ALGEBRA

II The University of the State of New York

REGENTS HIGH SCHOOL EXAMINATION

ALGEBRA II
Thursday, August 16, 2018 — 12:30 to 3:30 p.m., only

Student Name: _________________________________________________________

School Name: ________________________________________________________________

The possession or use of any communications device is strictly prohibited when taking
this examination. If you have or use any communications device, no matter how briefly,
your examination will be invalidated and no score will be calculated for you.

Print your name and the name of your school on the lines above.
A separate answer sheet for Part I has been provided to you. Follow the instructions from the
proctor for completing the student information on your answer sheet.
This examination has four parts, with a total of 37 questions. You must answer all questions in this
examination. Record your answers to the Part I multiple-choice questions on the separate answer
sheet. Write your answers to the questions in Parts II, III, and IV directly in this booklet. All work
should be written in pen, except graphs and drawings, which should be done in pencil. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts,
etc. Utilize the information provided for each question to determine your answer. Note that diagrams
are not necessarily drawn to scale.
The formulas that you may need to answer some questions in this examination are found at the
end of the examination. This sheet is perforated so you may remove it from this booklet.
Scrap paper is not permitted for any part of this examination, but you may use the blank spaces
in this booklet as scrap paper. A perforated sheet of scrap graph paper is provided at the end of this
booklet for any question for which graphing may be helpful but is not required. You may remove
this sheet from this booklet. Any work done on this sheet of scrap graph paper will not be scored.
When you have completed the examination, you must sign the statement printed at the end of
the answer sheet, indicating that you had no unlawful knowledge of the questions or answers
prior to the examination and that you have neither given nor received assistance in answering any of
the questions during the examination. Your answer sheet cannot be accepted if you fail to sign this
declaration.

Notice…
A graphing calculator and a straightedge (ruler) must be available for you to use while
taking this examination.

DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.

ALGEBRA II
 Part I

Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial
credit will be allowed. Utilize the information provided for each question to determine your
answer. Note that diagrams are not necessarily drawn to scale. For each statement or question,
choose the word or expression that, of those given, best completes the statement or answers
the question. Record your answers on your separate answer sheet. [48]

Use this space for

1 The solution of 87e0.3x  5918, to the nearest thousandth, is computations.
(1) 0.583 (3) 4.220
(2) 1.945 (4) 14.066

2 A researcher randomly divides 50 bean plants into two groups.

He puts one group by a window to receive natural light and
the second group under artificial light. He records the growth of
the plants weekly. Which data collection method is described in this
situation?
(1) observational study (3) survey
(2) controlled experiment (4) systematic sample

3 If f(x)  x2  9 and g(x)  x  3, which operation would not result

in a polynomial expression?
(1) f(x)  g(x) (3) f(x) • g(x)
(2) f(x)  g(x) (4) f(x)  g(x)

Algebra II – Aug. ’18 [2]

 Use this space for
3 2
4 Consider the function p(x)  3x  x  5x and the graph of computations.
y  m(x) below.
y

1
x
–2 –1 –1 1 2

–10

Which statement is true?

(1) p(x) has three real roots and m(x) has two real roots.
(2) p(x) has one real root and m(x) has two real roots.
(3) p(x) has two real roots and m(x) has three real roots.
(4) p(x) has three real roots and m(x) has four real roots.

2 x4  8 x3  25 x2  6 x  14
5 Which expression is equivalent to ?
x 6
86
(1) 2x3  4x2  x  12 
x6
(2) 2x3  4x2  x  14
14
(3) 2x3  4x2  x 
x6
(4) 2x3  4x2  x

Algebra II – Aug. ’18 [3] [OVER]

 Use this space for
1
6 Given f(x)  _2_ x  8, which equation represents the inverse, g(x)? computations.
(1) g(x)  2x  8 (3) g(x)  _12_ x  8

