot J ?
253 In ABC , a = 15, b = 14, and c = 13, as shown in
the diagram below. What is the m∠C , to the
nearest degree?
258 What is the period of the function

1  x
y = sin  − π  ?
2 3

259 The roots of the equation 2x 2 + 7x − 3 = 0 are
260 The sides of a parallelogram measure 10 cm and 18
cm. One angle of the parallelogram measures 46
degrees. What is the area of the parallelogram, to
the nearest square centimeter?
261 Factored completely, the expression
12x 4 + 10x 3 − 12x 2 is equivalent to
3 2 1
x − x − 4 is subtracted from
2
4
5 2 3
x − x + 1, the difference is
4
2
254 When
262 The expression log 8 64 is equivalent to
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 23 Name: ______________________
www.jmap.org
263 What is the radian measure of the smaller angle
formed by the hands of a clock at 7 o’clock?
268 The expression 2i 2 + 3i 3 is equivalent to
269 The graph of y = f(x) is shown below.
264 For which equation does the sum of the roots equal
−3 and the product of the roots equal 2?
265 The expression
sin 2 θ + cos 2 θ
is equivalent to
1 − sin 2 θ
266 Samantha constructs the scatter plot below from a
set of data.
Which set lists all the real solutions of f(x) = 0?
270 If a function is defined by the equation f(x) = 4 x ,
which graph represents the inverse of this function?
Based on her scatter plot, which regression model
would be most appropriate?
267 The value of x in the equation 4 2x + 5 = 8 3x is
271 Akeem invests $25,000 in an account that pays
4.75% annual interest compounded continuously.
Using the formula A = Pe rt , where A = the amount
in the account after t years, P = principal invested,
and r = the annual interest rate, how many years, to
the nearest tenth, will it take for Akeem’s
investment to triple?
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 24 Name: ______________________
www.jmap.org
 −5
w
272 When simplified, the expression  −9
w

equivalent to
1
 2

 is


275 The solution set of
3x + 16 = x + 2 is
276 Which expression is equivalent to
3 +5
3 −5
?
273 Which equation is represented by the graph below?
277 Twenty different cameras will be assigned to
several boxes. Three cameras will be randomly
selected and assigned to box A. Which expression
can be used to calculate the number of ways that
three cameras can be assigned to box A?
278 The lengths of 100 pipes have a normal distribution
with a mean of 102.4 inches and a standard
deviation of 0.2 inch. If one of the pipes measures
exactly 102.1 inches, its length lies
 1 
279 The expression log 5   is equivalent to
 25 
274 Which ratio represents csc A in the diagram below?
280 What is the formula for the nth term of the
sequence 54,18,6,. . .?
281 An auditorium has 21 rows of seats. The first row
has 18 seats, and each succeeding row has two
more seats than the previous row. How many seats
are in the auditorium?
Algebra 2/Trigonometry Regents Exam Bimodal Questions Worksheet # 25 Name: ______________________
www.jmap.org
282 Which equation represents the circle shown in the
graph below that passes through the point (0,−1)?
287 What is the fifteenth term of the sequence
5,−10,20,−40,80,. . .?
288 What is the fifteenth term of the geometric
sequence − 5, 10 ,−2 5 ,. . .?
289 If sin A =
2
where 0° < A < 90°, what is the value
3
of sin2A?
290 What are the values of θ in the interval
0° ≤ θ < 360° that satisfy the equation
tan θ − 3 = 0?
283 The solution set of the equation
x + 3 = 3 − x is
284 For which equation does the sum of the roots equal
3
and the product of the roots equal −2?
4
291 The expression cos 4x cos 3x + sin4x sin 3x is
equivalent to
292 The graph below shows the function f(x).
−
285 The expression x
2
5
is equivalent to
286 How many distinct triangles can be formed if
m∠A = 35, a = 10, and b = 13?
Which graph represents the function f(x + 2)?
ID: A
Algebra 2/Trigonometry Regents Bimodal Worksheets
Answer Section
1 ANS:
1
log 6 + log a
2
log x 2 = log 3a + log 2a
2 logx = log 6a 2
log x =
log 6 log a 2
+
2
2
log x =
2 loga
1
log 6 +
2
2
log x =
1
log 6 + log a
2
PTS: 2
REF: 011224a2
KEY: splitting logs
2 ANS:
0
STA: A2.A.19
TOP: Properties of Logarithms
PTS: 2
3 ANS:
3π
2
REF: 061222a2
STA: A2.A.50
TOP: Solving Polynomial Equations
REF: 061212a2
STA: A2.A.61
TOP: Arc Length
s=θr=
2π
3π
⋅6 =
8
2
PTS: 2
KEY: arc length
4 ANS:
6 C 4 ⋅4 C 2
PTS: 2
REF: 061523a2
STA: A2.S.9
TOP: Differentiating Permutations and Combinations
5 ANS:
3sinx 2
PTS: 2
KEY: variables
REF: 061216a2
STA: A2.A.42
TOP: Compositions of Functions
ID: A
6 ANS:
3
2
3y
3y
3y − 9 3(y − 3) 3
9
9
+
=
−
=
=
=
2y − 6 6 − 2y 2y − 6 2y − 6 2y − 6 2(y − 3) 2
PTS: 2
7 ANS:
{y | y ≥ 2}
REF: 011325a2
STA: A2.A.16
TOP: Addition and Subtraction of Rationals
PTS: 2
KEY: real domain
8 ANS:
5
12 − 7 = 5
REF: 011222a2
STA: A2.A.39
TOP: Domain and Range
PTS: 2
REF: 011525a2
STA: A2.S.4
KEY: range, quartiles, interquartile range, variance
9 ANS:
1
3xy 3
TOP: Dispersion
PTS: 2
REF: 011306a2
STA: A2.A.8
10 ANS:
cot A
1 + cos 2A 1 + 2 cos 2 A − 1 cos A
=
=
= cot A
sin 2A
2 sinA cos A
sinA
TOP: Negative and Fractional Exponents
PTS: 2
KEY: simplifying
11 ANS:
1
16a 4
REF: 061522a2
STA: A2.A.77
TOP: Double Angle Identities
PTS: 2
12 ANS:
23
32
REF: 061402a2
STA: A2.A.8
TOP: Negative and Fractional Exponents
 3  2 32 9
23
cos 2A = 1 − 2 sin A = 1 − 2   =
−
=
32 32 32
 8
2
PTS: 2
KEY: evaluating
REF: 011510a2
STA: A2.A.77
TOP: Double Angle Identities
ID: A
13 ANS:
0.5
1
If sin x = 0.8, then cos x = 0.6. tan x =
2
PTS: 2
14 ANS:
831,600
11 P 11
3!2!2!2!
REF: 061220a2
=
1 − 0.6
=
1 + 0.6
0.4
= 0.5.
1.6
STA: A2.A.77
TOP: Half Angle Identities
STA: A2.S.10
TOP: Permutations
39,916,800
= 831,600
48
PTS: 2
15 ANS:
2b − a − 1
log 9 − log 20
REF: 081512a2
log 3 2 − log(10 ⋅ 2)
2 log 3 − (log 10 + log 2)
2b − (1 + a)
2b − a − 1
PTS: 2
REF: 011326a2
STA: A2.A.19
KEY: expressing logs algebraically
16 ANS:
4xi
(x + i) 2 − (x − i) 2 = x 2 + 2xi + i 2 − (x 2 − 2xi + i 2 ) = 4xi
TOP: Properties of Logarithms
PTS: 2
REF: 011327a2
STA: A2.N.9
TOP: Multiplication and Division of Complex Numbers
17 ANS:
−39,321
S8 =
3(1 − (−4) 8 ) 196,605
=
= −39,321
5
1 − (−4)
PTS: 2
KEY: geometric
18 ANS:
6b
− 2
a
3
− a3b4
32
6b
= − 2
1 5 3
a
a b
64
PTS: 2
REF: 061304a2
STA: A2.A.35
TOP: Summations
REF: 061326a2
STA: A2.A.31
TOP: Sequences
ID: A
19 ANS:
4,845
20 C 4 = 4,845
PTS: 2
20 ANS:
1.5057
REF: 011509a2
STA: A2.S.11
TOP: Combinations
PTS: 2
21 ANS:
y = f(x + 7) − 3
REF: 061217a2
STA: A2.A.66
TOP: Determining Trigonometric Functions
PTS: 2
REF: 061516a2
STA: A2.A.46
TOP: Transformations with Functions and Relations
22 ANS:
225
512
 5  2  3  1 225
    =
3 C2 
 8   8 
512
   
