GEORGIAPERIMETER COLLEGE MATHEMATICS ACADEMIC GROUP TEACHINGGUIDE-MATH1111

I.Course Title: College Algebra

II.Prerequisite:Placementinto college-level mathematics

III.College Algebra, 1st edition,by Julie Miller, McGraw Hill, 2014

IV.CatalogDescription:

This course provides an in-depth study of the properties of algebraic, exponential and logarithmic functions as needed for calculus. Emphasis is on using algebraic and graphical techniques for solving problems involving linear, quadratic, piece-wise defined, rational, polynomial, exponential, and logarithmic functions.

V.Course Objective:

This courseprovidesabasis forthestudyofscienceorprecalculus.

VI.General Notes

For homework assignments instructors are encouraged to select items from those listed and to not simplyassign the entireset.Different assignments arepermitted as longas theyaresimilarin scopeand coverageoftopics. At the instructor’s discretion, students should be able to do some topicsbyhand without usingacalculator.

VII.Calculator

TheTI-83 orTI-84graphingcalculatoris therequired calculator forthis course. With instructor approval, othercalculators with thesame capabilities maybeused. Thegraphing calculatoris availableinthe collegebookstoreandin other retail stores.Instructors will be provided agraphing calculatorbythedepartment foruseduringterms theyareteachingMath 1111. Most classrooms are also equippedwith TI-SmartView, an onlineversion ofthe calculator. Contactyourdepartment chairifyou need assistance with thecalculator.

Students should be ableto solvethe equations andinequalities covered in the course algebraically, using graphical support.

VIII.Standards for Topics in Math 1111

Standardforfunction shifting in Math 1111

Students should be ableto perform vertical and horizontal shifts, vertical stretches and

compressionsand xand yaxis reflections on given functions. Theyshould be ableto perform combinations ofup to threetransformations (excludinganythat havetwo"inside changes”). Theyshould be ableto look at a function rulesuch as f(x)=3(x+1)2−5andverbally describe whatchanges havebeen madewithout lookingat thegraph on acalculator.

Standardforpolynomial functions in Math 1111

Students will be ableto graph byhand quadraticfunctions ofthe form

1.bycompletingthesquareto determinethevertexand

2.byfindingtheintercepts.

Students will recognizethevertexas amaximum orminimum and be ableto interpret the vertexand theinterceptsin applied settings.

Students will be ableto

1.identifypower functions and polynomial (3rd degreeorgreater) functions,

2.graph byhand power functions, transformations ofpowerfunctions, and simple polynomialfunctionswherethepolynomialisfactored,e.g.(x−2)(x+3)(x−3),

3.describetheend behaviorofpolynomials and therelationship betweenend behavior and thedegreeofthepolynomial.

4.usea calculatortographboth short-term and end-behaviorofanypolynomial,

5.determineintercepts offactored polynomials exactly.

6.usetechnologyto approximatex-intercepts and turningpoints ofpolynomials,

7.usetechnologyto solvepolynomial inequalities (graphically, that is).

Standardfor Rational functions in Math 1111

Students will study only transformations of yand y .

For suchtransformations,theywill be ableto do the following:

1.identifyand sketch them(byhand)

2.recognize from agraph vertical and horizontal asymptotes (calculatorgraphs or graphs wheretheasymptotes arenot explicitlydrawn)

3.determinethe equations forverticaland horizontal asymptotes

4.describetheend behaviorofthe function (e.g.,as x→∞, f(x)→a)

5.use arrownotation to describethebehaviorofthefunction nearvertical asymptotes(e.g., as x→a from the right, f(x)→∞)

Students should be ableto solve rational inequalities graphically.

Standardfor composition in Math 1111

Instructors should emphasizethemechanics of composition.Students should spend most of

theirtime with algebraicproblems ratherthan arithmetic (e.g., f(g(x)), ratherthan f(g(2)).

Theissueofsimpledomain restrictions should becovered duringthis work (e.g. If , then will have a restricted domain that is neither the domain of nor the domain of ).

Students should also be ableto evaluate when only given thegraphsofand.This puts composition in adifferent setting, which deepens theirunderstanding of composition (as well as graphsand function notation).

StandardforInverseFunctions in Math 1111

Students should be ableto

1.evaluateinverse function notation (e.g)

2.recognize which functions have an inverse function,

3.use composition to checkiftwo functions areinverses ofeach other,

4.find function rules forinverse functions, and

5.statethedomain and rangeofboth theoriginal and inverse functions.

Most ofthe functions should haveonlyobvious domain restrictions (e.g. theinverseof

f(x) has an obvious domain restriction) or the restriction should be obvious because the original function is not 1 – 1 (e.g. ).

Hand sketchingand symmetryacrossy=xshould be covered to help them understand whythe function needs to be1-to-1, and toget them used to being ableto reflect across adiagonal line beforetheyare asked tograpple with themorein-depth sketchingin 1113.

