Chabot College
Fall 2010
Course Outline for Mathematics 54L
APPLIED INTERMEDIATE ALGEBRA WITH LAB
Catalog Description:
54L – Applied Intermediate Algebra With Lab
5.5 units
Functions in the context of real data; rates of change of linear functions; linear systems; laws of rational
exponents; mathematical models (including graphs) using exponential, logarithmic, power, and linear,
quadratic and other polynomial functions; solution of exponential and logarithmic equations. Includes
laboratory and study group time to reinforce and enhance the learning of applied intermediate algebra
skills. Prerequisites: Mathematics 65 or 65B or 65L (completed with a grade of “C” or higher) or an
appropriate skill level demonstrated through the Mathematics Assessment process. May not receive
credit if Mathematic 54 has been completed. 5 hours lecture, 1.5 hours laboratory.
[Typical contact hours: lecture 87.5, laboratory 26.25]
Prerequisite Skills:
Before entering the course the student should be able to:
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write set theory notation;
apply order of operations to simplify algebraic expressions;
solve linear equations in one variable;
solve and graph linear inequalities in one variable;
graph linear equations in two variables by various methods;
add, subtract, multiply, and divide polynomials;
apply the formula for squaring a binomial;
factor special products, general trinomials, and polynomials with four terms;
add, subtract, multiply, divide and simplify rational expressions;
apply algebraic methods to solve word problems;
solve quadratic equations by factoring, using the principle of square roots, and using the
quadratic formula;
solve systems of equations by graphing, substitution and elimination;
apply the properties of integral exponents;
solve formulas for any given variable;
solve rational equations;
find the slope of a line from the graph, from the definition and from the slope-intercept
equation of the line;
find the equation of a line using the point-slope equation;
convert between scientific notation and standard notation.
Expected Outcomes for Students:
Upon the completion of the course the student should be able to:
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describe data using concepts of frequency and measures of central tendency;
identify functions, find domain and range, and use function notation in the context of real data;
identify the slope of a line using that it is parallel to another line;
find average rates of change;
graph and find the equations of linear functions in the context of real data;
solve problems involving direct and inverse proportionality;
find linear models for data;
find linear system models for data and interpret solutions to these linear systems;
perform operations using the properties of rational exponents;
graph exponential functions and interpret real growth and decay situations and data with
exponential functions;
solve exponential equations using logarithms;
analyze real situations and data by using exponential functions with base e and natural
logarithmic functions;
find inverse functions and compose functions in the context of real data;
graph quadratic, power, and logarithmic functions;
Chabot College
Course Outline for Mathematics 54L, Page 2
Fall 2010
15. analyze real situations and data using quadratic functions;
16. choose an appropriate model for a realistic situation given a choice of mathematical models.
Course Content (Lecture):
1. Mean and median
2. Frequency and relative frequency
3. Functions
a. Domain and range
b. Identify functions
c. Represent functions with words, tables, graphs, and words
d. Language
e. Notation
f. Inverse functions
g. Composition
4. Types of functions
a. Linear
b. Quadratic and other polynomial
c. Power
d. Exponential
e. Logarithmic
1) Natural logarithmic
5. Graphs of linear equations
a. Review slope
b. Review horizontal and vertical lines
c. Parallel lines
6. Average rate of change
7. Direct and inverse proportionality
8. Rational exponents
a. Properties
b. Perform operations
9. Review solution of quadratic equations
a. By applying the quadratic formula
b. By factoring
10. Solve exponential equations by using logarithms
11. Model and analyze real world data
a. With linear functions
b. With non-linear functions
1) Quadratic
2) Power
3) Exponential
4) Logarithmic
c. With inverse functions
d. With composite functions
e. With linear systems
1) Review solution by graphing
2) Review solution by substitution method
3) Review solution by elimination method
4) Interpret solutions
Course Content (Laboratory):
1. Basic use of a graphing calculator
a. Function graphing
b. Setting windows
c. Tracing graphs
d. Using tables
e. Making scatterplots
Chabot College
Course Outline for Mathematics 54L, Page 3
Fall 2010
2. Applying graphing calculator techniques
a. Line fitting by trial and error
b. Linear regression
c. Interpolation and extrapolation
d. Comparing graphical, tabular, and algebraic representations
e. Choosing appropriate scales for graphs
3. Linear systems on the graphing calculator
a. Graphical solutions of systems of equations
b. Graphical solutions of systems of inequalities
c. Applications of systems
4. Calculator techniques for exponential and logarithmic functions
a. Notation for large and small numbers
b. Fractional exponents
c. Base ten and base e for exponential functions
d. Base ten and base e for logarithmic functions
e. Different types of compound interest
f. Half-life and doubling time
g. Other applications
5. Calculator techniques for quadratic functions
a. Graphical solutions of maximization problems
b. Graphical solutions of quadratic equations
6. Introduction to statistical software
a. Types of data
b. Data display using tables
c. Data display using graphs
d. Interpreting graphs
Methods of Presentation:
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Lectures
Class discussion of problems, solutions and students’ questions
Audio-visual materials
Laboratory
Collaborative small groups
Assignments and Methods of Evaluating Student Progress:
1. Typical Assignments
a. The accompanying table and graph show the change in median age of the U.S.
population from 1850 through the present and projected into the next century. (In the text,
the table and graph show every tenth year from 1850 to 2050 with the corresponding
median age.)
1) Using the given data, specify the longest time period over which the median age has
been increasing. Calculate the average rate of change between the two end points of
this time period.
2) Calculate the average rate of change between 1850 and 1900, 1900 and 1950, and
1950 and 2000 and the projected average rate of change between 2000 and 2050.
Write a paragraph comparing these results.
3) Does an increase in median age necessarily mean that more people are living longer?
What changes in society could make this change in median age possible?
b. Perform an experiment with water and coffee filters and model with an exponential function.
2. Methods of Evaluating Student Progress
a. Homework
b. Quizzes
c. Midterms
Chabot College
Course Outline for Mathematics 54L, Page 4
Fall 2010
d. Group work
e. Final Examination
Textbook(s) (Typical):
Intermediate Algebra: Functions and Authentic Applications, Lehmann, Jay, 3rd ed., Prentice Hall,
2008
Special Student Materials:
Will require scientific or graphing calculator and/or computer lab fee.
AW:al
New 10/2004
Updated by dh: 9/2009
Updated by aw: 10/2009