Advertisement
| exponential equations worksheet with answers: Beginning and Intermediate Algebra Tyler Wallace, 2018-02-13 Get Better Results with high quality content, exercise sets, and step-by-step pedagogy! Tyler Wallace continues to offer an enlightened approach grounded in the fundamentals of classroom experience in Beginning and Intermediate Algebra. The text reflects the compassion and insight of its experienced author with features developed to address the specific needs of developmental level students. Throughout the text, the author communicates to students the very points their instructors are likely to make during lecture, and this helps to reinforce the concepts and provide instruction that leads students to mastery and success. The exercises, along with the number of practice problems and group activities available, permit instructors to choose from a wealth of problems, allowing ample opportunity for students to practice what they learn in lecture to hone their skills. In this way, the book perfectly complements any learning platform, whether traditional lecture or distance-learning; its instruction is so reflective of what comes from lecture, that students will feel as comfortable outside of class as they do inside class with their instructor. |
| exponential equations worksheet with answers: Algebra Teacher's Activities Kit Judith A. Muschla, Gary R. Muschla, Erin Muschla-Berry, 2015-11-30 Help your students succeed with classroom-ready, standards-based activities The Algebra Teacher's Activities Kit: 150 Activities That Support Algebra in the Common Core Math Standards helps you bring the standards into your algebra classroom with a range of engaging activities that reinforce fundamental algebra skills. This newly updated second edition is formatted for easy implementation, with teaching notes and answers followed by reproducibles for activities covering the algebra standards for grades 6 through 12. Coverage includes whole numbers, variables, equations, inequalities, graphing, polynomials, factoring, logarithmic functions, statistics, and more, and gives you the material you need to reach students of various abilities and learning styles. Many of these activities are self-correcting, adding interest for students and saving you time. This book provides dozens of activities that Directly address each Common Core algebra standard Engage students and get them excited about math Are tailored to a diverse range of levels and abilities Reinforce fundamental skills and demonstrate everyday relevance Algebra lays the groundwork for every math class that comes after it, so it's crucial that students master the material and gain confidence in their abilities. The Algebra Teacher's Activities Kit helps you face the challenge, well-armed with effective activities that help students become successful in algebra class and beyond. |
| exponential equations worksheet with answers: College Algebra Jay Abramson, 2018-01-07 College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they've learned. Coverage and Scope In determining the concepts, skills, and topics to cover, we engaged dozens of highly experienced instructors with a range of student audiences. The resulting scope and sequence proceeds logically while allowing for a significant amount of flexibility in instruction. Chapters 1 and 2 provide both a review and foundation for study of Functions that begins in Chapter 3. The authors recognize that while some institutions may find this material a prerequisite, other institutions have told us that they have a cohort that need the prerequisite skills built into the course. Chapter 1: Prerequisites Chapter 2: Equations and Inequalities Chapters 3-6: The Algebraic Functions Chapter 3: Functions Chapter 4: Linear Functions Chapter 5: Polynomial and Rational Functions Chapter 6: Exponential and Logarithm Functions Chapters 7-9: Further Study in College Algebra Chapter 7: Systems of Equations and Inequalities Chapter 8: Analytic Geometry Chapter 9: Sequences, Probability and Counting Theory |
| exponential equations worksheet with answers: Intermediate Algebra 2e Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, 2020-05-06 |
| exponential equations worksheet with answers: Mathematics Standard Level for IB Diploma Exam Preparation Guide Paul Fannon, Vesna Kadelburg, Ben Woolley, Stephen Ward, 2014-03-27 A new series of Exam Preparation guides for the IB Diploma Mathematics HL and SL and Mathematical Studies. This exam preparation guide for the IB Diploma Mathematics Standard Level course breaks the course down into chapters that summarise material and present revision questions by exam question type, so that revision can be highly focused to make best use of students' time. Students can stretch themselves to achieve their best with 'going for the top' questions for those who want to achieve the highest results. Worked solutions for all the mixed and 'going for the top' questions are included, plus exam hints throughout. Guides for Mathematics Higher Level and Mathematical Studies are also available. |
| exponential equations worksheet with answers: Puzzling Algebra Steve Hiner, 2014-09-06 This book was written to provide math teachers with supplemental resources they can use in their classrooms. This book can also be used by students to improve their skills. Tutorials are included with many of the activities so you can learn at your own pace. Topics can be used for Alg 1 and 2, as well as Integrated Math I, II, and III. Topics include: order of operations, solving many types of equations, exponents, mult/divide scientific notation, percentages, distance formula, Pythagorean Theorem, area of triangles from determinants, basic circles, square roots, mean, median, mode, geometric mean, box and whisker plots, matrices (cryptography and inverses), plotting points, graphing circles, lines, and parabolas, long and synthetic division of polynomials, FOIL, Quadratic Formula, logarithms, factoring, and the Binary number system. |
| exponential equations worksheet with answers: Precalculus Jay P. Abramson, Valeree Falduto, Rachael Gross (Mathematics teacher), David Lippman, Melonie Rasmussen, Rick Norwood, Nicholas Belloit, Jean-Marie Magnier, Harold Whipple, Christina Fernandez, 2017 Precalculus is adaptable and designed to fit the needs of a variety of precalculus courses. It is a comprehensive text that covers more ground than a typical one- or two-semester college-level precalculus course. The content is organized by clearly-defined learning objectives and includes worked examples that demonstrate problem-solving approaches in an accessible way. |
