The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA II (Common Core) Wednesday, June 1, 2016 — 9:15 a.m. to 12:15 p.m., only Student Name:________________________________________________________ School Name: ______________________________________________________________ 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. ALGEBRA II (COMMON CORE) DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN. Notice… A graphing calculator and a straightedge (ruler) must be available for you to use while taking this examination. ALGEBRA II (COMMON CORE) 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.
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The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
ALGEBRA II (Common Core)Wednesday, June 1, 2016 — 9:15 a.m. to 12:15 p.m., only
School Name: ______________________________________________________________
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 answersheet.
This examination has four parts, with a total of 37 questions. You must answerall questions in this examination. Record your answers to the Part I multiple-choicequestions on the separate answer sheet. Write your answers to the questions inParts II, III, and IV directly in this booklet. All work should be written in pen, exceptgraphs and drawings, which should be done in pencil. Clearly indicate the necessarysteps, 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 examinationare found at the end of the examination. This sheet is perforated so you may removeit from this booklet.
Scrap paper is not permitted for any part of this examination, but you may usethe blank spaces in this booklet as scrap paper. A perforated sheet of scrap graphpaper is provided at the end of this booklet for any question for which graphing maybe helpful but is not required. You may remove this sheet from this booklet. Anywork done on this sheet of scrap graph paper will not be scored.
When you have completed the examination, you must sign the statement printedat the end of the answer sheet, indicating that you had no unlawful knowledge of thequestions 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.
ALGEBRA II (COMMON CORE)
DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.
Notice…
A graphing calculator and a straightedge (ruler) must be available for you to use while taking thisexamination.
ALGEBRA II (COMMON CORE)
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 examinationwill be invalidated and no score will be calculated for you.
Algebra II (Common Core) – June ’16 [2]
Part I
Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partialcredit will be allowed. Utilize the information provided for each question to determine youranswer. 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 answersthe question. Record your answers on your separate answer sheet. [48]
Use this space forcomputations.
1 When b � 0 and d is a positive integer, the expression isequivalent to
(1) (3)
(2) (4)
2 Julie averaged 85 on the first three tests of the semester in hermathematics class. If she scores 93 on each of the remaining tests, her average will be 90. Which equation could be used to determinehow many tests, T, are left in the semester?
(1) (3)
(2) (4)
3 Given i is the imaginary unit, (2 � yi)2 in simplest form is
(1) y2 � 4yi � 4 (3) �y2 � 4
(2) �y2 � 4yi � 4 (4) y2 � 4
255 903
93� �TT
255 903
93��
�TT
255 933
90� �TT
255 933
90��
�TT
3b( )d
32
bd( )
1
3bd( )2
1
3bd
(3 )b2d
Algebra II (Common Core) – June ’16 [3] [OVER]
Use this space forcomputations.4 Which graph has the following characteristics?
• three real zeros
• as x → � ∞, f(x) → � ∞
• as x → ∞, f(x) → ∞
5 The solution set for the equation is
(1) {�8,7} (3) {7}
(2) {�7,8} (4) { }
56 � �x x
y
x
(1)
y
x
(3)
y
x
(2)
y
x
(4)
Algebra II (Common Core) – June ’16 [4]
Use this space forcomputations.6 The zeros for f(x) � x4 � 4x3 � 9x2 � 36x are
(1) {0,�3,4} (3) {0,�3,�4}
(2) {0,3,4} (4) {0,3,�4}
7 Anne has a coin. She does not know if it is a fair coin. She flippedthe coin 100 times and obtained 73 heads and 27 tails. She ran a computer simulation of 200 samples of 100 fair coin flips. Theoutput of the proportion of heads is shown below.
Given the results of her coin flips and of her computer simulation,which statement is most accurate?
(1) 73 of the computer’s next 100 coin flips will be heads.
(2) 50 of her next 100 coin flips will be heads.
(3) Her coin is not fair.
(4) Her coin is fair.
8 If g(c) � 1 � c2 and m(c) � c � 1, then which statement is not true?
(1) g(c) • m(c) � 1 � c � c2 � c3
(2) g(c) � m(c) � 2 � c � c2
(3) m(c) � g(c) � c � c2
(4) m cg c c
( )( )
11��
�
0.500 0.35 0.40
10
20
0.45
30
0.55 0.60
Samples � 200Mean � 0.497SD � 0.050
Algebra II (Common Core) – June ’16 [5] [OVER]
Use this space forcomputations.9 The heights of women in the United States are normally distributed
with a mean of 64 inches and a standard deviation of 2.75 inches.The percent of women whose heights are between 64 and 69.5 inches,to the nearest whole percent, is
(1) 6 (3) 68
(2) 48 (4) 95
10 The formula below can be used to model which scenario?
a1 � 3000
an � 0.80an � 1
(1) The first row of a stadium has 3000 seats, and each row thereafterhas 80 more seats than the row in front of it.
(2) The last row of a stadium has 3000 seats, and each row before ithas 80 fewer seats than the row behind it.
(3) A bank account starts with a deposit of $3000, and each year itgrows by 80%.
(4) The initial value of a specialty toy is $3000, and its value each ofthe following years is 20% less.
11 Sean’s team has a baseball game tomorrow. He pitches 50% of the games. There is a 40% chance of rain during the game tomorrow.If the probability that it rains given that Sean pitches is 40%, it canbe concluded that these two events are
(1) independent (3) mutually exclusive
(2) dependent (4) complements
Algebra II (Common Core) – June ’16 [6]
12 A solution of the equation 2x2 � 3x � 2 � 0 is
(1) (3)
(2) (4)
13 The Ferris wheel at the landmark Navy Pier in Chicago takes 7 minutes to make one full rotation. The height, H, in feet, above the ground of one of the six-person cars can be modeled by
H(t) � 70 sin � 80, where t is time, in minutes. Using
H(t) for one full rotation, this car’s minimum height, in feet, is
(1) 150 (3) 10
(2) 70 (4) 0
14 The expression is equivalent to
(1) 2x2 � 3x � 7 � (3) 2x2 � 2.5x � 5 �
(2) 2x2 � 3x � 7 � (4) 2x2 � 2.5x � 5 �
15 Which function represents exponential decay?
(1) y � 20.3 t (3) y �
(2) y � 1.23 t (4) y � 5�t
� �34
14
7
� �34
74
i 12
� �34
14
7i
12
⎛
⎝⎜
⎞
⎠⎟�t
112 3x �
202 3x �
312 3x �
152 3x �
4 5 102 3
3x xx
� ��
27� �( . )t 1 75
⎛⎝⎜
⎞⎠⎟
Use this space forcomputations.
Algebra II (Common Core) – June ’16 [7] [OVER]
Use this space forcomputations.
16 Given f �1(x) � � x � 2, which equation represents f(x)?
(1) f(x) � x � (3) f(x) � x � 2
(2) f(x) � � x � (4) f(x) � � x � 2
17 A circle centered at the origin has a radius of 10 units. The terminalside of an angle, �, intercepts the circle in Quadrant II at point C.The y-coordinate of point C is 8. What is the value of cos �?
(1) (3)
(2) (4)
18 Which statement about the graph of c(x) � log6x is false?
(1) The asymptote has equation y � 0.
(2) The graph has no y-intercept.
(3) The domain is the set of positive reals.
(4) The range is the set of all real numbers.
19 The equation 4x2 � 24x � 4y2 � 72y � 76 is equivalent to
(1) 4(x � 3)2 � 4(y � 9)2 � 76
(2) 4(x � 3)2 � 4(y � 9)2 � 121
(3) 4(x � 3)2 � 4(y � 9)2 � 166
(4) 4(x � 3)2 � 4(y � 9)2 � 436
45�
34
35�
35
43
83
34
43
83
34
34
Algebra II (Common Core) – June ’16 [8]
20 There was a study done on oxygen consumption of snails as a functionof pH, and the result was a degree 4 polynomial function whosegraph is shown below.
Which statement about this function is incorrect?
(1) The degree of the polynomial is even.
(2) There is a positive leading coefficient.
(3) At two pH values, there is a relative maximum value.
(4) There are two intervals where the function is decreasing.
21 Last year, the total revenue for Home Style, a national restaurantchain, increased 5.25% over the previous year. If this trend were tocontinue, which expression could the company’s chief financial officeruse to approximate their monthly percent increase in revenue? [Let m represent months.]
(1) (1.0525)m (3) (1.00427)m
(2) (4)(1.0525)12m (1.00427)12
m
0.10
0.08
0.06
0.04
0.00
0.02
6 7 8 9 10
pH
Oxy
gen
Co
nsu
mp
tio
n (
cc/h
r)
Use this space forcomputations.