The concept "if(1,-2)ison thegraph off, then (-2,1)is on thegraph off-inverse"should be stressed. This reinforcesthe algebraicideaofswappingthexandyand also is helpful when sketching/graphicallycheckinginversefunctions.

StandardforExponential and LogarithmicFunctions in Math 1111

Students should be expected to master all exponential and logarithmicproperties and be able to solve exponential and logarithmicequations. The emphasis in 1111 should beput on algebraicmanipulation and solving ratherthan on graphingthe functions. Composition and inversefunctions should be reviewed in this context.

Compound interest applications should be covered thoroughly(other applications can wait until 1113) and inequalities solved graphically.

Standardfor Circles in Math 1111

The students should learn to find the radius and center of a circle written in both the form

and in the form . The student should be required to find the equation of a circle given its center and radius. In addition, the student should be required to find the equation of a circle given its center and one other point on the circle.

SuggestedHomeworkProblems

College Algebra, 1st edition,by Julie Miller, McGraw Hill, 2014

Section / Problems
1.1 / 15-20, 25-34, 43-48, 53-68
1.4 / 15-51 odd, 57-68 odd, 81-103 odd
1.6 / 11-26, 31-34, 39-50, 55-62
1.7 / 13-30
2.1 / 45-66
2.2 / 15-32, 43-54
2.3 / 15-71 odd, 73-81 eoo, 83, 85-93 odd, 95-111 eoo
2.4 / 19-29 odd, 35-43 eoo, 45-91 odd, 93,97
Applications 31-44 odd
2.5 / 11-27 eoo, 29-53eoo, 55, 57, 61, 63, 67
2.6 / 15- 79 odd
2.7 / 13-25 odd, 26, 27-71 eoo, 85-103 odd, 105, 109, 113
2.8 / 11-47 odd, 51-77 odd, 81-91 odd
3.1 / 1-29 odd, 30; Applications 31-43 odd
3.2 / 1-28, 29-45 eoo, 48, 63-74
3.5 / 7, 8, 9, 23-26, 55-62
3.6 / 27-35, 39, 40, 59, 60, 63-81 odd, 86, 88, 89
4.1 / 11-33 odd, 37, 39, 41, 47-71 odd, 77-91odd
4.2 / 3-17 odd, 21, 31-43odd, 47,49, 55, 59, 65, 69, 87
4.3
4.6 / 1-51eoo, 57-91eoo, 97, 99, 115, 116, 121
4.4 / 1-15 odd, 17-77 eoo, 89-99, 101, 107, 111
4.5 / 1-5, 11-59, eoo, 63, 65, 74, 81, 85, 87, 113
4.6 / 1-13eoo, 23, 27, 31,33,38,39
5.1 / 15-47 odd, 55, 56, 60
6.1 / 39-65 odd

eoo means every other odd

SuggestedPacing Guide – Four Tests

College Algebra, 1st edition,by Julie Miller, McGraw Hill, 2014

Day / Section(s) Covered
1 / 1.1 Linear Equations and Rational Equations
2 / 1.4 Quadratic Equations
3 / 1.6 More Equations and Applications
4 / 1.7 Linear Inequalities and Compound Inequalities
5 / 2.1 The Rectangular Coordinate System and Graphing Utilities
2.2 Circles
6 / Review
7 / Test 1
8 / 2.3 Functions and Relations
9 / 2.4 Linear Equations in Two Variables and Linear Functions
2.5 Applications of Linear Equations and Modeling
10 / 2.6 Transformations of Graphs
11 / 2.7 Analyzing Graphs & Piecewise-defined Functions
12 / 2.8 Algebra of Functions and Composition
13 / Review
14 / Test 2
15 / 3.1 Quadratic Functions and Applications
16 / 3.2 Introduction to Polynomial Functions
17 / 3.5 Rational Functions
18 / 3.6 Polynomial and Rational Inequalities
19 / 4.1 Inverse Functions
20 / Review
21 / Test 3
22 / 4.2 Exponential Functions
23 / 4.3 Logarithmic Functions
4.4 Properties of Logs
24 / 4.5 Exponential and Logarithmic Equations
25 / 4.6 Modeling with Exponential and Logarithmic Functions
26 / 5.1 Systems of Linear Equations in Two Variables and Applications
6.1 Solving Systems of Linear Equations Using Matrices
27 / Review
28 / Test 4
29 / Review for Final Exam

IX.Evaluation Methods:

The coursegrade will bedetermined bytheindividual instructorusing avarietyof evaluation methods. Aportion ofthe coursegrade will bedetermined through theuseoffrequent assessment usingsuch means as tests, quizzes, projects, orhomework asdeveloped bytheinstructor. Someofthesemethods will requirethestudent to demonstrate abilityin problem solvingandcritical thinkingas evidenced by explainingand interpretingsolutions. A comprehensive final examination is required which must count at least one-fifth and nomorethan one-third ofthe coursegrade.

X. Effective Date: Fall 2015 ApprovedDate: June 2015