Code: MATH 151 Title: INTERMEDIATE ALGEBRA

Transcription

1 Cde: MATH 151 Title: INTERMEDIATE ALGEBRA Divisin: MATHEMATICS Department: MATHEMATICS Curse Descriptin: This curse prepares students fr curses that require algebraic skills beynd thse taught in Elementary Algebra. Tpics include equatins, inequalities, linear systems in tw and three variables, cmplex numbers, and applicatins f functins: linear, expnential, lgarithmic, quadratic, plynmial, ratinal, and radical. In additin, the curse prvides a basic intrductin t right triangle trignmetry. Prblems are apprached frm a variety f perspectives, including graphical, numerical, verbal, and algebraic. A graphing calculatr is required; the specific mdel is determined by the department. Prerequisites: MATH 022 (Algebra Skills) r MATH 025 (Elementary Algebra) r satisfactry cmpletin f the cllege s basic skills requirement in algebra Credits: 4 Lecture Hurs: 4 Lab/Studi Hurs: 0 REQUIRED TEXTBOOK/MATERIALS: 1. Textbk: Rckswld, Gary and Krieger, Terry, Intermediate Algebra with Applicatins and Visualizatin, Third Editin, Pearsn Addisn Wesley, Supplement: Rckswld, Gary, Algebra and Trignmetry with Mdeling and Visualizatin, Trignmetry Supplement fr Brkdale Cmmunity Cllege, custm available in the Brkdale Cllege Bkstre. Nte: MathXL will be required fr nline hmewrk in sme sectins. Check with yur instructr. The Cllege bkstre sells the textbk in a bundle which includes a MathXL access cde and the Trignmetry Supplement. 3. Graphing Calculatr: The calculatr fr this curse is the TI-83 (any versin) r TI-84 (any versin). The use f any ther calculatr shuld be discussed with the instructr. The TI-89 and TI-92 may nt be used fr testing. RECOMMENDED MATERIALS: Optinal: Slutins Manual fr the text ADDITIONAL TIME REQUIREMENTS: OTHER TIME COMMITMENTS: In additin t the regular class hurs, yu will need t set aside time each week fr hmewrk. The weekly time will vary by tpic and level f difficulty, but as an estimate, yu shuld expect tw hmewrk hurs fr each class hur per week. Fr example, if yur class meets fr fur hurs per week, yu shuld expect t spend abut eight hurs per week n hmewrk. If yu are having any difficulty with the curse material, yu may need t allw time t see yur instructr during ffice hurs r t get help in the Math Lab. Page 1 f 7

2 COURSE LEARNING OUTCOMES: Upn cmpletin f this curse, students will be able t: Demnstrate the mathematical skills apprpriate t this curse. (M) Identify and characterize the fllwing functins: linear, expnential, lgarithmic, quadratic, ratinal, and radical by interpreting verbal, graphical, numerical, and symblic representatins. (M) Use the apprpriate functin mdel t analyze and slve applicatin prblems. (M) Interpret slutins in the cntext f the prblem. (M) Use a graphing calculatr t understand cncepts and t explre and slve prblems. (M) Learning Outcme(s) supprt the fllwing General Educatin Knwledge Areas: (M) Mathematics GRADING STANDARD: In this curse, yu will be evaluated by means f tests, quizzes, labs, and pssibly hmewrk. A. TESTS There will be fur tests, ne after each unit. Each test cnsists f tw parts: a nncalculatr part and a graphing calculatr part. Students may nt use any type f calculatr n the nn-calculatr parts f the fur tests. Tests will be cumulative. All supprting wrk must be shwn n tests in rder fr yur instructr t prperly assess yur understanding f the material. The tests will be given in class and it is expected that yu will be in class t take the test n the day it is given. If yu are very ill (verifiable with a dctr s nte) r yu have sme ther emergency, yu must cntact yur instructr immediately. B. LABS/QUIZZES/HOMEWORK There are labs in this curse t be cmpleted in class. They are dne in grups and may be assessed either individually r as a grup assignment. The activities cntain prblems that reinfrce the cncepts and skills learned in class. There are als peridic quizzes, and yur instructr may als chse t use hmewrk assignments fr evaluatin. GRADING Each test is graded n the basis f 100 pints. Yur final curse average is determined by a weighted average as fllws: Test 1 10% Test 2 20% Test 3 20% Test 4 25% Labs, Quizzes, Hmewrk 25% Page 2 f 7

