nys regents algebra 1 reference sheet

Try the Pythagorean Theorem out yourself with these practice questions on Albert: The quadratic formula is one of the most important and useful formulas in all of math. Now, the width and height make up the legs of the right triangle and the diagonal is the unknown hypotenuse. Add 15! This gives us a total average snowfall of 0.59 inches. Please note: You must use Adobe Acrobat Reader/Professional X or higher to open the secure PDF files of scoring materials. $25.00. ii, regent algebra test algebra 1 common core regents exam, weird math 30 earns a passing grade in nys algebra, rubrics for new regents examination in english language, august 2015 regents examination scoring nysed, update on common core regents exams new york state, spring 2014 regents examination in mathematics algebra i, new york state . "Then it started snowing again at an average rate of one-half inch per hour for the next 4 hours until the storm was over.". Since we know the ratio of the width to the height of the given rectangle is 16{:}9, we can calculate the width to be about 36.6 from the height of 20.6. <> 0000017029 00000 n Here's an example of a student's correct response: This part isn't as tricky as it looks and mostly consists of easy addition, multiplication, and division. Title. 0 Thinking with Mathematical Models. From the diameter of, A pyramid is a three-dimensional figure with a polygon base and triangular faces that meet at a point, This problem presents a right pyramid whose base is a square. support JMAP by making a donation! NYSED / P-12 / OCAET / OSA / Past Examinations / Mathematics / Algebra II Regents Examination in Algebra I Spanish Translated Editions Please note: You must use Adobe Acrobat Reader/Professional X or higher to open the secure PDF files of scoring materials. So if there were, say, 10 people on Bryan's hockey team, that would be ten $\$23$ jerseys, or $10*23$. Since a rhombus is a type of parallelogram, we can use the area formula for parallelograms to solve this problem. Ask below and we'll reply! Use the formula when trying to solve a quadratic equation in the general form: If a quadratic equation is not in the standard form listed above, it must be rearranged before applying the quadratic formula. The Rock Cycle Reference Chart. One of these exams is Algebra 1 Regents, which tests your understanding of an array of algebra-related concepts and laws, from exponents and equations to functions and probability. %%EOF Comprehensive test covering all topics. As a result, the $x$-axis is divided up by hour, while the $y$-axis is divided up by half inch. endobj Since we know the ratio of the width to the height of the given rectangle is, Foundations of Algebra / Shapes: Pythagorean Theorem /, Level 1: Pythagorean Theorem with right triangles, Level 2: Pythagorean Theorem with isosceles triangles, Level 3: Problem solving with Pythagorean Theorem, The quadratic formula is most often using on the Algebra 1 and Algebra 2 Regents exams. For each Regents End of Course exam in mathematics, students have access to the official High School Math Reference Sheet for the duration of the assessment. endstream Thats why weve created a guide for what students need to remember and practice to best use the, Foundations of Algebra / Area of Polygons /, A parallelogram is a four sided polygon with opposite sides parallel, Types of parallelograms include squares, rectangles, and rhombuses, January 2020 Geometry Regents, Question 18, This is a multistep problem that ultimately asks us to find the area of a circles sector, but we must start by finding the area of the given circle. There are many ways to find the roots of a quadratic, but were going to focus on using the quadratic formula. Common Core High School Math Reference Sheet (Algebra I, Geometry, Algebra II) CONVERSIONS 1 inch = 2.54 centimeters 1 kilometer = 0.62 mile 1 cup = 8 fluid ounces 1 meter = 39.37 inches 1 pound = 16 ounces 1 pint = 2 cups 1 mile = 5280 feet 1 pound = 0.454 kilograms 1 quart = 2 pints 1 mile = 1760 yards 1 kilogram = 2.2 pounds 1 gallon = 4 . 