PTS: 2
REF: 011221a2
KEY: spinner
23 ANS:
53.2%
34.1% + 19.1% = 53.2%
STA: A2.S.15
PTS: 2
REF: 011212a2
STA: A2.S.5
KEY: probability
24 ANS:
1
11 − x
(x + 11)(x − 2)
−1
−1
x 2 + 9x − 22
÷ (2 − x) =
⋅
=
2
(x + 11)(x − 11) x − 2 x − 11
x − 121
PTS: 2
KEY: Division
REF: 011423a2
STA: A2.A.16
TOP: Binomial Probability
TOP: Normal Distributions
TOP: Multiplication and Division of Rationals
ID: A
25 ANS:
(x − 2)(x − 3)(x + 3)
x 3 − 2x 2 − 9x + 18
x 2 (x − 2) − 9(x − 2)
(x 2 − 9)(x − 2)
(x + 3)(x − 3)(x − 2)
PTS: 2
REF: 011511a2
26 ANS:
There was a strong relationship.
STA: A2.A.7
TOP: Factoring by Grouping
PTS: 2
27 ANS:
II
STA: A2.S.8
TOP: Correlation Coefficient
REF: 081502a2
PTS: 2
REF: 061502a2
STA: A2.M.1
28 ANS:
4a 2 − 20a + 30
(a − 1) 2 + (a − 2) 2 + (a − 3) 2 + (a − 4) 2
TOP: Radian Measure
(a 2 − 2a + 1) + (a 2 − 4a + 4) + (a 2 − 6a + 9) + (a 2 − 8a + 16)
4a 2 − 20a + 30
PTS: 2
KEY: advanced
29 ANS:
4x 2 − 9x + 3 = 0
sum of the roots,
REF: 011414a2
STA: A2.N.10
TOP: Sigma Notation
−b −(−9) 9
c 3
=
= . product of the roots, =
4
4
a 4
a
PTS: 2
KEY: basic
30 ANS:
(x + 1)(x − 1)(x + 2)
REF: 061208a2
STA: A2.A.21
TOP: Roots of Quadratics
REF: 011426a2
STA: A2.A.7
TOP: Factoring by Grouping
x 2 (x + 2) − (x + 2)
(x 2 − 1)(x + 2)
(x + 1)(x − 1)(x + 2)
PTS: 2
ID: A
31 ANS:
4 2 9 4
x −
y
16
25
The binomials are conjugates, so use FL.
PTS: 2
REF: 061201a2
STA: A2.N.3
32 ANS:
ac + b
cd − b
b
ac + b
a+
c
c
ac + b
c
ac + b
=
=
⋅
=
c
cd − b cd − b
b
cd − b
d−
c
c
TOP: Operations with Polynomials
PTS: 2
33 ANS:
1
17
2
STA: A2.A.17
TOP: Complex Fractions
STA: A2.N.1
TOP: Negative and Fractional Exponents
PTS: 2
REF: 061426a2
KEY: splitting logs
35 ANS:
x 3 + 2x 2 − 5x + 4
STA: A2.A.19
TOP: Properties of Logarithms
PTS: 2
REF: 011314a2
36 ANS:
30
3 C 1 ⋅5 C 2 = 3 ⋅ 10 = 30
STA: A2.N.3
TOP: Operations with Polynomials
PTS: 2
37 ANS:
30 C 3 ⋅20 C 2
STA: A2.S.12
TOP: Combinations
REF: 011405a2
1
2
f(16) = 4(16) + 16 + 16
= 4(4) + 1 +
= 17
0
−
1
4
1
2
1
2
PTS: 2
34 ANS:
log2 + 3logx
REF: 081503a2
log2x 3 = log 2 + log x 3 = log2 + 3logx
REF: 061422a2
PTS: 2
REF: 011417a2
STA: A2.S.9
TOP: Differentiating Permutations and Combinations
ID: A
38 ANS:
90º and 270º
PTS: 1
REF: 011312a2
KEY: degrees, common angles
39 ANS:
3,780
362,880
9 P9
=
= 3,780
96
4!⋅ 2!⋅ 2!
STA: A2.A.56
TOP: Determining Trigonometric Functions
PTS: 2
40 ANS:
(−5,10)
STA: A2.S.10
TOP: Permutations
REF: 061511a2
x+y = 5
. −5 + y = 5
y = −x + 5
y = 10
(x + 3) 2 + (−x + 5 − 3) 2 = 53
x 2 + 6x + 9 + x 2 − 4x + 4 = 53
2x 2 + 2x − 40 = 0
x 2 + x − 20 = 0
(x + 5)(x − 4) = 0
x = −5,4
PTS: 2
KEY: equations
41 ANS:
1 3
− i
2 2
REF: 011302a2
STA: A2.A.3
TOP: Quadratic-Linear Systems
PTS: 2
42 ANS:
(x + 2)(x − 2)(x + 3)
REF: 011213a2
STA: A2.N.8
TOP: Conjugates of Complex Numbers
REF: 061214a2
STA: A2.A.7
TOP: Factoring by Grouping
x 3 + 3x 2 − 4x − 12
x 2 (x + 3) − 4(x + 3)
(x 2 − 4)(x + 3)
(x + 2)(x − 2)(x + 3)
PTS: 2
ID: A
43 ANS:
2
tan30 =
3
3
= 30
. Arc cos
3
k
3
k
= cos 30
k =2
PTS: 2
KEY: advanced
44 ANS:
REF: 061323a2
STA: A2.A.64
TOP: Using Inverse Trigonometric Functions
2 3
3
sin 120 =
3
2
csc 120 =
⋅
2
3
PTS: 2
45 ANS:
y3
3
3
=
2 3
3
REF: 081505a2
STA: A2.A.59
TOP: Reciprocal Trigonometric Relationships
PTS: 2
46 ANS:
84
9 C 3 = 84
REF: 061324a2
STA: A2.A.9
TOP: Negative Exponents
PTS: 2
47 ANS:
13.9
1000 = 500e .05t
REF: 081513a2
STA: A2.S.11
TOP: Combinations
REF: 061313a2
STA: A2.A.6
TOP: Exponential Growth
REF: 061506a2
STA: A2.A.9
TOP: Negative Exponents
2x 2
2 = e .05t
ln 2 = ln e .05t
ln 2 .05t ⋅ ln e
=
.05
.05
13.9 ≈ t
PTS: 2
48 ANS:
y6
x3
PTS: 2
ID: A
49 ANS:
less than 2
PTS: 2
KEY: real domain
50 ANS:
28°4'
sin S =
REF: 011521a2
STA: A2.A.39
TOP: Domain and Range
REF: 061311a2
STA: A2.A.55
TOP: Trigonometric Ratios
8
17
S = sin −1
8
17
S ≈ 28°4'
PTS: 2
51 ANS:
7
−
24
7
−
25
sin A
7
7
24
=
= −
If sin A = − , cos A = , and tanA =
cos A
24
24
25
25
25
PTS: 2
KEY: advanced
52 ANS:
{135°,225°}
REF: 011413a2
STA: A2.A.64
TOP: Using Inverse Trigonometric Functions
PTS: 2
REF: 011322a2
KEY: reciprocal functions
STA: A2.A.68
TOP: Trigonometric Equations
− 2 sec x = 2
sec x = −
2
2
cos x = −
2
2
x = 135,225
ID: A
53 ANS:
51
p(5) − p(0) = 17(1.15)
2(5)
PTS: 2
54 ANS:
1
2π
=π
2
− 17(1.15)
2(0)
≈ 68.8 − 17 ≈ 51
REF: 061527a2
STA: A2.A.12
TOP: Evaluating Exponential Expressions
π
=1
π
PTS: 2
REF: 061519a2
STA: A2.A.69
TOP: Properties of Graphs of Trigonometric Functions
55 ANS:
6x 8 i 5
KEY: period
−180x 16 = 6x 8 i 5
PTS: 2
REF: 081524a2
56 ANS:
x 2 − 6x − 6 = 0
2(x − 3) x(x − 3)
5x
−
=
x(x − 3) x(x − 3) x(x − 3)
STA: A2.N.6
TOP: Square Roots of Negative Numbers
STA: A2.A.23
TOP: Solving Rationals
STA: A2.A.27
TOP: Exponential Equations
5x − 2x + 6 = x 2 − 3x
0 = x 2 − 6x − 6
PTS: 2
REF: 011522a2
KEY: irrational and complex solutions
57 ANS:
14
−
5
8 3k + 4 = 4 2k − 1 .
(2 3 ) 3k + 4 = (2 2 ) 2k − 1
2 9k + 12 = 2 4k − 2
9k + 12 = 4k − 2
5k = −14
k= −
14
5
PTS: 2
REF: 011309a2
KEY: common base not shown
ID: A
58 ANS:
4 + 11
4+
11
11 4 +
11
5
4−
⋅
PTS: 2
59 ANS:
{60°,300°}
=
5(4 + 11) 5(4 + 11)
=
= 4+
16 − 11
5
REF: 061509a2
11
STA: A2.N.5
TOP: Rationalizing Denominators
2 cos θ = 1
cos θ =
1
2
θ = cos −1
1
= 60, 300
2
PTS: 2
KEY: basic
60 ANS:
TS
REF: 061203a2
STA: A2.A.68
TOP: Trigonometric Equations
PTS: 2
61 ANS:
REF: 011315a2
STA: A2.A.55
TOP: Trigonometric Ratios
REF: 061209a2
STA: A2.A.1
TOP: Absolute Value Inequalities
REF: 011427a2
STA: A2.M.2
TOP: Radian Measure
4x − 5
4x − 5
< −1
> 1 or
3
3
4x − 5 > 3
4x > 8
x>2
PTS: 2
KEY: graph
62 ANS:
286
180
5⋅
≈ 286
4x − 5 < −3
4x < 2
x<
1
2
π
PTS: 2
KEY: degrees
ID: A
63 ANS:
12.0
1
42 = (a)(8) sin 61
2
42 ≈ 3.5a
12 ≈ a
PTS: 2
REF: 011316a2
KEY: basic
64 ANS:
−448x 5
8−3
⋅ (−2) 3 = 56x 5 ⋅ (−8) = −448x 5
8 C3 ⋅ x
STA: A2.A.74
PTS: 2
REF: 011308a2
STA: A2.A.36
65 ANS:
−2
x − 2 = 3x + 10 −6 is extraneous. x − 2 = −3x − 10
−12 = 2x
4x = −8
−6 = x
x = −2
TOP: Using Trigonometry to Find Area
TOP: Binomial Expansions
PTS: 2
REF: 061513a2
STA: A2.A.1
66 ANS:
domain: {x | − 3 ≤ x ≤ 3}; range: {y | 0 ≤ y ≤ 3}
TOP: Absolute Value Equations
PTS: 2
REF: 011313a2
KEY: real domain
67 ANS:
13
(−3 − 2i)(−3 + 2i) = 9 − 4i 2 = 9 + 4 = 13
TOP: Domain and Range
STA: A2.A.39
PTS: 2
REF: 011512a2
STA: A2.N.9
TOP: Multiplication and Division of Complex Numbers
68 ANS:
log4 + 2logm
log4m2 = log 4 + log m2 = log4 + 2 logm
PTS: 2
REF: 061321a2
STA: A2.A.19
TOP: Properties of Logarithms
KEY: splitting logs
69 ANS:
cos θ
sin(θ + 90) = sin θ ⋅ cos 90 + cos θ ⋅ sin90 = sin θ ⋅ (0) + cos θ ⋅ (1) = cos θ
PTS: 2
KEY: identities
REF: 061309a2
STA: A2.A.76
TOP: Angle Sum and Difference Identities
ID: A
70 ANS:
A = 18,000e 0.0125 • 2
PTS: 2
REF: 061416a2
STA: A2.A.12
71 ANS:
732
Top 6.7% = 1.5 s.d. + σ = 1.5(104) + 576 = 732
TOP: Evaluating Exponential Expressions
PTS: 2
KEY: predict
72 ANS:
25b 4
a3
REF: 011420a2
STA: A2.S.5
TOP: Normal Distributions
PTS: 2
REF: 011514a2
73 ANS:
{x | x > 4} and {y | y > 0}
STA: A2.A.9
TOP: Negative Exponents
PTS: 2
KEY: real domain
74 ANS:
35 + (n − 1)(4)
REF: 011416a2
STA: A2.A.39
TOP: Domain and Range
PTS: 2
REF: 061520a2
75 ANS:
(x + 4) 2 + (y − 2) 2 = 20
STA: A2.A.29
TOP: Sequences
5 2 a −3 b 4 =
25b 4
a3
PTS: 2
REF: 011513a2
STA: A2.A.49
76 ANS:
x
x+2
4
1−
x(x − 4)
x
x2
x 2 − 4x
x
× 2 = 2
=
=
(x
−
4)(x
+
2)
x
+2
2
8
x − 2x − 8
x
1− − 2
x x
PTS: 2
REF: 061305a2
STA: A2.A.17
TOP: Equations of Circles
TOP: Complex Fractions
ID: A
77 ANS:
{x | x > 3 or x < −3}
or x + 3 < 0 and x − 3 < 0
9 − x2 < 0
x < −3 and x < 3
x2 − 9 > 0
x < −3
(x + 3)(x − 3) > 0
x + 3 > 0 and x − 3 > 0
x > −3 and x > 3
x>3
PTS: 2
REF: 061507a2
KEY: one variable
78 ANS:
124
40 − 10 30
=
= 6 a n = 6n + 4
5
6−1
a 20 = 6(20) + 4 = 124
STA: A2.A.4
TOP: Quadratic Inequalities
PTS: 2
79 ANS:
STA: A2.A.32
TOP: Sequences
STA: A2.N.2
TOP: Operations with Radicals
PTS: 2
REF: 061418a2
81 ANS:
4
 1  1
g   =
= 2. f(2) = 4(2) − 2 2 = 4
2
1
 