3 FINAL GRADE Yur final grade is determined as fllws: If yur final curse average is Yur final grade is A A B B B C C D** Belw 60 F ** T use this curse as a prerequisite fr anther mathematics curse, yu must have a grade f C r better. Incmplete INC is nly given at the discretin f yur instructr. This may ccur in dcumented cases f hardship r emergency. In this case, yu must meet with the instructr t discuss the wrk that must be cmpleted t earn a grade in the curse. All wrk must be cmpleted within 21 days after the end f the term, exclusive f fficial cllege clsings. Withdrawal Yu may withdraw frm the curse, withut penalty, up t a date set by the Cllege. If yu d nt withdraw frm the curse but stp attending, yur grade at the end f the semester will be F. COURSE CONTENT: (TEXT SECTION) Unit 1: In this unit, yu will study functins, use functin ntatin, and study linear functins and systems f linear equatins (in tw and three variables) in depth. The unit cncludes with right triangle trignmetry. Unit 1 Outcmes: Yu will: Define a functin (2.1) Evaluate functins and use functin ntatin (2.1) Determine whether a graph r table represents a functin (2.1) Find slpes frm tables and graphs (2.2) Draw graphs f linear functins bth by hand and with the graphing calculatr (Chapter 2) Represent linear mdels symblically, graphically, and numerically. (2.3) Interpret the slpe as a rate in the cntext f a prblem situatin. (2.3) Slve applicatin prblems invlving linear functins. (Chapter 2) Interpret linear slutins in the cntext f the applicatin. (Chapter 2) Slve linear equatins graphically, numerically, and symblically. (3.1) Slve linear inequalities graphically, numerically, and symblically. (3.3) Slve cmpund inequalities graphically, numerically, and symblically (3.4) Slve abslute value equatins graphically, numerically, and symblically. (3.5) Page 3 f 7

4 Slve systems f tw linear equatins graphically, numerically, and symblically. (4.1) Slve applicatin prblems by setting up and slving a system f tw linear equatins. (4.1, 4.2) Slve systems f three linear equatins symblically. (4.5). Define straight, acute, btuse, and right angles. (TRIG SUPPLEMENT 1.1) Define radians, and cnvert between degrees and radians. (TRIG SUPPLEMENT 1.1) Review the Pythagrean Therem. (TRIG SUPPLEMENT R.1) Sketch an angle in standard psitin, and name c-terminal angles. (TRIG SUPPLEMENT 1.1) Define the six trignmetric ratis (sine, csine, tangent, ctangent, secant, and csecant) f an angle in a right triangle. (TRIG SUPPLEMENT 1.2) Develp and remember the tw special triangles ( and ) and their trignmetric ratis. (TRIG SUPPLEMENT 1.2) Slve trignmetric applicatin prblems using angles f elevatin and depressin invlving right triangles. (TRIG SUPPLEMENT 1.2) Interpret trignmetric slutins in the cntext f the prblem situatin. (TRIG SUPPLEMENT 1.2) Unit 2: In this unit, yu will study plynmial and ratinal expressins and functins. Yu will slve plynmial and ratinal equatins frm a variety f perspectives: graphically, numerically, and symblically. Unit 2 Outcmes: Yu will: Define a plynmial expressin and functin. (5.1) Add and subtract plynmial expressins. (5.1) Identify which functins are plynmial functins. (5.2) Evaluate plynmial functins graphically, numerically, and symblically. (5.1) Multiply plynmial expressins. (5.2) Factr plynmial expressins. (5.3, 5.4, 5.5) Slve plynmial equatins symblically, graphically, r numerically. (5.7) Slve applicatin prblems invlving plynmial functins, and interpret slutins in the cntext f the applicatin. (5.7) Define a ratinal expressin and a ratinal functin. (6.1) Define a vertical asymptte. (6.1) Determine the equatins f the vertical asympttes f a ratinal functin. (6.1) Multiply and divide ratinal expressins. (6.2) Add and subtract ratinal expressins. (6.3) Slve ratinal equatins graphically, numerically, and symblically. (6.4) Simplify cmplex fractins. (6.5) Analyze and slve applicatin prblems invlving ratinal functins and interpret the results in the cntext f the prblem. (6.1, 6.2, 6.5) Unit 3: In this unit, yu will study the prperties and applicatins f radical expressins and functins and quadratic functins. Yu will define cmplex numbers and perfrm calculatins with them. Page 4 f 7

