Download MATH096_Outline_Fall2015 - Web4students

MONTGOMERY COLLEGE
Department of Mathematics
Rockville Campus
COURSE OUTLINE: MATH096 – Intermediate Algebra Revised Fall 2015
COURSE CHAIRS:
Yan Zhao
Office: SC 254H
Phone: 240-567-5223
[email protected]
Okkyung Cho
Office: SC 454P
Phone: 240-567-5210
[email protected]
TEXTBOOK: Intermediate Algebra, 6th Edition by Elayn Martin-Gay
MathXL is required for this course. Access can be purchased in the bookstore (ISBN 0201726114) or on
the website www.mathxl.com. Students who plan to continue to Math 110, Math 150 or Math 165 are
encouraged to purchase access for at least 12 months since students will use MathXL in those courses and
can continue working under the same code.
Since the textbook is imbedded in the MathXL homework for that section, students may decide to just use
the text in MathXL rather than purchasing it separately. If they choose to purchase it separately:
ISBN: 0321785045 (Hardbound) or ISBN: 0321785924 (Loose-leaf)
COURSE DESCRIPTION: An examination of algebraic skills and concepts intended to prepare
students for MATH130, MATH150, MATH165. Algebraic, graphical, numerical, and verbal approaches
are used in working with a variety of functions and their applications, including linear, polynomial,
exponential, logarithmic, rational, and radical functions. Solve systems of equations.
PREREQUISITE: A grade of C or better in MATH080, MA094, MA091, MA091A, MA091D; or
appropriate score on the mathematics assessment test; or consent of department.
Assessment level: READ120. Four hours each week.
MATH093 VS. MATH096: Some students are confused about whether they should take MATH093 or
MATH096. Discuss the differences briefly on the first day of class to ensure students are properly
placed. In addition, some statement should be put into the syllabus explaining the difference. A
possibility is the following, although the first paragraph is sufficient.
MATH096 is the prerequisite for MATH130, MATH150, and (along with Trigonometry)
MATH165. MATH130 is for elementary school teachers. MATH150 is Elementary Applied
Calculus, and MATH165 is Precalculus. Students who are certain they will never take any of
these courses might be better off taking MATH093.
MATH093 is only a prerequisite for four courses (Survey of College Math, Intro to Probability,
Elements of Statistics, or Mathematical Ideas.) One of these courses satisfies the math
requirement for many programs. MATH093 costs less money and meets for less time than
MATH096. If you are certain you belong in MATH093 rather than MATH96, please switch
immediately. (MATH096 is an alternative prerequisite for these courses.)
CALCULATORS: A graphing calculator is required and should be allowed for in-class assessments.
However, students still need to show algebraic work when calculators are used. Please be advised that
some four-year institutions do not allow the use of calculators on their exams. You may consider
giving part of your exam without calculators and part with calculators.
1
The minimal graphing calculator objectives are:
1.
2.
3.
4.
Deal with these mechanics: screen contrast, battery replacement, and common error messages.
Be able to apply the proper order of operations and use parentheses appropriately.
Be able to create and view a graph.
Know and be able to use some of the features on the following menus:
WINDOW, Y=, ZOOM, CALC, and TABLE .
5. Given a formula for f(x) and a number a, be able to evaluate f(a).
6. Be able to use the CALC menu to find intersections and real zeros.
7. Be able to enter and recognize scientific notation.
HOMEWORK: You must assign AND count homework as part of the overall grade. Homework
must count between 5% and 10% of the overall grade. It is required that MathXL be used to assess
student homework. There is a MathXL course available for copying.
EXAMS AND QUIZZES: Instructors are expected to give at least three exams in addition to the final
exam. In addition, it is recommended to give short, frequent quizzes, so that students receive early and
immediate feedback on their performance.
EVALUATION RECOMMENDATIONS: The following percentages may be used to calculate a
student's grade.