2
STA: A2.A.51
TOP: Domain and Range
PTS: 2
REF: 011204a2
KEY: numbers
82 ANS:
2a + 3
(4a + 4) − (2a + 1) = 2a + 3
STA: A2.A.42
TOP: Compositions of Functions
STA: A2.A.30
TOP: Sequences
4ab 2
3
3
REF: 081510a2
a2
64a 5 b 6 =
3
PTS: 2
80 ANS:
0.97 ≤ y ≤ 2.38
PTS: 2
4 3 a 3 a 2 b 6 = 4ab 2
3
a2
REF: 011516a2
REF: 011401a2
ID: A
83 ANS:
π
3
2π
π
=
6
3
PTS: 2
REF: 061413a2
STA: A2.A.69
TOP: Properties of Graphs of Trigonometric Functions
84 ANS:
2
8
5
57.98 + 32 < 180
=
sin 32 sinE
(180 − 57.98) + 32 < 180
E ≈ 57.98
KEY: period
PTS: 2
85 ANS:
7
8
15 C 8 (3x) (2y)
REF: 011419a2
STA: A2.A.75
TOP: Law of Sines - The Ambiguous Case
PTS: 2
86 ANS:
1
8
REF: 081525a2
STA: A2.A.36
TOP: Binomial Expansions
 3  2
 9 
9 8 1
cos 2θ = 2   − 1 = 2   − 1 = − =
 4 
8 8 8
16
 
PTS: 2
KEY: evaluating
87 ANS:
8 P3
REF: 081522a2
STA: A2.A.77
TOP: Double Angle Identities
PTS: 2
REF: 011310a2
STA: A2.S.9
TOP: Differentiating Permutations and Combinations
88 ANS:
3x − 2


 3
   3
  3
   3

 x − 1    x + 1  −  x − 1   =  x − 1  (2) = 3x − 2
2
   2
 2
   2



 
 

PTS: 2
89 ANS:
f(x) = |x | + 3
REF: 011524a2
STA: A2.N.3
TOP: Operations with Polynomials
PTS: 2
REF: 011502a2
STA: A2.A.52
TOP: Identifying the Equation of a Graph
ID: A
90 ANS:
2
sum = ; product = −2
3
−b 4 2
c −12
= = . product: =
= −2
sum:
6 3
6
a
a
PTS: 2
91 ANS:
4 − 12 x + 9x
REF: 011209a2
STA: A2.A.20
TOP: Roots of Quadratics
PTS: 2
92 ANS:
−0.999
REF: 061407a2
STA: A2.N.3
TOP: Operations with Polynomials
STA: A2.S.8
TOP: Correlation Coefficient
.
PTS: 2
93 ANS:
7
9
REF: 061225a2
2
 1 
2 7
cos 2A = 1 − 2 sin2 A = 1 − 2   = 1 − =
3
9 9
 
PTS: 2
REF: 011311a2
STA: A2.A.77
KEY: evaluating
94 ANS:
1254
n
19
S n = [2a + (n − 1)d] =
[2(3) + (19 − 1)7] = 1254
2
2
TOP: Double Angle Identities
PTS: 2
KEY: arithmetic
95 ANS:
1
y = 3 sin x
2
2π
= 4π
b
TOP: Summations
b=
REF: 011202a2
STA: A2.A.35
1
2
PTS: 2
REF: 011425a2
STA: A2.A.69
TOP: Properties of Graphs of Trigonometric Functions
KEY: period
ID: A
96 ANS:
−i 2
9
−1
2−
−1
16
PTS: 2
97 ANS:
{2,4}
2 = 3i 2 − 4i 2 = −i 2
REF: 061404a2
STA: A2.N.6
TOP: Square Roots of Negative Numbers
2x − 4 = x − 2
2x − 4 = x 2 − 4x + 4
0 = x 2 − 6x + 8
0 = (x − 4)(x − 2)
x = 4,2
PTS: 2
REF: 061406a2
STA: A2.A.22
KEY: extraneous solutions
98 ANS:
$5805.92
4 ⋅5

