Algebra 2 regents questions and answers

Regents Exam Questions A2.A.29: Sequences. What is a formula for the nth term of sequence B shown below? 10,12,14,16,... 62.5. Which formula represents the nth term in the sequence? What is the formula for the nth term of the sequence 54,18,6,...? ̃ Ë ̄ 3. In an arithmetic sequence, a4 19 and a7 31. Determine a formula for an, the nth term ...

Algebra 2 regents questions and answers. The New York State High School Mathematics Testing Program is designed to measure student progress on the Next Generation Mathematics Learning Standards following the implementation timeline for the Regents Examinations as follows: June 2024: Algebra I. June 2025: Geometry. June 2026: Algebra II.

Algebra II Rating Guide – June ’19 [2] Mechanics of Rating The following procedures are to be followed for scoring student answer papers for the Regents Examination in Algebra II. More detailed information about scoring is provided in the publication Information Booklet for Scoring the Regents Examination in Algebra II.

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 ...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 …Apr 21, 2020 ... Algebra 2 Regent August 2019 Part 1. 6.6K views · 4 years ago ...more. Math Recipe. 67. Subscribe. 57. Share. Save.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 ...Apr 21, 2020 ... Algebra 2 Regent August 2019 Part 1. 6.6K views · 4 years ago ...more. Math Recipe. 67. Subscribe. 57. Share. Save.Answer all 27 questions in this part. Each correct answer will receive 2 credits. 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.[54] Use this space for computations.Use this space for computations. Algebra I – Aug. ’19 [7] [OVER] 20 The length of a rectangular patio is 7 feet more than its width, w.The area of a patio, A(w), can be represented by the function (1) A(w) w 7 (3) A(w) 4w 14 (2) A(w) w2 2 7w (4) A(w) 4w 28w 21 A dolphin jumps out of the water and then back into the water. His jump could be …May 18, 2022 ... January 2020 #33-37 Algebra 2 Regents Exam. 1.8K views · 1 year ago ...more. Ashley. 114. Subscribe. 27. Share. Save. Report. Comments1.

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 ...The following are questions from the past paper Regents High School Algebra 2, January 2017 Exam (pdf). Download the questions and try them, then scroll down the page to check your answers with the step by step solutions. Algebra 2 - January 2017 Regents - Questions and solutions 1 - 12This 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 workFor exponential models, express as a logarithm the solution to ab ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. WORKSHEETS: AII: Regents-Express Exponentials as Logarithms AII: 1: TST PDF DOC: Regents-Exponential Equations 1 A2/B/SIII common base shown: 3/2/19: TST PDF …This ex~ination 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 …Answer aJI 24 questions in this part. Each correct answer will receive 2 credits. No partial credit will he 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 ...

Mechanics of Rating. The following procedures are to be followed for scoring student answer papers for the Regents Examination in Algebra II. More detailed information about scoring is provided in the publication Information Booklet for Scoring the Regents Examination in Algebra II. Do not attempt to correct the student’s work by making ... 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 ...There’s so much more to know about trigonometric functions, but understanding these two vocabulary terms will give you a leg up on the Algebra 2 Regents exam. Example question: Source: Regents Algebra 2 Exam, August 2019, Question #12. 3 Strategies and Tips for Multiple Choice Questions on Regents Algebra 2 Exams 1. Use the process of eliminationSample spaces and The Counting Principle. Independent and dependent events. Mutualy exclusive events. Permutations. Combinations. Permutations vs combinations. Probability using permutations and combinations. Free Algebra 2 worksheets created with Infinite Algebra 2. Printable in convenient PDF format.Algebra II Rating Guide – Jan. ’23 [2] Mechanics of Rating The following procedures are to be followed for scoring student answer papers for the Regents Examination in Algebra II. More detailed information about scoring is provided in the publication Information Booklet for Scoring the Regents Examination in Algebra II.

