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SINCLAIR COMMUNITY COLLEGE DAYTON, OHIO DEPARTMENT SYLLABUS FOR COURSE IN MAT COLLEGE ALGEBRA (4 SEMESTER HOURS)

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SINCLAIR COMMUNITY COLLEGE DAYTON, OHIO

DEPARTMENT SYLLABUS FOR COURSE IN MAT 1470 - COLLEGE ALGEBRA

(4 SEMESTER HOURS)

1. COURSE DESCRIPTION: Polynomial, radical, rational, exponential, and logarithmic functions and their graphs; roots of polynomial functions, rational and polynomial inequalities; conic sections; systems of linear and nonlinear equations; matrices; sequences and series; and applications.

2. COURSE OBJECTIVES: To develop in the student the theories, skills, and techniques that form the foundation for algebra, to provide the student opportunities to apply their knowledge of algebra in a variety of contexts, to build within the student the mathematical sophistication necessary for the study of calculus and other courses/disciplines that require the use of algebra.

3. PREREQUISITE: Satisfactory score on Mathematics Placement Test or a grade of "C" or better in either MAT 1370 or MAT 1365.

4. ASSESSMENT: In addition to required exams as specified on the syllabus, instructors are encouraged to include other components in computing final course grades such as homework, quizzes, and/or special projects. However, 80% of the student’s course grade must be based on in-class proctored exams.

5. TEXT: College Algebra and Trigonometry, Third Edition Ratti/McWaters

Pearson

Adopted: Fall 2015

MyMathLab is a required component of this course. It will give students access to the online version of the textbook, as well as a set of homework assignments and quizzes.

6. CALCULATOR POLICY: A scientific calculator is required. Graphing calculators are not allowed on exams.

7. INTERNSHIP: Please include the following in your syllabus:

Experiencing an internship in your field of study is the best way to begin a career. Companies offer opportunities throughout the year for students to practice what they learned in the classroom to solve real world of work

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7. PREPARED BY: Kinga Oliver -point of contact, David Hare, Susan Harris, Craig Birkemeier, Kay Cornelius, Najat Baji, David Stott, Effective: Fall 2015

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SINCLAIR COMMUNITY COLLEGE DAYTON, OHIO

CLASS SCHEDULE FOR COURSE IN MAT 1470 – COLLEGE ALGEBRA

(4 SEMESTER HOURS)

CLASSES MEETING 2 TIMES A WEEK

Lecture Sections Topics

1

2.4

Introduction to the Class Functions 2 2.5 2.6 Properties of Functions A Library of Functions 3 2.7 Transformations of Functions

4 2.8 Combining Functions; Composite Functions 5 2.9 Inverse Functions

6

3.1

REVIEW FOR TEST 1 Quadratic Functions

7 TEST 1 [ 2.4–2.9]

8 3.1

3.2

Quadratic Functions

Polynomial Functions and Models

9 3.2

3.3

Polynomial Functions Dividing Polynomials

10 3.4 The Real Zeros of a Polynomial Function

11 3.5 3.6

Complex Zeros of a Polynomial Function Rational Functions

12 3.6 Rational Functions 13 1.5* Inequalities*

14

4.1

REVIEW FOR TEST 2 Exponential Functions 15 TEST 2 [1.5, 3.1–3.6] 16 4.1 4.2 Exponential Functions Logarithmic Functions

* Note to instructors regarding section 1.5: Cover only quadratic and higher degree inequalities, and rational functions.

(4)

MAT 1470 – College Algebra

2 TIMES A WEEK SECTIONS CLASS SCHEDULE (continued)

Lecture Sections Topics

17 4.3 Rules of Logarithms

18 4.3

4.4**

Rules of Logarithms

Exponential and Logarithmic Equations and Inequalities** 19 4.4** Exponential and Logarithmic Equations and Inequalities**

20 8.1

8.2

Systems of Linear Equations in Two Variables Systems of Linear Equations in Three Variables 21 CATCH-UP TIME / Holiday

22 9.1 Matrices and Systems of Equations

REVIEW FOR TEST 3

23

10.1/10.2

TEST 3 [4.1–4.4, 8.1-8.2, 9.1] Conic Sections: Overview/ Parabolas

24 10.2 Parabolas

25 2.2*** 10.3

Graphs of Equations (Circles only***) Ellipses

26 10.4

8.4

Hyperbolas

Systems of Nonlinear Equations 27 CATCH-UP TIME / Holiday

28 11.1

11.2

Sequences and Series

Arithmetic Sequences; Partial Sums

29 11.3 Geometric Sequences and Series

REVIEW FOR TEST 4

30 TEST 4 [2.2, 8.4, 10.1–10.4, 11.1-11.3]

Finals Week

31 REVIEW FOR FINAL EXAM

32 COMPREHENSIVE FINAL EXAM

** Note to instructors regarding section 4.4: Please do not cover Logarithmic and Exponential Inequalities. *** Note to instructors regarding section 2.2: Please cover only circles as a special case of an ellipse where

a = b = r, from the middle of page 171 through page 174.