| exponential equations worksheet with answers: Introductory Statistics 2e Barbara Illowsky, Susan Dean, 2023-12-13 Introductory Statistics 2e provides an engaging, practical, and thorough overview of the core concepts and skills taught in most one-semester statistics courses. The text focuses on diverse applications from a variety of fields and societal contexts, including business, healthcare, sciences, sociology, political science, computing, and several others. The material supports students with conceptual narratives, detailed step-by-step examples, and a wealth of illustrations, as well as collaborative exercises, technology integration problems, and statistics labs. The text assumes some knowledge of intermediate algebra, and includes thousands of problems and exercises that offer instructors and students ample opportunity to explore and reinforce useful statistical skills. This is an adaptation of Introductory Statistics 2e by OpenStax. You can access the textbook as pdf for free at openstax.org. Minor editorial changes were made to ensure a better ebook reading experience. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License. |
| exponential equations worksheet with answers: Advanced Algebra Anthony W. Knapp, 2007-10-11 Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a global view of algebra and its role in mathematics as a whole. |
| exponential equations worksheet with answers: Introductory Business Statistics 2e Alexander Holmes, Barbara Illowsky, Susan Dean, 2023-12-13 Introductory Business Statistics 2e aligns with the topics and objectives of the typical one-semester statistics course for business, economics, and related majors. The text provides detailed and supportive explanations and extensive step-by-step walkthroughs. The author places a significant emphasis on the development and practical application of formulas so that students have a deeper understanding of their interpretation and application of data. Problems and exercises are largely centered on business topics, though other applications are provided in order to increase relevance and showcase the critical role of statistics in a number of fields and real-world contexts. The second edition retains the organization of the original text. Based on extensive feedback from adopters and students, the revision focused on improving currency and relevance, particularly in examples and problems. This is an adaptation of Introductory Business Statistics 2e by OpenStax. You can access the textbook as pdf for free at openstax.org. Minor editorial changes were made to ensure a better ebook reading experience. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License. |
| exponential equations worksheet with answers: Applied Stochastic Differential Equations Simo Särkkä, Arno Solin, 2019-05-02 With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice. |
| exponential equations worksheet with answers: 411 SAT Algebra and Geometry Questions , 2006 In order to align the SAT with the math curriculum taught in high schools, the SAT exam has been expanded to include Algebra II materials. 411 SAT Algebra and Geometry Questions is created to offer you a rigorous preparation for this vital section. If you are planning to take the SAT and need extra practice and a more in-depth review of the Math section, here's everything you need to get started. 411 SAT Algebra and Geometry Questions is an imperative study tool tailored to help you achieve your full test-taking potential. The most common math skills that you will encounter on the math portion of the SAT are covered in this book. Increase your algebra and geometry skills with proven techniques and test your grasp of these techniques as you complete 411 practice questions, including a pre- and posttest. Follow up by reviewing our comprehensive answer explanations, which will help measure your overall improvement. The questions are progressively more difficult as you work through each set. If you can handle the last question on each set, you are ready for the SAT! Book jacket. |
| exponential equations worksheet with answers: Integrated Math, Course 1, Student Edition CARTER 12, McGraw-Hill Education, 2012-03-01 Includes: Print Student Edition |
| exponential equations worksheet with answers: Common Core Algebra II Kirk Weiler, 2016-06-01 |
| exponential equations worksheet with answers: Exercises And Problems In Linear Algebra John M Erdman, 2020-09-28 This book contains an extensive collection of exercises and problems that address relevant topics in linear algebra. Topics that the author finds missing or inadequately covered in most existing books are also included. The exercises will be both interesting and helpful to an average student. Some are fairly routine calculations, while others require serious thought.The format of the questions makes them suitable for teachers to use in quizzes and assigned homework. Some of the problems may provide excellent topics for presentation and discussions. Furthermore, answers are given for all odd-numbered exercises which will be extremely useful for self-directed learners. In each chapter, there is a short background section which includes important definitions and statements of theorems to provide context for the following exercises and problems. |
| exponential equations worksheet with answers: The Classroom Chef John Stevens, Matt Vaudrey, 2016-03-30 I just don't get math. If you're a math teacher, you probably can't count the number of times you've heard students, parents, and even fellow teachers make a disparaging statement about your subject. As math teachers and instructional coaches, John Stevens and Matt Vaudrey know how discouraging it feels to look out into a classroom full of disinterested and confused students. But they also know how amazing it feels to see comprehension dawn in their students' eyes - when a concept suddenly makes sense and math becomes meaningful. In The Classroom Chef, John and Matt share their secret recipes, ingredients, and tips for serving up lessons that engage students and help them get math. You can use these ideas and methods as-is, or better yet, tweak them and create your own enticing educational meals. The message the authors want to convey is that, with imagination and preparation, every teacher can be a Classroom Chef. Far from bland or boring, the lessons and ideas in The Classroom Chef spark curiosity-and occasionally bewilderment and awe (yes, in math class). After all, mullets, ziplines, and sharks aren't standard topics for typical math classes. But maybe they should be. |
| exponential equations worksheet with answers: Advanced Calculus (Revised Edition) Lynn Harold Loomis, Shlomo Zvi Sternberg, 2014-02-26 An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds. |
| exponential equations worksheet with answers: Introduction to Probability Joseph K. Blitzstein, Jessica Hwang, 2014-07-24 Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment. |
| exponential equations worksheet with answers: Helping Children Learn Mathematics National Research Council, Division of Behavioral and Social Sciences and Education, Center for Education, Mathematics Learning Study Committee, 2002-07-31 Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society. |
