Mathematics Science A Student And Family Guide To Grade 10
GRADEGRADESTUDY GUIDEMathematics ScienceTexas Education AgencyTX00000163A Student and Family Guide to Grade 10Mathematics Science
Gr10 Math/Science Guide4/22/038:25 AMTexas AssessmentPage 1STUDY GUIDETexas Assessment of Knowledge and SkillsGrade 10Mathematics and ScienceA Student and Fa mily GuideCopyright 2003, Texas Education Agency. All rights reserved. Reproduction of all or portions of this work is prohibitedwithout express written permission from Texas Education Agency.
Gr10 Math/Science Guide4/22/038:26 AMPage 2Cover photo credits: Top left Jose Luis Pelaez, Inc./CORBIS; Top right Marc Asnin/CORBIS SABA;Bottom right Jose Luis Pelaez, Inc./CORBIS; Bottom left Ariel Skelley/CORBIS.
Gr10 Math/Science Guide4/22/038:26 AMPage 3A Letter from the Associate Commissioner of EducationDear Student and Parent:The Texas Assessment of Knowledge and Skills (TAKS) is a comprehensive testingprogram for public school students in grades 3–11. TAKS replaces the Texas Assessmentof Academic Skills (TAAS) and is designed to measure to what extent a student haslearned, understood, and is able to apply the important concepts and skills expectedat each tested grade level. In addition, the test can provide valuable feedback tostudents, parents, and schools about student progress from grade to grade.Students are tested in mathematics in grades 3–11; reading in grades 3–9; writing ingrades 4 and 7; English language arts in grades 10 and 11; science in grades 5, 10, and11; and social studies in grades 8, 10, and 11. Every TAKS test is directly linked to theTexas Essential Knowledge and Skills (TEKS) curriculum. The TEKS is the statemandated curriculum for Texas public school students. Essential knowledgeand skills taught at each grade build upon the material learned in previous grades.By developing the academic skills specified in the TEKS, students can build a strongfoundation for future success.The Texas Education Agency has developed this study guide to help studentsstrengthen the TEKS-based skills that are taught in class and tested on TAKS. Theguide is designed for students to use on their own or for students and families towork through together. Concepts are presented in a variety of ways that will helpstudents review the information and skills they need to be successful on TAKS. Everyguide includes explanations, practice questions, detailed answer keys, and studentactivities. At the end of this book is an evaluation form for you to complete and mailback when you have finished the guide. Your comments will help us improve futureversions of this guide.There are a number of resources available for students and families who would likemore information about the TAKS testing program. Information booklets are availablefor every TAKS subject and grade. Brochures are also available that explain the StudentSuccess Initiative promotion requirements and the new graduation requirements foreleventh-grade students. To obtain copies of these resources or to learn more aboutthe testing program, please contact your school or visit the Texas Education Agencywebsite at www.tea.state.tx.us.Texas is proud of the progress our students have made as they strive to reach theiracademic goals. We hope the study guides will help foster student learning, growth,and success in all of the TAKS subject areas.Sincerely,Ann SmiskoAssociate CommissionerCurriculum, Assessment, and TechnologyTexas Education Agency3
Gr10 Math/Science Guide4/22/038:26 AMPage 4ContentsMathematicsIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Mathematics Chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Objective 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Objective 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Objective 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Objective 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106Objective 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130Objective 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147Objective 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158Objective 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180Objective 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201Objective 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220Mathematics Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . 2244
Gr10 Math/Science Guide4/22/038:26 AMPage 5ContentsScienceIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245Objective 1: The Nature of ScienceSkill Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260Objective 2: The Organization of Living SystemsSkill Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276Objective 3: The Interdependence of Organisms and theEnvironmentSkill Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286Objective 4: The Structures and Properties of MatterSkill Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303Objective 5: Motion, Forces, and EnergySkill Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306Practice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321Science Cluster Practice QuestionsCluster 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324Cluster 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326Science ActivityThe Floating Rubber Band: A Scientific Trick . . . . . . . . . . . . . 328Science Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3335