Algebra II (Common Core) – June ’16 [9] [OVER]
22 Which value, to the nearest tenth, is not a solution of p(x) � q(x) ifp(x) � x3 � 3x2 � 3x � 1 and q(x) � 3x � 8?
(1) �3.9 (3) 2.1
(2) �1.1 (4) 4.7
23 The population of Jamesburg for the years 2010 – 2013, respectively,was reported as follows:
250,000 250,937 251,878 252,822
How can this sequence be recursively modeled?
(1) jn � 250,000(1.00375)n � 1
(2) jn � 250,000 � 937(n � 1)
(3) j1 � 250,000jn � 1.00375 jn � 1
(4) j1 � 250,000jn � jn � 1 � 937
24 The voltage used by most households can be modeled by a sinefunction. The maximum voltage is 120 volts, and there are 60 cyclesevery second. Which equation best represents the value of the voltageas it flows through the electric wires, where t is time in seconds?
(1) V � 120 sin (t) (3) V � 120 sin (60π t)
(2) V � 120 sin (60 t) (4) V � 120 sin (120π t)
Use this space forcomputations.
25 Solve for x: 1 13
13x x
� � �
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 correctnumerical 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]
Algebra II (Common Core) – June ’16 [10] [OVER]
26 Describe how a controlled experiment can be created to examine the effect of ingredient X in a toothpaste.
Algebra II (Common Core) – June ’16 [11] [OVER]
27 Determine if x � 5 is a factor of 2x3 � 4x2 � 7x � 10. Explain your answer.
Algebra II (Common Core) – June ’16 [12]
28 On the axes below, graph one cycle of a cosine function with amplitude 3, period , midline y � �1, and passing through the point (0,2).
�2
y
x
Algebra II (Common Core) – June ’16 [13] [OVER]
29 A suburban high school has a population of 1376 students. The number of students whoparticipate in sports is 649. The number of students who participate in music is 433. If
the probability that a student participates in either sports or music is , what is the probability
that a student participates in both sports and music?
9741376
Algebra II (Common Core) – June ’16 [14]
30 The directrix of the parabola 12(y � 3) � (x � 4)2 has the equation y � �6. Find the coordinatesof the focus of the parabola.
Algebra II (Common Core) – June ’16 [15] [OVER]
31 Algebraically prove that , where x �2.xx x
3
3 398
18
1�
� �� �
Algebra II (Common Core) – June ’16 [16]
32 A house purchased 5 years ago for $100,000 was just sold for $135,000. Assuming exponentialgrowth, approximate the annual growth rate, to the nearest percent.
Algebra II (Common Core) – June ’16 [17] [OVER]
33 Solve the system of equations shown below algebraically.
(x � 3)2 � (y � 2)2 � 16
2x � 2y � 10
Algebra II (Common Core) – June ’16 [18]
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 correctnumerical 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]
34 Alexa earns $33,000 in her first year of teaching and earns a 4% increase in each successive year.
Write a geometric series formula, Sn, for Alexa’s total earnings over n years.
Use this formula to find Alexa’s total earnings for her first 15 years of teaching, to the nearest cent.
Algebra II (Common Core) – June ’16 [19] [OVER]
35 Fifty-five students attending the prom were randomly selected to participate in a survey about the music choice at the prom. Sixty percent responded that a DJ would be preferred over a band.Members of the prom committee thought that the vote would have 50% for the DJ and 50% forthe band.
A simulation was run 200 times, each of sample size 55, based on the premise that 60% of the students would prefer a DJ. The approximate normal simulation results are shown below.
Using the results of the simulation, determine a plausible interval containing the middle 95% ofthe data. Round all values to the nearest hundredth.
Members of the prom committee are concerned that a vote of all students attending the prommay produce a 50% – 50% split. Explain what statistical evidence supports this concern.
����
����
0.40
4
8
12
16
20
24
28
����� ���������0.45 0.50 0.55 0.60 0.65 0.750.70
Mean = 0.602S.D. = 0.066
Algebra II (Common Core) – June ’16 [20]
36 Which function shown below has a greater average rate of change on the interval [�2, 4]? Justifyyour answer.
x f(x)
−4 0.3125
−3 0.625
−2 1.25
−1 2.5
0 5
1 10
2 20
3 40
4 80
5 160
6 320
g(x) � 4x3 � 5x2 � 3
Algebra II (Common Core) – June ’16 [21] [OVER]
37 Drugs break down in the human body at different rates and therefore must be prescribed bydoctors carefully to prevent complications, such as overdosing. The breakdown of a drug isrepresented by the function N(t) � N0(e)�r t, where N(t) is the amount left in the body, N0 is the initial dosage, r is the decay rate, and t is time in hours. Patient A, A(t), is given 800 milligramsof a drug with a decay rate of 0.347. Patient B, B(t), is given 400 milligrams of another drug witha decay rate of 0.231.
Write two functions, A(t) and B(t), to represent the breakdown of the respective drug given toeach patient.
Graph each function on the set of axes below.
y
t
Algebra II (Common Core) – June ’16 [22]
Part IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly indicatethe 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 only1 credit. All answers should be written in pen, except for graphs and drawings, which shouldbe done in pencil. [6]
To the nearest hour, t, when does the amount of the given drug remaining in patient B begin toexceed the amount of the given drug remaining in patient A?
The doctor will allow patient A to take another 800 milligram dose of the drug once only 15% of the original dose is left in the body. Determine, to the nearest tenth of an hour, how long patient Awill have to wait to take another 800 milligram dose of the drug.
Algebra II (Common Core) – June ’16 [23]
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FOR TEACHERS ONLYThe University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
ALGEBRA II (Common Core)Wednesday, June 1, 2016 — 9:15 a.m. to 12:15 p.m., only
SCORING KEY AND RATING GUIDE
Mechanics of RatingThe following procedures are to be followed for scoring student answer papers for
the Regents Examination in Algebra II (Common Core). More detailed information about scoring is provided in the publication Information Booklet for Scoring the RegentsExamination in Algebra II (Common Core).
Do not attempt to correct the student’s work by making insertions or changes of anykind. In scoring the constructed-response questions, use check marks to indicate studenterrors. Unless otherwise specified, mathematically correct variations in the answers will beallowed. Units need not be given when the wording of the questions allows such omissions.
Each student’s answer paper is to be scored by a minimum of three mathematics teachers. No one teacher is to score more than approximately one-third of the constructed-response questions on a student’s paper. Teachers may not score their own students’ answerpapers. On the student’s separate answer sheet, for each question, record the number ofcredits earned and the teacher’s assigned rater/scorer letter.
Schools are not permitted to rescore any of the open-ended questions on thisexam after each question has been rated once, regardless of the final exam score.Schools are required to ensure that the raw scores have been added correctly andthat the resulting scale score has been determined accurately.
Raters should record the student’s scores for all questions and the total raw score on the student’s separate answer sheet. Then the student’s total raw score should be convertedto a scale score by using the conversion chart that will be posted on the Department’s web siteat: http://www.p12.nysed.gov/assessment/ by Thursday, June 23, 2016. Because scale scorescorresponding to raw scores in the conversion chart may change from one administration to another, it is crucial that, for each administration, the conversion chart provided for thatadministration be used to determine the student’s final score. The student’s scale scoreshould be entered in the box provided on the student’s separate answer sheet. The scale scoreis the student’s final examination score.
(1) . . . . . 4 . . . . .
(2) . . . . . 3 . . . . .
(3) . . . . . 2 . . . . .
(4) . . . . . 3 . . . . .
(5) . . . . . 3 . . . . .
(6) . . . . . 1 . . . . .
(7) . . . . . 3 . . . . .
(8) . . . . . 4 . . . . .
(9) . . . . . 2 . . . . .
(10) . . . . . 4 . . . . .
(11) . . . . . 1 . . . . .
(12) . . . . . 1 . . . . .
(13) . . . . . 3 . . . . .
(14) . . . . . 2 . . . . .
(15) . . . . . 4 . . . . .
(16) . . . . . 2 . . . . .
(17) . . . . . 1 . . . . .
(18) . . . . . 1 . . . . .
(19) . . . . . 4 . . . . .
(20) . . . . . 2 . . . . .
(21) . . . . . 3 . . . . .
(22) . . . . . 4 . . . . .
(23) . . . . . 3 . . . . .
(24) . . . . . 4 . . . . .
Updated information regarding the rating of this examination may be posted on the NewYork State Education Department’s web site during the rating period. Check this web site at:http://www.p12.nysed.gov/assessment/ and select the link “Scoring Information” for anyrecently posted information regarding this examination. This site should be checked beforethe rating process for this examination begins and several times throughout the RegentsExamination period.