| exponential equations worksheet with answers: Precalculus Jay Abramson, 2018-01-07 Precalculus is adaptable and designed to fit the needs of a variety of precalculus courses. It is a comprehensive text that covers more ground than a typical one- or two-semester college-level precalculus course. The content is organized by clearly-defined learning objectives, and includes worked examples that demonstrate problem-solving approaches in an accessible way. Coverage and Scope Precalculus contains twelve chapters, roughly divided into three groups. Chapters 1-4 discuss various types of functions, providing a foundation for the remainder of the course. Chapter 1: Functions Chapter 2: Linear Functions Chapter 3: Polynomial and Rational Functions Chapter 4: Exponential and Logarithmic Functions Chapters 5-8 focus on Trigonometry. In Precalculus, we approach trigonometry by first introducing angles and the unit circle, as opposed to the right triangle approach more commonly used in College Algebra and Trigonometry courses. Chapter 5: Trigonometric Functions Chapter 6: Periodic Functions Chapter 7: Trigonometric Identities and Equations Chapter 8: Further Applications of Trigonometry Chapters 9-12 present some advanced Precalculus topics that build on topics introduced in chapters 1-8. Most Precalculus syllabi include some of the topics in these chapters, but few include all. Instructors can select material as needed from this group of chapters, since they are not cumulative. Chapter 9: Systems of Equations and Inequalities Chapter 10: Analytic Geometry Chapter 11: Sequences, Probability and Counting Theory Chapter 12: Introduction to Calculus |
| exponential equations worksheet with answers: Algebraic Reasoning Paul Gray, Jacqueline Weilmuenster, Jennifer Hylemon, 2016-09-01 Algebraic Reasoning is a textbook designed to provide high school students with a conceptual understanding of algebraic functions and to prepare them for Algebra 2.. |
| exponential equations worksheet with answers: The Busyness Delusion Chris Gardener, 2018-06-17 When your business is a job in disguise and feels like a hamster wheel it's time to get smarter. How to have financial security, freedom and fulfilment ... without being so stupidly busy. When people find out you run your own business you know what they'll ask: How's it going? Are you busy? Somehow, busy has come to mean successful. But you didn't wake up this morning thinking my main aim today is to be as busy as possible! You don't have your business to be busy ... so why DO you work so hard? We all have our businesses for the same reason. The same three reasons actually - to have financial security, freedom and fulfilment - the 3Fs. But these aren't the outcomes for most small businesses. Instead, the common experience feels like you're on a hamster wheel, where the hours are long and the rewards mediocre. Self-esteem is threatened and life, love and relationships impacted. This book explains why this happens and how to approach work in a smarter way, to have a better business with less busyness and more certain results, so you can get back to living and loving life again. How, by climbing off the hamster wheel and escaping The Busyness Delusion, you can take the easier, more certain route to turn your own business into one that does give you all 3Fs. It covers: Why the hustle method is seductive but flawed, and how to use a smarter approach Why most self-employed people unwittingly choose the hardest way to earn, and what the easier options are. How to overcome the biggest obstacle to a smarter business and better life. What financial security really means and how to achieve it quicker and more easily. How to get better results by applying a simple model of how the brain works to give you more control. How to eliminate your competition to make it easier to get better results. Providing a new framework, illustrated in clear diagrams and told through a compelling story, this book reveals why copying others creates the hamster wheel effect, and precisely what to do to have a business and life you deserve. This book nails the problem with most small businesses. The solutions are time-tested principles, for the first time pulled together in an original and enjoyable way that's easy to understand and implement. Dan Sager |
| exponential equations worksheet with answers: Algebra and Trigonometry Jay P. Abramson, Valeree Falduto, Rachael Gross (Mathematics teacher), David Lippman, Rick Norwood, Melonie Rasmussen, Nicholas Belloit, Jean-Marie Magnier, Harold Whipple, Christina Fernandez, 2015-02-13 The text is suitable for a typical introductory algebra course, and was developed to be used flexibly. While the breadth of topics may go beyond what an instructor would cover, the modular approach and the richness of content ensures that the book meets the needs of a variety of programs.--Page 1. |
| exponential equations worksheet with answers: Precalculus Michael Sullivan, 2018-01-11 NOTE: Before purchasing, check with your instructor to ensure you select the correct ISBN. Several versions of the MyLab(tm)and Mastering(tm) platforms exist for each title, and registrations are not transferable. To register for and use MyLab or Mastering, you may also need a Course ID, which your instructor will provide. Used books, rentals, and purchases made outside of Pearson If purchasing or renting from companies other than Pearson, the access codes for the MyLab platform may not be included, may be incorrect, or may be previously redeemed. Check with the seller before completing your purchase. For courses in precalculus. Ties concepts together using a functions approach The Concepts Through Functions Series introduces functions at the start of each text, and maintains a continuous theme by introducing/developing a new function in every chapter. Known for their ability to connect with today's students, acclaimed authors Sullivan and Sullivan focus on the fundamentals - preparing for class, practice with homework, and reviewing key concepts - encouraging students to master basic skills and develop the conceptual understanding needed for this and future courses. Graphing utility coverage is optional, and can be included at the discretion of each instructor based on course needs. Also available with MyLab Math MyLab(tm) Math is the teaching and learning platform that empowers instructors to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab personalizes the learning experience and improves results for each student. Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information. If you would like to purchase both the physical text and MyLab Math, search for: 0134859030 / 9780134859033 Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry Plus MyLab Math with eText -- Title-Specific Access Card Package, 4/e Package consists of: 0134686985 / 9780134686981 Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry 0134852184 / 9780134852188 MyLab Math with Pearson eText - Standalone Access Card - for Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry |
| exponential equations worksheet with answers: Differential Equations with Boundary-value Problems Dennis G. Zill, Michael R. Cullen, 2005 Now enhanced with the innovative DE Tools CD-ROM and the iLrn teaching and learning system, this proven text explains the how behind the material and strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This accessible text speaks to students through a wealth of pedagogical aids, including an abundance of examples, explanations, Remarks boxes, definitions, and group projects. This book was written with the student's understanding firmly in mind. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations. |