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Algebra II Regents Exam Questions by Common Core State Standard: Topic www.jmap.org 1 Algebra II Regents Exam Questions by Common Core State Standard: Topic GRAPHS AND STATISTICS S.IC.A.2, S.IC.B.4-6: ANALYSIS OF DATA 1 Anne has a coin. She does not know if it is a fair coin. She flipped the coin 100 times and obtained 73 …Algebra II Regents Exam Questions by State Standard: Topic www.jmap.org 3 5 The function N(x) =90(0.86)x +69 can be used to predict the temperature of a cup of hot chocolate in degrees Fahrenheit after x minutes. What is the approximate average rate of change of the temperature of the hot chocolate, in degrees per minute, over the interval [0,6]?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,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 ...Jul 11, 2015 ... Name: Algebra 2 and Trigonometry: Regents Review Test 2 1 The . ... Solving Systems Word Problems HW. <strong> ... answers to a survey), in support ...

Algebra 2 Regents Topics Explained: We’ve developed many Algebra 2 Regents prep resources, so you can understand advanced algebra, trigonometry, and it’s functions. Polynomial Functions Properties of Exponents Dividing Polynomials Factoring Polynomial Functions Graphing Polynomial Functions Rational Exponents & Functions Nth Roots Rational Exponent Properties Operations & Composition ...The following are past exam questions, videos, walkthroughs, examples, and solutions for the Regents Common Core Exam. Regents High School Exam - Algebra 1 (Common Core) Regents Exam - Algebra I. Regents High School Exam - Algebra 2 (Common Core) Regents Exam - Algebra II. Regents High School Exam - Geometry (Common Core) …Are trigonometry and algebra 2 the same? No, not even close. Though both work with variables in some instances and other mathematical techniques, such as logarithms and algebraic manipulation, algebra is mostly equation solving to get the variables value, though trig has equations, while trig is the study of triangular and circular …Apr 21, 2020 ... Algebra 2 Regent August 2019 Part 1. 6.6K views · 4 years ago ...more. Math Recipe. 67. Subscribe. 57. Share. Save.Algebra II Regents Exam Questions by State Standard: Topic www.jmap.org 3 5 The function N(x) =90(0.86)x +69 can be used to predict the temperature of a cup of hot chocolate in degrees Fahrenheit after x minutes. What is the approximate average rate of change of the temperature of the hot chocolate, in degrees per minute, over the interval [0,6]?Mathematics Regents Examinations Algebra I. Geometry. Algebra II. Archive. Integrated Algebra. Geometry (2005 Standard) Algebra 2/Trigonometry. Mathematics A.REGENTS HIGH SCHOOL EXAMINATION ALGEBRA II (Common Core) Wednesday, June 1, 2016 - 9:15 a.m. to 12:15 p.m., only ... questions or answers prior to the examination and that you have neither given ... Algebra II (Common Core) -June '16 [2] Use this space for computations.In today’s fast-paced world, staying updated with the latest general knowledge (GK) is crucial. Whether you are preparing for an exam, job interview, or simply want to expand your ...II. ALGEBRA. Print your name and the name of your school on the lines above. A separate answer sheet for Part Ihas 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.Sample spaces and The Counting Principle. Independent and dependent events. Mutualy exclusive events. Permutations. Combinations. Permutations vs combinations. Probability using permutations and combinations. Free Algebra 2 worksheets created with Infinite Algebra 2. Printable in convenient PDF format.Jan 24, 2018 · Mathematics Regents Examinations Algebra I. Geometry. Algebra II. Archive. Integrated Algebra. Geometry (2005 Standard) Algebra 2/Trigonometry. Mathematics A. Algebra 2/Trigonometry Standards. The December 2014 memorandum, “Transition to Common Core Regents Examinations in English Language Arts and Mathematics” provides information on the phase-in schedule for all Mathematics Regents Examinations in Algebra I, Geometry (Common Core), and Algebra II. This memorandum can be found at:

To find answers to questions using Algebra Nation, go to the official website, click on “Enter Algebra Nation,” sign in using a Facebook user name and password and post the questio...

