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Department of Mathematics
MONTGOMERY COLLEGE
Rockville Campus
Course Outline
Ma 101 – Intermediate Algebra for Liberal Arts
Course Chair:
Stephanie Pepin
240-567-5207
[email protected]
TEXT: Jay Lehman, INTERMEDIATE ALGEBRA 3rd edition, Functions and Authentic
Applications. Prentice Hall, 2007
Our text is a departure form traditional texts and brings functions and modeling to the
forefront, although it still gives due attention to developing algebraic skills. Especially
noticeable and important is the early treatment of exponential and logarithmic functions.
Curve fitting is an integral part of the course.
MA 101 is a point in our curriculum where graphing calculators are introduced and
utilized as an integral teaching tool for conceptual understanding. See the graphing
calculator objectives at the end of this outline and use the calculator support offered in
the text. The TI-83, TI- 83+, and the TI – 84 are recommended and supported by the
department. Symbol-manipulating calculators such as the TI-89 and TI –92 are not
permitted.
Appendix B, pg 637 in the text, is an excellent practical introduction to the TI – 82/83,
especially for students using a graphing calculator for the first time. Instructors and
students alike will find pp. 640 – 641 helpful with scattergrams.
The following outline will be helpful in planning your semester schedule. It is a guide
offering suggestions for pacing and depth of coverage.
Chapter 1 – Linear Equations and Functions, sections 1 through 6
5 days
Many topics in this chapter are review. Cover 1.1 – 1.5 creating connections between
numerical and graphical representations. Integrate calculator support as algebraic
concepts are introduced. Focus on 1.5 and 1.6 (Finding equations and functions) Slope
of perpendicular lines is omitted (section 1.3, example 9). Finding equations of lines
perpendicular to a given line are also omitted (1.5 example 6, 7).
Chapter 2 – Modeling with Linear Functions, Sections 1 through 4
4 days
Students must be able to find the equation of a line algebraically (without calculator) if
given 2 or more points. It is a recommended activity to have students graph points in a
scattergram, draw a line for a scatter plot that looks like the best- fit line, calculate slope
and y intercept by hand, and find a linear model; Use linear regression function on the
calculator to support algebraic work and for predictions.. Section 2.3 may require 2 days,
Highlight interpretation of slope (Section 2.4) as a rate of change. Students should be
encouraged to write interpretation in complete sentences using context of problem.
Chapter 4 – Exponential Functions, Sections 1 through 4
5 days
Section 1, properties of exponents need review. Attention to negative exponents should
be given. Scientific notation focus is placed on entering and reading numbers in
scientific notation on the calculator. Section 4.2, HW such as # 51 – 58 may be omitted.
Section 4.3, omit material on stretching and reflecting graphs (ex. 4), expectation is on
basic graphs of exponential functions. Section 4.4; find an equation of an exponential
function passing through two points ONLY if one point is the y intercept. (Omit example
6). Modeling exponential functions; problems 1, 4, 5, 7, 9 from section 5 (pg. 207-208)
are worthwhile and easily incorporated.
Chapter 5 – Logarithmic Functions, Sections 1 – 4, and section 6
5 days
Sections 5.1: inverse functions (examples 5,6,7,8 are key) and 5.2 (def of Log function)
can be informal and quick as an introduction to Section 5.3.(Solving exponential
equations) Focus on 5.4, power property and modeling for prediction.
Omit 5.5
Section 5.6 (natural logarithms) can be combined with 5.4 in lecture.
Chapter 6 – Polynomial Functions, Sections 2 through 6
6 days
6.2 (examples 1 – 9) quickly review multiplication of polynomials as intro to factoring.
6.3 – 6.5 factoring techniques, 6.4 (grouping ex 1 – 4) should be reviewed quickly.
Section 6.5 examples 1, 2 and 5 step strategy review on page 314 for factoring techniques
covered in 6.2-6.4. 6.6 (Solving quadratics only – ex 1 – 8) should use a variety of
factoring techniques, with connections of solutions to graphs. Modeling should be
included.(ex 12) Omit ex 9, 10, 11.
Chapter 7 – Using Quadratic Functions to Model Data, Sections 1, 3, 6
Omit sections 2,4,5
In section 1, omit vertex form and emphasize graphs of the form y  ax 2 and
y  ax 2  c ; (ex 1, 2, 3). Domain and range can be discussed within ex 1,2,3)
6 days
Section 2 sketch the graph of a quadratic and find the vertex by using method not
requiring completing the square or the method1 outlined in text: use method 2 pg 350
b
 b 
vertex formula: x   . y  f  
2a
 2a 
Focus on modeling and interpretations (max/min, predictions from models)
Section 7.3, rationalize denominators, and solving by extracting square roots now
required. Complex solutions are introduced here in preparation for Quadratic
formula
Omit 7.4, 7.6
7.5 briefly introduce use of discriminant. Review quadratic formula: Reinforce
 b  b 2  4ac
with emphasis on including “ x  ” and the
2a
division bar not beginning just under the square root sign. Modeling (Ex 9) should be a
continued theme.
notation/concept of x 
7.7 is a wrap up of modeling process and choosing an appropriate model. Additional
work here would be appropriate.