0000025998 00000 n Regents Examination in Algebra II OSA NYSED / P-12 / OCAET / OSA / Past Examinations / Mathematics / Algebra II Regents Examination in Algebra II Please note: You must use Adobe Acrobat Reader/Professional X or higher to open the secure PDF files of scoring materials. This problem presents a right pyramid whose base is a square. endstream endobj 24 0 obj<>stream \dfrac{ \text{area of sector}}{ \text{area of full circle}} = \dfrac{\dfrac{ 512 \pi}{3 }}{256 \pi }. Common Core High School Math Reference Sheet (Algebra I, Geometry, Algebra II) . A passing score on Algebra Regents is a 65, equal to about 27 credits on the test. regents books. Since the diameter of this hemisphere is, Since a hemisphere is half of a sphere, the volume of the given hemisphere would be equal to half of, This prompt provides the volume of a right circular cone and the diameter of its base. Were told the first term of the sequence is 8, so: Were also told the fourth term is 216, so we know: We can use the geometric sequence formula to solve for the common ratio of this sequence: Alright were making progress! Geometry Regents is a four-part exam consisting of 35 questions, and you'll have three hours to complete it. 0000008545 00000 n <> 0000001808 00000 n Note that this formula only works for right circular cones. complex numbers cheat sheet. The following equipment must be provided to you for the Algebra 1 Regents exam: In the back of the test booklet will be a "High School Math Reference Sheet" containing common formulas and conversions. Sitio oficial de TUDN, con la cobertura total del futbol y el deporte en Mxico y el mundo: noticias, reportajes, estadsticas, fotos y videos. This rock cycle reference chart shows the three types of rock (igneous, sedimentary, metamorphic), describes each rock type, and explains how heat, pressure, weathering, and erosion change rocks over time. Learn about these tests with our expert articles on Earth Science Regents, Chemistry Regents, and Living Environment Regents. The College Entrance Examination BoardTM does not endorse, nor is it affiliated in any way with the owner or any content of this site. The formula were working with is called the explicit formula (there is another version of the formula called the recursive formula that is not included on the regents formula sheet). hbbd```b``:"A$fv D2O{jdX.lo,"$4H* hbkI@yUs.a``?W m 56 0 obj<>stream Lets substitute the values of a, b, and c like this: x=\dfrac{-(-5)\pm\sqrt{(-5)^2-4(1)(-4)}}{2(1)}. During the August 2022 Regents Examination period (August 16-17, 2022) 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 being administered this week. The height is the distance between \overline{CD} and \overline{AB}, which is also equal to 5\text{ units}. For an advanced Regents diploma, students need three math exams with a 65 or higher this means Algebra 1 is just 33% of what they need to obtain this diploma. This is a multistep problem that ultimately asks us to find the area of a circles sector, but we must start by finding the area of the given circle. Is 10 inches of snow enough for a fox to submerge its head in? To find this, multiply the number of eggs her chickens lay each day (that's 16) by 7 days: Allysa's chickens lay 112 eggs a week. High School Regents Examinations General Information Implementation Schedule for New Regents Examinations in Mathematics, Science, and English Language Arts Education Requirements and Diploma Requirements Listing of Department Approved Alternative Assessments Acceptable for Meeting Requirements for a Local or Regents Diploma Take a NY Regents Algebra 1 practice test. Source: January 2016 Geometry Regents, Question 32. You will be given one sheet of scrap graph paper. Now that we have the value of $D$, we can plug this value of 8 into our equation and solve for $A$: The algebra shows that Allysa bought 8 Delaware chickens and 4 Americana chickens. common core high school math reference sheet algebra i, august 2015 regents examination scoring nysed, regents review algebra i, spring 2014 regents examination in . jmap resource archives ai/geo/aii (2015-now) ia/ge/a2 (2007-17) math a/b (1998-2010) regents resources. NYS Mathematics Regents Preparation is a non-for-profit organization. Source: August 2017 Geometry Regents, Question 23. Dec 2, 2021 | cheddar cheese dumplings | willy caballero retire. We can thus use the formula for area of a parallelogram, where b=8 and h=3.5. . Since the coffee is cooling at a constant rate of, To find how long it will take for the coffee to be at a safe temperature of, Rounding to the nearest full minute, our final answer is, Exponential Growth and Decay (topic quiz), Quickly review popular literary works like. Hello New York State Algebra 2 students! 