Chabot College
Fall 2013
Course Outline for Mathematics 53
APPLIED ALGEBRA AND DATA ANALYSIS
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Catalog Description:
MTH 53 - Applied Algebra and Data Analysis
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6.00 units
Equations and formulas; linear, exponential, logarithmic and variation functions; measurement and
conversion of units; exponents and scientific notation; introduction to descriptive statistics including graphical
methods; introduction to probability; measures of risk. Intended for students who do not need calculus.
Prerequisite: MTH 104 (completed with a grade of "C" or higher) or an appropriate skill level demonstrated
through the Mathematics Assessment process.
Strongly Recommended: ENGL 102 or , ENGL 101B
Units
Contact Hours
Week
Term
6.00
Lecture
Laboratory
Clinical
Total
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6.00
6.00
1.00
0.00
7.00
105.00
17.50
0.00
122.50
Prerequisite Skills:
Before entry into this course, the student should be able to:
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apply the commutative, associative and distributive laws;
perform computations with signed numbers without a calculator;
apply order of operations in evaluating algebraic expressions;
simplify exponential expressions with whole number exponents;
create, interpret, and solve simple linear equations;
find area, circumference, diameter and radius of a circle;
solve a right triangle using Pythagorean Theorem;
simplify square roots of perfect squares;
solve problems using percents;
find the areas, perimeters, and volumes of geometric figures and objects;
translate between words and the mathematical symbols for variables and operations;
interpret operations and variables in algebraic expressions;
graph simple relationships between two variables;
solve word problems, including those using formulas and linear equations.
Expected Outcomes for Students:
Upon completion of this course, the student should be able to:
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use formulas and the metric system to find areas and volumes;
use dimensional analysis to perform multi-step unit conversions;
use scientific notation to perform calculations and make comparisons;
create and solve linear equations involving fractions, decimals, and percents;
interpret absolute value;
interpret and apply formulas involving several variables and parameters;
create, apply, and interpret graphs and equations of linear and piecewise linear functions;
create, apply, and interpret graphs and equations of exponential functions;
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create, apply, and interpret graphs and equations of variation functions, including square root
functions;
apply and interpret logarithmic models;
apply proportional reasoning appropriately in real-life situations;
calculate and interpret linear and exponential rates of growth;
create appropriate graphical displays of univariate quantitative and categorical data;
create and interpret scatterplots of bivariate quantitative data
calculate and interpret the mean and median for a set of data;
create and interpret frequency and relative frequency tables;
interpret two-way tables for bivariate categorical data;
apply and interpret the relative frequency definition of probability;
use two-way tables to calculate and interpret conditional probabilities;
calculate and interpret weighted averages;
recognize the Normal distribution as an example of a probability distribution;
apply the empirical rule for the Normal distribution in real-life situations;
use a graphing calculator and statistical software as tools in problem solving.
Course Content:
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Variables, expressions, equations, and functions
A. Order of operations
B. Distance and absolute value
C. Linear equations and inequalities
a. Review of equation solving principles
b. Word problems with decimals, fractions, and percents
c. Solving inequalities
D. Formulas
a. Parameters and variables
b. Solving for one variable in terms of another
E. Laws of Exponents
a. Interpreting exponents
b. Negative exponents and reciprocals
F. Functions
a. Function notation
b. Evaluating for given values of the independent variable
c. Finding the value of independent variable for a given value of dependent variable
Geometry and measurement
A. Dimension
B. Common three-dimensional figures
C. Metric System
a. Powers of ten and metric prefixes
b. Relationship among meters, liters, and grams
c. Comparison with U.S. customary system
d. One-step unit conversion
e. Dimensional analysis and multi-step unit conversion
D. Issues in measurement
a. Absolute and relative measurement error
b. Accuracy and precision
c. Scientific notation for very large and small numbers
d. Order of magnitude
Proportional reasoning
A. Rates and Ratios
a. Difference between rates and ratios
b. Simplify rates and ratios