5 Unit 3 Outcmes: Yu will: Define square rt and nth rt expressins. (7.1) Review the prperties f expnents. (7.1, 7.2) Simplify, add, subtract, multiply, and divide radical expressins. (7.2, 7.3) Define the square and cube rt functins, adding them t the library f functins. State their dmains and ranges. (7.4) Slve applicatin prblems that invlve square and cube rt functins. (7.4) Interpret the results f radical prblems in the cntext f the prblem situatin. (7.4) Slve equatins invlving radical expressins. (7.5) Define a cmplex number. (7.6) Add, subtract, multiply and divide cmplex numbers. (7.6) Recgnize the graphs f quadratic functins. (8.1) Write a quadratic functin in standard and vertex frm. (8.2) Use the terminlgy (vertex, axis f symmetry) related t graphs f quadratic functins. (8.2) Find the vertex and the equatin f the axis f symmetry f a quadratic functin. (8.2) Slve quadratic equatins using a variety f techniques (factring, square rt prperty, cmpleting the square, tables, and graphs). (8.2) State and use the quadratic frmula t slve quadratic equatins. (8.3) Use the discriminant t determine the number f real number slutins t a quadratic equatin. (8.3) Slve quadratic equatins that have nn-real slutins. (8.3) Mdel applicatin prblems with quadratic functins and slve the related equatins graphically, numerically, and symblically. (Chapter 8) Interpret the results f quadratic prblems in the cntext f the prblem situatin. (Chapter 8) Unit 4: In this unit, yu will study the prperties and applicatins f expnential and lgarithmic expressins and functins. Unit 4 Outcmes: Yu will: Define an expnential functin. (9.2) Determine whether a table culd represent a linear r an expnential functin (9.2) If a table represents an expnential functin, find the grwth r decay factr and write the functin rule. (9.2) Apply previusly studied cncepts (dmain, range) and new cncepts (hrizntal asymptte, grwth and decay) related t expnential functins. (9.2) Define a lgarithm. (9.3) Evaluate lgarithms with and withut a calculatr. (9.3) Apply previusly studied cncepts (dmain, range) and new cncepts (vertical asymptte) related t lgarithmic functins. (9.3) Use the prperties f lgarithms t simplify expressins. (9.4) Cnvert equatins between expnential frm and lgarithmic frm. (9.5) Slve expnential and lgarithmic equatins graphically, numerically, and symblically.(9.5) Mdel applicatin prblems with expnential r lgarithmic functins and slve the related equatins graphically, numerically, and symblically. (9.5) Interpret the results f expnential r lgarithmic prblems in the cntext f the prblem situatin. (9.5) Page 5 f 7