Question Formats. The Regents Examination in Algebra II (Common Core) contains four parts: one with multiple-choice questions and three with constructed-response questions. For multiple-choice questions, students select …May 10, 2018 ... While 48% of the likely voters in this poll said that they would vote for Mayor Ortega, this is only a sample of all the voters and there is a ...regents exams. worksheets. jmap on jumbled an online platform for the above algebra i resources. regents books. ai lesson plans. worksheet generators. extras. regents exam archives 1866-now. jmap resource archives ai/geo/aii (2015-now) ia/ge/a2 (2007-17) math a/b (1998-2010) regents resources. interdisciplinary exams. nyc teacher resourcesAlgebra 2 Regents Topics Explained: We’ve developed many Algebra 2 Regents prep resources, so you can understand advanced algebra, trigonometry, and it’s functions. Polynomial Functions Properties of Exponents Dividing Polynomials Factoring Polynomial Functions Graphing Polynomial Functions Rational Exponents & Functions Nth Roots Rational Exponent Properties Operations & Composition ...regents exams. worksheets. jmap on jumbled an online platform for the above algebra i resources. regents books. ai lesson plans. worksheet generators. extras. regents exam archives 1866-now. jmap resource archives ai/geo/aii (2015-now) ia/ge/a2 (2007-17) math a/b (1998-2010) regents resources. interdisciplinary exams. nyc teacher resourcesState the number of solutions to the equation f(x) g(x). 33On the set of axes below, graph y f(x) and y g(x) for the given functions. f(x) x33x2. g(x) 2x5. Algebra II – June ’22[43] Question 33 Score 4:The student gave a complete and correct response. State the number of solutions to the equation f(x) g(x).In today’s fast-paced world, staying updated with the latest general knowledge (GK) is crucial. Whether you are preparing for an exam, job interview, or simply want to expand your ...

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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 ... Barron's Let's Review Regents: Algebra I gives students the step-by-step review and practice they need to prepare for the Regents exam. This updated edition is an ideal companion to high school textbooks and covers all Algebra I topics prescribed by the New York State Board of Regents. Features include: In-depth Regents exam preparation, …Algebra I – Jan. ’19 [2] Use this space for computations. 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,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 ...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,Algebra I – Jan. ’20 [2] Use this space for computations. 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,Jan 24, 2018 · Mathematics Regents Examinations Algebra I. Geometry. Algebra II. Archive. Integrated Algebra. Geometry (2005 Standard) Algebra 2/Trigonometry. Mathematics A. Algebra 2/Trigonometry – June ’13 [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. For all questions in this part, a correct numerical answer with no work shown will receive only 1 ...Regents High School Algebra 2, June 2022 Exam (pdf). Download the questions and try them, then scroll down the page to check your answers with the step by step solutions. Algebra 2 - June 2022 Regents - Solutions for Questions 1 - 24. Solutions for Questions 25 - 37. For all positive values of x, which expression is equivalent to x 3/4. Algebra II Regents Exam Questions by State Standard: Topic www.jmap.org 3 6 Irma initially ran one mile in over ten minutes. She then began a training program to reduce her one-mile time. She recorded her one-mile time once a week for twelve consecutive weeks, as modeled in the graph below. Which statement regarding Irma’s one-mile ….