Homework: 5% - 10%
Exams and Quizzes: 45% - 60%
Final Exam: 25% - 35%
Other: 0% - 10%
FORMULAS: All formulas should be memorized. No notes or formula sheets are allowed for in class
assessments. Students should already be familiar with the slope formula, the slope-intercept formula, rules
of integer exponents, and the quadratic formula.
The following formulas should also be memorized by students in MATH096:
Quadratic Functions:
The x  
Exponential/Logarithmic Functions:
If b
x
b
formula for the vertex of a parabola
2a
 N , then x  logb N
logb x P  P logb x
ADDITIONAL INFORMATION: You can find course materials such as class handouts, sample exams
etc. on a Blackboard Community for MATH096 (still in working progress). The significant digits
document is also there.
2
MATH096 Suggested Semester Schedule
CHAPTER
SECTIONS
Chapter 2
Equations, Inequalities, and Problem Solving
NUMBER OF
70-MIN
CLASSES
(MWF)
3
(2.1-2.3 optional reviews)
2.4 - 2.7 (2.4 – Interval notations, 2.5 – Three part inequality only)
App.D
and
Graphing Calculator Introduction (Note: This is just an introduction. Incorporate
Handout
the graphing calculator into the rest of the course and be sure to cover the graphing
calculator objectives.)
Significant Digits
Chapter 3
Graphs and Functions
1
3
(3.1 optional review)
3.2 - 3.5
Chapter 4
Systems of Linear Equations
2
4.1, 4.3
Chapter 5
Exponents, Polynomials, and Polynomial Functions
4
(5.1 - 5.4 optional reviews)
5.5-5.8
Chapter 6
Rational Expressions
4
6.1 - 6.3, 6.5 - 6.6
Note: Section 6.3 is an optional topic.
Chapter 7
Rational Exponents, Radicals, and Complex Numbers
5
7.1 - 7.7
Chapter 8
Quadratic Equations and Functions
4
8.1 - 8.3, 8.5 - 8.6
Note: Section 8.3 is an optional topic.
Chapter 9
Exponential and Logarithmic Functions
8
9.1 - 9.8
Note: Omit all logarithmic equations except those that can be solved by directly
converting to exponential form. Cover section 9.4 Exponential Growth and Decay
lightly with one example for each.
Chapter 10
Solving Non-Linear Systems of Equations
1
10.3
NOTES: This gives 35 seventy minute classes, leaving 7 seventy minute classes for quizzes, tests and
reviews. Unless you have taught from this book before and were able to finish everything, consider doing
any optional material at the end of the course, if at all.
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MATH096 Intermediate Algebra Objectives
Topics
Objectives
The student will be able to
The Function Concept
A. Define relation.
B. Define function.
1. Use and interpret algebraic, verbal, numeric and
graphic definitions.
2. Determine whether a function is a relation numerically,
graphically or algebraically.
C. Identify the domain and range of a function.
1. Describe domain and range using interval notation.
2. Describe domain and range using inequality symbols.
D. Apply and interpret function notation to include
1. Evaluation of functions, f ( a ) ;
2. Solving f ( x)  b for x; and
3. Finding and interpreting x- and y-intercepts.
E. Find
1. The inverse of a function defined by a table or a graph.
2. The inverse of linear and exponential formulas.
Linear Functions and Equations
A. Solve linear systems
1. By using a graphing calculator.
2. Algebraically by the substitution and elimination
methods.
B. Determine if a linear system has one solution, no solution,
or infinitely many solutions.
C. Interpret the slope as a rate of change.
D. Determine if a function could be linear given an equation,
graph or a table of ordered pairs.
E. Write the equation of a line parallel to a given line through
a given point.
F. Interpret the slope and intercepts in the context of
applications.
G. Construct linear models.
H. Make conclusions and predictions based on a linear
model.
Quadratic Functions and
Equations
A. Factor quadratics that are
1. The difference of squares.
2. Perfect square trinomials.
3. Trinomials of the form x2  bx  c .
4. Trinomials of the form ax  bx  c, a  1.
B. Solve quadratic equations by
1. Using the zero-product rule and factoring.
2. The Quadratic Formula.
3. Completing the square.
4. Using a graphing calculator.
2
(continue on next page)
4
C. Analyze the graphs of a quadratic function to include
1. Finding the vertex of a parabola using completing the
square and the formula x 
b
.