| exponential equations worksheet with answers: Algebra 1, Student Edition McGraw Hill, 2012-07-06 The only program that supports the Common Core State Standards throughout four-years of high school mathematics with an unmatched depth of resources and adaptive technology that helps you differentiate instruction for every student. Connects students to math content with print, digital and interactive resources. Prepares students to meet the rigorous Common Core Standards with aligned content and focus on Standards of Mathematical Practice. Meets the needs of every student with resources that enable you to tailor your instruction at the classroom and indivdual level. Assesses student mastery and achievement with dynamic, digital assessment and reporting. Includes Print Student Edition |
| exponential equations worksheet with answers: Financial Mathematics For Actuarial Science Richard James Wilders, 2020-01-24 Financial Mathematics for Actuarial Science: The Theory of Interest is concerned with the measurement of interest and the various ways interest affects what is often called the time value of money (TVM). Interest is most simply defined as the compensation that a borrower pays to a lender for the use of capital. The goal of this book is to provide the mathematical understandings of interest and the time value of money needed to succeed on the actuarial examination covering interest theory Key Features Helps prepare students for the SOA Financial Mathematics Exam Provides mathematical understanding of interest and the time value of money needed to succeed in the actuarial examination covering interest theory Contains many worked examples, exercises and solutions for practice Provides training in the use of calculators for solving problems A complete solutions manual is available to faculty adopters online |
| exponential equations worksheet with answers: Tested Studies for Laboratory Teaching Association for Biology Laboratory Education. Workshop/Conference, 1991 |
| exponential equations worksheet with answers: SpringBoard Mathematics , 2015 |
| exponential equations worksheet with answers: Mathematics Framework for California Public Schools California. Curriculum Development and Supplemental Materials Commission, 1999 |
| exponential equations worksheet with answers: Calculus Volume 3 Edwin Herman, Gilbert Strang, 2016-03-30 Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations. |
| exponential equations worksheet with answers: Big Ideas Math Ron Larson, Laurie Boswell, 2018 |
| exponential equations worksheet with answers: Core Connections , 2016 |
| exponential equations worksheet with answers: Algebra 2, Student Edition McGraw Hill, 2002-03-06 Glencoe Algebra 2 strengthens student understanding and provides the tools students need to succeed , from the first day your students begin to learn the vocabulary of algebra until the day they take final exams and standardized tests. |
| exponential equations worksheet with answers: New York Math: Math B , 2000 |
| exponential equations worksheet with answers: MathLinks 9 Bruce McAskill, 2009 |
| exponential equations worksheet with answers: Financial Modeling Using Excel and VBA Chandan Sengupta, 2004-04-01 Comprehensive instruction on developing real-world financial models This book, designed for self-study, classroom use, and reference, presents a com-prehensive approach to developing simple to sophisticated financial models in all major areas of finance. The approach is based on the author's 20 years of experience of developing such models in the business world and teaching a popular MBA class in financial modeling. The book assumes only basic knowledge of Excel and teaches all advanced features of Excel and VBA from scratch using a unique simple method. A companion CD includes all working versions of all the models presented in the book and additional useful reference material. |
| exponential equations worksheet with answers: The Parallel Curriculum in the Classroom, Book 2 Carol Ann Tomlinson, Sandra N. Kaplan, Jeanne H. Purcell, Jann H. Leppien, Deborah E. Burns, Cindy A. Strickland, 2005-09-08 Learn to design exemplary Parallel Curriculum Units from the experts—classroom teachers! What is the best way to incorporate the four parallels into your Parallel Curriculum Unit? How do teachers using the Parallel Curriculum Model (PCM) craft units based on the PCM and why do they utilize certain elements and downplay others? What does a complete Parallel Curriculum Unit look like? This compilation of Parallel Curriculum Units provides a close-up look into the development of PCM units and how those units work in actual classroom settings. The Parallel Curriculum in the Classroom, Book 2 reflects a variety of Parallel Curriculum units spanning primary, elementary, middle, and high school levels of instruction and encompassing the disciplines of social studies, science, art, math, and language arts. Across each unit, the authors present a framework of three essential components in an effective Parallel Curriculum Unit: The big picture of grade level, subject, goals, and standards The unpacking, or step-by-step explanation of the unit The reasoning behind the unit design Whether using each parallel independently or combining all four parallels into curriculum design, teachers will find the units included here are exemplary models for creating their own parallel curriculum units. Use them as professional development tools to help plan thoughtful curriculum based upon the Parallel Curriculum Model! |
| exponential equations worksheet with answers: Into Algebra 2 Edward B. Burger, Juli K. Dixon, Timothy D. Kanold, Robert Kaplinsky, Matthew R. Larson, Steve Leinwand, 2020 |
| exponential equations worksheet with answers: Common Core Algebra I Kirk Weiler, Garrett Matula, 2015-08-01 |
Solving Exponential Equations with Logarithms - Kuta Software
Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com.
EXPONENTIALS & LOGARITHMS PRACTICE - MadAsMaths
Solve each of the following equations, leaving your final answers as expressions involving natural logarithms in their simplest form. a) e 4x = b) e 92y = c) 2e 1 9−z + = d) 4e 7 572w− = e) 2e 7 …
AS/A Level Mathematics Exponentials and Logarithms - Maths …
Answers should be given to three significant figures unless otherwise stated. use this as a guide as to how much time to spend on each question. Read each question carefully before you start …
Solving Exponential Equations Worksheet - Paulding County …
Worksheet by Kuta Software LLC Algebra 2 Solving Exponential Equations Worksheet Name_____ ©r F2I0N1[7R SKLumt[aX SS\oqf[tzwxaUrgex GL`LjCx.t i XAklulP grXiJgThUt^sX …
Solving Exponential and Logarithmic Equations - WordPress.com
Worksheet by Kuta Software LLC Algebra 2 Honors - Mr. Allen-Black ... EXPONENTIAL EQUATIONS: Solve each equation. 1) 53a = 52a + 2 2) 322x = 24 EXPONENTIAL …
Exponential Equations and Logarithms - Effortless Math
Math Worksheets Name: _____ Date: _____ … So Much More Online! Please visit: www.EffortlessMath.com Exponential Equations and Logarithms Solve each equation for the …
Worksheet Section 7.3: Solving Exponential Equations - Ms.