regents exams. worksheets. jmap on jumbled an online platform for the above algebra i resources. regents books. ai lesson plans. worksheet generators. extras. regents exam archives 1866-now. jmap resource archives ai/geo/aii (2015-now) ia/ge/a2 (2007-17) math a/b (1998-2010) regents resources. interdisciplinary exams. nyc teacher resourcesThe Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. Khan Academy's Algebra 1 course is built to deliver a comprehensive, illuminating, engaging, and Common Core aligned experience!The more challenging Algebra 1 problems are quadratic equations of the form ax^2 +bx +c =0, where the general solution is given by the quadratic formula: x = (-b +/- sqrt(b^2-4ac))... Sample spaces and The Counting Principle. Independent and dependent events. Mutualy exclusive events. Permutations. Combinations. Permutations vs combinations. Probability using permutations and combinations. Free Algebra 2 worksheets created with Infinite Algebra 2. Printable in convenient PDF format. regents exams. worksheets. jmap on jumbled an online platform for the above algebra i resources. regents books. ai lesson plans. worksheet generators. extras. regents exam archives 1866-now. jmap resource archives ai/geo/aii (2015-now) ia/ge/a2 (2007-17) math a/b (1998-2010) regents resources. interdisciplinary exams. nyc teacher resourcesThe Educator Guide to the Regents Examination in Algebra II (Common Core) has been designed to support educators by providing an overview of the new test design. Information about how the assessment shifts has informed test development and how the CCLS will be measured on the new Regents Exam is specified. This test guide …Algebra I Regents Exam Questions by State Standard: Topic. www.jmap.org. 34 182 Graph the inequality y>2x−5 on the set of axes below. State the coordinates of a point in its solution. 183 Graph the inequality y+4 <−2(x−4) on the set of axes below. 184 Shawn incorrectly graphed the inequality −x−2y≥8 as shown below.REGENTS HIGH SCHOOL EXAMINATION ALGEBRA II Thursday, August 16, 2018 - 12:30 to 3:30 p.m., only ... The formulas that you may need to answer some questions in this examination are found at the ... (2) 0.3648 Algebra II - Aug. '18 l~ 0.57 ~0.8 [10] Use this space for compt1tions. 7Algebra 2 Regents Topics Explained: We’ve developed many Algebra 2 Regents prep resources, so you can understand advanced algebra, trigonometry, and it’s functions. Polynomial Functions Properties of Exponents Dividing Polynomials Factoring Polynomial Functions Graphing Polynomial Functions Rational Exponents & Functions Nth Roots Rational Exponent Properties Operations & Composition ...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 … Algebra 2 regents questions and answers, Excel is a powerful tool that can help you get ahead in your studies. Whether you’re preparing for an upcoming exam or just want to brush up on your skills, these Excel quiz questi..., State the number of solutions to the equation f(x) g(x). 33On the set of axes below, graph y f(x) and y g(x) for the given functions. f(x) x33x2. g(x) 2x5. Algebra II – June ’22[43] Question 33 Score 4:The student gave a complete and correct response. State the number of solutions to the equation f(x) g(x)., The following are questions from the past paper Regents High School Algebra 2, June 2019 Exam (pdf). Download the questions and try them, then scroll down the page to check your answers with the step by step solutions. Algebra 2 - June 2019 Regents - Questions and solutions 1 - 12. A sociologist reviews randomly selected …, January 2011. August 2010. June 2010. Algebra 2/ Trigonometry Information. Last Updated: August 29, 2022. Algebra 2/Trigonometry Regents Exam (2005 Standard), The Department is providing supplemental scoring guidance, the “Model Response Set,” for the Regents Examination in Algebra II. This guidance is intended to be part of the scorer training. Schools are encouraged to incorporate the Model Response Sets into the scorer training or to use them as additional information during scoring., 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 …, In this video I go through the Algebra 2 Regents January 2023, part 1, questions 1-24. Here is a link to the practice exam:https://www.nysedregents.org/algeb..., This downward trend seems to suggest that Algebra 1 Regents is getting easier, not harder, as a test. Since the exam is scored out of 86 points, students only need to score 31%, compared to 34% back in 2016. Educators that believe the test is becoming easier say so because of the way raw scores get converted to scaled scores., Regents Examination in Living Environment Regular size version (1.61 MB) Large type version (1.77 MB) Scoring Key PDF version (37 KB) Excel version (21 ... Questions 35, 75, and 79, Spanish Edition Only (9 KB) Notice to Teachers: June 2012 Regents Examination in Living Environment, Question 77, Chinese Edition Only (64 …, May 27, 2022 ... Algebra 2 Regents August 2022 (Part 1 Questions 1 - 24) ... 