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Chabot College
Spring 2012
Course Outline for Mathematics 62
APPLIED ALGEBRA AND DATA ANALYSIS
Catalog Description:
62– Applied Algebra and Data Analysis
6 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 not majoring in
mathematics, science, or engineering. Prerequisite: Mathematics 104 (completed with a grade of “C” or
higher) or an appropriate skill level demonstrated through the Mathematics Assessment process. 6 hours
lecture, 1 hour laboratory.
[Typical contact hours: lecture 105, laboratory 17.5]
Prerequisite Skills:
Before entering the course the student should be able to:
1. apply the commutative, associative and distributive laws;
2. perform computations with signed numbers without a calculator;
3. apply order of operations in evaluating algebraic expressions;
4. simplify exponential expressions with whole number exponents;
5. create, interpret, and solve simple linear equations;
6. find area, circumference, diameter and radius of a circle;
7. solve a right triangle using Pythagorean Theorem;
8. simplify square roots of perfect squares;
9. solve problems using percents;
10. find the areas, perimeters, and volumes of geometric figures and objects;
11. translate between words and the mathematical symbols for variables and operations;
12. interpret operations and variables in algebraic expressions;
13. graph simple relationships between two variables;
14. solve word problems, including those using formulas and linear equations.
Expected Outcomes for Students:
Upon completion of the course the students should be able to:
1. use formulas and the metric system to find areas and volumes;
2. use dimensional analysis to perform multi-step unit conversions;
3. use scientific notation to perform calculations and make comparisons;
4. create and solve linear equations involving fractions, decimals, and percents;
5. interpret absolute value;
6. interpret and apply formulas involving several variables and parameters;
7. create, apply, and interpret graphs and equations of linear and piecewise linear functions;
8. create, apply, and interpret graphs and equations of exponential functions;
9. create, apply, and interpret graphs and equations of variation functions, including square root
functions;
10. apply and interpret logarithmic models;
11. apply proportional reasoning appropriately in real-life situations;
12. calculate and interpret linear and exponential rates of growth;
13. create appropriate graphical displays of univariate quantitative and categorical data;
14. create and interpret scatterplots of bivariate quantitative data
15. calculate and interpret the five-number summary for a set of data;
Chabot College
Course Outline for Mathematics 62, Page 2
Spring 2012
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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;
estimate risk and probability from data;
use two-way tables to calculate and interpret conditional probabilities;
calculate and interpret weighted averages and expected values;
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 as a tool in problem solving.
Course Content (Lecture):
1. Variables, expressions, equations, and functions
a. Order of operations
b. Distance and absolute value
c. Linear equations and inequalities
1) Review of equation solving principles
2) Word problems with decimals, fractions, and percents
3) Solve inequalities
d. Formulas
1) Parameters and variables
2) Solving for one variable in terms of another
e. Laws of Exponents
1) Interpretation of exponents
2) Negative exponents and reciprocals
f. Functions
1) Function notation
2) Evaluating for given values of the independent variable
3) Finding the value of independent variable for a given value of dependent variable
2. Geometry and measurement
a. Dimension
b. Common three-dimensional figures
c. Formulas for area and volume using function notation
d. Metric System
1) Powers of ten and metric prefixes
2) Relationship among meters, liters, and grams
3) Comparison with U.S. customary system
4) One-step unit conversion
5) Dimensional analysis and multi-step unit conversion
e. Issues in measurement
1) Absolute and relative measurement error
2) Accuracy and precision
3) Scientific notation for very large and small numbers
4) Order of magnitude
3. Linear functions and graphs
a. Cartesian coordinate system
1) Creating scatterplots from ordered pairs and data
2) Interpreting scatterplots
b. Rate of change
1) Calculating rate of change from data
2) Visualizing rate of change from graph
3) Interpreting rate of change
c. Linear Functions
1) Relationship between equations and graphs
Chabot College
Course Outline for Mathematics 62, Page 3
Spring 2012
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2) Interpreting slope and intercept
3) Intersecting lines
4) Linear models for real situations
d. Piecewise linear functions
1) Domain and range
2) Graphs and equations
3) Interpretation
Proportional reasoning and variation
a. Rates and Ratios
1) Difference between rates and ratios
2) Simplifying rates and ratios
3) Unit conversion for rates
b. Proportionality
1) Solving proportions
2) Applications of proportional reasoning
c. Variation functions
1) Linear direct variation functions
2) Interpretation of rational exponents
3) Non-linear variation functions including square root functions
Data summary and interpretation
a. Variables and data
1) Categorical and quantitative variables
2) Bivariate and univariate data
3) Raw and summarized data
b. Frequency and relative frequency tables
1) Creating from raw data
2) Interpreting
c. Pie charts, bar graphs, and histograms
1) Choosing appropriate representations
2) Creating from raw or summarized data
3) Interpreting
d. Two-way tables
1) Creating from raw data
2) Interpreting
3) Calculating relative frequencies
e. Mean and five-number summary
1) Calculating from raw data
2) Interpreting
Probability and risk
a. Basic probability
1) Relative frequency definition
2) Simulation
b. Probability distributions
1) Normal distributions
2) Center and spread of Normal distributions
3) Empirical rule for Normal distributions
c. Risk
1) Measures of risk
2) Calculating risk from data
d. Conditional probability from two-way tables
e. Weighted averages and expected value
Exponential and Logarithmic Functions
a. Equations of exponential functions
b. Exponential models for real-world situations
c. Graphs of exponential and logarithmic functions
Chabot College
Course Outline for Mathematics 62, Page 4
Spring 2012
d. Calculations with logarithms
e. Formulas involving logarithms
Course Content (Laboratory):
1. 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
2. Calculator techniques for exponential and logarithmic functions
a. Notation for large and small numbers
b. Using logarithms to solve problems
c. Other applications
3. Introduction to statistical software
a. Types of data
b. Data display using tables
c. Data display using graphs
Methods of Presentation:
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Lectures
Presentations on the use of technology
Class discussion of problems, solutions and students’ questions
Group work
Student presentations
Assignments and Methods of Evaluating Student Progress:
1. Typical Assignments
a. 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.)
b. Group collaborative: Use your graphing calculator or Minitab to 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.
2. Methods of Evaluating Student Progress
a. Homework
b. Quizzes
c. Class participation
d. Group problem-solving and presentations
e. Individual and group activities applying technology
f. Midterms
g. Final examination
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Textbook(s) (Typical):
Using and Understanding Mathematics, Bennett and Briggs, 5th ed., Addison Wesley, Pearson Publishing,
2011
Chabot College
Course Outline for Mathematics 62, Page 5
Spring 2012
Special Student Materials:
A graphing calculator is required.
Access to a statistical computer package in an on-campus laboratory is provided.
A. Wah and I. Chaudhuri
New September 23, 2011