Section 7.8 objectives 1 and 2. Briefly discuss HW #10 as it is a nice lead in to Chapter 3
(systems of equations).
***Chapter 3 – Systems of Linear Equations, Sections 1 – 3
Chapter 11.8 – nonlinear systems
3 days
Section 3.1 and 3.2. (3.2 omit ex 6) Focus on 3.3, modeling (ex’s 1, 2, 3) Section 11.8
focus is on graphing two parabolas or a parabola and a line. (ex 1 only)
***Additional work on modeling should be included within sections: 2.3, 4.5, 5.4,
5.6, 7.5, 7.8
*** indicates additional material covered by Rockville Campus based on relevance to
respective academic programs.
Content days
Reviews/explorations
Tests
Final
34
3
4
1
Total
42
MA 101 MINIMAL GRAPHING CALCULATOR OBJECTIVES
1. Deal with these mechanics: screen contrast, battery replacement, common error
messages.
2. Be able to apply the proper order of operations and use parentheses
appropriately.
3. Be able to create and view a graph.
4. 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.
Students should be able to enter data into lists for use in linear regression, Quadratic
regression, and exponential regression modeling.
Math 101 Formula List
Topic
Lines, linear functions
Formulas we expect students
to know upon entering MA
100
The slope formula
Formulas that students will learn in
MA 100 to be tested without notes
or calculator
The slope-intercept formula
Exponents,
exponential functions
Rules of integer exponents
If b x  N , then x  logb N
logb x P  P logb x
Quadratic equations and
functions
The quadratic formula
The x  
b
formula for the vertex
2a
of a parabola
Students are expected to know these formulas and they should not be provided for them
on tests or quizzes. You may choose to briefly review the formulas in the second
column.
Department of Mathematics
Rockville Campus
Objectives MA101
Course Objectives: The student will be able to:
Linear Equations and functions:
A. Interpret the slope as a rate of change and in the context of applications.
B. Determine if a function is linear given an equation, graph, or a table of ordered pairs
C. Interpret intercepts in the context of applications.
D. Sketch the graphs of lines.
E. Find linear equations given:
1. the slope and a point on the line; two points on the line;
2. the equation of a line parallel to a given line through a given point; or
3. a linear model.
Functions:
A. Determine if a relation is a function numerically, graphically, or algebraically.
B. Apply and interpret algebraic, verbal, numeric and graphic definitions of functions.
C. Apply and interpret function notation to include:
1. Evaluating functions, f (a ) ;
2. Solving f ( x)  b for x; and
3. Finding and interpreting x- and y-intercepts.
D.
Identify the domain of a function.
Exponential equations and Functions:
A. Simplify and evaluate expressions containing rational exponents.
B. Graph exponential functions of the form f ( x)  ab x .
C. Solve exponential equations algebraically or by using a graphing calculator.
D. Solve exponential growth and decay problems.
Logarithmic Functions:
A. Define logarithms and the relationship between exponential and logarithmic form.
B. Define and apply the power rule to solve exponential equations.
Quadratic Equations and Funcitons:
A. Solve quadratic equations by
1. Factorization
2. Square root method
3. Quadratic Formula
B. Analyze the graphs of Quadratic Functions to include:
1. Graphing parabolas;
b
2. Finding and interpreting the vertex using x 
; and
2a
3. Finding and interpreting intercepts.
Applications and Calculator use:
A. Model real-world applications using linear, exponential, and quadratic equations.
B. Create and analyze scatter plots from data.
A.
B.
C.
D.
E.
Enter a function and adjust the graphing window.
Evaluate a function.
Find x-intercept(s) and y-intercept.
Find turning points on a graph.
Find the intersection of two graphs.
Systems of Equations:
A. Solve linear and nonlinear systems of equations.
Additional notes:
Students registered for MA101 are preparing for MA115, MA116, MA113, MA110.
Reading and writing across the curriculum are part of the General Education
competencies that many students have difficulty with in MA116, MA116. Considering
that many of our students progress to these courses, a goal of the MA101 course should
be to prepare students for these competencies by interspersing reading and writing
assignments along with computational skills. Small examples are: having students write
answers in complete sentences including context and units (if applicable) of original
problem, Having students read journal articles, watch videos and summarize the
mathematics, use focused writing prompts, class journal writing. If you need some
guidance, please feel free to stop by or drop me an e mail.
Attempt to connect the concepts in the course. Students see chapters as independent
topics with no relationship. Try to lead students to see the relationships by spiraling
previous topics into the new concepts and by continually reinforcing previous material
with new material through quizzes and tests.