Course Outline for Mathematics 53B
Intermediate Applied Algebra and Data Analysis

Effective: Spring 2018
SLO Rev: 03/14/2017
Catalog Description:

MTH 53B - Intermediate Applied Algebra and Data Analysis

3.00 Units

Formulas; inverse, exponential, and logarithmic functions; introduction to descriptive statistics including graphical methods; introduction to probability. Intended for students who do not need calculus.
Prerequisite: MTH 53A or an appropriate skill level demonstrated through the Mathematics Assessment process. , Strongly Recommended: ENGL 102 or ENGL 101B.
1701.00 - Mathematics, General
Optional
Type Units Inside of Class Hours Outside of Class Hours Total Student Learning Hours
Lecture 3.00 54.00 108.00 162.00
Laboratory 0.00 18.00 0.00 18.00
Total 3.00 72.00 108.00 180.00
Measurable Objectives:
Upon completion of this course, the student should be able to:
  1. create graphs and find equations of exponential functions;
  2. apply and interpret linear and exponential models in context of the real data or situations;
  3. calculate and interpret exponential rates of growth;
  4. calculate and interpret the mean and median for a set of data;
  5. create and interpret frequency and relative frequency tables;
  6. interpret two-way tables for bivariate categorical data;
  7. apply and interpret the relative frequency definition of probability;
  8. use scientific notation to perform calculations and make comparisons;
  9. apply proportional reasoning appropriately in real-life situations;
  10. model real growth and decay situations and data with exponential graphs and functions;
  11. solve exponential equations using logarithms;
  12. analyze data and determine the appropriate model for the situation;
  13. interpret absolute error and relative error in real life situations;
  14. solve systems of equations using graphing and the substitution methods;
  15. use a graphing calculator as a tool in problem solving.
Course Content:

Lecture

  1. Data summary and interpretation
    1. Variables and data
      1. Categorical and quantitative variables
      2. Bivariate and univariate data
      3. Raw and summarized data
    2. Frequency and relative frequency tables
      1. Create from raw data
      2. Interpret
    3. Pie charts, bar graphs, and histograms
      1. Choose appropriate representations
      2. Interpret
    4. Two-way tables
      1. Interpret
      2. Calculate relative frequencies
    5. Mean and median
      1. Calculate from raw data
      2. Interpret
  2. Basic Probability
    1. Relative frequency definition
    2. Venn diagrams
  3. Exponents
    1. Laws of exponents
    2. Interpret exponents
    3. Negative exponents and reciprocals
    4. Rational exponents
    5. Scientific notation
  4. Exponential and Logarithmic Functions
    1. Equations of exponential functions
    2. Exponential models for real-world situations
    3. Graphs of exponential and logarithmic functions
    4. Evaluate logarithms
    5. Applications involving logarithms
    6. Interpret the coefficient and base of an exponential model
    7. Use logarithms to solve exponential equations
  5. Systems of Linear Equations
    1. Solve by graphing
    2. Solve by substitution method
    3. Applications

Lab

  1. Graphing calculator techniques for statistics
  2. Calculator techniques for exponential and logarithmic functions
    1. Notation for large and small numbers
    2. Use logarithms to solve problems
    3. Find exponentional regression equations
    4. Other applications
  3. Graphing calculator techniques for solving systems of equations
Methods of Instruction:
  1. Lecture/Discussion
  2. Demonstration
  3. Class and group discussions
  4. Group Activities
  5. Presentation
Assignments and Methods of Evaluating Student Progress:
  1. 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.
  2. 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?
  3. 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.
  1. Homework
  2. Quizzes
  3. Class Participation
  4. Class Work
  5. Lab Activities
  6. Midterm Examination
  7. Final Examination
Upon the completion of this course, the student should be able to:
  1. Critically analyze mathematical problems using a logical methodology.
  2. Communicate mathematical ideas, understand definitions, and interpret concepts.
  3. Increase confidence in understanding mathematical concepts, communicating ideas and thinking analytically.
Textbooks (Typical):
  1. Bennett, J., W. Briggs (2011). Using and Understanding Mathematics: A Quantitative Reasoning Approach (5th). Addison-Wesley.
  2. Lehmann, J (2011). Elementary and Intermediate Algebra: Functions and Authentic Applications Prentice Hall.
  3. Custom (2016). Applied Algebra and Data Analysis (3rd). Pearson Publishing.
  • A graphing calculator is required.
  • Access code for the required on-line homework system.
Abbreviated Class Schedule Description:
Formulas; inverse, exponential, and logarithmic functions; introduction to descriptive statistics including graphical methods; introduction to probability. Intended for students who do not need calculus.
Prerequisite: MTH 53A or an appropriate skill level demonstrated through the Mathematics Assessment process. , Strongly Recommended: ENGL 102 or ENGL 101B.
Discipline:
Mathematics*