The COMPREHENSIVE FINAL exam will be in two parts. One part will be prepared by the department. It will be a 14-question, 50-minute, multiple-choice test. It will be sent to the instructor in the mail. Another part is to be prepared by the instructor. It may be of any format but should be 50 minutes long. The instructor should count the departmental part for 50% of the final exam score and the other part for 50%. The total final exam score should count for 20% of the final course grade. The other four exams should count for 15% each, and the homework and quizzes should count for 20% total. The instructor will be asked to report the scores on the departmental part and the final course grades back to the department.

(5)

SINCLAIR COMMUNITY COLLEGE DAYTON, OHIO

CLASS SCHEDULE FOR COURSE IN MAT 1470 – COLLEGE ALGEBRA

(4 SEMESTER HOURS)

CLASSES MEETING 3 TIMES A WEEK

Lecture Sections Topics

1

2.4

Introduction to the Class, Functions

2 2.4/2.5 Functions/ Properties of Functions

3 2.5/2.6 Properties of Functions/ A Library of Functions 4 2.7 Transformations of Functions

5 2.7/2.8 Transformations of Functions/ Combining Functions; Composite Functions 6 2.8 Combining Functions; Composite Functions

7 2.9 Inverse Functions

8 2.9 Inverse Functions

REVIEW FOR TEST 1 9 3.1 Quadratic Functions 10 TEST 1 [ 2.4–2.9] 11 3.1 Quadratic Functions 12 3.2 Polynomial Functions 13 3.2 Polynomial Functions 14 3.3 Dividing Polynomials

(6)

MAT 1470 – College Algebra

3 TIMES A WEEK SECTIONS CLASS SCHEDULE (continued)

Lecture Sections Topics

16 3.5 Complex Zeros of a Polynomial Function 17 3.6 Rational Functions

18 3.6 Rational Functions 19 1.5* Inequalities*

20 REVIEW FOR TEST 2

21 4.1 Exponential Functions 22 TEST 2 [1.5, 3.1–3.6] 23 4.1 Exponential Functions 24 4.2 Logarithmic Functions 25 4.3 Rules of Logarithms 26 4.3 Rules of Logarithms

27 4.4** Exponential and Logarithmic Equations and Inequalities** 28 4.4** Exponential and Logarithmic Equations and Inequalities** 29 8.1 Systems of Linear Equations in Two Variables

30 8.2 Systems of Linear Equations in Three Variables 31 CATCH-UP TIME / Holiday

32 9.1 Matrices and Systems of Equations

33 REVIEW FOR TEST 3

* Note to instructors regarding section 1.5: Cover only quadratic and higher degree inequalities, and rational functions.

(7)

MAT 1470 – College Algebra

3 TIMES A WEEK SECTIONS CLASS SCHEDULE (continued)

Lecture Sections Topics

34 TEST 3 [4.1–4.4, 8.1-8.2, 9.1]

35 10.1

10.2

Conic Sections: Overview Parabolas

36 10.2 Parabolas

37 2.2*** 10.3

Graphs of Equations (Circles only***) Ellipses

38 10.4 Hyperbolas

39 10.4

8.4

Hyperbolas

Systems of Nonlinear Equations 40 CATCH-UP TIME / Holiday 41 11.1 Sequences and Series

42 11.2 Arithmetic Sequences; Partial Sums 43 11.3 Geometric Sequences and Series

44 REVIEW FOR TEST 4

45 TEST 4 [2.2, 8.4, 10.1–10.4, 11.1-11.3]

Finals Week

46 REVIEW FOR FINAL EXAM

47 COMPREHENSIVE FINAL EXAM (part 1)

48 COMPREHENSIVE FINAL EXAM (part 2)

*** Note to instructors regarding section 2.2: Please cover only circles as a special case of an ellipse where a = b = r, from the middle of page 171 through page 174.

The COMPREHENSIVE FINAL exam will be in two parts. One part will be prepared by the department. It will be a 14-question, 50-minute, multiple-choice test. It will be sent to the instructor in the mail. Another part is to be prepared by the instructor. It may be of any format but should be 50 minutes long. The instructor should count the departmental part for 50% of the final exam score and the other part for 50%. The total final exam score should count for 20% of the final course grade. The other four exams should count for 15% each, and the homework and quizzes should count for 20% total. The instructor will be asked to report the scores on the departmental part and

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DAYTON, OHIO

CLASS SCHEDULE FOR COURSE IN MAT 1470 – COLLEGE ALGEBRA

(4 SEMESTER HOURS)

SUMMER CLASSES MEETING 3 TIMES A WEEK

Week Sections Topics

1

2.4

Introduction to the Class, Functions

2.5 Properties of Functions 2.6 A Library of Functions 2.7 Transformations of Functions

2 2.8 Combining Functions; Composite Functions 2.9 Inverse Functions

REVIEW FOR TEST 1

3 TEST 1 [ 2.4–2.9]

3.1 Quadratic Functions 3.2 Polynomial Functions 4 3.3 Dividing Polynomials

3.4 The Real Zeros of a Polynomial Function

3.5 3.6

Complex Zeros of a Polynomial Function Rational Functions

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MAT 1470 – College Algebra

SUMMER CLASSES MEETING 3 TIMES A WEEK (continued)