.03 


5000  1 +
= 5000(1.0075) 20 ≈ 5805.92

4


TOP: Solving Radicals
PTS: 2
99 ANS:


 3,1 
STA: A2.A.12
TOP: Evaluating Exponential Expressions
x = 2⋅
3
=
2
REF: 011410a2
3 y = 2⋅
1
=1
2
PTS: 2
100 ANS:
60
6 P6
720
=
= 60
3!2!
12
REF: 061525a2
STA: A2.A.62
TOP: Determining Trigonometric Functions
PTS: 2
101 ANS:
2
REF: 011324a2
STA: A2.S.10
TOP: Permutations
PTS: 2
REF: 061510a2
STA: A2.A.5
TOP: Inverse Variation
ID: A
102 ANS:
117
1
(22)(13) sin 55 ≈ 117
2
PTS: 2
KEY: basic
103 ANS:
y = 2 cos 3x
REF: 061403a2
STA: A2.A.74
TOP: Using Trigonometry to Find Area
PTS: 2
REF: 011320a2
STA: A2.A.72
TOP: Identifying the Equation of a Trigonometric Graph
104 ANS:
−2 ± 3i
(x + 2) 2 = −9
x + 2 =± −9
x = −2 ± 3i
PTS: 2
105 ANS:
(−6,−2)
REF: 011408a2
x = 2y . y 2 − (3y) 2 + 32 = 0
STA: A2.A.24
TOP: Completing the Square
. x = 3(−2) = −6
y 2 − 9y 2 = −32
−8y 2 = −32
y2 = 4
y = ±2
PTS: 2
KEY: equations
106 ANS:
III
REF: 061312a2
STA: A2.A.3
TOP: Quadratic-Linear Systems
PTS: 2
107 ANS:
(−∞,∞)
REF: 061412a2
STA: A2.A.60
TOP: Finding the Terminal Side of an Angle
PTS: 2
KEY: real domain
108 ANS:
f −1 (x) = 4 x
REF: 081517a2
STA: A2.A.39
TOP: Domain and Range
REF: 061521a2
STA: A2.A.44
TOP: Inverse of Functions
PTS: 2
KEY: equations
ID: A
109 ANS:
15 out of 25
15 C 5 = 3,003.
25
C 5 = 25 C 20 = 53,130.
25
C 15 = 3,268,760.
PTS: 2
110 ANS:
−1 ≤ x ≤ 6
REF: 061227a2
STA: A2.S.11
TOP: Combinations
PTS: 2
111 ANS:
p3
REF: 061202a2
STA: A2.A.51
TOP: Domain and Range
t2
r
PTS: 2
REF: 061207a2
STA: A2.A.19
TOP: Properties of Logarithms
KEY: antilogarithms
112 ANS:
4a 2 − 14a + 13
(3 − 2a) 0 + (3 − 2a) 1 + (3 − 2a) 2 = 1 + 3 − 2a + 9 − 12a + 4a 2 = 4a 2 − 14a + 13
PTS: 2
KEY: advanced
113 ANS:
1 1 1 1
, , ,
2 2 2 2
REF: 061526a2
STA: A2.N.10
TOP: Sigma Notation
PTS: 2
114 ANS:
x4 y5
3
REF: 081520a2
STA: A2.A.33
TOP: Sequences
PTS: 2
REF: 061210a2
STA: A2.A.9
115 ANS:
$73.73

 4 ⋅ 12
.0325


A = 50  1 +
= 50(1.008125) 48 ≈ 73.73

4


PTS: 2
REF: 081511a2
STA: A2.A.12
TOP: Negative Exponents
TOP: Evaluating Exponential Expressions
ID: A
116 ANS:
4a 2 + 7a + 4
f a + 1 = 4(a + 1) 2 − (a + 1) + 1
= 4(a 2 + 2a + 1) − a
= 4a 2 + 8a + 4 − a
= 4a 2 + 7a + 4
PTS: 2
REF: 011527a2
117 ANS:
{30°,150°,270°}
(2 sinx − 1)(sinx + 1) = 0
STA: A2.A.41
TOP: Functional Notation
PTS: 2
REF: 081514a2
KEY: quadratics
118 ANS:
11.4
1
(7.4)(3.8) sin 126 ≈ 11.4
2
STA: A2.A.68
TOP: Trigonometric Equations
PTS: 2
REF: 011218a2
KEY: basic
119 ANS:
−4 and 5
20(−2) = x(−2x + 2)
STA: A2.A.74
TOP: Using Trigonometry to Find Area
STA: A2.A.5
TOP: Inverse Variation
sin x =
1
,−1
2
x = 30,150,270
−40 = −2x 2 + 2x
2x 2 − 2x − 40 = 0
x 2 − x − 20 = 0
(x + 4)(x − 5) = 0
x = −4,5
PTS: 2
REF: 011321a2
ID: A
120 ANS:
131 − 175
x ±σ
153 ± 22
131 − 175
PTS: 2
KEY: interval
121 ANS:
300
REF: 011307a2
STA: A2.S.5
TOP: Normal Distributions
PTS: 2
122 ANS:
1
1
− x2 + x + 2
4
2
REF: 011205a2
STA: A2.A.6
TOP: Exponential Growth
PTS: 2
123 ANS:
−5x − 4i
REF: 061515a2
STA: A2.N.3
TOP: Operations with Polynomials
PTS: 2
124 ANS:
5
−
2
2x 2 − 7x − 5 = 0
REF: 061219a2
STA: A2.N.8
TOP: Conjugates of Complex Numbers
REF: 061414a2
STA: A2.A.20
TOP: Roots of Quadratics
320 = 10(2)
32 = (2)
t
60
t
60
log 32 = log(2)
log 32 =
t
60
t log 2
60
60 log 32
=t
log 2
300 = t
c −5
=
a
2
PTS: 2
ID: A
125 ANS:
23
s=θr=
2π
⋅ 18 ≈ 23
5
PTS: 2
KEY: arc length
126 ANS:
{−3,−1,2}
REF: 011526a2
STA: A2.A.61
TOP: Arc Length
PTS: 2
127 ANS:
$150
3 ⋅ 400 = 8x
REF: 081501a2
STA: A2.A.50
TOP: Solving Polynomial Equations
REF: 081507a2
STA: A2.A.5
TOP: Inverse Variation
STA: A2.A.36
TOP: Binomial Expansions
150 = x
PTS: 2
128 ANS:
6x 4 y 2
3
C 2 (2x 4 ) 1 (−y) 2 = 6x 4 y 2
PTS: 2
129 ANS:
6ab 2
3
27a 3 ⋅
REF: 011215a2
4
16b 8 = 3a ⋅ 2b 2 = 6ab 2
PTS: 2
REF: 061504a2
STA: A2.A.14
TOP: Operations with Radicals
KEY: with variables | index > 2
130 ANS:
2x 2 + 17x + 36
f(g(x)) = 2(x + 5) 2 − 3(x + 5) + 1 = 2(x 2 + 10x + 25) − 3x − 15 + 1 = 2x 2 + 17x + 36
PTS: 2
REF: 061419a2
KEY: variables
131 ANS:
(x + 3) 2 + (y − 1) 2 = 13
PTS: 2
REF: 061318a2
STA: A2.A.42
TOP: Compositions of Functions
STA: A2.A.49
TOP: Equations of Circles
ID: A
132 ANS:
a2b
log x = log a 2 + log b
log x = log a 2 b
x = a2b
PTS: 2
REF: 061517a2
KEY: antilogarithms
133 ANS:
4a 5 3 a
3
STA: A2.A.19
TOP: Properties of Logarithms
STA: A2.A.13
TOP: Simplifying Radicals
4 3 a 15 a = 4a 5 3 a
PTS: 2
KEY: index > 2
134 ANS:
{4}
5x + 29 = (x + 3) 2
REF: 061204a2
. (−5) + 3 shows an extraneous solution.
5x + 29 = x 2 + 6x + 9
0 = x 2 + x − 20
0 = (x + 5)(x − 4)
x = −5,4
PTS: 2
REF: 061213a2
KEY: extraneous solutions
135 ANS:
h
tan4.76° =
15
STA: A2.A.22
TOP: Solving Radicals
PTS: 2
136 ANS:
STA: A2.A.55
TOP: Trigonometric Ratios
REF: 061514a2
π
2π
=π
2
PTS: 2
REF: 081519a2
STA: A2.A.69
TOP: Properties of Graphs of Trigonometric Functions
KEY: period
ID: A
137 ANS:
 π 
y = −3 cos  x  + 5
 15 
2π
= 30
b
b=
π
15
PTS: 2
REF: 011227a2
STA: A2.A.72
TOP: Identifying the Equation of a Trigonometric Graph
138 ANS:
a n = 4(2.5) n − 1
10
= 2.5
4
PTS: 2
139 ANS:
1.84
REF: 011217a2
60 = −16t 2 + 5t + 105 t =
−5 ±
STA: A2.A.29
TOP: Sequences
5 2 − 4(−16)(45) −5 ± 53.89
≈
≈ 1.84
2(−16)
−32
0 = −16t 2 + 5t + 45
PTS: 2
140 ANS:
−1
sec θ =
REF: 061424a2
x2 + y2
=
x
PTS: 2
141 ANS:
33
65
cos(A − B) =
STA: A2.A.25
TOP: Quadratics with Irrational Solutions
(−4) 2 + 0 2
4
=
= −1
−4
−4
REF: 011520a2
STA: A2.A.62
TOP: Determining Trigonometric Functions
 5   3   12   4 
   −  +     = − 15 + 48 = 33
 13   5   13   5 
65 65 65
     