Practice Worksheet: Solving Exponential Equations
Solve the exponential equation using ANY METHOD. Give answers as exact values. Show all work.
Exponential Equations Worksheet #1 Name Solve the …
Exponential Equations Worksheet #1 Name_____ Solve the Exponential Equation. Author: Brooklyn Eve Punziano Created Date: 3/4/2013 11:17:35 AM
Exponential Equations with Logarithms Date Period - Kuta Software
Worksheet by Kuta Software LLC Kuta Software - Infinite Precalculus Exponential Equations with Logarithms Name_____ Date_____ Period____-1-Solve each equation. Round your answers …
Exponential Expressions and Equations - MrBertman.com
Exponential Expressions and Equations Level 1 – 2 1. Complete the following by writing on the dotted line a) 4𝑥=2… b) 1 6𝑥 =6… c) 5…=1 d) 7𝑥∙72=7… 𝑥 e) 32÷3 =3… ( ) f) 2𝑥3=2… g) 3 …∙4𝑥=12 𝑥 …
xponentials & Logs: Exponential Equations E …
xponentials & Logs: Exponential Equations E PhysicsAndMathsTutor.com Edexcel 6 1. Most candidates completed part (a) successfully (sometimes by ‘trial and error’), but sometimes a …
Exponential equations: Exercises 612 - Math-Grain.de
Exponential equations: Solutions 11,12 The function exp (x) is positive everywhere. The condition can not be satisfied. There is one solution only :
Solve each equation. - Math and Computer Science
EXPONENTIAL & LOGARITHMIC EQUATIONS - Mt. San …
1998. Use the exponential decay model y e 0. 001t 0 = − to answer the following. a) How many inhabitants will there be by 2005, round your answer to the nearest whole number. b) How …
Exponential Equations Sample Problems - Marta Hidegkuti
21 Aug 2024 · Lecture Notes Exponential Equations page 1 Sample Problems 1.Simplify each of the following expressions. a) 32x+1 9x−1 b) 8b−2 2b+1 r 42b−3 c) 52x−3 ·251−x d) 23x−1 …
Exponential Equations Not Requiring Logarithms Date Period
©S _2o0x1h6C HKLuYtJaQ cSsoUfHtowlacrseh zLELFCq.f g bAzlJle LrtipgRhgtQsh frre]sKekrVvCe\da.T W GMHaHdheK JwiiRtZhU gIZnzf^ivnOitthe^ fPrr]eucba]lhcSuylluGsp.
Exponential equations - ibmathematics.org
We will learn how to solve basic exponential equations. We will deal with the equations of the form. where a; b > 0 and f ; g are real-valued functions. In our examples these will be simple …
Exponential Equations & Inequalities Worksheet Name Solve the …
Exponential Equations & Inequalities Worksheet Name_____ Solve the Exponential Equation or Inequality. Check your solution.
Exponents Mixed Practice Worksheet 1 - Riverside Math
riversidemath.com Exponents – Mixed Practice Worksheet 1 Answers Simplify the expression. Do not leave any negative exponents in your final answer. 1. 4∙ 7= 11 3. 514 58 =56 5. (3 9 3)2=9 18 6 16 7. −5∙ −11=1 16 9.
logarithms practice - MadAsMaths
Solve each of the following exponential equations. a) 3 11x = b) 4 18y−1 = c) 2 802 1z+ = d) 5 303w = e) 6 77767 2 ...
indices exam questions - MadAsMaths
a) Evaluate the following indicial expressions, giving the final answers as exact simplified fractions. i. 2 8− −5 2− . ii. ( ) 3 4 2 9. b) Solve the equation 1 y 3 8 − = . C1G , 1 64, 8 27, 1 512 Question 6 (**+) Evaluate the following indicial expression, giving the final answers as an exact simplified fraction. 2 1 1 3 36 162 4 − +
Worksheet 1 Memo: Exponents and Surds Grade 11 Mathematics …
Worksheet 1 Memo: Exponents and Surds Grade 11 Mathematics 1. i) When the same bases are multiplied the exponents are added → ii) When the same bases are divided the exponents are subtracted → iii) (When a power is raised to an exponent, the exponents are multiplied → ) iv) When a power is under a root sign the exponent is divided by the ...
xponentials & Logs: Exponential Equations E …
xponentials & Logs: Exponential Equations E PhysicsAndMathsTutor.com Edexcel 7 recommended procedure for this type of question. Part (b) was one of the most discriminating parts of the paper. Whilst a reassuringly high proportion of candidates did achieve full marks here many incorrect procedures were seen.