2a
2. Finding and identifying the intercepts.
D. Interpret intercepts and the vertex for quadratic models in
context.
E. Define complex numbers.
1. Identify real, rational, irrational, and complex numbers.
2. Simplify radicals leading to complex numbers.
F. Find and interpret algebraic and graphical solutions of
systems of functions.
Rational Functions and
Equations
A. Find least common denominators and reduce, multiply,
divide, add, and subtract algebraic fractions with binomial
and trinomial denominators.
B. Identify the domain of a rational function.
C. Solve equations containing rational functions with
denominators that are binomials or easily factorable
quadratic trinomials and identify extraneous solutions if
they exist.
Exponential and Logarithmic
Functions and Equations
A. Simplify and evaluate expressions containing rational
exponents.
1. Interpret rational exponents as roots.
2. Convert between exponential and radical forms.
B. Recognize functions of the form f ( x)  Ab .
1. Determine if a function could be exponential given an
equation, graph or a table of values.
2. Graph for b  1, and for 0  b  1 .
3. Find the equation if given two points.
4. Evaluate f ( a ) .
C. Use and interpret the number e.
x
Radical Functions and
Equations
A.
B.
C.
D.
E.
F.
1. Recognize functions of the form f ( x)  Ae .
2. Evaluate f ( a ) on the calculator.
Define logarithms.
1. Use base b and base e.
2. Convert between exponential and logarithmic
equations.
3. Solve exponential equations using logarithms.
4. Solve growth and decay problems.
Simplify radicals.
Add, subtract, and multiply numerical radical expressions.
Rationalize denominators.
Find the domain of a radical function.
Solve radical equations containing one radical.
Identify extraneous solutions if they exist.
Graphing Calculator Skills
A.
B.
C.
D.
Enter a function and adjust a graphing window.
Evaluate a function.
Find x-intercept(s) and y-intercept.
Find turning points on a graph.
kx
D.
5
E. Find the intersection of two graphs.
F. Find the zeros of a function.
Analysis
A. Recognize and reproduce a typical example of each
function studied.
B. Compare linear, quadratic, and exponential growth.
Applications
A. Solve linear, quadratic, exponential, and simultaneous
equations.
B. Model real world applications using linear, polynomial,
exponential, and simultaneous equations.
C. Apply significant digits. (This is not in our textbook)
Montgomery College
MATH096 Course Outcomes
Approved spring 2008
#
Outcome: Upon completion of this course a student will be able to:
1
Define functions verbally, numerically, graphically and algebraically.
2
Use the numerical or graphical representation of a relation to determine whether the relation is a
function.
3
Identify the domain and range of a given function in both interval notation and set-builder
notation.
4
Understand the relationship between a function and its inverse in terms of domains, ranges, and
graphs.
5
Find an inverse of linear, exponential, and logarithmic functions.
6
Identify whether a function given symbolically is linear, quadratic, radical, exponential, or
logarithmic.
7
Identify linear, quadratic, exponential, and logarithmic functions, and systems of equations from
their graphs.
8
Solve linear, quadratic, rational, exponential, and simple radical equations, as well as systems of
equations.
9
Simplify rational, radical, exponential, and simple logarithmic expressions using appropriate
properties.
10
Graph linear, quadratic, exponential, and logarithmic functions, and systems of equations.
11
Find and identify the vertex, axis of symmetry, minimum or maximum, x-intercepts, and yintercept of a quadratic function from its symbolic representation or its graph.
12
Model real world applications using linear, quadratic, rational, logarithmic, exponential functions,
and systems of linear equations.
13
Use a graphing calculator to enter and graph linear, quadratic, radical, exponential, and
logarithmic functions, and systems of equations and interpret and analyze the graph.
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