2 (#25-32) ... NYS Algebra 2 [Common Core] January 2018 Regents Exam || Parts 2-4 ANSWERS., Jul 7, 2015 ... Algebra 2/Trigonometry Regents at Random Worksheets. ... Questions <strong>at</strong> <strong>Random ... answers were given. Whichstudent answer ..., Moved Permanently. The document has moved here., Algebra 2 Lessons and Practice is a free site for students (and teachers) studying a second year of high school algebra., The Algebra 2 Regents Exam is a standardized test administered in New York State. It is designed to assess students’ understanding and mastery of algebraic concepts and skills. The exam consists of multiple-choice questions, extended-response questions, and constructed-response questions. It covers a wide range of topics, including linear ... , Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial credit will he 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 ..., Algebra I Regents Exam Questions at Random Worksheet # 1 NAME:_____ www.jmap.org Algebra I Regents at Random Worksheets 1 The table below represents the height of a bird above the ground during flight, with P(t) representing height in feet and t representing time in seconds. t P(t) 0 6.71 3 6.26 46 9 3.41, 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 ..., 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, The following are questions from the past paper Regents High School Algebra 2, June 2018 Exam (pdf). Download the questions and try them, then scroll down the page to check your answers with the step by step solutions. Algebra 2 - June 2018 Regents - Questions and solutions 1 - 12. The graphs of the equations y = x 2 + 4x - 1 …, Answer all 27 questions in this part. Each correct answer will receive 2 credits. 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.[54] Use this space for computations., Algebra II Rating Guide – Jan. ’23 [2] Mechanics of Rating The following procedures are to be followed for scoring student answer papers for the Regents Examination in Algebra II. More detailed information about scoring is provided in the publication Information Booklet for Scoring the Regents Examination in Algebra II., If you are taking the Algebra 2 exam in order to satisfy the graduation requirements for a Regents diploma, you need to answer 33% of the questions on the exam correctly to pass. If you are attempting to graduate with honors, you would need to correctly answer at or near 88% of the questions in order to achieve the requisite score., The sample questions are teaching tools for educators and can be shared freely with students and parents. They are designed to help clarify the way the Common Core should drive instruction and how students will be assessed on the Regents Examination in Algebra II measuring CCLS beginning in June 2016. NYSED is eager for feedback on these sample ..., 60 82 4 31 68 3 2 7 1 59 82 4 30 67 3 1 3 1 58 81 4 29 66 3 0 0 1 Schools are not permitted to rescore any of the open-ended questions on this exam 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 and that the resulting scale score has been ..., Regents Examination Guides and Samplers. Past Regents Examinations. English Language Arts. Mathematics. Revised Test Design for the Regents Examination in Geometry. Social Studies. United States History and Government (Framework) Regents Exam in Global History and Geography II., regents exams. worksheets. jmap on jumbled an online platform for the above algebra i resources. regents books. ai lesson plans. worksheet generators. extras. regents exam archives 1866-now. jmap resource archives ai/geo/aii (2015-now) ia/ge/a2 (2007-17) math a/b (1998-2010) regents resources. interdisciplinary exams. nyc teacher resources, Learn Algebra 2 skills for free! Choose from hundreds of topics including complex numbers, polynomials, trigonometry, logarithms, and more. Start now!, Learn Algebra 2 skills for free! Choose from hundreds of topics including complex numbers, polynomials, trigonometry, logarithms, and more. Start now!, Algebra II Regents Exam Questions by Common Core State Standard: Topic www.jmap.org 1 Algebra II Regents Exam Questions by Common Core State Standard: Topic GRAPHS AND STATISTICS S.IC.A.2, S.IC.B.4-6: ANALYSIS OF DATA 1 Anne has a coin. She does not know if it is a fair coin. She flipped the coin 100 times and obtained 73 heads and 27 tails., Physical Setting/Earth Science. Friday, 1/27/23 - 9:15 a.m. Physical Setting/Chemistry. During the January 2023 Regents Examination period (January 24-27, 2023) and for a period of time thereafter, this site will provide, as needed, timely information and guidance on the administration and scoring of each of the Regents Examinations …, JMAP offers math teachers resources that simplify the integration of Regents Exam questions into their curriculum. Resources may be downloaded using the links in the left column or below. ... JMAP has partnered with www.JumblED.it, an online platform that offers the Algebra I Regents Exam questions for free. ... Answers & Conversion Charts ..., Regents Exam Questions A2.A.29: Sequences. What is a formula for the nth term of sequence B shown below? 10,12,14,16,... 62.5. Which formula represents the nth term in the sequence? What is the formula for the nth term of the sequence 54,18,6,...? ̃ Ë ̄ 3. In an arithmetic sequence, a4 19 and a7 31. Determine a formula for an, the nth term ..., Answer all 27 questions in this part. Each correct answer will receive 2 credits. 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.[54] Use this space for computations.