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Gr10 Math/Science Guide4/22/038:27 AMPage 7Each objective is organized into review sectionsand a practice section. The review sectionspresent examples and explanations of themathematics skills for each objective. Thepractice sections feature mathematics problemsthat are similar to the ones used on the TAKStest.What Is This Book?This is a study guide to help you strengthen theskills tested on the Grade 10 Texas Assessment ofKnowledge and Skills (TAKS). TAKS is a statedeveloped test administered with no time limit.It is designed to provide an accurate measure oflearning in Texas schools.By acquiring all the skills taught in tenth grade,you will be better prepared to succeed on theGrade 10 TAKS test and during the next schoolyear. This study guide is organized into twosections. This section is about mathematics.How Can I Use This Book?First look at your Confidential Student Report.This is the report the school gave you thatshows your TAKS scores. This report will tellyou which TAKS subject-area test(s) you passedand which one(s) you did not pass. Use yourreport to determine which skills needimprovement. Once you know which skillsneed to be improved, you can read through theinstructions and examples that support thoseskills. You may also choose to work through allthe sections. Pace yourself as you work throughthe study guide. Work in short sessions. If youbecome frustrated, stop and start again later.What Are Objectives?Objectives are goals for the knowledge and skillsthat you should achieve. The specific goals forinstruction in Texas schools were provided bythe Texas Essential Knowledge and Skills (TEKS).The objectives for TAKS were developed basedon the TEKS.How Is the Mathematics SectionOrganized?The mathematics section of this study guide isdivided into the ten objectives tested on TAKS.A statement at the beginning of each objectivelists the mathematics skills you need to acquire.The study guide covers a large amount ofmaterial. You should not expect to complete itall at once. It may be best to work through oneobjective at a time.7MATHEMATICSM AT H E M AT I C S
MATHEMATICSGr10 Math/Science Guide4/22/038:27 AMPage 8What Are the Helpful Features of theMathematics Section? There are several words in the mathematicssection that are important for you tounderstand. These words are boldfaced inthe text and are defined when they areintroduced. Locate the boldfaced wordsand review the definitions. Examples are contained inside shadedboxes. Each objective has “Try It” problemsbased on the examples in the reviewsections. A Mathematics Chart for the Grade 10TAKS test is included on pages 10–11and also as a tear-out page in the backof the book. This chart includes usefulmathematics information. The tear-outMathematics Chart in the back of thebook also provides both a metric and acustomary ruler to help solve problemsrequiring measurement of length.Look for the following features in themargin:Ms. Mathematics provides importantinstructional information for a topic.Do you see that . . .points to asignificantsentence inthe instruction.How Should the “Try It” Problems BeUsed?“Try It” problems are found throughout thereview sections of the mathematics study guide.These problems provide an opportunity for youto practice skills that have just been covered inthe instruction. Each “Try It” problem featureslines for your responses. The answers to the “TryIt” problems are found immediately followingeach problem.Calculatorsuggests thatusing a graphingcalculator mightbe helpful.While completing a “Try It” problem, cover upthe answer portion with a sheet of paper. Thencheck the answer.Memoprovides pagereferences in thisstudy guide foradditionalinformation.8
Gr10 Math/Science Guide4/22/038:27 AMPage 9The mathematics study guide contains questionssimilar to those found on the Grade 10 TAKStest. There are two types of questions in themathematics section. Multiple-Choice Questions: Most of thepractice questions are multiple choicewith four answer choices. These questionspresent a mathematics problem usingnumbers, symbols, words, a table, adiagram, or a combination of these. Readeach problem carefully. If there is a tableor diagram, study it. You should read eachanswer choice carefully before choosingthe best answer.Griddable Questions: Some practicequestions use an eight-column answergrid like those used on the Grade 10TAKS 5556666666777777788888889999999Where Can Correct Answers to thePractice Questions Be Found?The answers to the practice questions are inthe answer key at the back of the mathematicssection (pages 224–244). Each question includesa reference to the page number in the answerkey for the answer to the problem. The answerkey explains the correct answer, and it alsoincludes some explanations for incorrectanswers. After you answer the practicequestions, you can check your answers.How Do You Use an Answer Grid?The answer grid contains eight columns, whichinclude three decimal places: tenths, hundredths,and thousandths.Suppose 5708.61 is the answer to a problem.First write the number in the blank spaces. Besure to use the correct place value. For example,5 is in the thousands place, 7 is in the hundredsplace, 0 is in the tens place, 8 is in the onesplace, 6 is in the tenths place, and 1 is in thehundredths place.If you still do not understand the correct answerafter reading the answer explanations, ask afriend, family member, or teacher for help. Evenif you have chosen the correct answer, it is agood idea to read the answer explanationbecause it may help you better understand whythe answer is correct.Then fill in the correct bubble under each digit.Notice that if there is a zero in the answer, youneed to fill in the bubble for the zero.9MATHEMATICSThe grid shows 5708.61 correctly entered. Thezero in the tens place is bubbled in because it ispart of the answer. It is not necessary to bubblein the zero in the thousandths place, becausethis zero will not affect the value of the correctanswer.What Kinds of Practice Questions Are inthe Study Guide?