(2) g(x)  2x  16 (4) g(x)  _12_ x  16

7 The value(s) of x that satisfy x 2  4 x  5  2 x  10 are

(1) {5} (3) {5, 7}
(2) {7} (4) {3, 5, 7}

8 Stephanie found that the number of white-winged crossbills in an

area can be represented by the formula C  550(1.08)t, where t
represents the number of years since 2010. Which equation
correctly represents the number of white-winged crossbills in terms
of the monthly rate of population growth?
__
t
t
(1) C  550(1.00643) (3) C  550(1.00643) 12

(4) C  550(1.00643)t  12
12t
(2) C  550(1.00643)

9 The roots of the equation 3x2  2x  7 are

1 1 2i兹苵5苵
(1) 2, __ (3)  __  _____
3 3 3
7 1 兹苵苵
11
(2)  __
3
,1 (4)  __
3
 ____
3

Algebra II – Aug. ’18 [4]

 Use this space for
10 The average depreciation rate of a new boat is approximately 8% per computations.
year. If a new boat is purchased at a price of $75,000, which model
is a recursive formula representing the value of the boat n years after
it was purchased?
n n
(1) an  75,000(0.08) (3) an  75,000(1.08)
(2) a0  75,000 (4) a0  75,000
n
an  (0.92) an  0.92(an  1)

7
11 Given cos θ  __ , where θ is an angle in standard position terminating
25
in quadrant IV, and sin2 θ  cos2 θ  1, what is the value of tan θ?
24 24
(1)  ___
25
(3) ___
25

24 24
(2)  ___
7
(4) ___
7

3 2
x i x5
12 For x  0, which expression is equivalent to 6
?
x

(1) x (3) x3
3
__
(2) x 2 (4) x10

Algebra II – Aug. ’18 [5] [OVER]

 Use this space for
13 Jake wants to buy a car and hopes to save at least $5000 for a down computations.
payment. The table below summarizes the amount of money he
plans to save each week.

Week 1 2 3 4 5
Money Saved,
2 5 12.5 31.25 …
in Dollars

Based on this plan, which expression should he use to determine

how much he has saved in n weeks?
n n
2  2(2 . 5 ) 1  2.5
(1) (3)
1  2.5 1 − 2.5
n− 1 n− 1
2  2(2 . 5 ) 1  2.5
(2) (4)
1  2.5 1  2.5

14 Which expression is equivalent to x6 y4(x4  16)  9(x4  16)?

(1) x10y4  16x6y4  9x4  144
(2) (x6y4  9)(x  2)3(x  2)
(3) (x3 y2  3)(x3 y2  3)(x  2)2(x  2)2
(4) (x3 y2  3)(x3 y2  3)(x2  4)(x2  4)

15 If A  3  5i, B  4  2i, and C  1  6i, where i is the imaginary

unit, then A  BC equals
(1) 5  17i (3) 19  17i
(2) 5  27i (4) 19  27i

Algebra II – Aug. ’18 [6]

 Use this space for
y computations.
16 Which sketch best represents the graph of x  3 ?
y y

x x

(1) (3)

y y

x x

(2) (4)

Algebra II – Aug. ’18 [7] [OVER]

 Use this space for
17 The graph below represents national and New York State average computations.
gas prices.
3.78
3.68
3.58
Average Gas Price ($)

3.48
3.38
3.28
3.18
3.08
2.98
2.88
2.78
2.68
2.58
2.48
2.38
2.28
2.18
Aug Oct Dec Feb Apr Jun Aug
2014 2014 2014 2015 2015 2015 2015

Key
NYS National

If New York State’s gas prices are modeled by G(x) and C  0, which
expression best approximates the national average x months from
August 2014?
(1) G(x  C) (3) G(x  C)
(2) G(x)  C (4) G(x)  C

18 Data for the students enrolled in a local high school are shown in the
Venn diagram below.

Algebra II Sophomores

210 85 320

985

If a student from the high school is selected at random, what is the

probability that the student is a sophomore given that the student is
enrolled in Algebra II?
85 85
(1) ____ (3) ____
210 405
85 85
(2) ____
295
(4) _____
1600