Worksheet 2 7 Logarithms and Exponentials - Macquarie University
Worksheet 2:7 Logarithms and Exponentials Section 1 Logarithms The mathematics of logarithms and exponentials occurs naturally in many branches of science. It is very important in solving problems related to growth and decay. The growth and decay may be that of a plant or a population, a crystalline structure or money in the bank. Therefore
2.13A Exponential and Logarithmic Equations and Inequalities
2.13A Exponential and Logarithmic Equations and Inequalities AP Precalculus CALCULATOR ACTIVE: Instructions: Solve each equation. Have exact answer and answer rounded to nearest thousandth. 1) !"#
Simplifying Exponential Expressions Date Period
Simplifying Exponential Expressions Simplify. Your answer should contain only positive exponents. 1) 4 ⋅ 45 2) 3−1 ⋅ 33 3) (4−4) −2 4) (4−4) 0 5) 35 3 6) 4−5 40 ... .X 9 zAEl slp nrDiIghWtFsx mrBeQsxe Vr9voe rd 1.f h AM8a 1dMek Ww9ijt uhz oI lnbf Gigndi4tjeH UAnlQgte lb Irua 2 e2c. g Worksheet by Kuta Software LLC
00i ALG1SN TP SE 890844 - McGraw Hill Education
Study Notebook 000i_ALG1SN_TP_SE_890844.indd 10i_ALG1SN_TP_SE_890844.indd 1 66/10/08 11:59:06 PM/10/08 11:59:06 PM
4.5 Solving Exponential Equations using Logarithms
4.5 Solving Exponential Equations using Logarithms Name_____ Period____ ©u [2[0S1t8f AKquGtNaC wSMoQfetMwwawrve` TLvLfCl.O x SAGlhlB ^rniDgehutssf grKeRsdeTrNvEerdp. ... Worksheet by Kuta Software LLC-3-Answers to 4.5 Solving Exponential Equations using Logarithms 1) 2) log183) log574) ln32 5) ln816) log 8 897) log 14 59 8) log 8 26 8 9) log 2 ...
LINEAR/QUADRATIC/EXPONENTIAL TABLES - Ms. Shultis
The graph is exponential and is verified at right. (In this case, the difference pattern was exactly the same as the y-values. This is not always necessary.) ... Answers 1. linear 2. exponential 3. quadratic 4. linear 5. linear 6. quadratic 7. exponential 8. exponential 9. quadratic 10. linear 11. exponential 12. neither 13. ...
Worksheet 3: Exponents Grade 8 Mathematics - Maths At Sharp
Worksheet 3: Exponents Grade 8 Mathematics 1. Label the letters a, b and c in the diagram below: 2. Find the answers for each of these – do not use your calculator:
Equations with exponents - K5 Learning
Answers 1) 0 2) 171 3) 0 4) 89 5) 22 6) 1144 7) 57 8) 319 9) 0 10) 36 11) 1 22 12) 169. Title: Grade 6 Exponents Worksheet - Equations with exponents Author: K5 Learning Subject: Grade 6 Exponents Worksheet Keywords: Grade 6 Exponents Worksheet - Equations with exponents math practice printable elementary school
Worksheet: Logarithmic Function - Department of Mathematics
Vanier College Sec V Mathematics Department of Mathematics 201-015-50 Worksheet: Logarithmic Function 1. Find the value of y. (1) log 5 25 = y (2) log 3 1 = y (3) log 16 4 = y (4) log 2 1 8 = y (5) log
Homework #9-6: Exponential Modeling - Denton ISD
Pre-AP Algebra 2 Unit 9 - Lesson 6 – Exponential Modeling Objectives: Students will be able to model word problems with exponential functions and use logs to solve exponential models. Materials: Hw #9-5 answers overhead; quiz #2; pair work and answer overhead; board collaborations; hw #9-6 Time Activity 5 min Check Homework Put the answers to hw #9-5 on …
AP Calculus AB Unit 11: Differential Equations - Santa Ana …
AP Calculus AB - Worksheet 95 Solving Differential Equations – Separation of Variables Solve each differential equation by using separation of variables. 1. dy xy2 dx 2. 9 dy y dx 3. cos dy yx dx 4. 2 dy x dx Use separation of variables to find the solution to the initial value problem. Indicate the domain over which the solution is valid 5 ...
4.5B Solving Exponential and Logarithmic Equations Date ...
Worksheet by Kuta Software LLC Algebra 2 4.5B Solving Exponential and Logarithmic Equations Name_____ Date_____ Period____ ©F u2a0o1R8Q lKFuFttas [SEo_fPtjwXaGrFeu JLaLFCM.V E WAvlulA CrRiDgzhMtosp nrPe`sVeDrnv`eSde. Solve each equation. Round your answers to the nearest thousandth. 1) 16-n = 64 2) 53 - 2k = 1 125
DOMAIN AND RANGE OF EXPONENTIAL FUNCTIONS
© Cosenza & Associates, LLC EXPONENTIAL FUNCTIONS AND EQUATIONS 185 EXAMPLE 3:c " c!+ *"c) c c* +-c) c 1*)( (-# &c .( -#)(c#c#,c,")0(Ic 1 1 1 1 1 1 1 1 1 1 ï
5.2D Exponential Word Problems - Mrs. Crumpley Math Tutoring
5.2D Exponential Word Problems Name_____ Date_____ Period____ ©i v2g0W1m7e HKCuZtma` IS[oyfUtewLaIr^e^ [LCLACd.n P ZAtlMlQ trMilg_hWttsv wrCeHsXeyrlveeydf. ... Worksheet by Kuta Software LLC-2-Expontential Decay: 5) The groundskeeper of a local high school estimates that due to heavy usage by the baseball and softball teams, the pitcher's
5.5 Solving Exponential and Logarithmic Equations - Big Ideas …
Section 5.5 Solving Exponential and Logarithmic Equations 281 Solving Exponential and Logarithmic Equations Work with a partner. Match each equation with the graph of its related system of equations. Explain your reasoning. Then use the graph to solve the equation. a. e x = 2 b. ln x = −1 c. 2x = 3−x d. log 4 x = 1 e. log 5 x = 1 — 2 f ...