The Department is providing supplemental scoring guidance, the “Model Response Set,”for the Regents Examination in Algebra II (Common Core). This guidance is recommendedto be part of the scorer training. Schools are encouraged to incorporate the Model ResponseSets into the scorer training or to use them as additional information during scoring. Whilenot reflective of all scenarios, the model responses selected for the Model Response Set illustrate how less common student responses to constructed-response questions may bescored. The Model Response Set will be available on the Department’s web site athttp://www.nysedregents.org/algebratwo/.
Algebra II (Common Core) Rating Guide – June ’16 [2]
If the student’s responses for the multiple-choice questions are being hand scored prior to beingscanned, the scorer must be careful not to make any marks on the answer sheet except to recordthe scores in the designated score boxes. Marks elsewhere on the answer sheet will interfere withthe accuracy of the scanning.
Part I
Allow a total of 48 credits, 2 credits for each of the following.
Algebra II (Common Core) Rating Guide – June ’16 [3]
General Rules for Applying Mathematics Rubrics
I. General Principles for RatingThe rubrics for the constructed-response questions on the Regents Examination in Algebra II (CommonCore) are designed to provide a systematic, consistent method for awarding credit. The rubrics are not tobe considered all-inclusive; it is impossible to anticipate all the different methods that students might useto solve a given problem. Each response must be rated carefully using the teacher’s professional judgmentand knowledge of mathematics; all calculations must be checked. The specific rubrics for each question mustbe applied consistently to all responses. In cases that are not specifically addressed in the rubrics, raters mustfollow the general rating guidelines in the publication Information Booklet for Scoring the RegentsExamination in Algebra II (Common Core), use their own professional judgment, confer with other mathematics teachers, and/or contact the State Education Department for guidance. During each RegentsExamination administration period, rating questions may be referred directly to the Education Department.The contact numbers are sent to all schools before each administration period.
II. Full-Credit ResponsesA full-credit response provides a complete and correct answer to all parts of the question. Sufficient workis shown to enable the rater to determine how the student arrived at the correct answer.When the rubric for the full-credit response includes one or more examples of an acceptable method forsolving the question (usually introduced by the phrase “such as”), it does not mean that there are no additional acceptable methods of arriving at the correct answer. Unless otherwise specified, mathematicallycorrect alternative solutions should be awarded credit. The only exceptions are those questions that specifythe type of solution that must be used; e.g., an algebraic solution or a graphic solution. A correct solutionusing a method other than the one specified is awarded half the credit of a correct solution using the specified method.
III. Appropriate WorkFull-Credit Responses: The directions in the examination booklet for all the constructed-response questionsstate: “Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,charts, etc.” The student has the responsibility of providing the correct answer and showing how that answerwas obtained. The student must “construct” the response; the teacher should not have to search through agroup of seemingly random calculations scribbled on the student paper to ascertain what method the student may have used.Responses With Errors: Rubrics that state “Appropriate work is shown, but…” are intended to be used withsolutions that show an essentially complete response to the question but contain certain types of errors,whether computational, rounding, graphing, or conceptual. If the response is incomplete; i.e., an equationis written but not solved or an equation is solved but not all of the parts of the question are answered, appropriate work has not been shown. Other rubrics address incomplete responses.
IV. Multiple ErrorsComputational Errors, Graphing Errors, and Rounding Errors: Each of these types of errors results in a 1-credit deduction. Any combination of two of these types of errors results in a 2-credit deduction. No more than2 credits should be deducted for such mechanical errors in a 4-credit question and no more than 3 credits should be deducted in a 6-credit question. The teacher must carefully review the student’s work to determinewhat errors were made and what type of errors they were.Conceptual Errors: A conceptual error involves a more serious lack of knowledge or procedure. Examplesof conceptual errors include using the incorrect formula for the area of a figure, choosing the incorrecttrigonometric function, or multiplying the exponents instead of adding them when multiplying terms withexponents.If a response shows repeated occurrences of the same conceptual error, the student should not be penalizedtwice. If the same conceptual error is repeated in responses to other questions, credit should be deductedin each response.For 4- and 6-credit questions, if a response shows one conceptual error and one computational, graphing, orrounding error, the teacher must award credit that takes into account both errors. Refer to the rubric forspecific scoring guidelines.
(25) [2] 4, and correct work is shown.
[1] Appropriate work is shown, but one computational error is made.
or
[1] Appropriate work is shown, but one conceptual error is made.
or
[1] 4, but no work is shown.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.
(26) [2] A correct description of a controlled experiment is written, such as indicatingtwo randomly assigned groups, one with ingredient X and one without ingredient X.
[1] One conceptual error is made.
or
[1] An incomplete description of a controlled experiment is written.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.
(27) [2] No, and correct work is shown, and a correct explanation is written.
[1] Appropriate work is shown, but one computational error is made.
or
[1] Appropriate work is shown, but one conceptual error is made.
or
[1] Correct work is shown, but no explanation or an incorrect explanation is written.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.
Part II
For each question, use the specific criteria to award a maximum of 2 credits. Unlessotherwise specified, mathematically correct alternative solutions should be awarded appropriate credit.
Algebra II (Common Core) Rating Guide – June ’16 [4]
Algebra II (Common Core) Rating Guide – June ’16 [5]
(28) [2] A correct graph is drawn.
[1] One graphing error is made.
or
[1] One conceptual error is made, such as graphing more than one cycle.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.
(29) [2] or an equivalent fraction, and correct work is shown.
[1] Appropriate work is shown, but one computational error is made.
or
[1] Appropriate work is shown, but one conceptual error is made.
or
[1] , but no work is shown.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.
(30) [2] (4,0), and correct work is shown.
[1] Appropriate work is shown, but one computational error is made.
or
[1] Appropriate work is shown, but one conceptual error is made.
or
[1] (4,0), but no work is shown.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.
1081376
1081376
(31) [2] A correct algebraic proof is shown.
[1] Appropriate work is shown, but one computational or simplification error ismade.
or
[1] Appropriate work is shown, but one conceptual error is made.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.
(32) [2] 6, and correct work is shown.
[1] Appropriate work is shown, but one computational or rounding error is made.
or
[1] Appropriate work is shown, but one conceptual error is made.
or
[1] 6, but no work is shown.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.
Algebra II (Common Core) Rating Guide – June ’16 [6]
(33) [4] (7,�2) and (3,2) or equivalent solutions, and correct algebraic work is shown.
[3] Appropriate work is shown, but one computational, factoring, or substitutionerror is made.
or
[3] Appropriate work is shown, but only one correct solution is found or only the x-values or y-values are found.
[2] Appropriate work is shown, but two or more computational, factoring, orsubstitution errors are made.
or
[2] Appropriate work is shown, but one conceptual error is made.
or
[2] A correct substitution into the quadratic formula is made, but no further correct work is shown.
or
[2] (7,�2) and (3,2), but a method other than algebraic is used.
[1] Appropriate work is shown, but one conceptual error and one computational,factoring, or substitution error are made.
or
[1] A correct quadratic equation in one variable is written, but no further correctwork is shown.
or
[1] (7,�2) and (3,2), but no work is shown.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.
Algebra II (Common Core) Rating Guide – June ’16 [7]
Part III
For each question, use the specific criteria to award a maximum of 4 credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit.
(34) [4] Sn � or an equivalent equation is written and 660,778.39,
and correct work is shown.
[3] Appropriate work is shown, but one computational or simplification error ismade.
or
[3] Appropriate work is shown, but one notation error is made, such as writing
the expression , or not using n.
[2] Appropriate work is shown, but two or more computational, notation, or simplification errors are made.
or
[2] Appropriate work is shown, but one conceptual error is made.
or
[2] Sn � , but no further correct work is shown.
[1] Appropriate work is shown, but one conceptual error and one computational,notation, or simplification error are made.
or
[1] 660,778.39, but no work is shown.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.
33 0001
, 33,000(1.04)1.04
��
n
33 0001
, 33,000(1.04)1.04
��
n
33 0001
, 33,000(1.04)1.04
��
n
Algebra II (Common Core) Rating Guide – June ’16 [8]
(35) [4] (0.47, 0.73) and correct work is shown, and a correct statistical explanation iswritten.
[3] Appropriate work is shown, but one computational error is made.
or
[3] Correct work is shown to find (0.47, 0.73), but the explanation is incompleteor nonstatistical.
[2] Appropriate work is shown, but two or more computational errors are made.
or
[2] Appropriate work is shown, but one conceptual error is made.
or
[2] Appropriate work is shown to find (0.47, 0.73), but no further correct work isshown.
or
[2] A correct statistical explanation is written, but no further correct work is shown.
[1] Appropriate work is shown, but one conceptual error and one computationalerror are made.
or
[1] (0.47, 0.73), but no work is shown.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.
Algebra II (Common Core) Rating Guide – June ’16 [9]
(36) [4] g, and a correct justification is given.
[3] Appropriate work is shown, but one computational error is made.
or
[3] Correct rates of change are computed, but no function is indicated.
