MAPÚA INSTITUTE OF TECHNOLOGY
Department of Mathematics
a.
b.
c.
VISION
Mapua shall be among the best universities in the world.
MISSION
The Institute shall provide a learning environment in order for its students to acquire the attributes
that will make them globally competitive.
The Institute shall engage in economically viable research, development, and innovation.
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 SYLLABUS
1.
Course Code:
MATH10-4
2.
Course Title:
Advanced Algebra
3.
Pre-requisite:
MATH10-3
4.
Co-requisite:
none
5.
Credit:
3 units
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.
6.
7.
Student Outcomes and Relationship to Program Educational Objectives
Student Outcomes
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
an ability to apply knowledge of mathematics, science, and engineering
an ability to design and conduct experiments, as well as to analyze and interpret
from data
an ability to design a system, component, or process to meet desired needs
an ability to function on multidisciplinary teams
an ability to identify, formulate, and solve engineering problems
an understanding of professional and ethical responsibility
an ability to communicate effectively
the broad education necessary to understand the impact of engineering solutions
in the global and societal context
a recognition of the need for, and an ability to engage in life-long learning
a knowledge of contemporary issues
an ability to use the techniques, skills, and modern engineering tools necessary for
engineering practice
knowledge and understanding of engineering and management principles as a
member and leader in a team, to manage projects and in multidisciplinary
Course Title:
ADVANCED ALGEBRA
Date Effective:
Date Revised:
2nd Term
AY 2014-2015
Oct 2014
Prepared by:
Cluster I
Committee
Program Educational Objectives
1
2
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
Approved by:
Page 1 of 6
LD SABINO
Subject Chair
environments
8.
Course Outcomes (COs) and Relationship to Student Outcomes
Course Outcomes
After completing the course, the student must be able to:
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.
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.
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.
* Level: I- Introduced, R- Reinforced, D- Demonstrated
9.
Course Coverage
WEEK TOPIC
a
b
Student Outcomes*
d e
f
g h
i
c
D
D
D
D
D
D
D
D
D
TLA
AT
j
k
COURSE
OUTCOME
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
1
2
Relations, Functions and Graphs
 Relations and Functions
 Domain and Range
 Evaluation of Functions
 Operations on Functions
 Odd and Even functions
 Inverse functions
 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
CO1
Guided Learning /
Working through
Examples
Assignment 1 (A)
Exercise 1 (Exr)
Date Effective:
Date Revised:
2nd Term
AY 2014-2015
Oct 2014
Prepared by:
Cluster I
Committee
Approved by:
Page 2 of 6
LD SABINO
Subject Chair
l
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
LONG QUIZ 1 (Q1)
4
5
6
7
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
Systems of Equations and Inequalities
 Definition of Terms
 Systems of Linear Equations in Two Variables
 Systems of Linear Equations in Three
Variables
 Nonlinear Systems of Equations
 Applications of Systems of Equations
 Inequalities in Two Variables and Systems of
Inequalities
 Linear Programming
 Partial Fractions
Cooperative
Learning/Group
Discussion
Assignment 2 (A2)
Guided Discovery /
Class Discussion
Exercise 2 (Exr2)
CO2
Guided Discovery /
Class Discussion
LONG QUIZ 2 (Q2)
8
9
10
Sequences and Series
 Definition of terms
 Summation Notation
 Arithmetic Sequence and Series
 Harmonic Sequence
 Geometric Sequence and Series
 Applications of Sequences and Series
Factorial of a Number
Mathematical Induction
 Principle of Mathematical Induction
Binomial Theorem
th
 n term of Binomial Expansion
 Pascal’s Triangle
Permutation and Combination
 Fundamental Counting Principle
 Permutation
 Combination
Dyadic Discussion
Guided Discovery /
Class Discussion
Assignment 3 (A3)
CO3
Dyadic Discussion
Guided Discovery /
Class Discussion
Exercise 3 (Exr 3)
Guided Discovery /
Class Discussion
LONG QUIZ 3 (30% online, 70% written)
PROJECT (Prj)
11
FE1
FE2
FE3
SUMMATIVE ASSESSMENT - FINAL EXAMINATION
10.
CO1
CO2
CO3
Opportunities to Develop Lifelong Learning Skill
Course Title:
ADVANCED ALGEBRA
Date Effective:
Date Revised:
2nd Term
AY 2014-2015
Oct 2014
Prepared by:
Cluster I
Committee
Approved by:
Page 3 of 6
LD SABINO
Subject Chair
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
General Education
Basic Sciences and Mathematics
:
:
0%
0%
100%
:
th
12.