c. Unit conversion for rates
B. Proportionality
a. Solving proportions
b. Applications of proportional reasoning
Linear functions and graphs
A. Cartesian coordinate system
a. Creating scatterplots from ordered pairs and data
b. Interpreting scatterplots
B. Rate of change
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a. Calculating rate of change from data
b. Visualizing rate of change from graph
c. Interpreting rate of change
C. Linear Functions
a. Relationship between equations and graphs
b. Interpreting slope and intercept
c. Domain and range in applications
d. Intersecting lines
e. Linear models for real situations
Data summary and interpretation
A. Variables and data
a. Categorical and quantitative variables
b. Bivariate and univariate data
c. Raw and summarized data
B. Frequency and relative frequency tables
a. Creating from raw data
b. Interpreting
C. Pie charts, bar graphs, and histograms
a. Choosing appropriate representations
b. Creating from raw or summarized data
c. Interpreting
D. Two-way tables
a. Creating from raw data
b. Interpreting
c. Calculating relative frequencies
E. Mean and median
a. Calculating from raw data
b. Interpreting
c. Weighted averages
Probability
A. Basic probability
a. Relative frequency definition
b. Simulation
c. Conditional probability from two-way tables
B. Probability distributions
a. Normal distributions
b. Center and spread of Normal distributions
c. Empirical rule for Normal distributions
Exponential and Logarithmic Functions
A. Equations of exponential functions
B. Exponential models for real-world situations
C. Graphs of exponential and logarithmic functions
D. Calculations with logarithms
E. Formulas involving logarithms
Other Non-linear functions
A. Power and Variation functions
a. Linear direct variation functions
b. Interpretation of rational exponents
c. Non-linear variation functions including square root functions
B. Piecewise linear functions
a. Domain and range
b. Graphs and equations
c. Interpretation
Technology Skills (Lab)
A. Basic use of a graphing calculator
a. Function graphing
b. Setting windows
c. Choosing appropriate scales for graphs
d. Tracing graphs
e. Using tables
f. Making scatterplots
g. Graphical equation-solving
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Methods of Presentation
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Calcultor techniques for exponential and logarithmic functions
a. Notation for large and small numbers
b. Using logarithms to solve problems
c. Other applications
Introduction to statistical software
a. Types of data
b. Data display using tables
c. Data display using graphs
Lecture/Discussion
Demonstration
Class and group discussions
Group Activities
Problem Solving
Presentation
Assignments and Methods of Evaluating Student Progress
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Exercises from the textbook: You are riding an exercise bicycle at a fitness center. The
readout states that you are using 500 Calories per hour. Are you generating enough
power to light a 100-watt bulb? (Note that 1 Calorie = 4184 joules and 1 watt = 1 joule per
second.)
Group collaborative: Use your graphing calculator or statistical software, make a
scatterplot of the bivariate data given in the table. Identify the two variables, give their
units, and explain how you chose the independent and dependent variables. With your
group, write at least three sentences describing any trends, patterns, or striking features of
the data that are visible from the scatterplot.
Lab Assignments: (a) Collaborative exercises using the graphing calculator to make
scatterplots and to fit function to data. (b) Collaborative exercises using the graphing
calculator to graph functions. (c) Collaborative exercises using computer applications to
better understand the concept of mean vs. median. (d) Collaborative exercises using
computer applications to learn various distribution shapes. (e) Collaborative exercises
using computer applications to better understand the center and spread of a Normal
distribution. (f) Collaborative exercises using computer applications to better understand
the Empirical Rule for Normal distributions. (g) Collaborative exercises applying piecewise
functions to utility bills and income taxes.
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Textbooks (Typical):
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Homework
Quizzes
Class Participation
Lab Activities
Midterm Examination
Final Examination
Bennett, J., W Briggs (2011). Using and Understanding Mathematics: A Quantitative Reasoning
Approach (5th/e). Addison-Wesley.
Lehmann, J (2011). Elementary and Intermediate Algebra: Functions and Authentic Applications
Prentice Hill.
Custom (2012). Combined custom text from above Pearson Publishing.
Special Student Materials
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A graphing calculator is required.
Access is provided to a statistical computer package in an on-campus laboratory.