Chabot College
Fall 2013
Course Outline for Mathematics 53B
INTERMEDIATE APPLIED ALGEBRA AND DATA ANALYSIS
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Catalog Description:
MTH 53B - Intermediate Applied Algebra and Data Analysis
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3.00 units
Formulas; exponential, logarithmic functions, variation and piecewise linear function; introduction to
descriptive statistics including graphical methods; introduction to probability; measures of risk. Intended for
students who do not need calculus.
Prerequisite: MTH 53A (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
3.00
Lecture
Laboratory
Clinical
Total
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3.00
3.00
1.00
0.00
4.00
52.50
17.50
0.00
70.00
Prerequisite Skills:
Before entry into this course, the student should be able to:
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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 and apply formulas involving several variables and parameters;
create, apply, and interpret graphs and equations of linear functions;
create, apply, and interpret graphs and equations of simple inverse variation functions;
apply proportional reasoning appropriately in real-life situations;
calculate, interpret, and apply constant rate of change;
create and interpret scatterplots of bivariate quantitative data;
use a graphing calculator as a tool in problem solving.
Expected Outcomes for Students:
Upon completion of this course, the student should be able to:
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interpret and apply formulas involving several variables and parameters;
create, apply, and interpret graphs and equations piecewise linear functions;
create, apply, and interpret graphs and equations of exponential functions;
create, apply, and interpret graphs and equations of variation functions, including square root
functions;
5. apply and interpret logarithmic models;
6. calculate and interpret exponential rates of growth;
7. create appropriate graphical displays of univariate quantitative and categorical data;
8. create and interpret scatterplots of bivariate quantitative data
9. calculate and interpret the mean and median for a set of data;
10. create and interpret frequency and relative frequency tables;
11. interpret two-way tables for bivariate categorical data;
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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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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 distribution
a. Normal distributions
b. Center and spread of Normal distributions
c. Empirical rule for Normal distribution
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. Review of direct and inverse 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. Interpretatio
Technology Skills (Lab)
A. Graphing calculator techniques for probability and statistics
B. Calculator techniques for exponential and logarithmic functions
a. Notation for large and small numbers
b. Using logarithms to solve problems
c. Other applications
C. Introduction to statistical software
a. Types of data
b. Data display using tables
c. Data display using graphs
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Methods of Presentation
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Lecture/Discussion
Demonstration
Class and group discussions
Group Activities
Presentation
Assignments and Methods of Evaluating Student Progress
1. Typical Assignments
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Exercises from the textbook: An archeologist discovers a tool made of wood. (i) If 50% of
the wood’s carbon-14 remains, how old is the wood? Explain how you can find this result
without using an equation. The half-life of carbon-14 is 5720 years. (ii) Answer question
(a), again without an equation, if 25% of the carbon-14 remains. (iii) If 10% of the wood’s
carbon-14 remains, how old is the wood? First, guess an approximate age without solving
an equation. Explain how you decided on your estimate. Then use an equation to find the
age.
Group collaborative: Refer to the two-way table on in problem 69 on page 48 of your
textbook. Make a copy of the table and complete, filling in the margins. Then discuss the
following questions in your group. (i) Which had more individuals with disease, the group
of coffee drinkers, or the non-drinkers of coffee? (ii) Which had a larger percentage of
individuals with disease, the coffee drinkers or the non-drinkers? (iii) What is the overall
rate of disease among all the people in the study?
Lab Assignments: (a) Collaborative exercises using the graphing calculator to graph and
analyze functions and to fit function to data. (b) Collaborative exercises using computer
applications to better understand the concept of mean vs. median. (c) Collaborative
exercises using computer applications to learn various distribution shapes. (d)
Collaborative exercises using computer applications to better understand the center and
spread of a Normal distribution. (e) Collaborative exercises using computer applications to
better understand the Empirical Rule for Normal distributions. (f) Collaborative exercises
applying piecewise functions to utility bills and income taxes.
2. Methods of Evaluating Student Progress
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Textbooks (Typical):
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Homework
Quizzes
Class Participation
Class Work
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 Hall.
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.