PTS: 2
KEY: evaluating
142 ANS:
y = −2 cos 2x
REF: 011214a2
STA: A2.A.76
PTS: 2
REF: 061306a2
STA: A2.A.72
TOP: Identifying the Equation of a Trigonometric Graph
TOP: Angle Sum and Difference Identities
ID: A
143 ANS:
y≤0
PTS: 2
REF: 061308ge
144 ANS:
b2 + a2
cos(x − y) = cos x cos y + sin x siny
STA: A2.A.51
TOP: Domain and Range
= b ⋅b +a ⋅a
= b2 + a2
PTS: 2
KEY: simplifying
145 ANS:
3
−
4
c −3
=
4
a
REF: 061421a2
STA: A2.A.76
TOP: Angle Sum and Difference Identities
PTS: 2
146 ANS:
48 3
REF: 011517a2
STA: A2.A.20
TOP: Roots of Quadratics
STA: A2.A.74
TOP: Using Trigonometry to Find Area
K = 8 ⋅ 12 sin120 = 96 ⋅
3
= 48 3
2
PTS: 2
REF: 061508a2
KEY: parallelograms
147 ANS:
12 − 12mi
(3i)(2i) 2 (m + i)
(3i)(4i 2 )(m + i)
(3i)(−4)(m + i)
(−12i)(m + i)
−12mi − 12i 2
−12mi + 12
PTS: 2
REF: 061319a2
STA: A2.N.9
TOP: Multiplication and Division of Complex Numbers
ID: A
148 ANS:
24x 4 y 2
 3 
 2x  3
 8x 
a 4 = 3xy 5   = 3xy 5  3  = 24x 4 y 2
 y 
 y 


PTS: 2
REF: 061512a2
149 ANS:
h 2 = 6 2 + 9 2 − 2(6)(9) cos 57°
STA: A2.A.33
TOP: Sequences
PTS: 2
REF: 011501a2
STA: A2.A.73
KEY: side, without calculator
150 ANS:
129
g(−2) = 3(−2) − 2 = −8 f(−8) = 2(−8) 2 + 1 = 128 + 1 = 129
TOP: Law of Cosines
PTS: 2
REF: 061503a2
KEY: numbers
151 ANS:
x2 1
−
16 9
The binomials are conjugates, so use FL.
STA: A2.A.42
TOP: Compositions of Functions
PTS: 2
152 ANS:
STA: A2.N.3
TOP: Operations with Polynomials
REF: 011206a2
x + 16 7(x − 2)
−
≤ 0 −6x + 30 = 0 x − 2 = 0 . Check points such that x < 2, 2 < x < 5, and x > 5. If x = 1 ,
x−2
x−2
x=2
−6x = −30
−6x + 30
≤0
x−2
x=5
−6(1) + 30 24
−6(3) + 30 12
=
= −24, which is less than 0. If x = 3,
=
= 12, which is greater than 0. If x = 6 ,
−1
1
1−2
3−2
−6(6) + 30 −6
3
=
= − , which is less than 0.
4
2
6−2
PTS: 2
153 ANS:
5
h(−8) =
REF: 011424a2
STA: A2.A.23
TOP: Rational Inequalities
1
1
(−8) − 2 = −4 − 2 = −6. g(−6) = (−6) + 8 = −3 + 8 = 5
2
2
PTS: 2
KEY: numbers
REF: 011403a2
STA: A2.A.42
TOP: Compositions of Functions
ID: A
154 ANS:
7+
11
38
7+
11
11 7 +
11
1
7−
⋅
=
PTS: 2
155 ANS:
7 + 11 7 + 11
=
49 − 11
38
REF: 011404a2
STA: A2.N.5
TOP: Rationalizing Denominators
STA: A2.A.1
TOP: Absolute Value Inequalities
2x − 1 > 5. 2x − 1 < −5
2x > 6
2x > −4
x>3
x < −2
PTS: 2
REF: 061307a2
KEY: graph
156 ANS:
1
3
2 2 ⋅ 3 = 12 . 6 2 d = 12
42 ⋅
36d = 12
3
= 12
4
1
d=
3
PTS: 2
157 ANS:
3
−
2
3
4
3
= −
2
1
−
2
REF: 061310a2
STA: A2.A.5
TOP: Inverse Variation
PTS: 2
158 ANS:
25
3 3
10 ⋅ = p
2 5
REF: 011508a2
STA: A2.A.31
TOP: Sequences
REF: 011226a2
STA: A2.A.5
TOP: Inverse Variation
15 =
3
p
5
25 = p
PTS: 2
ID: A
159 ANS:
{0,±2,±2i}
3x 5 − 48x = 0
3x(x 4 − 16) = 0
3x(x 2 + 4)(x 2 − 4) = 0
3x(x 2 + 4)(x + 2)(x − 2) = 0
PTS: 2
160 ANS:
3x
REF: 011216a2
STA: A2.A.26
TOP: Solving Polynomial Equations
PTS: 2
161 ANS:
−8
20 ⋅ 2 = −5t
REF: 061411a2
STA: A2.A.30
TOP: Sequences
PTS: 2
162 ANS:
−2
4
= −2
−2
REF: 011412a2
STA: A2.A.5
TOP: Inverse Variation
PTS: 2
163 ANS:
REF: 011304a2
STA: A2.A.31
TOP: Sequences
−8 = t
4a
3
3
6a 4 b 2 + 3 (27 ⋅ 6)a 4 b 2
a
6ab 2
3
6ab 2 + 3a
4a
3
3
6ab 2
6ab 2
PTS: 2
164 ANS:
288
8π 180
⋅
= 288
5
π
REF: 011319a2
STA: A2.N.2
TOP: Operations with Radicals
PTS: 2
KEY: degrees
165 ANS:
1.12
REF: 061302a2
STA: A2.M.2
TOP: Radian Measure
PTS: 2
REF: 081509a2
STA: A2.S.4
KEY: basic, group frequency distributions
TOP: Dispersion
ID: A
166 ANS:
(x + 4)(x − 4)(3x − 5)
3x 3 − 5x 2 − 48x + 80
x 2 (3x − 5) − 16(3x − 5)
(x 2 − 16)(3x − 5)
(x + 4)(x − 4)(3x − 5)
PTS: 2
167 ANS:
360
REF: 011317a2
STA: A2.A.7
TOP: Factoring by Grouping
π
2⋅
180
π
=
360
π
PTS: 2
REF: 011220a2
STA: A2.M.2
TOP: Radian Measure
KEY: degrees
168 ANS:
−21
−b −(−4)
=
= 4. If the sum is 4, the roots must be 7 and −3.
a
1
PTS: 2
REF: 011418a2
KEY: advanced
169 ANS:
1
x
1
1+x
+1
−1
x
x
x +1
1
=
=
=
x+1
x+1
x+1
x
STA: A2.A.21
PTS: 2
REF: 011211a2
STA: A2.A.9
170 ANS:
6x 2 3 2
 3
 

 27x 2   3 16x 4  = 3 3 3 ⋅ 2 4 ⋅ x 6 = 3 ⋅ 2 ⋅ x 2 3 2 = 6x 2 3 2

 

PTS: 2
REF: 011421a2
STA: A2.N.2
TOP: Roots of Quadratics
TOP: Negative Exponents
TOP: Operations with Radicals
ID: A
171 ANS:
4
4 ⋅ 0 + 6 ⋅ 1 + 10 ⋅ 2 + 0 ⋅ 3 + 4k + 2 ⋅ 5
=2
4 + 6 + 10 + 0 + k + 2
4k + 36
=2
k + 22
4k + 36 = 2k + 44
2k = 8
k =4
PTS: 2
172 ANS:
none
REF: 061221a2
STA: A2.S.3
TOP: Average Known with Missing Data
34
12
=
sin 30 sinB
B = sin −1
≈ sin −1
12 sin30
34
6
5.8
PTS: 2
173 ANS:
1
64
2
 1  1  
  −   = 1
 2  4  
64
  