Algebra II – Aug. ’18 [8]

 Use this space for
19 If p(x)  2 ln(x)  1 and m(x)  ln(x  6), then what is the solution computations.
for p(x)  m(x)?
(1) 1.65 (3) 5.62
(2) 3.14 (4) no solution

20 Which function’s graph has a period of 8 and reaches a maximum

height of 1 if at least one full period is graphed?
π
(1) y  4 cos __( )
x 3 (3) y  4 cos(8x)  3
4
π
(2) y  4 cos (__
4 )
x 5 (4) y  4 cos(8x)  5

21 Given c(m)  m3  2m2  4m  8, the solution of c(m)  0 is

(1) 2 (3) 2i,2
(2) 2, only (4) 2i,2

22 The height above ground for a person riding a Ferris wheel after
π
t seconds is modeled by h(t)  150sin ___
( )
t  67.5  160 feet.
45
How many seconds does it take to go from the bottom of the wheel
to the top of the wheel?
(1) 10 (3) 90
(2) 45 (4) 150

Algebra II – Aug. ’18 [9] [OVER]

 Use this space for
1
23 The parabola described by the equation y  ___ (x  2)2  2 has the computations.
12
directrix at y  1. The focus of the parabola is
(1) (2,1) (3) (2,3)
(2) (2,2) (4) (2,5)

24 A fast-food restaurant analyzes data to better serve its customers.

After its analysis, it discovers that the events D, that a customer uses
the drive-thru, and F, that a customer orders French fries, are
independent. The following data are given in a report:

P(F)  0 . 8
P(F ∩ D)  0 . 456

Given this information, P(F|D) is

(1) 0.344 (3) 0.57
(2) 0.3648 (4) 0.8

Algebra II – Aug. ’18 [10]

 Part II
Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [16]

25 Over the set of integers, factor the expression x4  4x2  12.

Algebra II – Aug. ’18 [11] [OVER]

 3
2x 2
26 Express the fraction 1 in simplest radical form.
(16x )
4 4

Algebra II – Aug. ’18 [12]

 27 The world population was 2560 million people in 1950 and 3040 million in 1960 and can be
modeled by the function p(t)  2560e0.017185t, where t is time in years after 1950 and p(t) is the
population in millions. Determine the average rate of change of p(t) in millions of people per year,
from 4 ≤ t ≤ 8. Round your answer to the nearest hundredth.

28 The scores of a recent test taken by 1200 students had an approximately normal distribution with
a mean of 225 and a standard deviation of 18. Determine the number of students who scored
between 200 and 245.

Algebra II – Aug. ’18 [13] [OVER]

 29 Algebraically solve for x:

3  1  x  1
x3 2 6 2

Algebra II – Aug. ’18 [14]

 30 Graph t(x)  3sin(2x)  2 over the domain [0,2π] on the set of axes below.

t(x)

Algebra II – Aug. ’18 [15] [OVER]

 31 Solve the following system of equations algebraically.

x2  y2  400
y  x  28

Algebra II – Aug. ’18 [16]

 32 Some smart-phone applications contain “in-app” purchases, which allow users to purchase special
content within the application. A random sample of 140 users found that 35 percent made in-app
purchases. A simulation was conducted with 200 samples of 140 users assuming 35 percent of the
samples make in-app purchases. The approximately normal results are shown below.

25
Mean = 0.350
SD = 0.042
20

15

10

0
0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52
Proportion of In-App Purchases

Considering the middle 95% of the data, determine the margin of error, to the nearest hundredth,
for the simulated results. In the given context, explain what this value represents.

