math 10-4 advanced algebra

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  • Course Title:

    ADVANCED ALGEBRA

    Date Effective:

    2nd

    Term AY 2014-2015

    Date Revised:

    Oct 2014

    Prepared by:

    Cluster I Committee

    Approved by:

    LD SABINO Subject Chair

    Page 1 of 6

    MAPA INSTITUTE OF TECHNOLOGY Department of Mathematics

    COURSE SYLLABUS

    1. Course Code: MATH10-4

    2. Course Title: Advanced Algebra

    3. Pre-requisite: MATH10-3 4. Co-requisite: none 5. Credit: 3 units

    6. Course Description: This course prepares students for studying higher level algebraic processes. The course

    discussions starts with functions and relations, polynomial equations, matrices and determinants, systems of linear and non-linear equations and inequalities and its applications, partial fractions, sequences and series, factorial of a number, binomial theorem and its applications, counting principles and mathematical induction.

    7. Student Outcomes and Relationship to Program Educational Objectives

    Student Outcomes Program Educational Objectives

    1 2

    (a) an ability to apply knowledge of mathematics, science, and engineering

    (b) an ability to design and conduct experiments, as well as to analyze and interpret from data

    (c) an ability to design a system, component, or process to meet desired needs

    (d) an ability to function on multidisciplinary teams

    (e) an ability to identify, formulate, and solve engineering problems

    (f) an understanding of professional and ethical responsibility

    (g) an ability to communicate effectively

    (h) the broad education necessary to understand the impact of engineering solutions in the global and societal context

    (i) a recognition of the need for, and an ability to engage in life-long learning

    (j) a knowledge of contemporary issues

    (k) an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice

    (l) knowledge and understanding of engineering and management principles as a member and leader in a team, to manage projects and in multidisciplinary

    VISION Mapua shall be among the best universities in the world.

    MISSION

    a. The Institute shall provide a learning environment in order for its students to acquire the attributes

    that will make them globally competitive.

    b. The Institute shall engage in economically viable research, development, and innovation.

    c. The Institute shall provide state-of-the-art solutions to problems of industries.

    PROGRAM EDUCATIONAL OBJECTIVES (CONSTRUCTION ENGINEERING AND MANAGEMENT, SERVICE

    ENGINEERING AND MANAGEMENT)

    MISSION

    a b C

    1. To enable our graduates to practice as successful engineers and managers for the advancement of society.

    2. To promote professionalism in the engineering and management practice.

  • Course Title:

    ADVANCED ALGEBRA

    Date Effective:

    2nd

    Term AY 2014-2015

    Date Revised:

    Oct 2014

    Prepared by:

    Cluster I Committee

    Approved by:

    LD SABINO Subject Chair

    Page 2 of 6

    environments

    8. Course Outcomes (COs) and Relationship to Student Outcomes

    Course Outcomes After completing the course, the student must be able to:

    Student Outcomes*

    a b c d e f g h i j k l

    1. Identify relations and functions, and find its domain and range; evaluate and perform operations on functions; interpret its graphs; and find roots of polynomial functions.

    D D D

    2. Identify types of matrices and evaluate determinants; solve systems of linear and nonlinear equations and inequalities and its applications; and decomposing fractions to sum of partial fractions.

    D D D

    3. Solve application problems involving sequence and series; find specific term of a binomial expansion; and solve problems using the fundamental principles of counting, permutation and combination.

    D D D

    * Level: I- Introduced, R- Reinforced, D- Demonstrated 9. Course Coverage

    WEEK TOPIC TLA AT COURSE OUTCOME

    1

    Mission and Vision of Mapua Institute of Technology

    Orientation and Introduction to the Course

    Discussion on COs, TLAs, and ATs of the course

    Overview on student-centered learning and eclectic approaches to be used in the course

    Relations, Functions and Graphs

    Relations and Functions

    Domain and Range

    Evaluation of Functions

    Operations on Functions

    Odd and Even functions

    Inverse functions

    Guided Learning / Working through

    Examples

    Assignment 1 (A)

    Exercise 1 (Exr)

    CO1

    2

    Linear Functions - Slopes of Lines - Equations of Lines

    General Form Point Slope Form Two point Form Slope Intercept Form Intercept Form

    Quadratic Functions - Standard Form of Quadratic

    Function - Maximum and Minimum of

    Quadratic Function - Vertical and Horizontal Translation

    Absolute value functions

    Piecewise defined functions

    Greatest Integer Functions

  • Course Title:

    ADVANCED ALGEBRA

    Date Effective:

    2nd

    Term AY 2014-2015

    Date Revised:

    Oct 2014

    Prepared by:

    Cluster I Committee

    Approved by:

    LD SABINO Subject Chair

    Page 3 of 6

    3

    Polynomial Functions and Equations

    Remainder Theorem

    Factor Theorem

    Zeroes of Polynomials

    Types of algebraic curves and its functions - Properties of graphs - Symmetry - Intercepts - Asymptotes

    Guided Learning / Working through Examples

    4

    LONG QUIZ 1 (Q1)

    Matrices and Determinants

    Introduction to Matrices - Kinds of Matrices

    Addition/Subtraction of Matrices

    Scalar and Matrix Multiplication

    Determinants of 2x2 and 3x3 Matrices - Arrow/Basket Method - Minors and Cofactors

    Cooperative Learning/Group Discussion

    Assignment 2 (A2)

    Exercise 2 (Exr2)

    CO2

    5 Systems of Equations and Inequalities

    Definition of Terms

    Systems of Linear Equations in Two Variables

    Systems of Linear Equations in Three Variables

    Guided Discovery / Class Discussion

    6 Nonlinear Systems of Equations

    Applications of Systems of Equations

    Inequalities in Two Variables and Systems of Inequalities

    Guided Discovery / Class Discussion

    7

    Linear Programming

    Partial Fractions

    LONG QUIZ 2 (Q2)

    8 Sequences and Series

    Definition of terms

    Summation Notation

    Arithmetic Sequence and Series

    Harmonic Sequence

    Geometric Sequence and Series

    Applications of Sequences and Series

    Dyadic Discussion

    Guided Discovery / Class Discussion

    Assignment 3 (A3)

    Exercise 3 (Exr 3)

    CO3

    9 Factorial of a Number

    Dyadic Discussion

    Guided Discovery / Class Discussion

    Mathematical Induction

    Principle of Mathematical Induction

    Binomial Theorem

    nth

    term of Binomial Expansion

    Pascals Triangle

    10

    Permutation and Combination

    Fundamental Counting Principle

    Permutation

    Combination

    Guided Discovery / Class Discussion

    LONG QUIZ 3 (30% online, 70% written)

    PROJECT (Prj)

    11

    SUMMATIVE ASSESSMENT - FINAL EXAMINATION

    FE1 CO1

    FE2 CO2

    FE3 CO3

    10. Opportunities to Develop Lifelong Learning Skill

  • Course Title:

    ADVANCED ALGEBRA

    Date Effective:

    2nd

    Term AY 2014-2015

    Date Revised:

    Oct 2014

    Prepared by:

    Cluster I Committee

    Approved by:

    LD SABINO Subject Chair

    Page 4 of 6

    To help students understand and apply the mathematical principles of Advanced Algebra and provide them with the needed working knowledge of the different mathematical concepts and methods for them to fully understand the relationship of Advanced Algebra with the increasingly complex world.

    11. Contribution of Course to Meeting the Professional Component

    Engineering Topics : 0 % General Education : 0 % Basic Sciences and Mathematics : 100%

    12. Textbook: College Algebra and Trigonometry, 7

    th edition

    Richard N. Aufmann, Vernon C. Barker, Richard D. Nation 13. Course Evaluation Student performance will be rated based on the following:

    Assessment Tasks Weight (%)

    Minimum Average for Satisfactory Performance (%)

    CO 1

    Assignment 1 A 3.34

    16.331

    Long Quiz 1 Q 16.67

    Exercise 1 Exr 3.33

    CO 2

    Assignment 2 A2 3.33

    16.331 Long Quiz 2 Q2 16.67

    Exercise 2 Exr2 3.33

    CO 3

    Assignment 3 A3 3.33

    19.83

    Long Quiz 3 on-line Ex 5

    Long Quiz 3 written Q3 11.67

    Exercise 3 Exr3 3.33

    Project Prj 5.0

    Summative Assessment: Final Examination

    FE1 9

    17.50 FE2 8

    FE3 8

    TOTAL 100 70

    The final grades will correspond to the weighted average scores shown below:

    Final Average Final Grade

    96 x < 100 1.00

    93 x < 96 1.25

    90 x < 93 1.50

    86 x < 90 1.75

    83 x < 86 2.00

    80 x < 83 2.25

    76 x < 80 2.50

    73 x < 76 2.75

  • Course Title:

    ADVANCED ALGEBRA

    Date Effective:

    2nd

    Term AY 2014-2015

    Date Revised:

    Oct 2014

    Prep