[2] Appropriate work is shown, but two or more computational errors are made.
or
[2] Appropriate work is shown, but one conceptual error is made.
or
[2] Appropriate work is shown to find the rate of change for f is 13.125 or the rate of change for g is 38, but no further correct work is shown.
[1] Appropriate work is shown, but one conceptual error and one computationalerror are made.
or
[1] 13.125 and 38, but no work is shown.
[0] 13.125 or 38, but the rates of change are not labeled, and no further correctwork is shown.
or
[0] g, but no work is shown.
or
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.
Algebra II (Common Core) Rating Guide – June ’16 [10]
Algebra II (Common Core) Rating Guide – June ’16 [11]
(37) [6] A(t) � 800e�0.347t and B(t) � 400e�0.231t, correct graphs are drawn and at leastone is labeled, 6, 5.5, and correct work is shown.
[5] Appropriate work is shown, but one computational, graphing, labeling, orrounding error is made.
[4] Appropriate work is shown, but two computational, graphing, labeling, orrounding errors are made.
or
[4] Appropriate work is shown, but one conceptual error is made.
[3] Appropriate work is shown, but three or more computational, graphing, labeling, or rounding errors are made.
or
[3] Appropriate work is shown, but one conceptual error and one computational,graphing, labeling, or rounding error are made.
[2] Appropriate work is shown, but two conceptual errors are made.
or
[2] Correct graphs are drawn and at least one is labeled, but no further correctwork is shown.
or
[2] 5.5 and correct work is shown, but no further correct work is shown.
or
[2] 6 and 5.5, but no work is shown.
[1] Appropriate work is shown, but two conceptual errors and one computational,graphing, labeling, or rounding errors are made.
or
[1] A(t) � 800e�0.347t and B(t) � 400e�0.231t, but no further correct work is shown.
or
[1] A(t) or B(t) is graphed correctly, but no further correct work is shown.
or
[1] 6 or 5.5, but no work is shown.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.
Part IV
For this question, use the specific criteria to award a maximum of 6 credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit.
Algebra II (Common Core) Rating Guide – June ’16 [12]
Map to the Common Core Learning Standards Algebra II (Common Core)
June 2016
Question Type Credits Cluster
1 Multiple Choice 2 N-RN.A
2 Multiple Choice 2 A-CED.A
3 Multiple Choice 2 N-CN.A
4 Multiple Choice 2 F-IF.C
5 Multiple Choice 2 A-REI.A
6 Multiple Choice 2 A-APR.B
7 Multiple Choice 2 S-IC.A
8 Multiple Choice 2 F-BF.A
9 Multiple Choice 2 S-ID.A
10 Multiple Choice 2 F-BF.A
11 Multiple Choice 2 S-CP.A
12 Multiple Choice 2 N-CN.C
13 Multiple Choice 2 F-IF.B
14 Multiple Choice 2 A-APR.D
15 Multiple Choice 2 F-IF.C
16 Multiple Choice 2 F-BF.B
17 Multiple Choice 2 F-TF.A
18 Multiple Choice 2 F-IF.C
19 Multiple Choice 2 A-SSE.A
20 Multiple Choice 2 F-IF.B
Algebra II (Common Core) Rating Guide – June ’16 [13]
21 Multiple Choice 2 A-SSE.B
22 Multiple Choice 2 A-REI.D
23 Multiple Choice 2 F-BF.A
24 Multiple Choice 2 F-TF.B
25 Constructed Response 2 A-REI.A
26 Constructed Response 2 S-IC.B
27 Constructed Response 2 A-APR.B
28 Constructed Response 2 F-IF.C
29 Constructed Response 2 S-CP.B
30 Constructed Response 2 G-GPE.A
31 Constructed Response 2 A-SSE.A
32 Constructed Response 2 F-LE.A
33 Constructed Response 4 A-REI.C
34 Constructed Response 4 A-SSE.B
35 Constructed Response 4 S-IC.B
36 Constructed Response 4 F-IF.C
37 Constructed Response 6 A-REI.D
Algebra II (Common Core) Rating Guide – June ’16 [14]
Regents Examination in Algebra II (Common Core)
June 2016
Chart for Converting Total Test Raw Scores toFinal Examination Scores (Scale Scores)
Online Submission of Teacher Evaluations of the Test to the DepartmentSuggestions and feedback from teachers provide an important contribution to the test
development process. The Department provides an online evaluation form for State assessments. It contains spaces for teachers to respond to several specific questions and tomake suggestions. Instructions for completing the evaluation form are as follows:
1. Go to http://www.forms2.nysed.gov/emsc/osa/exameval/reexameval.cfm.
2. Select the test title.
3. Complete the required demographic fields.
4. Complete each evaluation question and provide comments in the space provided.
5. Click the SUBMIT button at the bottom of the page to submit the completed form.
The Chart for Determining the Final Examination Score for the June 2016 Regents Examination in Algebra II (Common Core) will be posted on the Department’sweb site at: http://www.p12.nysed.gov/assessment/ by Thursday, June 23, 2016.
Regents Examination in
Algebra II (Common Core)
Selected Questions with Annotations
June 2016
1
THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY 12234
New York State Testing Program Regents Examination in Algebra II (Common Core)
Selected Questions with Annotations With the adoption of the New York P-12 Common Core Learning Standards (CCLS) in ELA/Literacy and Mathematics, the Board of Regents signaled a shift in both instruction and assessment. In Spring 2014, New York State administered the first set of Regents Exams designed to assess student performance in accordance with the instructional shifts and the rigor demanded by the Common Core State Standards (CCSS). To aid in the transition to new tests, New York State released a number of resources including sample questions, test blueprints and specifications, and criteria for writing test questions. These resources can be found at http://www.engageny.org/resource/regents-exams. New York State administered the first Algebra II (Common Core) Regents Exam in June 2016 and is now annotating a portion of the questions from this test available for review and use. These annotated questions will help students, families, educators, and the public better understand how the test has changed to assess the instructional shifts demanded by the Common Core and to assess the rigor required to ensure that all students are on track to college and career readiness. Annotated Questions Are Teaching Tools
The annotated questions are intended to help students, families, educators, and the public understand how the Common Core is different. The annotated questions demonstrate the way the Common Core should drive instruction and how tests have changed to better assess student performance in accordance with the instructional shifts demanded by the Common Core. They are also intended to help educators identify how the rigor of the Regents Examinations can inform classroom instruction and local assessment. The annotations will indicate common student misunderstandings related to content clusters; educators should use these to help inform unit and lesson planning. In some cases, the annotations may offer insight into particular instructional elements (conceptual thinking, mathematical modeling) that align to the Common Core that may be used in curricular design. It should not be assumed, however, that a particular cluster will be measured with identical items in future assessments. The annotated questions include both multiple-choice and constructed-response questions. With each multiple-choice question annotated, a commentary is available to demonstrate why the question measures the intended cluster. The rationales describe why the correct answer is correct and why the wrong answer choices are plausible but incorrect, based on common misconceptions or common procedural errors. While these rationales speak to a possible and likely reason for the selection of the incorrect option by the student, these rationales do not contain definitive statements as to why the student chose the incorrect option, or what we can infer about the knowledge and skills of the student based on the student’s selection of an incorrect response. These multiple-choice questions are designed to assess student proficiency, not to diagnose specific misconceptions/errors with each and every incorrect option.
For each constructed-response question, there is a commentary describing how the question measures the intended cluster, plus sample student responses representing possible student errors or misconceptions at each possible score point. The annotated questions do not represent the full spectrum of standards assessed on the State test, nor do they represent the full spectrum of how the Common Core should be taught and assessed in the classroom. Specific criteria for writing test questions as well as test information are available at http://www.engageny.org/resource/regents-exams. Understanding Math Annotated Questions
All questions on the Regents Exam in Algebra II (Common Core) are designed to measure the Common Core Learning Standards identified by the PARCC Model Content Framework for Algebra II. More information about the relationship between the New York State Testing Program and PARCC can be found here: http://www.p12.nysed.gov/assessment/math/ccmath/parccmcf.pdf. Multiple Choice
Multiple-choice questions will primarily be used to assess procedural fluency and conceptual understanding. Multiple-choice questions measure the Standards for Mathematical Content and may incorporate Standards for Mathematical Practices and real-world applications. Some multiple-choice questions require students to complete multiple steps. Likewise, questions may measure more than one cluster, drawing on the simultaneous application of multiple skills and concepts. Within answer choices, distractors will all be based on plausible missteps. Constructed Response
Constructed-response questions will require students to show a deep understanding of mathematical procedures, concepts, and applications. The Regents Examination in Algebra II (Common Core) contains 2-, 4-, and 6-credit constructed-response questions. 2-credit constructed-response questions require students to complete a task and show their work. Like multiple-choice questions, 2-credit constructed-response questions may involve multiple steps, the application of multiple mathematics skills, and real-world applications. These questions may ask students to explain or justify their solutions and/or show their process of problem solving. 4-credit and 6-credit constructed-response questions require students to show their work in completing more extensive problems that may involve multiple tasks and concepts. Students will be asked to make sense of mathematical and real-world problems in order to demonstrate procedural and conceptual understanding. For 6-credit constructed-response questions, students will analyze, interpret, and/or create mathematical models of real-world situations to solve multi-step problems that connect multiple major clusters or a major cluster to supporting or additional content.