Name: GCSE (1 – 9) Trig and Exponential Graphs - Maths Genie
Trig and Exponential Graphs Name: _____ Instructions • Use black ink or ball-point pen. • Answer all questions. • Answer the questions in the spaces provided – there may be more space than you need. • Diagrams are NOT accurately drawn, unless otherwise indicated. • You must show all your working out. Information
Logarithmic Equations Date Period - Kuta Software
©d 92f0 p1t2 x uK7uUtoar 7S3oIf2tEw 0a Tr1e P uLcLMC6. t Y WAml7lr krBi Ogsh ctMsT aroeNsyeyr ev0e YdV.a I uM Na bdMer Mw7i Otnh T pITnwfli4nri ct0e T LAlsgZe 2b Xr6aj O2 T.z Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Logarithmic Equations Date_____ Period____
General Mathematics - DepEd Tambayan
1. distinguish exponential function, exponential equation, and exponential inequality; and 2. formulate own examples of exponential functions, equations, and inequalities. What I Know Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper. 1.
Name: MATH MONKS Properties of Exponents: Practice Worksheet …
Properties of Exponents: Practice Worksheet ... Answers 5a2y(2a4y-3) 1 Oa6 2x3y-3 . 2x-ly3 4x2 3x3y-lz- xyz . Created Date: 20220715083824Z ...
9.1 Graphing Exponential Functions - Allegany-Limestone High …
Worksheet by Kuta Software LLC Intermediate Algebra 9.1 Graphing Exponential Functions ... Create a table of values for each exponential function. Then sketch the graph of each function. 1) f (x) = (1 2) x x y-6-4-2246 2 4 6 8 10 12 14 16 18 20 2) f (x) = 2x x y-6-4-2246 2 4 6 8 10 12 14 16 18 20 3) f (x) = 4x x y-6-4-2246 2 4 6 8 10 12 14 16 18 20
CAMI Mathematics: :: : Grade 11 - camiweb.com
GRADE 11_Exponential equations GRADE 11_Exponential equations 11.4 Exponential equations11.4 Exponential equations 1. Solve the following1. Solve the following equations equations equations (a) 4y =1 (b) 625 1 25 x = (c) 8 1 16 p = (d) 32 z =4 (e) 5.25 d =3125 2. Solve the following equations 2. Solve the following equations
Solving Exponential Equations w-same Base - hasdk12.org
I 3 oM1a Od8ei 2wdiEtYhr EIQnWfji En JiZtMek PAKl4gie CbBrYae K2l. Q Worksheet by Kuta Software LLC ... ZMmahdce 1 CwciqtZh 8 aIunZf PiTnyi pt wez xA8l HgPe mbbrIa 0 W2H.l Worksheet by Kuta Software LLC Answers to Assignment (ID: 1) 1 ... {1 2} 10) { All real numbers. } Title Solving Exponential Equations w-same Base Author: Jeffco Created Date ...
Exponential Functions: Applications & Graphs - WordPress.com
Worksheet by Kuta Software LLC Algebra 1 - Mr. Allen-Black & Mrs. Gulamali Exponential Functions: Applications & Graphs Name_____ Date_____ Period____ ©\ F2W0N2w1` eK`ubtpas lSaovfhtqwLahrLeG vLyLQCW.] L wA^lYlx QroiAg]hjtZsr Arce_sDewrwvmegdZ.-1- 1) In order to control plant eating insects, Mr. Wilson released 17 ladybugs in the DA Sculpture ...
Chapter 3 Indices and surds Worksheet A - Math Seven
4 Simplify the following and express your answers using positive indices.
Infinite Algebra 2 - Extra Practice Rational Exponents & Radical ...
Worksheet by Kuta Software LLC Algebra 2 Extra Practice Rational Exponents & Radical Expressions Name_____ ID: 1 ©e Y2d0T1O7J RK`uPtvaN hScoAfstAwoaBrpeL zLTLoCX._ d KAYl_lZ UrLiFgPh]tesX Arne^speBrfv\e_dE.-1-Write each expression in exponential form. 1) 3 3n 2) 3 2a 3) (4 b) 5 4) 6 n2 5) (3 6k) 2 6) (2p) 5 7) (5 3n) 7 8) 6 10n2
9.8 Compare Linear, Exponential, and Quadratic Models
x y 2 1 EXAMPLE 3 Write an equation for a function Tell whether the table of values represents a linear function, an exponential function, or a quadratic function.Then write an equation for the function. x 22 21 012 y 2 0.5 0 0.5 2 Solution STEP 1 Determine which type of function the table of values represents. First differences: 21.5 20.5 0.5 1.5 Second differences: 1 1 1
Transformations of Exponential Functions - Worksheet
Transformations of Exponential Functions - Worksheet 1. Graph each set of functions on the same axes by applying the appropriate transformations. a) b) 2. For each transformation below, state the base (parent) function and then describe the transformations in the order in …
Solving Exponential Equations - Big Ideas Learning
332 Chapter 6 Exponential Functions and Sequences SELF-ASSESSMENT 1 I do not understand. 2 I can do it with help. 3 I can do it on my own. 4 I can teach someone else. EXAMPLE 1 Solving Exponential Equations with the Same Base Solve each equation. a. 3x + 1 = 35 b. 6 = 62x − 3 c. 103x = 102x + 3 SOLUTION a. 3x + 1 = 35 Write the equation. x + 1 = 5 …
Exponential Growth and DecayWorksheet - Coppin Academy …
12 Feb 2018 · ANSWER KEY 1. A. Exponential Growth B. 1200 C. 0.3 or 30% 2. A. Exponential Decay B. 55 C. 0.02 or 2% 3. A. Exponential Growth B. 100 C. 0.25 or 25% 4. A. Exponential Decay B. 5575 C. 0.35 or 35% 5. A. Exponential Growth B. 2000 C. 0.05 or 5% 6. A. Exponential Decay B. 14000 C. 0.08 or 8% 7. A. Exponential Decay B. 2250 C. 0.9or 90% 8. A. …
Worksheet 3: Functions – Exponential and Logarithmic
9. Study the functions and their inverses in question 8. What do you notice about: a) when and where the graphs intersect? b) the domain and range of the function and inverse function.