0000004159 00000 n 0000004471 00000 n The ultimate review guides for AP subjects to help you plan and structure your prep. Source: June 2017 Geometry Regents, Question 26. As Part 3's instructions tell us, Delaware chickens lay 1 egg a day, whereas Americana chickens lay 2 eggs a day. We now know the common ratio (r) is 3. No new snow means nothing changes vertically (on the y-axis), giving us a horizontal line. 0000109597 00000 n We are given the length of the radius as, To finish this problem, we would now set up a proportion that compares the, Level 1: Radius, diameter, circumference of circles, A prism is a three-dimensional figure with two congruent and parallel end faces, January 2020 Geometry Regents, Question 14, This question provides enough information for us to calculate the volume of a rectangular prism and then asks us to take it one step further and calculate its weight. So, the correct answer is, Algebra 1 / Solve Quadratic Equations by Using Quadratic Formula /, Level 1: Solving quadratics by quadratic formula (free), Level 2: Predicting solutions with discriminant (free), Algebra 2 / Quadratic Formula and the Discriminant /, has a consistent amount (called the common difference) being added between each consecutive term, August 2018 Algebra 1 Regents, Question 20, Level 1: Determining common difference (free), Level 2: Determining the nth arithmetic term (free), Level 3: Determining an arithmetic formula (free), has a consistent amount (called the common ratio) that is multiplied between consecutive terms, August 2019 Algebra 1 Regents, Question 24, Level 2: Determining the nth geometric term (free), Level 3: Determining a geometric formula (free), is the sum of the terms in a geometric sequence, This formula is most often used on the Algebra 2 Regents exam, We use the geometric series formula anytime were trying to find the sum of a geometric sequence. Noticias, telenovelas, entretenimiento, espectculos,mundo y cultura, series, deportes y ftbol en vivo 7 das a la semana las 24 horas al da . The Algebra 1 Regents exam is a three-hour math test consisting of 37 questions across four parts. HWM cr $x?UVervM(_YE#^vC_W~yiOO%-wg_@SimRWaY^scr%,9D:WbUimMol8vZ= U{Heh]YU(|{K}hZoRnBzFD7 j9s['gi'?o?zAR|Xm]W(k_Cm}+uSry{op/Kw:5;^he_Kjr^+\l/v9-w=Rtru/sKC!" ghr=6Ll cw nAn%7&J>|b^RdCYG>zaQL:d+pjoqb"kNPHW=]*(!QFG}7| Quickly review popular literary works like The Great Gatsby and more, See how scores on each section impacts your overall SAT score, See how scores on each section impacts your overall ACT score. GEO Here's an overview of the format: Each multiple-choice question has four answer choices (labeled 1-4) from which you will choose one and then record it on a separate answer sheet. 1. Bring Albert to your school and empower all teachers with the world's best question bank for: For each Regents End of Course exam in mathematics, students have access to the official . Regents Examination in Geometry Please note: You must use Adobe Acrobat Reader/Professional X or higher to open the secure PDF files of scoring materials. First we need to find the area of the base of the prism, which we know is a rectangle. If you put down just the correct answer, you'll net 1 pointbut that's it. Check out these practice problems on Albert so that you can try out the area of a triangle formula for yourself: Use this formula when you know or are able to calculate two of the following three attributes of a parallelogram: its height, its base, and its area. A sample of questions from this year's New York Regents Algebra I exam, which was aligned with the Common Core curriculum. Lets calculate the volume of this shape as if it was an entire sphere with the same dimensions. To pass the Algebra 1 Regents Exam, a student must demonstrate a level of understanding of mathematical concepts equivalent to the Common Core Learning Standards. RESOURCES BY STANDARD Since were adding 15 between consecutive terms in the sequence, the common difference, d, is 15. It also serves as a handy reference guide for math teachers and college To achieve the Regents Diploma, students must achieve the 4+1 options requirement by scoring 65 or higher in at least 4 Regents examsone per subjectand pass one additional Regents exam in any subject as shown below: . Materials coo rdinate with state assessments. Source: June 2018 Geometry Regents, Question 22. Not a fan of Algebra 1 Regents? A quick run-through of the kinds of questions you'll see on the exam will pinpoint the concepts you know and don't know. is one of the most important and useful formulas in all of math. 1. We use the relationship between radians and degrees in a variety of different problems involving angle measurements. Algebra I. Source: June 2019 Geometry Regents, Question 10. The test has 37 questions spread out across four sections: the first is a multiple-choice section, and the other three are constructed-response sections that require you to show your work in order to earn credit. ga('send', 'pageview'); Please The next Algebra 2 Regents exam will take place on Thursday, January 23, 2020, at 1:15 pm. Ideally, you'll also have plenty of time at the end of the exam to check your answers. It's most effective to take one practice test in the beginning of your prep, one in the middle of your prep, and one right before test day. While this problem is ultimately asking for the length of an arc of the given circle, we first need to find the circles circumference. This 20-page review packet covers 5 essential concepts for review for the NYS Algebra 1 Common Core Regents. . 