Score 2: The student gave a complete and correct response.
Algebra II (Common Core) – June ’16 [2]
Question 25
25 Solve for x: 1 13
13x x
� � �
Score 2: The student gave a complete and correct response.
Algebra II (Common Core) – June ’16 [3]
Question 25
25 Solve for x: 1 13
13x x
� � �
Score 1: The student only found a common denominator and combined like terms.
Algebra II (Common Core) – June ’16 [4]
Question 25
25 Solve for x: 1 13
13x x
� � �
Score 1: The student made an error reducing the first term.
Algebra II (Common Core) – June ’16 [5]
Question 25
25 Solve for x: 1 13
13x x
� � �
Score 0: The student made an error combining the fractions, and also made a transcription errorby omitting the negative.
Algebra II (Common Core) – June ’16 [6]
Algebra II (Common Core) – June ’16 [7]
Question 26
Score 2: The student wrote a correct description of a controlled experiment, including randomassignment and a control group.
26 Describe how a controlled experiment can be created to examine the effect of ingredient X in a toothpaste.
Algebra II (Common Core) – June ’16 [8]
Question 26
Score 2: The student gave a complete and correct response.
26 Describe how a controlled experiment can be created to examine the effect of ingredient X in a toothpaste.
Algebra II (Common Core) – June ’16 [9]
Question 26
Score 1: The student wrote an incomplete description by omitting the random assignment of two groups.
26 Describe how a controlled experiment can be created to examine the effect of ingredient X in a toothpaste.
Algebra II (Common Core) – June ’16 [10]
Question 26
Score 0: The student’s response lacked random assignment and had an insufficient explanationof a control group.
26 Describe how a controlled experiment can be created to examine the effect of ingredient X in a toothpaste.
Algebra II (Common Core) – June ’16 [11]
Question 27
Score 2: The student gave a complete and correct response.
27 Determine if x � 5 is a factor of 2x3 � 4x2 � 7x � 10. Explain your answer.
Algebra II (Common Core) – June ’16 [12]
Question 27
Score 2: The student gave a complete and correct response.
27 Determine if x � 5 is a factor of 2x3 � 4x2 � 7x � 10. Explain your answer.
Algebra II (Common Core) – June ’16 [13]
Question 27
Score 2: The student gave a complete and correct response.
27 Determine if x � 5 is a factor of 2x3 � 4x2 � 7x � 10. Explain your answer.
Algebra II (Common Core) – June ’16 [14]
Question 27
Score 2: The student gave a complete and correct response.
27 Determine if x � 5 is a factor of 2x3 � 4x2 � 7x � 10. Explain your answer.
Algebra II (Common Core) – June ’16 [15]
Question 27
Score 1: The student wrote no explanation.
27 Determine if x � 5 is a factor of 2x3 � 4x2 � 7x � 10. Explain your answer.
Algebra II (Common Core) – June ’16 [16]
Question 27
Score 1: The student made one error by substituting �5 instead of 5.
27 Determine if x � 5 is a factor of 2x3 � 4x2 � 7x � 10. Explain your answer.
Algebra II (Common Core) – June ’16 [17]
Question 27
Score 0: The student made multiple errors dividing and did not provide the explanation.
27 Determine if x � 5 is a factor of 2x3 � 4x2 � 7x � 10. Explain your answer.
Algebra II (Common Core) – June ’16 [18]
Question 28
Score 2: The student gave a complete and correct response.
28 On the axes below, graph one cycle of a cosine function with amplitude 3, period , midline y � �1, and passing through the point (0,2).
�2
y
x
Algebra II (Common Core) – June ’16 [19]
Question 28
Score 2: The student gave a complete and correct response.
28 On the axes below, graph one cycle of a cosine function with amplitude 3, period , midline y � �1, and passing through the point (0,2).
�2
y
x
Algebra II (Common Core) – June ’16 [20]
Question 28
Score 2: The student gave a complete and correct response.
28 On the axes below, graph one cycle of a cosine function with amplitude 3, period , midline y � �1, and passing through the point (0,2).
�2
y
x
Algebra II (Common Core) – June ’16 [21]
Question 28
Score 1: The student correctly graphed one cycle of a cosine function passing through (0,2) withperiod π–
2, but used an incorrect amplitude that affected the midline.
28 On the axes below, graph one cycle of a cosine function with amplitude 3, period , midline y � �1, and passing through the point (0,2).
�2
y
x
Algebra II (Common Core) – June ’16 [22]
Question 28
Score 1: The student did not label the axes with appropriate values.
28 On the axes below, graph one cycle of a cosine function with amplitude 3, period , midline y � �1, and passing through the point (0,2).
�2
y
x
Algebra II (Common Core) – June ’16 [23]
Question 28
Score 0: The student made multiple errors.
28 On the axes below, graph one cycle of a cosine function with amplitude 3, period , midline y � �1, and passing through the point (0,2).
�2
y
x
Algebra II (Common Core) – June ’16 [24]
Question 29
Score 2: The student gave a complete and correct response.
29 A suburban high school has a population of 1376 students. The number of students whoparticipate in sports is 649. The number of students who participate in music is 433. If
the probability that a student participates in either sports or music is , what is the probability
that a student participates in both sports and music?
9741376
Algebra II (Common Core) – June ’16 [25]
Question 29
Score 1: The student made an error by not subtracting from .9741376
29 A suburban high school has a population of 1376 students. The number of students whoparticipate in sports is 649. The number of students who participate in music is 433. If
the probability that a student participates in either sports or music is , what is the probability
that a student participates in both sports and music?
9741376
Algebra II (Common Core) – June ’16 [26]
Question 29
Score 0: The student made multiple errors.
29 A suburban high school has a population of 1376 students. The number of students whoparticipate in sports is 649. The number of students who participate in music is 433. If
the probability that a student participates in either sports or music is , what is the probability
that a student participates in both sports and music?
9741376
Algebra II (Common Core) – June ’16 [27]
Question 30
Score 2: The student gave a complete and correct response.
30 The directrix of the parabola 12(y � 3) � (x � 4)2 has the equation y � �6. Find the coordinatesof the focus of the parabola.
Algebra II (Common Core) – June ’16 [28]
Question 30
Score 2: The student gave a complete and correct response.
30 The directrix of the parabola 12(y � 3) � (x � 4)2 has the equation y � �6. Find the coordinatesof the focus of the parabola.
Algebra II (Common Core) – June ’16 [29]
Question 30
Score 1: The student found an incorrect vertex.
30 The directrix of the parabola 12(y � 3) � (x � 4)2 has the equation y � �6. Find the coordinatesof the focus of the parabola.
Algebra II (Common Core) – June ’16 [30]
Question 30
Score 1: The student misused the directrix.
30 The directrix of the parabola 12(y � 3) � (x � 4)2 has the equation y � �6. Find the coordinatesof the focus of the parabola.
Algebra II (Common Core) – June ’16 [31]
Question 30
Score 0: The student stated the vertex as the focus.
30 The directrix of the parabola 12(y � 3) � (x � 4)2 has the equation y � �6. Find the coordinatesof the focus of the parabola.
Algebra II (Common Core) – June ’16 [32]
Question 30
Score 0: The student stated a partially correct answer that was obtained by an incorrect procedure.
30 The directrix of the parabola 12(y � 3) � (x � 4)2 has the equation y � �6. Find the coordinatesof the focus of the parabola.
Algebra II (Common Core) – June ’16 [33]
Question 31
Score 2: The student gave a complete and correct response.
31 Algebraically prove that , where x � �2.xx x
3
3 398
18
1�
� �� �
Algebra II (Common Core) – June ’16 [34]
Question 31
Score 2: The student gave a complete and correct response.
31 Algebraically prove that , where x � �2.xx x
3
3 398
18
1�
� �� �
Algebra II (Common Core) – June ’16 [35]
Question 31
Score 2: The student gave a complete and correct response.
31 Algebraically prove that , where x � �2.xx x
3
3 398
18
1�
� �� �
Algebra II (Common Core) – June ’16 [36]
Question 31
Score 1: The student made an error by not manipulating expressions independently in analgebraic proof.
31 Algebraically prove that , where x � �2.xx x
3
3 398
18
1�
� �� �
Algebra II (Common Core) – June ’16 [37]
Question 31
Score 1: The student made an error by not manipulating expressions independently in an algebraicproof.