REF: 011523a2
STA: A2.A.75
TOP: Law of Sines - The Ambiguous Case
PTS: 2
174 ANS:
1
3x 2
REF: 081527a2
STA: A2.A.24
TOP: Completing the Square
PTS: 2
REF: 011402a2
STA: A2.A.8
TOP: Negative and Fractional Exponents
175 ANS:
−sinx
sin(180 + x) = (sin 180)(cos x) + (cos 180)(sin x) = 0 + (−sinx) = −sinx
PTS: 2
KEY: identities
REF: 011318a2
STA: A2.A.76
TOP: Angle Sum and Difference Identities
ID: A
176 ANS:
−20x 3 y 3
3
 x  3
  (−2y) 3 = 20 ⋅ x ⋅ −8y 3 = −20x 3 y 3
C
6 3
 2 
8
 
PTS: 2
REF: 061215a2
177 ANS:
2,494,800
39,916,800
11 P 11
=
= 2,494,800
16
2!2!2!2!
STA: A2.A.36
TOP: Binomial Expansions
PTS: 2
REF: 011518a2
STA: A2.S.10
TOP: Permutations
178 ANS:
{2}
(x + 3)(x − 3)
5(x + 3)
30
+
=
3 is an extraneous root.
(x + 3)(x − 3) (x + 3)(x − 3) (x − 3)(x + 3)
30 + x 2 − 9 = 5x + 15
x 2 − 5x + 6 = 0
(x − 3)(x − 2) = 0
x=2
PTS: 2
REF: 061417a2
KEY: rational solutions
179 ANS:
above the 95th percentile
91 − 82
= 2.5 sd
3.6
STA: A2.A.23
TOP: Solving Rationals
PTS: 2
REF: 081521a2
KEY: interval
180 ANS:
46 − 12x
4 + 3(2 − x) + 3(3 − x) + 3(4 − x) + 3(5 − x)
STA: A2.S.5
TOP: Normal Distributions
STA: A2.N.10
TOP: Sigma Notation
4 + 6 − 3x + 9 − 3x + 12 − 3x + 15 − 3x
46 − 12x
PTS: 2
KEY: advanced
REF: 061315a2
ID: A
181 ANS:
cos x
cos x
sinx
cot x
=
= cos x
csc x
1
sinx
PTS: 2
182 ANS:
y = 2 −x
REF: 061410a2
STA: A2.A.58
TOP: Reciprocal Trigonometric Relationships
PTS: 2
REF: 011301a2
183 ANS:
720x 3
5−2
(−3) 2 = 720x 3
5 C 2 (2x)
STA: A2.A.52
TOP: Identifying the Equation of a Graph
PTS: 2
184 ANS:
8
15
STA: A2.A.36
TOP: Binomial Expansions
REF: 011519a2
8
17
15
8
8
=
If sin θ = , then cos θ = . tan θ =
15 15
17
17
17
PTS: 2
KEY: advanced
185 ANS:
2
3−
6
3
3−
8
3
PTS: 2
⋅
3
3
=
REF: 081508a2
3 3−
3
24
=
STA: A2.A.64
3 3 −2 6
=
3
REF: 081518a2
3−
2
3
STA: A2.N.5
TOP: Using Inverse Trigonometric Functions
6
TOP: Rationalizing Denominators
ID: A
Algebra 2/Trigonometry Regents Bimodal Worksheets
Answer Section
186 ANS:
5
−
42
f 10 =
−10
−10
5
=
=−
2
84
42
(−10) − 16
PTS: 2
187 ANS:
33°33'
cos K =
REF: 061102a2
STA: A2.A.41
TOP: Functional Notation
REF: 061023a2
STA: A2.A.55
TOP: Trigonometric Ratios
5
6
K = cos −1
5
6
K ≈ 33°33'
PTS: 2
188 ANS:
3±3 5
2
3±
(−3) 2 − 4(1)(−9) 3 ± 45 3 ± 3 5
=
=
2(1)
2
2
PTS: 2
REF: 061009a2
STA: A2.A.25
TOP: Quadratics with Irrational Solutions
ID: A
189 ANS:
4
3
9 3x + 1 = 27 x + 2 .
(3 2 ) 3x + 1 = (3 3 ) x + 2
3 6x + 2 = 3 3x + 6
6x + 2 = 3x + 6
3x = 4
x=
4
3
PTS: 2
REF: 081008a2
KEY: common base not shown
190 ANS:
x2
log 3
y z
STA: A2.A.27
2logx − (3log y + log z) = log x 2 − log y 3 − logz = log
PTS: 2
191 ANS:
1
3
TOP: Exponential Equations
x2
y3z
REF: 061010a2
STA: A2.A.19
TOP: Properties of Logarithms
REF: 061011a2
STA: A2.A.10
TOP: Fractional Exponents as Radicals
(x 2 − 1) 2
PTS: 2
192 ANS:
1
3
π
3
PTS: 2
+
2π
π
3
2π
3
1
=
=
2π
3
REF: 011108a2
STA: A2.S.13
TOP: Geometric Probability
ID: A
193 ANS:
7 + 5i
PTS: 2
REF: 011111a2
STA: A2.N.8
194 ANS:
−38
Σ
n
3
4
5
2
2
2
2
−r + r −3 + 3 = −6 −4 + 4 = −12−5 + 5 = −20 −38
TOP: Conjugates of Complex Numbers
PTS: 2
REF: 061118a2
KEY: basic
195 ANS:
−720x 2
2
3
2
2
5 C 3 (3x) (−2) = 10 ⋅ 9x ⋅ −8 = −720x
STA: A2.N.10
TOP: Sigma Notation
PTS: 2
196 ANS:
y = csc x
STA: A2.A.36
TOP: Binomial Expansions
PTS: 2
REF: 011123a2
197 ANS:
6x 2 − 30
6(x 2 − 5) = 6x 2 − 30
STA: A2.A.71
TOP: Graphing Trigonometric Functions
PTS: 2
KEY: variables
198 ANS:
−1.3408
REF: 011109a2
STA: A2.A.42
TOP: Compositions of Functions
PTS: 2
199 ANS:
34
68% × 50 = 34
REF: 061115a2
STA: A2.A.66
TOP: Determining Trigonometric Functions
PTS: 2
KEY: predict
REF: 081013a2
STA: A2.S.5
TOP: Normal Distributions
REF: fall0919a2
ID: A
200 ANS:
10i 3
−300 =
100
−1
3
PTS: 2
REF: 061006a2
201 ANS:
120
7 2 = 3 2 + 5 2 − 2(3)(5) cos A
STA: A2.N.6
TOP: Square Roots of Negative Numbers
PTS: 2
REF: 081017a2
KEY: angle, without calculator
202 ANS:
8
−
9
1
−2
9
8
3
=
= −
−3
9
1
(−2)
−
8
STA: A2.A.73
TOP: Law of Cosines
PTS: 2
REF: 061003a2
203 ANS:
b n = 8 + 2n
common difference is 2. b n = x + 2n
STA: A2.N.1
TOP: Negative and Fractional Exponents
PTS: 2
REF: 081014a2
204 ANS:
1
1
2
log A + log B − log C
3
3
3
STA: A2.A.29
TOP: Sequences
PTS: 2
REF: 061120a2
KEY: splitting logs
205 ANS:
a6
b5
STA: A2.A.19
TOP: Properties of Logarithms
STA: A2.A.9
TOP: Negative and Fractional Exponents
49 = 34 − 30 cos A
15 = −30 cos A
1
− = cos A
2
120 = A
10 = x + 2(1)
8=x
PTS: 2
REF: fall0914a2
ID: A
206 ANS:
49
4
PTS: 2
REF: 061122a2
STA: A2.A.24
207 ANS:
3
1
f(4) = (4) − 3 = −1. g(−1) = 2(−1) + 5 = 3
2
TOP: Completing the Square
PTS: 2
KEY: numbers
208 ANS:
−2 − 3i
REF: fall0902a2
STA: A2.A.42
TOP: Compositions of Functions
PTS: 2
209 ANS:
15 C 2 ⋅5 C 1
30 C 3
REF: 081024a2
STA: A2.N.8
TOP: Conjugates of Complex Numbers
PTS: 2
REF: 011117a2
STA: A2.S.9
TOP: Differentiating Permutations and Combinations
210 ANS:
6,435
15 C 8 = 6,435
PTS: 2
211 ANS:
8
s = θ r = 2⋅4 = 8
REF: 081012a2
STA: A2.S.11
TOP: Combinations
PTS: 2
KEY: arc length
212 ANS:
8!
2!⋅ 2!
REF: fall0922a2
STA: A2.A.61
TOP: Arc Length
PTS: 2
REF: fall0925a2
STA: A2.S.10
213 ANS:
x−2
x 1
x2 − 4
−
(x + 2)(x − 2)
4 x
4x
8x
=
=
×
= x−2
1 1
2x + 4
4x
2(x + 2)
+
2x 4
8x
PTS: 2
REF: fall0920a2
STA: A2.A.17
TOP: Permutations
TOP: Complex Fractions
ID: A
214 ANS:
1
−
x
−(x − 1)
1
1−x
−1
x
x
x −1 x
1
=
=
=
= −
x−1
x−1
x−1
x−1
x
−1
PTS: 2
215 ANS:
7π
−
3
 π 
 = − 7π
−420 