0000112378 00000 n In this question, we are given the diameter of a hemisphere, which is a three-dimensional shape that comprises half of a sphere. This 20-page review packet covers 5 essential concepts for review for the NYS Algebra 1 Common Core Regents. nys regents algebra 1 reference sheet. Source: August 2018 Algebra 1 Regents, Question 20. /18Mm~^ v8YZn-6^7muG%=:VC=n[Plpa1hpZ(7t$637d_ l>s 62 0 obj <>stream This Regents Mathematics reference sheet provides students with the formulas and equations they need to know for the Algebra 1, Algebra 2, and Geometry Regents exams. The Best Algebra 1 Regents Review Guide 2022, Get Free Guides to Boost Your SAT/ACT Score, August 2019 administration of the Algebra 1 Regents exam, Engage NY via the New York State Education Department, official Algebra 1 Regents conversion charts, New York State Education Department website, Our in-depth guide goes over what these tests are for and who must take them, Reason quantitatively and use units to solve problems, Use properties of rational and irrational numbers, Write expressions in equivalent forms to solve problems, Arithmetic with Polynomials and Rational Expressions, Perform arithmetic operations on polynomials, Understand the relationship between zeros and factors of polynomials, Create equations that describe numbers or relationships, Reasoning with Equations and Inequalities, Understand solving equations as a process of reasoning and explain the reasoning, Solve equations and inequalities in one variable, Represent and solve equations and inequalities graphically, Understand the concept of a function and use function notation, Interpret functions that arise in application in terms of the context, Analyze functions using different representations, Build a function that models a relationship between two quantities, Build new functions from existing functions, Construct and compare linear, quadratic, and exponential models and solve problems, Interpret expressions for functions in terms of the situation they model, Interpreting Categorical and Quantitative Data, Summarize, represent and interpret data on two categorical and quantitative variables, Summarize, represent and interpret data on a single count or measurement variable, Calculate the average rate of snowfall per hour. I Resources below. Basically, you have to show your work! This prompt provides the volume of a right circular cone and the diameter of its base. Xc An online platform for JMAP's Algebra The exam requires that students show an understanding of mathematical concepts, use prior knowledge and prerequisite skills, and solve real world problems using tools and formulas. Algebra 1 Workbook: Algebra 1 Review and Practice Book for 8th and 9th Grade: [Over 350 Practice Problems] by Calvin Ferguson | Jul 5, 2020 4.1 (116) Paperback $849 FREE delivery Wed, Dec 14 on $25 of items shipped by Amazon Arrives before Christmas More Buying Choices $7.24 (4 used & new offers) Best Seller Read on to learn exactly what the Algebra 1 Regents exam entails, what kinds of questions you can expect, what topics you should know, and how you can ensure you pass it. From $(4, 2)$, draw an increasing line until hour 10 that goes up a whole inch every hour. Check out Tutorbase! www.commoncorestatestandards.org, RESOURCES BY TOPIC We now know the common ratio (, Radians and degrees are both units of measurement for angles, We can use the relationships given on the reference sheet to convert between radians and degrees, Radians and degrees are most often used on the Geometry and Algebra 2 Regents exam, August 2017 Geometry Regents, Question 23, We can now use that information to find the measure of the sector angle. The test builds on prior knowledge and asks students to work through real-world problems. This updated book prepares students for the new Algebra I (Common Core) exam. The volume of the given pyramid in cubic centimeters is 32{,}768.0. I recommend trying out some of the practice math questions from your algebra textbook that you didn't already do for homework or in-class practice. 