31 Algebraically prove that , where x � �2.xx x
3
3 398
18
1�
� �� �
Algebra II (Common Core) – June ’16 [38]
Question 31
Score 0: The student used an incorrect procedure by substituting a single value in for x.
31 Algebraically prove that , where x � �2.xx x
3
3 398
18
1�
� �� �
Algebra II (Common Core) – June ’16 [39]
Question 32
Score 2: The student gave a complete and correct response.
32 A house purchased 5 years ago for $100,000 was just sold for $135,000. Assuming exponentialgrowth, approximate the annual growth rate, to the nearest percent.
Algebra II (Common Core) – June ’16 [40]
Question 32
Score 1: The student wrote an incomplete solution.
32 A house purchased 5 years ago for $100,000 was just sold for $135,000. Assuming exponentialgrowth, approximate the annual growth rate, to the nearest percent.
Algebra II (Common Core) – June ’16 [41]
Question 32
Score 1: The student found the growth factor correctly, but incorrectly stated the annual growthrate percentage.
32 A house purchased 5 years ago for $100,000 was just sold for $135,000. Assuming exponentialgrowth, approximate the annual growth rate, to the nearest percent.
Algebra II (Common Core) – June ’16 [42]
Question 32
Score 1: The student found the growth factor correctly, but stated an incorrect annual growth ratepercentage.
32 A house purchased 5 years ago for $100,000 was just sold for $135,000. Assuming exponentialgrowth, approximate the annual growth rate, to the nearest percent.
Algebra II (Common Core) – June ’16 [43]
Question 32
Score 0: The student made an error by subtracting 100,000 and did not state a percentage.
32 A house purchased 5 years ago for $100,000 was just sold for $135,000. Assuming exponentialgrowth, approximate the annual growth rate, to the nearest percent.
Algebra II (Common Core) – June ’16 [44]
Question 33
Score 4: The student gave a complete and correct response.
33 Solve the system of equations shown below algebraically.
(x � 3)2 � (y � 2)2 � 16
2x � 2y � 10
Algebra II (Common Core) – June ’16 [45]
Question 33
Score 4: The student gave a complete and correct response.
33 Solve the system of equations shown below algebraically.
(x � 3)2 � (y � 2)2 � 16
2x � 2y � 10
Algebra II (Common Core) – June ’16 [46]
Question 33
Score 3: The student only found the correct x-values of the system.
33 Solve the system of equations shown below algebraically.
(x � 3)2 � (y � 2)2 � 16
2x � 2y � 10
Algebra II (Common Core) – June ’16 [47]
Question 33
Score 3: The student found only one correct solution of the system.
33 Solve the system of equations shown below algebraically.
(x � 3)2 � (y � 2)2 � 16
2x � 2y � 10
Algebra II (Common Core) – June ’16 [48]
Question 33
Score 2: The student obtained the correct solution, but used a method other than algebraic.
33 Solve the system of equations shown below algebraically.
(x � 3)2 � (y � 2)2 � 16
2x � 2y � 10
Algebra II (Common Core) – June ’16 [49]
Question 33
Score 2: The student made a transcription error by losing a �10x, and did not find y-values.
33 Solve the system of equations shown below algebraically.
(x � 3)2 � (y � 2)2 � 16
2x � 2y � 10
Algebra II (Common Core) – June ’16 [50]
Question 33
Score 2: The student made several computational errors.
33 Solve the system of equations shown below algebraically.
(x � 3)2 � (y � 2)2 � 16
2x � 2y � 10
Algebra II (Common Core) – June ’16 [51]
Question 33
Score 1: The student made a conceptual error squaring the first term and did not express bothordered pairs.
33 Solve the system of equations shown below algebraically.
(x � 3)2 � (y � 2)2 � 16
2x � 2y � 10
Algebra II (Common Core) – June ’16 [52]
Question 33
Score 0: The student made several errors and did not find the y-values.
33 Solve the system of equations shown below algebraically.
(x � 3)2 � (y � 2)2 � 16
2x � 2y � 10
Algebra II (Common Core) – June ’16 [53]
Question 33
Score 0: The student gave a completely incorrect response.
33 Solve the system of equations shown below algebraically.
(x � 3)2 � (y � 2)2 � 16
2x � 2y � 10
Algebra II (Common Core) – June ’16 [54]
Question 34
Score 4: The student gave a complete and correct response.
34 Alexa earns $33,000 in her first year of teaching and earns a 4% increase in each successive year.
Write a geometric series formula, Sn, for Alexa’s total earnings over n years.
Use this formula to find Alexa’s total earnings for her first 15 years of teaching, to the nearest cent.
Algebra II (Common Core) – June ’16 [55]
Question 34
Score 3: The student rounded too early.
34 Alexa earns $33,000 in her first year of teaching and earns a 4% increase in each successive year.
Write a geometric series formula, Sn, for Alexa’s total earnings over n years.
Use this formula to find Alexa’s total earnings for her first 15 years of teaching, to the nearest cent.
Algebra II (Common Core) – June ’16 [56]
Question 34
Score 3: The student failed to use parentheses when entering the expression into the calculator.
34 Alexa earns $33,000 in her first year of teaching and earns a 4% increase in each successive year.
Write a geometric series formula, Sn, for Alexa’s total earnings over n years.
Use this formula to find Alexa’s total earnings for her first 15 years of teaching, to the nearest cent.
Algebra II (Common Core) – June ’16 [57]
Question 34
Score 2: The student made a conceptual error interpreting the 4% increase.
34 Alexa earns $33,000 in her first year of teaching and earns a 4% increase in each successive year.
Write a geometric series formula, Sn, for Alexa’s total earnings over n years.
Use this formula to find Alexa’s total earnings for her first 15 years of teaching, to the nearest cent.
Algebra II (Common Core) – June ’16 [58]
Question 34
Score 2: The student only correctly wrote the geometric series formula.
34 Alexa earns $33,000 in her first year of teaching and earns a 4% increase in each successive year.
Write a geometric series formula, Sn, for Alexa’s total earnings over n years.
Use this formula to find Alexa’s total earnings for her first 15 years of teaching, to the nearest cent.
Algebra II (Common Core) – June ’16 [59]
Question 34
Score 1: The student made a computational error in the second part, having received no creditfor the first part.
34 Alexa earns $33,000 in her first year of teaching and earns a 4% increase in each successive year.
Write a geometric series formula, Sn, for Alexa’s total earnings over n years.
Use this formula to find Alexa’s total earnings for her first 15 years of teaching, to the nearest cent.
Algebra II (Common Core) – June ’16 [60]
Question 34
Score 0: The student made multiple errors.
34 Alexa earns $33,000 in her first year of teaching and earns a 4% increase in each successive year.
Write a geometric series formula, Sn, for Alexa’s total earnings over n years.
Use this formula to find Alexa’s total earnings for her first 15 years of teaching, to the nearest cent.
Algebra II (Common Core) – June ’16 [61]
Question 35
Score 4: The student gave a complete and correct response.
35 Fifty-five students attending the prom were randomly selected to participate in a survey about the music choice at the prom. Sixty percent responded that a DJ would be preferred over a band.Members of the prom committee thought that the vote would have 50% for the DJ and 50% forthe band.
A simulation was run 200 times, each of sample size 55, based on the premise that 60% of the students would prefer a DJ. The approximate normal simulation results are shown below.
Using the results of the simulation, determine a plausible interval containing the middle 95% ofthe data. Round all values to the nearest hundredth.
����
����
0.40
4
8
12
16
20
24
28
����� ���������0.45 0.50 0.55 0.60 0.65 0.750.70
Mean = 0.602S.D. = 0.066
Members of the prom committee are concerned that a vote of all students attending the prommay produce a 50% – 50% split. Explain what statistical evidence supports this concern.
Algebra II (Common Core) – June ’16 [62]
Question 35
Score 4: The student gave a complete and correct response.
35 Fifty-five students attending the prom were randomly selected to participate in a survey about the music choice at the prom. Sixty percent responded that a DJ would be preferred over a band.Members of the prom committee thought that the vote would have 50% for the DJ and 50% forthe band.
A simulation was run 200 times, each of sample size 55, based on the premise that 60% of the students would prefer a DJ. The approximate normal simulation results are shown below.
Using the results of the simulation, determine a plausible interval containing the middle 95% ofthe data. Round all values to the nearest hundredth.
����
����
0.40
4
8
12
16
20
24
28
����� ���������0.45 0.50 0.55 0.60 0.65 0.750.70
Mean = 0.602S.D. = 0.066
Members of the prom committee are concerned that a vote of all students attending the prommay produce a 50% – 50% split. Explain what statistical evidence supports this concern.