Algebra II – Aug. ’18 [17] [OVER]

 Part III
Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. Utilize the information provided for each question to determine your answer.
Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct
numerical answer with no work shown will receive only 1 credit. All answers should be
written in pen, except for graphs and drawings, which should be done in pencil. [16]

33 Solve the following system of equations algebraically for all values of x, y, and z.

2x  3y  4z  1
x  2y  5z  3
4x  y  z  16

Algebra II – Aug. ’18 [18]

 34 Evaluate j(1) given j(x)  2x4  x3 35x2  16x  48. Explain what your answer tells you about
x  1 as a factor.

Algebraically find the remaining zeros of j(x).

Algebra II – Aug. ’18 [19] [OVER]

 35 Determine, to the nearest tenth of a year, how long it would take an investment to double at a
3
3 __ % interest rate, compounded continuously.
4

Algebra II – Aug. ’18 [20]

 36 To determine if the type of music played while taking a quiz has a relationship to results,
16 students were randomly assigned to either a room softly playing classical music or a room softly
playing rap music. The results on the quiz were as follows:

Classical: 74, 83, 77, 77, 84, 82, 90, 89

Rap: 77, 80, 78, 74, 69, 72, 78, 69

John correctly rounded the difference of the means of his experimental groups as 7. How did John
obtain this value and what does it represent in the given context? Justify your answer.

To determine if there is any significance in this value, John rerandomized the 16 scores into two
groups of 8, calculated the difference of the means, and simulated this process 250 times as shown
below.
Classical vs. Rap
Frequency

5 0 5

Difference of the Means

Does the simulation support the theory that there may be a significant difference in quiz scores?
Explain.

Algebra II – Aug. ’18 [21] [OVER]

 Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate
the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.
Utilize the information provided to determine your answer. Note that diagrams are not
necessarily drawn to scale. A correct numerical answer with no work shown will receive only
1 credit. All answers should be written in pen, except for graphs and drawings, which should
be done in pencil. [6]

37 A major car company analyzes its revenue, R(x), and costs C(x), in millions of dollars over a
fifteen-year period. The company represents its revenue and costs as a function of time, in years, x,
using the given functions.

R(x)  550x3  12,000x2  83,000x  7000

C(x)  880x3  21,000x2  150,000x  160,000

The company’s profits can be represented as the difference between its revenue and costs.
Write the profit function, P(x), as a polynomial in standard form.

Question 37 is continued on the next page.

Algebra II – Aug. ’18 [22]

 Question 37 continued

Graph y  P(x) on the set of axes below over the domain 2 ≤ x ≤ 16.

Over the given domain, state when the company was the least profitable and the most profitable,
to the nearest year. Explain how you determined your answer.

Algebra II – Aug. ’18 [23]

Tear Here
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 High School Math Reference Sheet
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1 inch  2.54 centimeters 1 kilometer  0.62 mile 1 cup  8 fluid ounces

1 meter  39.37 inches 1 pound  16 ounces 1 pint  2 cups
1 mile  5280 feet 1 pound  0.454 kilogram 1 quart  2 pints
1 mile  1760 yards 1 kilogram  2.2 pounds 1 gallon  4 quarts
1 mile  1.609 kilometers 1 ton  2000 pounds 1 gallon  3.785 liters
1 liter  0.264 gallon
1 liter  1000 cubic centimeters

1 Pythagorean
Triangle A bh a2  b2  c2
2 Theorem

Quadratic b  b2  4ac
Parallelogram A  bh x
Formula 2a

Arithmetic
Circle A  πr 2 an  a1  (n  1)d
Sequence

Geometric
Circle C  πd or C  2πr a n  a 1r n  1
Sequence

Geometric a1  a1r n
General Prisms V  Bh Sn  where r  1
Series 1r

180
Cylinder V  πr 2h Radians 1 radian  degrees
π

4 3 π
Sphere V πr Degrees 1 degree  radians
3 180

1 2 Exponential
Cone V πr h A  A0ek(t  t0)  B0
3 Growth/Decay

1
Pyramid V Bh
3
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Algebra II – Aug. ’18 [27]

ALGEBRA II

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Printed on Recycled Paper

ALGEBRA II