Infinite Algebra 2 - Exponential Functions - DeKalb County …
Worksheet by Kuta Software LLC Algebra 2 Exponential Functions Name_____ Date_____ ©\ b2Y0u1\7d WKuuNtHaZ fS]okfttdwlaurbef JLML[C].h L EAalOle qrqihg\hQtssd XrmeCspewrAvnehdO.-1-Simplify. Product and power. Keep the same base and include the exponent. 1) 30 × 33 × 32 2) 22 × 23 3) 2 × 23 × 22 4) 9 × 30 5) (23) 3
Exponential Functions - Pathway
Section 6.3 Exponential Functions 307 STUDY TIP The graph of y = abx approaches the x-axis but never intersects it. Graphing Exponential Functions The graph of a function y = abx is a vertical stretch or shrink by a factor of ∣ a ∣ of the graph of the parent function y = bx.When a < 0, the graph is also refl ected in the x-axis.The y-intercept of the graph of y = abx is a.
4.5 Solving Exponential Equations using Logarithms
Worksheet by Kuta Software LLC-2-Solve each equation. Round your answers to the nearest ten-thousandth. 12) ... Answers to 4.5 Solving Exponential Equations using Logarithms 1) 2) log183) log574) ln32 5) ln816) log 8 897) log 14 59 8) log 8 26 8 9) log 2 58 9 + 710) …
Exponential and Logarithms IB Exam Practice Questions
2 5. Let f(x) = log 3 x, for x > 0. (a) Show that f–1(x) = 32x. (2) (b) Write down the range of f–1. (1) Let g(x) = log 3 x, for x > 0. (c) Find the value of (f –1 ° g)(2), giving your answer as an integer.(4) (Total 7 marks) 6. The number of bacteria, n, in a dish, after t minutes is given by n = 800e013t. (a) Find the value of n when t = 0. (2)
Exponential Growth and Decay - Kuta Software
Worksheet by Kuta Software LLC Kuta Software - Infinite Calculus Exponential Growth and Decay Name_____ Date_____ Period____ Solve each exponential growth/decay problem. 1) For a period of time, an island's population grows at a rate proportional to its population. If the growth rate is 3.8% per year and the current population is 1543, ...
1 EXPLORATION: Solving an Exponential Equation Graphically
Property of Equality for Exponential Equations Words Two powers with the same positive base b, where b ≠ 1,are equal if and only if their exponents are equal. Numbers If 2 2,x = 5 then x = 5. If x = 5, then 2 2.x = 5 Algebra If b > 0 and b ≠ 1, then bbx = y …
Matching Exponential Graphs and Equations - Mrs. PEASE
Microsoft Word - Matching Exponential Graphs and Equations.docx Created Date: 20141109213328Z ...
Worksheet 5: Exponents Grade 9 Mathematics - Maths At Sharp
www.mathsatsharp.co.za Worksheet 5: Exponents Grade 9 Mathematics 1. Represent the following expressions in exponential form a) b) c)
3.4 Solving Exponential and Logarithmic Equations Date ...
Worksheet by Kuta Software LLC Pre-Calculus 3.4 Solving Exponential and Logarithmic Equations Name_____ ID: 1 Date_____ Period____ ©w K2Q0W1J6S nKmuDtfaR mSlogfotHw\adrPe] LLiLOCf.] p CA]lQlr PrsixgBhRtBsp arBefsDehrlv_eHdt. ... Answers to 3.4 Solving Exponential and Logarithmic Equations (ID: 1) 1) {-4 5} 2) No solution. 3) {3 4} 4) {15 14}
Rational Exponent Equations - Kuta Software
©8 I2J0 n1T1 m WKJujt zak 7SKoDfxtIw6arde F 8LILrCe. n T eAFlJlE nrZi8gOhot PsA xr oecsveAr Ev 3eNdm.6 W WMoaRd8ej CwYigtoho HIYnhfLiNn0i0tLe 9 0AZlAgSecb tr XaH W2I. 7 Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Rational Exponent Equations Date_____ Period____
Sec 4.5 – Describing Characteristics of Exponential Functions …
3. )Create 3 different exponential functions of the form B( T= = ë+ > that have a range of y > 2. 4. Find the average rate of change of the function B( T) = 3 ë−2 from x = 1 to x = 2. 5. (Find the average rate of change of the function B T) = @ 5 6 A ë …
8.7 Solving Natural Log Equations - MS. HUGHES
Worksheet by Kuta Software LLC Algebra 2 8.7 Solving Natural Log Equations ... Round your answers to the nearest thousandth. 23) -8e-p = -4924) 2e8x = 45 25) ... 8.7 Solving Natural Log Equations Name_____ ©y a2V0`1x5g JKJuitQa[ CSkoNfitDwTaErpeV gL]LSCH.g N WA_l[lU Mr\iigBhztPs` RrleKsReGruvFeSdR. ...
Chapter 10: Exponential and Logarithmic Relations - math24seven
• Solve logarithmic equations using the properties of logarithms. Common Logarithms(pp. 547–553) 1 1 0.5 0.5 • Solve exponential equations and inequalities using common logarithms. • Evaluate logarithmic expressions using the Change of Base Formula. Follow-Up: Solving Exponential and Logarithmic Equations and Inequalities
Equations with exponents - K5 Learning
Answers 1) 176 2) 64 3) 4 4) 97 5) −87 6) 0 7) 11 8) −125 9) 81 10) 49 11) 9 12) 1 32. Title: Grade 6 Exponents Worksheet - Equations with exponents Author: K5 Learning Subject: Grade 6 Exponents Worksheet Keywords: Grade 6 Exponents Worksheet - Equations with exponents math practice printable elementary school