Algebra II (Common Core) – June ’16 [63]
Question 35
Score 4: The student gave a complete and correct response.
35 Fifty-five students attending the prom were randomly selected to participate in a survey about the music choice at the prom. Sixty percent responded that a DJ would be preferred over a band.Members of the prom committee thought that the vote would have 50% for the DJ and 50% forthe band.
A simulation was run 200 times, each of sample size 55, based on the premise that 60% of the students would prefer a DJ. The approximate normal simulation results are shown below.
Using the results of the simulation, determine a plausible interval containing the middle 95% ofthe data. Round all values to the nearest hundredth.
����
����
0.40
4
8
12
16
20
24
28
����� ���������0.45 0.50 0.55 0.60 0.65 0.750.70
Mean = 0.602S.D. = 0.066
Members of the prom committee are concerned that a vote of all students attending the prommay produce a 50% – 50% split. Explain what statistical evidence supports this concern.
Algebra II (Common Core) – June ’16 [64]
Question 35
Score 3: The student determined a correct interval, but provided contradictory statistical evidence.
35 Fifty-five students attending the prom were randomly selected to participate in a survey about the music choice at the prom. Sixty percent responded that a DJ would be preferred over a band.Members of the prom committee thought that the vote would have 50% for the DJ and 50% forthe band.
A simulation was run 200 times, each of sample size 55, based on the premise that 60% of the students would prefer a DJ. The approximate normal simulation results are shown below.
Using the results of the simulation, determine a plausible interval containing the middle 95% ofthe data. Round all values to the nearest hundredth.
����
����
0.40
4
8
12
16
20
24
28
����� ���������0.45 0.50 0.55 0.60 0.65 0.750.70
Mean = 0.602S.D. = 0.066
Members of the prom committee are concerned that a vote of all students attending the prommay produce a 50% – 50% split. Explain what statistical evidence supports this concern.
Algebra II (Common Core) – June ’16 [65]
Question 35
Score 2: The student gave no statistical explanation.
35 Fifty-five students attending the prom were randomly selected to participate in a survey about the music choice at the prom. Sixty percent responded that a DJ would be preferred over a band.Members of the prom committee thought that the vote would have 50% for the DJ and 50% forthe band.
A simulation was run 200 times, each of sample size 55, based on the premise that 60% of the students would prefer a DJ. The approximate normal simulation results are shown below.
Using the results of the simulation, determine a plausible interval containing the middle 95% ofthe data. Round all values to the nearest hundredth.
����
����
0.40
4
8
12
16
20
24
28
����� ���������0.45 0.50 0.55 0.60 0.65 0.750.70
Mean = 0.602S.D. = 0.066
Members of the prom committee are concerned that a vote of all students attending the prommay produce a 50% – 50% split. Explain what statistical evidence supports this concern.
Algebra II (Common Core) – June ’16 [66]
Question 35
Score 1: The student used only one standard deviation in the interval, rounded incorrectly, andprovided contradictory statistical evidence.
35 Fifty-five students attending the prom were randomly selected to participate in a survey about the music choice at the prom. Sixty percent responded that a DJ would be preferred over a band.Members of the prom committee thought that the vote would have 50% for the DJ and 50% forthe band.
A simulation was run 200 times, each of sample size 55, based on the premise that 60% of the students would prefer a DJ. The approximate normal simulation results are shown below.
Using the results of the simulation, determine a plausible interval containing the middle 95% ofthe data. Round all values to the nearest hundredth.
����
����
0.40
4
8
12
16
20
24
28
����� ���������0.45 0.50 0.55 0.60 0.65 0.750.70
Mean = 0.602S.D. = 0.066
Members of the prom committee are concerned that a vote of all students attending the prommay produce a 50% – 50% split. Explain what statistical evidence supports this concern.
Algebra II (Common Core) – June ’16 [67]
Question 35
Score 1: The student used the standard deviation as the center and rounded incorrectly. The studentgave an incomplete explanation.
35 Fifty-five students attending the prom were randomly selected to participate in a survey about the music choice at the prom. Sixty percent responded that a DJ would be preferred over a band.Members of the prom committee thought that the vote would have 50% for the DJ and 50% forthe band.
A simulation was run 200 times, each of sample size 55, based on the premise that 60% of the students would prefer a DJ. The approximate normal simulation results are shown below.
Using the results of the simulation, determine a plausible interval containing the middle 95% ofthe data. Round all values to the nearest hundredth.
����
����
0.40
4
8
12
16
20
24
28
����� ���������0.45 0.50 0.55 0.60 0.65 0.750.70
Mean = 0.602S.D. = 0.066
Members of the prom committee are concerned that a vote of all students attending the prommay produce a 50% – 50% split. Explain what statistical evidence supports this concern.
Algebra II (Common Core) – June ’16 [68]
Question 35
Score 0: The student made multiple conceptual and computational errors.
35 Fifty-five students attending the prom were randomly selected to participate in a survey about the music choice at the prom. Sixty percent responded that a DJ would be preferred over a band.Members of the prom committee thought that the vote would have 50% for the DJ and 50% forthe band.
A simulation was run 200 times, each of sample size 55, based on the premise that 60% of the students would prefer a DJ. The approximate normal simulation results are shown below.
Using the results of the simulation, determine a plausible interval containing the middle 95% ofthe data. Round all values to the nearest hundredth.
����
����
0.40
4
8
12
16
20
24
28
����� ���������0.45 0.50 0.55 0.60 0.65 0.750.70
Mean = 0.602S.D. = 0.066
Members of the prom committee are concerned that a vote of all students attending the prommay produce a 50% – 50% split. Explain what statistical evidence supports this concern.
Algebra II (Common Core) – June ’16 [69]
Question 36
Score 4: The student gave a complete and correct response.
36 Which function shown below has a greater average rate of change on the interval [�2, 4]? Justifyyour answer.
x f(x)
−4 0.3125
−3 0.625
−2 1.25
−1 2.5
0 5
1 10
2 20
3 40
4 80
5 160
6 320
g(x) � 4x3 � 5x2 � 3
Algebra II (Common Core) – June ’16 [70]
Question 36
Score 4: The student gave a complete and correct response.
36 Which function shown below has a greater average rate of change on the interval [�2, 4]? Justifyyour answer.
x f(x)
−4 0.3125
−3 0.625
−2 1.25
−1 2.5
0 5
1 10
2 20
3 40
4 80
5 160
6 320
g(x) � 4x3 � 5x2 � 3
Algebra II (Common Core) – June ’16 [71]
Question 36
Score 3: The student made a computational error when calculating the denominators.
36 Which function shown below has a greater average rate of change on the interval [�2, 4]? Justifyyour answer.
x f(x)
−4 0.3125
−3 0.625
−2 1.25
−1 2.5
0 5
1 10
2 20
3 40
4 80
5 160
6 320
g(x) � 4x3 � 5x2 � 3
Algebra II (Common Core) – June ’16 [72]
Question 36
Score 2: The student made a conceptual error by creating an appropriate model for f(x), but wrote an appropriate explanation for that model.
36 Which function shown below has a greater average rate of change on the interval [�2, 4]? Justifyyour answer.
x f(x)
−4 0.3125
−3 0.625
−2 1.25
−1 2.5
0 5
1 10
2 20
3 40
4 80
5 160
6 320
g(x) � 4x3 � 5x2 � 3
Algebra II (Common Core) – June ’16 [73]
Question 36
Score 2: The student found g(�2) and g(4) correctly, but made no comparison of the averagerates of change.
36 Which function shown below has a greater average rate of change on the interval [�2, 4]? Justifyyour answer.
x f(x)
−4 0.3125
−3 0.625
−2 1.25
−1 2.5
0 5
1 10
2 20
3 40
4 80
5 160
6 320
g(x) � 4x3 � 5x2 � 3
Algebra II (Common Core) – June ’16 [74]
Question 36
Score 1: The student made an error finding the average rates of change by not dividing by �x,and made one computational error.
36 Which function shown below has a greater average rate of change on the interval [�2, 4]? Justifyyour answer.
x f(x)
−4 0.3125
−3 0.625
−2 1.25
−1 2.5
0 5
1 10
2 20
3 40
4 80
5 160
6 320
g(x) � 4x3 � 5x2 � 3
Algebra II (Common Core) – June ’16 [75]
Question 36
Score 0: The student did not calculate an average rate of change and wrote an irrelevant explanation.
36 Which function shown below has a greater average rate of change on the interval [�2, 4]? Justifyyour answer.
x f(x)
−4 0.3125
−3 0.625
−2 1.25
−1 2.5
0 5
1 10
2 20
3 40
4 80
5 160
6 320
g(x) � 4x3 � 5x2 � 3
Algebra II (Common Core) – June ’16 [76]
Question 37
Score 6: The student gave a complete and correct response.