Week Sections Topics

5 3.6 Rational Functions 3.6 Rational Functions 1.5* Inequalities* 1.5* Inequalities*

REVIEW FOR TEST 2

6 TEST 2 [1.5, 3.1–3.6]

4.1 Exponential Functions 4.2 Logarithmic Functions 7 4.3 Rules of Logarithms

4.3 Rules of Logarithms

4.4** Exponential and Logarithmic Equations and Inequalities** 4.4** Exponential and Logarithmic Equations and Inequalities** 8 8.1 Systems of Linear Equations in Two Variables

8.2 Systems of Linear Equations in Three Variables CATCH-UP TIME / Holiday

REVIEW FOR TEST 3

* Note to instructors regarding section 1.5: Cover only quadratic and higher degree inequalities, and rational functions.

(10)

MAT 1470 – College Algebra

SUMMER CLASSES MEETING 3 TIMES A WEEK (continued)

Week Sections Topics

9 TEST 3 [4.1–4.4, 8.1-8.2, 9.1]

10.1/10.2 Conic Sections: Overview/ Parabolas 10.2 Parabolas

10 2.2*** 10.3

Graphs of Equations (Circles only***) Ellipses

10.4 Hyperbolas

8.4 Systems of Nonlinear Equations

11 11.1

11.2

Sequences and Series

Arithmetic Sequences; Partial Sums 11.3 Geometric Sequences and Series

REVIEW FOR TEST 4

CATCH-UP TIME / Holiday

12 TEST 4 [2.2, 8.4, 10.1–10.4, 11.1-11.3]

REVIEW FOR THE FINAL EXAM COMPREHENSIVE FINAL EXAM

*** Note to instructors regarding section 2.2: Please cover only circles as a special case of an ellipse where a = b = r, from the middle of page 171 through page 174.

The COMPREHENSIVE FINAL exam will be in two parts. One part will be prepared by the department. It will be a 14-question, 50-minute, multiple-choice test. It will be sent to the instructor in the mail. Another part is to be prepared by the instructor. It may be of any format but should be 50 minutes long. The instructor should count the departmental part for 50% of the final exam score and the other part for 50%. The total final exam score should count for 20% of the final course grade. The other four exams should count for 15% each, and the homework and quizzes should count for 20% total. The instructor will be asked to report the scores on the departmental part and the final course grades back to the department.

(11)

MAT 1470 Course Formulas

Prerequisite Formulas

Formulas of special importance that students are expected to know upon entering this course.

- Distance Formula d

x2x1

 

2 y2y1

2 - Midpoint Formula          2 , 2 2 1 2 1 x y y x M - Slope of a Line 1 2 1 2 x x y y m    - Forms of linear Equations

Slope-Intercept Form ymxb Point-Slope Form yy1m

xx1

Horizontal Line yb

Vertical Line xa

Course Formulas

- Formulas that students are required to memorize in this course:

Chapter 3 - Quadratic Function                   a b f a b c bx ax x f 2 , 2 vertex ; 2  x ax hk

 

h k f   2  ; vertex ,

- Quadratic Formula If ax2bx c 0, a0 then

a ac b b x 2 4 2    Chapter 4 - Rules of Exponents ( )

 

x x xy y x y x y x y x y x a a a a a a a a a a a   ,   ,  , 0 1,   1

(12)

Mat 1470 - College Algebra Course Formulas (Continued)

Chapter 4 (Cont)

- Laws of Logarithms

loga

MN

logaM loga N M N N M a a a log log log        M r a M r a log log 

- Change of Base Formula

b x x a a b log log log 

- Exponential Growth and Decay A(t) A0ekt,k 0 A(t) A0ekt,k 0 - Simple Interest: I Prt Future value P(t)PPrt - Compound Interest

 

nt n r P t A         1 Continuous Compounding A

 

tPert Chapter 10

- Equations of Conic Sections

Parabola

x h

2 4p y k

,

yk

2 4pxh Circle

xh

 

2  yk

2 r2 Ellipse 2 2 2 2 2 2 2 2 2 2 2 , 0 , 1 ) ( ) ( , 1 ) ( ) ( b a c b a a k y b h x b k y a h x             Hyperbola 2 2 2 2 2 2 2 2 2 2 2 , 1 ) ( ) ( , 1 ) ( ) ( b a c b h x a k y b k y a h x           Chapter 11 - Arithmetic Sequence: ana1(n1)d Geometric Sequence: 1 1   n n ar a - Partial sums of an Arithmetic Sequence Sn n

2a

n 1

d

2 1           2 1 n n a a n S

- Partial sums of a Geometric Sequence

r r a S n n   1 1 1 , 1  r

- Sum of an infinite Geometric Series 1 1 1    if r r a S

References

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