MATHEMATICSGr10 Math/Science Guide4/22/038:27 AMPage 10Grades 9, 10, and 11 Exit LevelMathematics ChartLENGTHMetricCustomary1 kilometer 1000 meters1 mile 1760 yards1 meter 100 centimeters1 mile 5280 feet1 centimeter 10 millimeters1 yard 3 feet1 foot 12 inchesCAPACITY AND VOLUMEMetricCustomary1 liter 1000 milliliters1 gallon 4 quarts1 gallon 128 ounces1 quart 2 pints1 pint 2 cups1 cup 8 ouncesMASS AND WEIGHTMetricCustomary1 kilogram 1000 grams1 ton 2000 pounds1 gram 1000 milligrams1 pound 16 ouncesTIME1 year 365 days1 year 12 months1 year 52 weeks1 week 7 days1 day 24 hours1 hour 60 minutes1 minute 60 secondsMetric and customary rulers can be found on the tear-out MathematicsChart in the back of this book.10
Gr10 Math/Science Guide4/22/038:27 AMPage 11PerimeterrectangleP 2l 2worCircumferencecircleC 2πrC πdArearectangleA lwtriangleA 2 bhoror112A circleA πr 2Surface Areacubecylinder (lateral)cylinder (total)cone (lateral)cone (total)sphereSSSSSSVolumeprism or cylinderV Bh*pyramid or coneV 3 Bh*sphereV 4 πr 3 A bhA bhor2(b1 b2)htrapezoidP 2(l w)orA 13π 3.14πor22π 7Pythagorean Theorema2 b2 c2Distance Formulad (x2 x1) 2 (y2 y1) 2Slope of a Liney2 y1m x x21Midpoint FormulaM Quadratic Formula2x b b 4ac2aSlope-Intercept Form of an Equationy mx bPoint-Slope Form of an Equationy y1 m(x x1)Standard Form of an EquationAx By CSimple Interest FormulaI prt1126s 22πrh2πrh 2πr 2 or S 2πr(h r)πrlπrl πr 2 or S πr(l r)4πr 2*B represents the area of the Base of a solid figure.Pi(b1 b2)hx1 x22(,y1 y22)MATHEMATICSGrades 9, 10, and 11 Exit Level Mathematics Chart
Gr10 Math/Science Guide4/22/038:27 AMPage 12MATHEMATICSObjective 1The student will describe functional relationships in a variety of ways.For this objective you should be able to recognize that a functionrepresents a dependence of one quantity on another and can bedescribed in a number of ways.What Is a Function?A function is a set of ordered pairs (x, y) in which each x-coordinate ispaired with only one y-coordinate. In a list of ordered pairs belongingto a function, no x-coordinate is repeated.When people eat at a restaurant, they often use a tip chart todetermine the amount of the tip to leave the server. A tip chartis a good example of a function.Tip ChartCostRecommendedof MealTip 5.00 1.00 6.00 1.20 7.00 1.40 8.00 1.60 9.00 1.80 10.00 2.00On the tip chart above, each meal cost listed has exactly onerecommended tip listed. Since the amount of the tip depends onhow much the meal costs, the recommended tip is a functionof the cost of the meal.In a functional relationship, for any given input there is a uniqueoutput.InputvaluexFunctiony OutputvalueInput an x-value andyou get a y-value.If you are given an x-value belonging to a function, you can find thecorresponding y-value.Do you seethat . . .If you input 5.00 into the above function, the output will be 1.00.12
Gr10 Math/Science Guide4/22/038:27 AMPage 13There are two ways to test a set of ordered pairs to see whether it is afunction.Examine the list of ordered pairs.If a set of ordered pairs is a function, no x-coordinate in the set isrepeated. No x-coordinate should be listed with two differenty-coordinates.Is this set of ordered pairs a function?{(1, 4), (5, 7), ( 1, 7), (10, 12)}Examine the set of ordered pairs. None of the x-coordinates in the set are repeated. Two ordered pairs, (5, 7) and ( 1, 7), have the samey-coordinate but different x-coordinates. This does not preventthis set of ordered pairs from being a functional relationship.This set of ordered pairs is a function.Is this set of ordered pairs a function?{(–2, 5), (0, 7), (1, 4), (–2, 6)} The number –2 is paired with 5; 0 is paired with 7; 1 is pairedwith 4; and –2 is paired with 6. Two ordered pairs, (–2, 5) and (–2, 6), have the samex-coordinate. In a functional relationship, no x-coordinateshould repeat.This set of ordered pairs is not a function.Examine a graph of the function.Use a vertical line to determine whether two points have the samex-coordinate. If two points in the function lie on the same vertical line,then they have the same x-coordinate, and the set of ordered pairs isnot a function.13Do you seethat . . .MATHEMATICSObjective 1