3
 180 
REF: 081018a2
STA: A2.A.9
TOP: Negative Exponents
PTS: 2
KEY: radians
216 ANS:
REF: 081002a2
STA: A2.M.2
TOP: Radian Measure
5+
13
3
5+
13
13 5 +
13
4
5−
⋅
PTS: 2
217 ANS:
446 + 16x
17 =
26 + x
=
4(5 + 13) 5 + 13
=
3
25 − 13
REF: 061116a2
STA: A2.N.5
TOP: Rationalizing Denominators
PTS: 2
REF: 061124a2
STA: A2.S.3
TOP: Average Known with Missing Data
218 ANS:
448
8 × 8 × 7 × 1 = 448. The first digit cannot be 0 or 5. The second digit cannot be 5 or the same as the first digit.
The third digit cannot be 5 or the same as the first or second digit.
PTS: 2
REF: 011125a2
STA: A2.S.10
TOP: Permutations
ID: A
219 ANS:
{−1,−3}
4x
2
2
+ 4x
2
x + 4x
(2 )
2
2
2x + 8x
= 2 −6 .
=2
−6
=2
−6
2x 2 + 8x = −6
2x 2 + 8x + 6 = 0
x 2 + 4x + 3 = 0
(x + 3)(x + 1) = 0
x = −3 x = −1
PTS: 2
REF: 061015a2
KEY: common base shown
220 ANS:
0, 4
x 2 − x − 6 = 3x − 6
STA: A2.A.27
TOP: Exponential Equations
STA: A2.A.3
TOP: Quadratic-Linear Systems
PTS: 2
REF: 011104a2
KEY: unit circle
222 ANS:
4
(3 + 5)(3 − 5) = 9 − 25 = 4
STA: A2.A.64
TOP: Using Inverse Trigonometric Functions
PTS: 2
REF: 081001a2
KEY: without variables | index = 2
223 ANS:
f(x) = e x and g(x) = lnx
STA: A2.N.4
TOP: Operations with Irrational Expressions
PTS: 2
KEY: equations
224 ANS:
3
REF: 081027a2
STA: A2.A.44
TOP: Inverse of Functions
REF: 061001a2
STA: A2.A.30
TOP: Sequences
x 2 − 4x = 0
x(x − 4) = 0
x = 0,4
PTS: 2
KEY: equations
221 ANS:
225
PTS: 2
REF: 081015a2
ID: A
225 ANS:
8
5
2 log 4 (5x) = 3
log 4 (5x) =
3
2
5x = 4
3
2
5x = 8
x=
8
5
PTS: 2
KEY: advanced
226 ANS:
−5ab 2b + 7ab
4ab
2b − 3a
REF: fall0921a2
STA: A2.A.28
TOP: Logarithmic Equations
6b
9b 2
2b + 7ab
6b = 4ab
PTS: 2
REF: fall0918a2
KEY: with variables | index = 2
227 ANS:
0,1,−2
x 3 + x 2 − 2x = 0
2b − 9ab
2b + 7ab
STA: A2.A.14
6b = −5ab
2b + 7ab
6b
TOP: Operations with Radicals
x(x 2 + x − 2) = 0
x(x + 2)(x − 1) = 0
x = 0,−2,1
PTS: 2
REF: 011103a2
STA: A2.A.26
TOP: Solving Polynomial Equations
228 ANS:
the method of choosing the students who were surveyed
Students entering the library are more likely to spend more time studying, creating bias.
PTS: 2
229 ANS:
150°
PTS: 2
KEY: basic
REF: fall0904a2
STA: A2.S.2
TOP: Analysis of Data
REF: 081007a2
STA: A2.A.64
TOP: Using Inverse Trigonometric Functions
ID: A
230 ANS:
2π
3
2π
2π
=
b
3
PTS: 2
REF: 061111a2
STA: A2.A.69
TOP: Properties of Graphs of Trigonometric Functions
231 ANS:
{x | x < − 2 or x > 5}
x 2 − 3x − 10 > 0
or
(x − 5)(x + 2) > 0
x − 5 < 0 and x + 2 < 0
x − 5 > 0 and x + 2 > 0
x < 5 and x < −2
x > 5 and x > −2
x < −2
KEY: period
x>5
PTS: 2
REF: 011115a2
KEY: one variable
232 ANS:
78.3 and 101.7
60.3
59.2
180 − 78.3 = 101.7
=
sin74 sinC
STA: A2.A.4
TOP: Quadratic Inequalities
PTS: 2
REF: 081006a2
233 ANS:
−6
The roots are −1,2,3.
STA: A2.A.75
TOP: Law of Sines - The Ambiguous Case
PTS: 2
234 ANS:
(−1,2)
STA: A2.A.50
TOP: Solving Polynomial Equations
C ≈ 78.3
REF: 081023a2
PTS: 2
REF: 081022a2
STA: A2.A.46
TOP: Transformations with Functions and Relations
235 ANS:
165
11π 180
⋅
= 165
12
π
PTS: 2
KEY: degrees
REF: 061002a2
STA: A2.M.2
TOP: Radian Measure
ID: A
236 ANS:
[2,∞)
PTS: 2
KEY: real domain
237 ANS:
67.3
REF: fall0923a2
STA: A2.A.39
PTS: 2
REF: fall0924a2
STA: A2.S.4
KEY: range, quartiles, interquartile range, variance
238 ANS:
period =
TOP: Domain and Range
TOP: Dispersion
2π
2π
2
=
=
b
3π
3
PTS: 2
KEY: recognize
239 ANS:
f(x) = 2 x
REF: 081026a2
STA: A2.A.70
TOP: Graphing Trigonometric Functions
PTS: 2
REF: 061004a2
240 ANS:
−5,376
6
3
6 3
9 C 3 a (−4b) = −5376a b
STA: A2.A.52
TOP: Identifying the Equation of a Graph
PTS: 2
REF: 061126a2
241 ANS:
{x | x ≥ −4}; {y | y ≥ 2}
STA: A2.A.36
TOP: Binomial Expansions
PTS: 2
242 ANS:
y≥7
REF: 081003a2
STA: A2.A.51
TOP: Domain and Range
REF: 061112a2
STA: A2.A.39
TOP: Domain and Range
PTS: 2
KEY: real domain
ID: A
243 ANS:
1
PTS: 2
244 ANS:
∅
REF: 061019a2
PTS: 2
245 ANS:
−x(x + 3)(x − 2)
REF: 011106a2
STA: A2.N.7
TOP: Imaginary Numbers
|  1 
|
 1 
4a + 6 = 4a − 10. 4a + 6 = −4a + 10. | 4   + 6 | − 4   = −10
||  2 
||
2
8a = 4
6 ≠ −10
8 − 2 ≠ −10
4 1
a= =
8 2
STA: A2.A.1
TOP: Absolute Value Equations
6x − x 3 − x 2 = −x(x 2 + x − 6) = −x(x + 3)(x − 2)
PTS: 2
REF: fall0917a2
KEY: single variable
246 ANS:
STA: A2.A.7
TOP: Factoring Polynomials
6x − 7 ≤ 5 6x − 7 ≥ −5
6x ≤ 12
x≤2
6x ≥ 2
x≥
1
3
PTS: 2
REF: fall0905a2
STA: A2.A.1
KEY: graph
247 ANS:
−40 − 42i
(3 − 7i)(3 − 7i) = 9 − 21i − 21i + 49i 2 = 9 − 42i − 49 = −40 − 42i
TOP: Absolute Value Inequalities
PTS: 2
REF: fall0901a2
STA: A2.N.9
TOP: Multiplication and Division of Complex Numbers
248 ANS:
78
1
K = (10)(18) sin 120 = 45 3 ≈ 78
2
PTS: 2
KEY: basic
REF: fall0907a2
STA: A2.A.74
TOP: Using Trigonometry to Find Area
ID: A
249 ANS:
210
10 C 4 = 210
PTS: 2
250 ANS:
y = 0.5 x
REF: 061113a2
STA: A2.S.11
TOP: Combinations
PTS: 2
251 ANS:
4
3
27r 4 − 1 = 64
REF: 061108a2
STA: A2.A.52
TOP: Identifying the Equation of a Graph
REF: 081025a2
STA: A2.A.31
TOP: Sequences
r3 =
64
27
r=
4
3
PTS: 2
252 ANS:
3
3
12 2 − 6 2 =
108 =
36
3 = 6 3 . cot J =
PTS: 2
REF: 011120a2
253 ANS:
53
13 2 = 15 2 + 14 2 − 2(15)(14) cos C
A
6
=
⋅
O 6 3
3
3
=
3
3
STA: A2.A.55
TOP: Trigonometric Ratios
REF: 061110a2
STA: A2.A.73
TOP: Law of Cosines
REF: 011114a2
STA: A2.N.3
TOP: Operations with Polynomials
169 = 421 − 420 cos C
−252 = −420 cos C
252
= cos C
420
53 ≈ C
PTS: 2
KEY: find angle
254 ANS:
1
x2 − x + 5
2
PTS: 2
ID: A
255 ANS:
24
n
2
n + 2n
Σ
0
1
2
0
2
2
2
2
12
0 +2 = 1 1 +2 = 3 2 +2 = 8
2
2 × 12 = 24
PTS: 2
KEY: basic
256 ANS:
625
x = 5 4 = 625
REF: fall0911a2
STA: A2.N.10
TOP: Sigma Notation
PTS: 2
REF: 061106a2
STA: A2.A.28
KEY: basic
257 ANS:
sin 2 θ
cos 2 θ − cos 2θ = cos 2 θ − (cos 2 θ − sin 2 θ) = sin 2 θ
TOP: Logarithmic Equations
PTS:
KEY:
258 ANS:
6π
2π
=
b
TOP: Double Angle Identities
2
simplifying
REF: 061024a2
STA: A2.A.77
2π
= 6π
1
3
PTS: 2
REF: 061027a2
STA: A2.A.69
TOP: Properties of Graphs of Trigonometric Functions
259 ANS:
KEY: period
−7 ± 73
4
−7 ±
7 2 − 4(2)(−3) −7 ± 73
=
2(2)
4
PTS: 2
REF: 081009a2
260 ANS:
129
K = (10)(18) sin46 ≈ 129
STA: A2.A.25
TOP: Quadratics with Irrational Solutions
PTS: 2
REF: 081021a2
KEY: parallelograms
STA: A2.A.74
TOP: Using Trigonometry to Find Area
ID: A
261 ANS:
2x 2 (2x + 3)(3x − 2)
12x 4 + 10x 3 − 12x 2 = 2x 2 (6x 2 + 5x − 6) = 2x 2 (2x + 3)(3x − 2)
PTS: 2
REF: 061008a2
KEY: single variable
262 ANS:
2
8 2 = 64
STA: A2.A.7
TOP: Factoring Polynomials
PTS: 2
REF: fall0909a2
263 ANS:
5π
6
5
10π
5π
2π ⋅
=
=
12
12
6
STA: A2.A.18
TOP: Evaluating Logarithmic Expressions
PTS: 2
REF: 061125a2
264 ANS:
2x 2 + 6x + 4 = 0
−b −6
c 4
=
= −3.
= =2
2
a
a 2
STA: A2.M.1
TOP: Radian Measure
PTS: 2
REF: 011121a2
KEY: basic
265 ANS:
sec 2 θ
sin 2 θ + cos 2 θ
1
=
= sec 2 θ
2
2
1 − sin θ
cos θ
STA: A2.A.21
TOP: Roots of Quadratics
PTS: 2
266 ANS:
logarithmic
REF: 061123a2
STA: A2.A.58
TOP: Reciprocal Trigonometric Relationships
REF: 061127a2
STA: A2.S.6
TOP: Regression
PTS: 2
ID: A
267 ANS:
2
4 2x + 5 = 8 3x
.
 2  2x + 5  3  3x
2 
= 2 
 