0000005603 00000 n And her 4 Americana chickens lay 8 total eggs as well (as 4 chickens multiplied by 2 eggs each per day = 8 eggs each day). But since this is arguably the easiest of the four sections, you'll want to make sure that you're not spending too much time on Part I. So, the height of this cone is 15\text{ cm}. Starting from the origin of the graph, or $(0, 0)$, draw an increasing line so that it goes up one-half inch every hour until hour 4; this should place you at a total of 2 inches of snowfall (that's $0.5*4$), or coordinates $(4, 2)$. Source: June 2018 Geometry Regents, Question 15. This resource is aligned to the CCSS standards. Option 1 is correct. 1 cup = 8 fluid ounces. Regents Algebra I (Common Core) test prep, practice tests and past exams. worksheet generators. 2 0 obj Get some prism practice of your own with these Albert topics: Use this formula when you know or are able to calculate two of the following attributes of a right circular cylinder and want to know the third: the radius of the base, the height, or the total volume. We know that a full circle is, This equation is used on the Algebra 2 Regents exam, because the sequence of values is continuously, August 2019 Algebra 2 Regents, Question 18, The problem above covers concepts of exponential change over time. From the diameter of 6.6\text{ cm}, we can calculate the radius as 3.3\text{ cm}. Please . Source: August 2019 Geometry Regents, Question 31. Now we can take the area of the sector and divide by the full area of the circle to find what portion of the entire circle is represented by the sector. 0000002384 00000 n . 0000004776 00000 n Select Page. Were told the first term of the sequence is, Alright were making progress! What can we do to get from -27 to -12? Each Albert question includes a detailed explanation: We use the arithmetic sequence formula anytime were trying to find a specific term in an arithmetic sequence. We first need to figure out what kind of sequence we are working with (arithmetic or geometric). %PDF-1.4 % 0000007284 00000 n Weve compiled the formulas from the Regents mathematics equation sheet. Algebra 2. Familiarizing yourself with the tools you'll be allowed to use on exam day should also be a part of your preparations. Source: June 2019 Algebra 1 Regents, Question 21. (1998-2010), JMAP ON JUMBLED When it comes to math, there is no such thing as a . So, the area of the base is 4{,}096\text{ cm}^2. algebra 1 midterm review packet 1 name multiple choice choose the one alternative that best completes the statement or answers the question write the set 1 e is the set of odd natural numbers between 3 and 10 a e 3 5 7 9 b e 5 7 9, 1 16 of 224 results for algebra regents review regents exams and answers algebra i barron s regents ny nov 1 2017 by "qU-4IVq?!T, VmqC2O(|gqQ&p94mbUR2ptv@L@\| ( **.- vnDPr_rL[oMv+\cjdQ#\*G'4V c]"i oe-"PQZ8r Well have to apply several mathematical concepts to solve this problem, including the Pythagorean Theorem. Well typically be given a specific number (, August 2019 Algebra 2 Regents, Question 2, We are asked to find the sum of the first, Lets first define a few of the variables we know. NYS Exams and Review. At least one science regents (Living Environment . Regents Examination Papers for the Academic Year 1895 (Classic Reprint) Jan 19 2022 Excerpt from Regents Click on the formulas in the table below to see our expert breakdown of each formula in action. 0000001590 00000 n NYSED General Information: (518) 474-3852, Office of Higher Education: (518) 486-3633, Office of the Professions: (518) 474-3817, 2015 - 2023 New York State Education Department, Accessibility | Internet Privacy Policy | Disclaimer|Terms of Use, Information Concerning Common Core Learning Standards and Assessments, Next Generation Learning Standards: ELA and Math, Teaching in Remote/Hybrid Learning Environments (TRLE), New York State Alternate Assessment (NYSAA), Testing Materials for Duplication by Schools, United States History and Government (Framework), Transition Examination in Global History and Geography, Implementation Schedule for New Regents Examinations in Mathematics, Science, and English Language Arts, Education Requirements and Diploma Requirements, Listing of Department Approved Alternative Assessments Acceptable for Meeting Requirements for a Local or Regents Diploma, Availability of Previously Released New York State Testing Program Assessments in Unified English Braille (UEB), Memo: Next-Day Completion of Testing for English Language Learners/ Multilingual Learners on Regents Examinations, Assurance of Next-Day Completion of Testing for English Language Learners/Multilingual Learners on Regents Examinations Form, New York State Test Administration Security Certificate (Form to Be Signed by Principal), New York State Test Administration Security Certificate (Form to Be Signed by Parent/Guardian), Information Concerning the June 2023 Examination Period, Memo: Procedures for Requesting and Storing the June 2023 Regents Examinations, School