MATHEMATICSGr10 Math/Science Guide4/22/038:27 AMPage 14Objective 1Do the ordered pairs graphed below represent a function?y987654321–9 –8 –7 –6 –5 –4 –3 –2 9The ordered pairs (2, 5) and (2, 7) lie on a common vertical line.They have the same x-coordinate, 2, but different y-coordinates, 5and 7.This graph does not represent a function because two points lie onthe same vertical line.In a function, the y-coordinate is described in terms of the x-coordinate.The value of the y-coordinate depends on the value of the x-coordinate.Suppose the number of miles you walk is equal to 4 times thenumber of hours you walk. Which is the dependent quantity inthis function?If you walked for 1 hour, you would have walked 4 miles.If you walked for 3 hours, you would have walked 12 miles.The distance you walk depends on, or is described in terms of, thenumber of hours you walk.Do you seethat . . .In this function, the number of hours you walk is the independentquantity. The distance you walk is the dependent quantity.An equation that describes this function is d 4h, whered represents the number of miles you walk, and h represents thenumber of hours. In this equation, d, the distance you walk,depends on h, the number of hours you walk. The variable h is the independent variable. The variable d is the dependent variable. The number 4 is a constant, a quantity in an equation that doesnot change.14
Gr10 Math/Science Guide4/22/038:27 AMPage 15Suppose the equation c 0.07m 0.25 describes c, the cost of aphone call, in terms of m, the number of minutes the phone calllasts.In this function, c is the dependent variable, m is the independentvariable, and 0.07 and 0.25 are constants.Jeremy works at an appliance store. He is paid 180.00 a week forhis base salary plus a commission equal to 5% of his total sales.The equation s 180 0.05d represents Jeremy’s weekly salary,s, in terms of d, his total weekly sales in dollars.Which variable is the dependent variable in this equation? Whatare the constants? Jeremy’s weekly salary, s, is the dependent quantity because itdepends on d, his total sales. The constants are 180, Jeremy’s base salary, and 0.05,his commission, because these numbers do not change.Try ItCara buys milk for her scout camp
grades 4 and 7; English language arts in grades 10 and 11; science in grades 5, 10, and 11; and social studies in grades 8, 10, and 11. Every TAKS test is directly linked to the Texas Essential Knowledge and Skills (TEKS) curriculum. The TEKS is the state-mandated curricu
IBDP MATHEMATICS: ANALYSIS AND APPROACHES SYLLABUS SL 1.1 11 General SL 1.2 11 Mathematics SL 1.3 11 Mathematics SL 1.4 11 General 11 Mathematics 12 General SL 1.5 11 Mathematics SL 1.6 11 Mathematic12 Specialist SL 1.7 11 Mathematic* Not change of base SL 1.8 11 Mathematics SL 1.9 11 Mathematics AHL 1.10 11 Mathematic* only partially AHL 1.11 Not covered AHL 1.12 11 Mathematics AHL 1.13 12 .
as HSC Year courses: (in increasing order of difficulty) Mathematics General 1 (CEC), Mathematics General 2, Mathematics (‘2 Unit’), Mathematics Extension 1, and Mathematics Extension 2. Students of the two Mathematics General pathways study the preliminary course, Preliminary Mathematics General, followed by either the HSC Mathematics .
2. 3-4 Philosophy of Mathematics 1. Ontology of mathematics 2. Epistemology of mathematics 3. Axiology of mathematics 3. 5-6 The Foundation of Mathematics 1. Ontological foundation of mathematics 2. Epistemological foundation of mathematics 4. 7-8 Ideology of Mathematics Education 1. Industrial Trainer 2. Technological Pragmatics 3.
GENERAL MATHEMATICS Subject General Mathematics Credit value 3 credits Prerequisites SSC Mathematics Course Description This course is designed to prepare Student Teachers for teaching mathematics in elementary grades. It provides opportunities for Student Teachers to strengthen their mathematical knowledge and skills and to gain confidence in .
o Grade 4: Reading and Mathematics. o Grade 5: Reading, Mathematics and Science. o Grade 6: Reading and Mathematics. o Grade 7: Reading and Mathematics. o Grade 8: Reading, Mathematics and Science. Grades 10-12 Ohio Graduation Tests Grade 10 March 12-25, 2012: Ohio Graduation Tests in reading, mathematics, wri
3rd Grade 4th Grade 5th Grade Mathematics Reading Mathematics Reading Mathematics Reading Science 100.0% 95.5% 95.9% 98.6% 96.6% 96.6% 96.6% 6th Grade 7th Grade 8th Grade Mathematics Reading Mathematics Reading Mathematics Science 95.6% 100.0% 97.0% 98.5% 98.6% 97.2% 94.4% Grades 3-5 Grade
Introduction to Science Section 2 The Branches of Science, continued The branches of science work together. -biological science: the science of living things botany, ecology -physical science: the science of matter and energy chemistry: the science of matter and its changes physics: the science of forces and energy -earth science: the science of the Earth, the
This handbook supplement applies to students entering the fourth year of their degree in Computer Science, Mathematics & Computer Science or Computer Science . Undergraduate Course Handbook 1.2 Mathematics & Computer Science The Department of Computer Science offers the following joint degrees with the Department of Mathematics: BA .