 
2 4x + 10 = 2 9x
4x + 10 = 9x
10 = 5x
2=x
PTS: 2
REF: 061105a2
KEY: common base not shown
268 ANS:
−2 − 3i
2i 2 + 3i 3 = 2(−1) + 3(−i) = −2 − 3i
STA: A2.A.27
TOP: Exponential Equations
PTS: 2
269 ANS:
{−2,0,3}
REF: 081004a2
STA: A2.N.7
TOP: Imaginary Numbers
PTS: 2
270 ANS:
REF: 061005a2
STA: A2.A.50
TOP: Solving Polynomial Equations
REF: fall0916a2
STA: A2.A.54
TOP: Graphing Logarithmic Functions
f −1 (x) = log 4 x
PTS: 2
ID: A
271 ANS:
23.1
75000 = 25000e .0475t
3 = e .0475t
ln 3 = ln e .0475t
ln 3
.0475t ⋅ ln e
=
.0475
.0475
23.1 ≈ t
PTS: 2
272 ANS:
w2
REF: 061117a2
STA: A2.A.6
TOP: Exponential Growth
1
1
 −5  2
 w 
4 2
 −9  = (w ) = w 2
 w 


PTS: 2
273 ANS:
y = sec x
REF: 081011a2
STA: A2.A.8
TOP: Negative and Fractional Exponents
PTS: 2
274 ANS:
25
7
REF: 061020a2
STA: A2.A.71
TOP: Graphing Trigonometric Functions
PTS: 2
275 ANS:
{3}
REF: 081010a2
STA: A2.A.55
TOP: Trigonometric Ratios
3x + 16 = (x + 2) 2
. −4 is an extraneous solution.
3x + 16 = x 2 + 4x + 4
0 = x 2 + x − 12
0 = (x + 4)(x − 3)
x = −4 x = 3
PTS: 2
REF: 061121a2
KEY: extraneous solutions
STA: A2.A.22
TOP: Solving Radicals
ID: A
276 ANS:
−
14 + 5 3
11
3 +5
3 −5
⋅
3 +5
3 +5
PTS: 2
277 ANS:
20 C 3
=
3 + 5 3 + 5 3 + 25 28 + 10 3
14 + 5 3
=
= −
3 − 25
−22
11
REF: 061012a2
STA: A2.N.5
TOP: Rationalizing Denominators
PTS: 2
REF: 061007a2
STA: A2.S.9
TOP: Differentiating Permutations and Combinations
278 ANS:
below the 16th percentile
PTS: 2
KEY: interval
279 ANS:
−2
REF: fall0915a2
STA: A2.S.5
TOP: Normal Distributions
PTS: 2
280 ANS:
 1  n − 1
a n = 54  
 3
REF: 011124a2
STA: A2.A.18
TOP: Evaluating Logarithmic Expressions
PTS: 2
REF: 061026a2
STA: A2.A.29
281 ANS:
798
n
21
S n = [2a + (n − 1)d] =
[2(18) + (21 − 1)2] = 798
2
2
TOP: Sequences
PTS: 2
REF: 061103a2
KEY: arithmetic
282 ANS:
(x − 3) 2 + (y + 4) 2 = 18
STA: A2.A.35
TOP: Series
STA: A2.A.49
TOP: Equations of Circles
PTS: 2
REF: 011126a2
ID: A
283 ANS:
{1}
PTS: 2
REF: 061018a2
KEY: extraneous solutions
284 ANS:
4x 2 − 3x − 8 = 0
−b −(−3) 3
c −8
= −2
S=
=
= . P= =
4
a
4
a
4
STA: A2.A.22
TOP: Solving Radicals
PTS: 2
KEY: basic
285 ANS:
1
STA: A2.A.21
TOP: Roots of Quadratics
PTS: 2
REF: 011118a2
286 ANS:
2
13
10
. 35 + 48 < 180
=
sin 35 sinB
35 + 132 < 180
B ≈ 48,132
STA: A2.A.10
TOP: Fractional Exponents as Radicals
PTS: 2
287 ANS:
81,920
a n = 5(−2) n − 1
STA: A2.A.75
TOP: Law of Sines - The Ambiguous Case
STA: A2.A.32
TOP: Sequences
5
x2
−
x
REF: fall0912a2
2
5
=
1
x
2
5
=
1
5
x2
REF: 011113a2
a 15 = 5(−2) 15 − 1 = 81,920
PTS: 2
288 ANS:
−128 5
REF: 011105a2
a n = − 5(− 2) n − 1
a 15 = − 5(− 2) 15 − 1 = − 5(− 2 ) 14 = − 5 ⋅ 2 7 = −128 5
PTS: 2
REF: 061109a2
STA: A2.A.32
TOP: Sequences
ID: A
289 ANS:
4 5
9
2
 2 
  + cos 2 A = 1
 3
 
sin 2A = 2 sinA cos A


 2   5 

= 2   
 3   3 
5
cos 2 A =
9
cos A = +
5
, sin A is acute.
3
PTS: 2
KEY: evaluating
290 ANS:
60º, 240º
tan θ −
4 5
9
REF: 011107a2
3 =0
tan θ =
=
.
STA: A2.A.77
TOP: Double Angle Identities
.
3
θ = tan−1
3
θ = 60, 240
PTS: 2
KEY: basic
291 ANS:
cos x
REF: fall0903a2
STA: A2.A.68
TOP: Trigonometric Equations
PTS: 2
KEY: simplifying
292 ANS:
REF: fall0910a2
STA: A2.A.76
TOP: Angle Sum and Difference Identities
PTS: 2
REF: fall0926a2
STA: A2.A.46
TOP: Transformations with Functions and Relations