Textbook: College Algebra and Trigonometry, 7 edition
Richard N. Aufmann, Vernon C. Barker, Richard D. Nation
13.
Course Evaluation
Student performance will be rated based on the following:
Assessment Tasks
Assignment 1
A
3.34
Long Quiz 1
Q
16.67
Exercise 1
Exr
3.33
Assignment 2
A2
3.33
Long Quiz 2
Q2
16.67
Exercise 2
Exr2
3.33
Assignment 3
A3
3.33
Long Quiz 3 on-line
Ex
5
Long Quiz 3 written
Q3
11.67
Exercise 3
Exr3
3.33
Project
Prj
5.0
FE1
FE2
FE3
9
8
8
CO 1
CO 2
CO 3
Weight
(%)
Summative Assessment:
Final Examination
TOTAL
Minimum Average for
Satisfactory Performance (%)
16.331
16.331
19.83
17.50
100
70
The final grades will correspond to the weighted average scores shown below:
Final Average
96  x < 100
93  x < 96
90  x < 93
86  x < 90
83  x < 86
80  x < 83
76  x < 80
73  x < 76
Course Title:
ADVANCED ALGEBRA
Final Grade
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
Date Effective:
Date Revised:
2nd Term
AY 2014-2015
Oct 2014
Prepared by:
Cluster I
Committee
Approved by:
Page 4 of 6
LD SABINO
Subject Chair
70  x < 73
Below 70
3.00
5.00 (Fail)
13.1. Other Course Policies
14.
a.
Attendance
According to CHED policy, total number of absences by the students should not be more than 20% of the total
number of meetings or 9 hrs for a three-unit-course. Students incurring more than 9 hours of unexcused absences
automatically gets a failing grade regardless of class standing.
b.
Submission of Assessment Tasks
Submission of students’ work should be on time. Late submittals will not be accepted.
c.
Written Examination
Long quizzes and final examination will be as scheduled. No special examination will be given unless for valid
reason subject to approval of the Department Chairman.
d.
Course Portfolio
Course portfolio will be collected at the end of the term.
e.
Language of Instruction
Lectures, discussion, and documentation will be in English. Written and spoken work may receive a lower mark if it
is, in the opinion of the instructor, deficient in English.
f.
Honor, Dress and Grooming Codes
All of us have been instructed on the Dress and Grooming Codes of the Institute. We have all committed to obey
and sustain these codes. It will be expected in this class that each of us will honor the commitments that we have
made.
For this course the Honor Code is that there will be no plagiarizing on written work and no cheating on exams.
Proper citation must be given to authors whose works were used in the process of developing instructional
materials and learning in this course. If a student is caught cheating on an exam, he or she will be given zero mark
for the exam. If a student is caught cheating twice, the student will be referred to the Prefect of Student Affairs
and be given a failing grade.
g.
Consultation Schedule
Consultation schedules with the Professor are posted outside the faculty room and in the Department’s web-page
(http://math.mapua.edu.ph). It is recommended that the student first set an appointment to confirm the
instructor’s availability.
Other References
14.1. Books
a, College Algebra and Trigonometry by Louis Leithold, International Ed., 2001
nd
b. College Algebra and Trigonometry by Matk Dugopolski, 2 Ed.
nd
c. College Algebra, enhances with Graphing Utilities by Michael Sullivan and Michael Sullivan III, 2 Ed.
th
d. College Algebra and Trigonometry by Nax Sobel and Lemer Norbert, 5 Ed., 1998
rd
e. Applied Algebra and Trigonometry by Linda Davis, 3 Ed., 2003
nd
f. Algebra and Trigonometry by James Stewart, Lothar Redlin and Saleem Watson, 2 ed, 2007
14.2
15.
Websites
Enhanced Web Assign Learning Management System
Course Materials Made Available
Course schedules for lectures and quizzes
Samples of assignment/Problem sets of students
Samples of written examinations of students
End-of-course self-assessment
Course Title:
ADVANCED ALGEBRA
Date Effective:
Date Revised:
2nd Term
AY 2014-2015
Oct 2014
Prepared by:
Cluster I
Committee
Approved by:
Page 5 of 6
LD SABINO
Subject Chair
16.
Committee Members:
Course Cluster Chair :
CQI Cluster Chair :
Member :
Course Title:
ADVANCED ALGEBRA
Dionisia M. Lanuza
Floro Deogracis G. Llacuna
Raquel B. Teodoro
Teresita L. Zapanta
Date Effective:
Date Revised:
2nd Term
AY 2014-2015
Oct 2014
Prepared by:
Cluster I
Committee
Approved by:
Page 6 of 6
LD SABINO
Subject Chair