6 1/14 DEPARTMENT POLICIES: The Math Department wants yu t be successful in this curse. Because f this, we have cmpiled a list f strategies and behavirs. Attendance and class participatin If yu want t be successful in this curse, attend every class. Cme t class n time, and stay fr the entire class perid. If yu are late r leave during class, yu will miss imprtant class material and yu will als distract yur classmates and yur instructr. (See the Student Cnduct Cde) Turn ff yur cell phne during class. Yu and yur classmates need t be free frm distractins. (See the Student Cnduct Cde) Bring yur bk and calculatr t every class. Respect yur classmates and yur instructr. Listen carefully t questins asked and answers given. Treat all questins with respect. Participate fully in class. Vlunteer answers, wrk prblems, take careful ntes, and engage in discussins abut the material. Abve all, stay n task. Cntribute yur share f wrk t yur in-class grup wrk and d yur best t make the grup experience a psitive ne fr all members. D yur wn wrk n tests and quizzes. Cheating will nt be tlerated. (See the Academic Integrity Cde.) Hmewrk Hmewrk is the way yu practice the ideas and skills that are intrduced in class. T be successful n the tests, yu must d the hmewrk. Hmewrk may be cllected and hmewrk questins may be included n quizzes r tests. All the hmewrk assignments are listed n the unit hmewrk assignment sheets. Hmewrk may be nline (see Required Materials) and may be graded. When yu d the hmewrk, write dwn all supprting wrk. Using the crrect prcess is at least as imprtant as getting the crrect answer, s yur wrk and steps are very imprtant. Remember t check yur answers. They will be in the back f the text r in the student s slutins manual. If there are questins yu can t get r dn t understand, ask abut them at the beginning f the next class. If yu have truble with mre than a few prblems, try starting yur hmewrk in the Math Lab, where help is available. Absence If yu are sick and an absence is unavidable, please call r yur instructr. Yu are still respnsible fr all material that was cvered during yur absence. Yu are expected t read the textbk and d the hmewrk. Make time t see yur instructr when yu return s that yu can get any papers yu missed. Remember that yu are expected t be in class fr the tests and quizzes. Getting Help After yu have tried the hmewrk, if yu need help, there are several things yu can d: Lk in yur text and yur class ntes fr examples similar t the prblems yu are finding difficult. Page 6 f 7

7 1/14 See yur instructr during ffice hurs r make an appintment. Bring the wrk yu have dne. Frm a study grup with ther class members. Wrking with ther students can be a great way t learn. If yu d have a grup t wrk with, cnsider exchanging phne numbers r addresses. Yur textbk may have a cmplete slutins manual available in the Math Lab. Yu may use this in the Math Lab. G t the Math Lab t get extra help n yur hmewrk r simply g and d yur hmewrk there. Smene will be there if yu get stuck. Yu dn t need an appintment. COLLEGE POLICIES: Fr infrmatin regarding: Brkdale s Academic Integrity Cde Student Cnduct Cde Student Grade Appeal Prcess Please refer t the BCC STUDENT HANDBOOK AND BCC CATALOG. NOTIFICATION FOR STUDENTS WITH DISABILITIES: Brkdale Cmmunity Cllege ffers reasnable accmmdatins and/r services t persns with disabilities. Students with disabilities wh wish t self-identify must cntact the Disabilities Services Office at (vice) r (TTY) t prvide apprpriate dcumentatin f the disability, and request specific accmmdatins r services. If a student qualifies, reasnable accmmdatins and/r services, which are apprpriate fr the cllege level and are recmmended in the dcumentatin, can be apprved. ADDITIONAL SUPPORT/LABS: Math Lab In the Math Lab, yu can: Obtain help n yur curse-related questins. Use vides r CDs related t yur cursewrk (with yur Brkdale ID) Use the slutins manual fr yur textbk (with yur Brkdale ID) Use the cmputers in the cmputer lab within the Math Lab t d wrk related t yur math curse. Yu can cnnect yur TI graphing calculatr t the cmputer and use sftware t print ut graphs and tables. During the Fall and Spring semesters, the hurs are: Mnday Thursday Friday Saturday 8:00am 8:45pm 8:00am 4:15pm 10:00am 3:00pm Yur instructr will infrm yu f Math Lab hurs during the Summer semesters. Curse Webpage The curse webpage has links t sites with helpful infrmatin. This webpage is at Page 7 f 7