37 Drugs break down in the human body at different rates and therefore must be prescribed bydoctors carefully to prevent complications, such as overdosing. The breakdown of a drug isrepresented by the function N(t) � N0(e)�r t, where N(t) is the amount left in the body, N0 is the initial dosage, r is the decay rate, and t is time in hours. Patient A, A(t), is given 800 milligramsof a drug with a decay rate of 0.347. Patient B, B(t), is given 400 milligrams of another drug witha decay rate of 0.231.
Write two functions, A(t) and B(t), to represent the breakdown of the respective drug given toeach patient.
Graph each function on the set of axes below.
y
t
Algebra II (Common Core) – June ’16 [77]
Question 37
To the nearest hour, t, when does the amount of the given drug remaining in patient B begin toexceed the amount of the given drug remaining in patient A?
The doctor will allow patient A to take another 800 milligram dose of the drug once only 15% of the original dose is left in the body. Determine, to the nearest tenth of an hour, how long patient Awill have to wait to take another 800 milligram dose of the drug.
Algebra II (Common Core) – June ’16 [78]
Question 37
Score 5: The student did not indicate which function models which patient.
37 Drugs break down in the human body at different rates and therefore must be prescribed bydoctors carefully to prevent complications, such as overdosing. The breakdown of a drug isrepresented by the function N(t) � N0(e)�r t, where N(t) is the amount left in the body, N0 is the initial dosage, r is the decay rate, and t is time in hours. Patient A, A(t), is given 800 milligramsof a drug with a decay rate of 0.347. Patient B, B(t), is given 400 milligrams of another drug witha decay rate of 0.231.
Write two functions, A(t) and B(t), to represent the breakdown of the respective drug given toeach patient.
Graph each function on the set of axes below.
y
t
Algebra II (Common Core) – June ’16 [79]
Question 37
To the nearest hour, t, when does the amount of the given drug remaining in patient B begin toexceed the amount of the given drug remaining in patient A?
The doctor will allow patient A to take another 800 milligram dose of the drug once only 15% of the original dose is left in the body. Determine, to the nearest tenth of an hour, how long patient Awill have to wait to take another 800 milligram dose of the drug.
Algebra II (Common Core) – June ’16 [80]
Question 37
Score 4: The student did not graph either function.
37 Drugs break down in the human body at different rates and therefore must be prescribed bydoctors carefully to prevent complications, such as overdosing. The breakdown of a drug isrepresented by the function N(t) � N0(e)�r t, where N(t) is the amount left in the body, N0 is the initial dosage, r is the decay rate, and t is time in hours. Patient A, A(t), is given 800 milligramsof a drug with a decay rate of 0.347. Patient B, B(t), is given 400 milligrams of another drug witha decay rate of 0.231.
Write two functions, A(t) and B(t), to represent the breakdown of the respective drug given toeach patient.
Graph each function on the set of axes below.
y
t
Algebra II (Common Core) – June ’16 [81]
Question 37
To the nearest hour, t, when does the amount of the given drug remaining in patient B begin toexceed the amount of the given drug remaining in patient A?
The doctor will allow patient A to take another 800 milligram dose of the drug once only 15% of the original dose is left in the body. Determine, to the nearest tenth of an hour, how long patient Awill have to wait to take another 800 milligram dose of the drug.
Algebra II (Common Core) – June ’16 [82]
Question 37
Score 3: The student drew a correct graph and gave a correct answer of 5.5 hours.
37 Drugs break down in the human body at different rates and therefore must be prescribed bydoctors carefully to prevent complications, such as overdosing. The breakdown of a drug isrepresented by the function N(t) � N0(e)�r t, where N(t) is the amount left in the body, N0 is the initial dosage, r is the decay rate, and t is time in hours. Patient A, A(t), is given 800 milligramsof a drug with a decay rate of 0.347. Patient B, B(t), is given 400 milligrams of another drug witha decay rate of 0.231.
Write two functions, A(t) and B(t), to represent the breakdown of the respective drug given toeach patient.
Graph each function on the set of axes below.
y
t
Algebra II (Common Core) – June ’16 [83]
Question 37
To the nearest hour, t, when does the amount of the given drug remaining in patient B begin toexceed the amount of the given drug remaining in patient A?
The doctor will allow patient A to take another 800 milligram dose of the drug once only 15% of the original dose is left in the body. Determine, to the nearest tenth of an hour, how long patient Awill have to wait to take another 800 milligram dose of the drug.
Algebra II (Common Core) – June ’16 [84]
Question 37
Score 2: The student correctly identified 6 hours and 5.5 hours.
37 Drugs break down in the human body at different rates and therefore must be prescribed bydoctors carefully to prevent complications, such as overdosing. The breakdown of a drug isrepresented by the function N(t) � N0(e)�r t, where N(t) is the amount left in the body, N0 is the initial dosage, r is the decay rate, and t is time in hours. Patient A, A(t), is given 800 milligramsof a drug with a decay rate of 0.347. Patient B, B(t), is given 400 milligrams of another drug witha decay rate of 0.231.
Write two functions, A(t) and B(t), to represent the breakdown of the respective drug given toeach patient.
Graph each function on the set of axes below.
y
t
Algebra II (Common Core) – June ’16 [85]
Question 37
To the nearest hour, t, when does the amount of the given drug remaining in patient B begin toexceed the amount of the given drug remaining in patient A?
The doctor will allow patient A to take another 800 milligram dose of the drug once only 15% of the original dose is left in the body. Determine, to the nearest tenth of an hour, how long patient Awill have to wait to take another 800 milligram dose of the drug.
Algebra II (Common Core) – June ’16 [86]
Question 37
Score 1: The student created and labeled correct functions.
37 Drugs break down in the human body at different rates and therefore must be prescribed bydoctors carefully to prevent complications, such as overdosing. The breakdown of a drug isrepresented by the function N(t) � N0(e)�r t, where N(t) is the amount left in the body, N0 is the initial dosage, r is the decay rate, and t is time in hours. Patient A, A(t), is given 800 milligramsof a drug with a decay rate of 0.347. Patient B, B(t), is given 400 milligrams of another drug witha decay rate of 0.231.
Write two functions, A(t) and B(t), to represent the breakdown of the respective drug given toeach patient.
Graph each function on the set of axes below.
y
t
Algebra II (Common Core) – June ’16 [87]
Question 37
To the nearest hour, t, when does the amount of the given drug remaining in patient B begin toexceed the amount of the given drug remaining in patient A?
The doctor will allow patient A to take another 800 milligram dose of the drug once only 15% of the original dose is left in the body. Determine, to the nearest tenth of an hour, how long patient Awill have to wait to take another 800 milligram dose of the drug.
Algebra II (Common Core) – June ’16 [88]
Question 37
Score 0: The student did not complete enough correct work in any part to receive credit.
37 Drugs break down in the human body at different rates and therefore must be prescribed bydoctors carefully to prevent complications, such as overdosing. The breakdown of a drug isrepresented by the function N(t) � N0(e)�r t, where N(t) is the amount left in the body, N0 is the initial dosage, r is the decay rate, and t is time in hours. Patient A, A(t), is given 800 milligramsof a drug with a decay rate of 0.347. Patient B, B(t), is given 400 milligrams of another drug witha decay rate of 0.231.
Write two functions, A(t) and B(t), to represent the breakdown of the respective drug given toeach patient.
Graph each function on the set of axes below.
y
t
Algebra II (Common Core) – June ’16 [89]
Question 37
To the nearest hour, t, when does the amount of the given drug remaining in patient B begin toexceed the amount of the given drug remaining in patient A?
The doctor will allow patient A to take another 800 milligram dose of the drug once only 15% of the original dose is left in the body. Determine, to the nearest tenth of an hour, how long patient Awill have to wait to take another 800 milligram dose of the drug.
The State Education Department / The University of the State of New York
Regents Examination in Algebra II (Common Core) – June 2016Chart for Converting Total Test Raw Scores to Final Exam Scores (Scale Scores)
To determine the student’s final examination score (scale score), find the student’s total test raw score in the columnlabeled “Raw Score” and then locate the scale score that corresponds to that raw score. The scale score is thestudent’s final examination score. Enter this score in the space labeled “Scale Score” on the student’s answer sheet.
RawScore
ScaleScore
Performance Level
ScaleScore
Performance Level
Performance Level
(Use for the June 2016 exam only.)
Schools are not permitted to rescore any of the open-ended questions on this exam after each question hasbeen rated once, regardless of the final exam score. Schools are required to ensure that the raw scores havebeen added correctly and that the resulting scale score has been determined accurately.
Because scale scores corresponding to raw scores in the conversion chart change from one administration to another,it is crucial that for each administration the conversion chart provided for that administration be used to determine thestudent’s final score. The chart above is usable only for this administration of the Regents Examination in Algebra II(Common Core).