Record of Examinations Requested - June 2023, Instructions for Submitting Your Examination Request Online - June 2023, Revised Test Design for the Regents Examination in Geometry, Summary of the Transition to the Common Core Regents Examinations, Transition to the Regents Examination in Algebra II (Common Core) and Phase-Out of the Regents Examination in Algebra 2/Trigonometry, Transition to the Regents Examination in Algebra II (Common Core), Transition to Common Core Regents Examinations - December 2014, Summary of the standard setting process that resulted in the approved cut scores to the Regents Exam in ELA and the Regents Exam in Algebra I (Common Core), Standard Setting Process in Educational Assessment, Memo: Scanning Regents Examination Answer Sheets: June 2011, History of Regents Examinations, 1865 to Present, ACT and SAT Test Scores Acceptable for Meeting Competency Requirements for a Local High School Diploma, Safe and Vault Specifications for Secondary-Level Examination Storage, Get information about my teacher certification, About the New York State Education Department, About the University of the State of New York (USNY), Business Portal for School Administrators. To do this, we must set up the two equations in such a way that one of them contains only one variable (either $\bi A$ or $\bi D$). See whether your teacher has any time after class to go over tricky concepts with you or give you advice on what graders look for when it comes to the constructed-response questions. We are given the length of the radius as 6 inches, so we can use the circumference formula. Pearson Success Net. The Regents Diploma. (12) $33.00. <>/ExtGState<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> sheets because they are practical.This book contains three courses in one: Integrated Algebra 1, Geometry, and Algebra 2/Trigonometry. {pr.>.(Lg:gb!t V9/=n > In the back of the test booklet will be a High School Math Reference Sheet containing common formulas and. The Algebra 1 Regents exam is one of three math Regents exams that high school students in New York can choose from to fulfill their graduation requirements. NY Regents ALGEBRA II Jan 2020 released items 37 questions | NY Regents. If you teach other regents level courses such as Algebra 1 and Geometry, visit our website at nysmathregentsprep to download those study guides too! Option 3 is correct. "For the first 4 hours, it snowed at an average rate of one-half inch per hour.". What can we do to get from 3 to 18? One of the best ways you can prepare for the Algebra 1 Regents exam is to use real, previously administered tests, which are available for free on the New York State Education Department website. If you are using an earlier version of Adobe Acrobat Reader/Professional, you will not be able to open the secure PDF files. '[ Put your sphere skills to the test with these practice questions on Albert: Use this formula when you know or can calculate two of the following three attributes of a cone and want to find the third: the radius of the circular base, the total height, and the cones volume. To do this, we'll have to divide the total amount of accumulated average snowfall (10 inches) by the total number of hours it snowed (17): Round your answer to the nearest hundredth of an inch, per the instructions in the problem. There are many subtopics and learning standards within algebra, and some take up more weight on the test . Source: August 2019 Algebra 1 Regents, Question 24. Allysa bought a total of 12 chickens, consisting of both Americana chickens and Delaware chickens. And since Parts II, III, and IV are harder and worth more points, you'll want to save as much time as you can for the constructed-response questions. NYS Algebra 2 - COMMON CORE - Regents June 2019 Part 1: 1 - 12 - YouTube PLEASE SUBSCRIBEVisit my Website at: www.mrkrausemath.comHey Everyone I hope you are enjoying OUR videos geared. So, the volume of the prism is 63 cubic inches. Examination. hbspt.cta.load(360031, '4efd5fbd-40d7-4b12-8674-6c4f312edd05', {}); Have any questions about this article or other topics? Source: January 2020 Geometry Regents, Question 14. We can now use that information to find the measure of the sector angle. endstream endobj 39 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text]/Properties<>>>/Subtype/Form>>stream Lets take a look at the arithmetic sequence formula: Were told in the prompt that a_1 (the first term in the sequence) is -27. Basic Algebra Algebra Basics Balancing Equations Multiplication Order of Operations (BODMAS) Order of Operations (PEMDAS) Substitution Equations vs Formulas Inequalities Exponents

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