Math 140: Unit 10

Target Date: Friday Dec. 11
Deadline: Friday Dec. 11

Note: The information on this page is for the 8th edition of the textbook.
Click here for the 7th edition information.
Click here for the 6th edition information.

Table of Contents:

Topics
Study Guidelines
Unit Pretest and Exam Description
Checklist

Topics

Unit 10 continues the work on systems of equations that was begun in Unit 9. A primary focus in this unit is applications. The unit starts with a study of real-world applications of 3x3 linear systems, and then continues with a mathematical application called the partial fraction decomposition. The partial fraction decomposition is a method of decomposing a complicated rational function into a sum of simpler ones. This technique is useful in a number of areas of mathematics (calculus in particular).

The unit concludes with a study of methods for solving nonlinear systems of equations (namely, 2x2 systems involving second-degree equations), and application of such systems.

• Systems of Linear Equations: three equations in three variables
  • Applications of 3x3 linear systems (11.1-2)
• Partial Fraction Decomposition (11.5)
• Nonlinear Systems Involving Second-Degree Equations (11.6)
  • Definition and number of solutions
  • Substitution method
  • Elimination method
  • Graphical solutions
  • Applications

Calculators may be used on this unit.

Unit 10 will be followed by the Final Exam.

Study Guidelines for the 8th edition of Sullivan's Precalculus

These reading and problem assignments are designed to help you learn the course material. You should complete all of these problems, check your answers in the back of the textbook, and get help with the problems that you missed. Most of the problems are odd-numbered, so you can check the solutions in the Solutions Manual.

The only way to learn mathematics is to do mathematics, so while these problems will not be collected or graded, you will probably not do well in the course if you do not complete these and check your work as described above. After completing these problems, go on to the Unit Exam Description below and follow directions.

• Sections 11.1 and 11.2: Applications of 3x3 Systems of Linear Equations
  • Reading: example 12 in section 11.1, and example 10 in section 11.2
  • Practice Problems: 11.1 #69, 70, 75-81
  • Practice Problems: 11.2 #73-81 odds
    
    
• Section 11.5: Partial Fraction Decomposition
  • Reading: section 11.5
    Read and work through examples 1-5 and their matched problems.
  • It is critical that you start with the correct form for a partial fraction decomposition, as described in Cases 1-4. If you choose the incorrect form, you will waste a lot of time and get the wrong answer. Read through the examples carefully. Partial fractions is just a mechanical procedure, but it takes practice to do it right.
  • More explanation and examples of partial fractions
  • Practice Problems: 11.5 #1-4, 5-45 odds
    
    
• Section 11.6: Systems of Nonlinear Equations
  • Reading: section 11.6
    Read and work through examples 1-6 and their matched problems.
  • Unlike the situation for linear systems, there is no one method that will work for all systems involving second-degree equations. Thus, you need to try the various techniques described in the textbook on lots of practice problems.
  • Practice Problems: 11.6 #1-4, 5, 9, 13, 15, 19, 23, 29, 37, 41, 47, 49, 53, 57, 61, 65, 69, 71-87 odds
    
• Supplementary material (optional):
  • Student Solutions Manual
  • Algebra Review booklet
  • CD lecture series (step-by-step video examples on CD)
  • For tutoring help, visit the Prentice Hall Tutor Center. Tutors can be contacted by phone, fax, or e-mail. To register, you will need the access code that came with your textbook.
  • Graphing Calculator Help

Unit 10 Pretest and Exam Description

After completing the above work, do the following:

1. Read the exam description:
   • This exam has 12 questions, and will count 15 points toward your grade. 
   • This exam has a one-hour time limit.
   • Calculators may be used on this unit.
   • Be sure to look under the entry box for the expected format of the answer.
     • Some problems ask you to solve a system of equations for which there may be more than one solution (for example, the systems in section 11.6). Each solution will be a point (x,y), so if there is more than one solution, you must separate the points with a semicolon. For example, if the system has solutions x=1,y=3 and x=5,y=-2, then your answer would be (1,3);(5,-2) or ( 5,-2);(1,3).
2. Complete the online Unit 10 Pretest assignment. You may use your book and notes if you wish.
   • Directions: Click on the link above, then choose the Unit 10 Pretest.
   • The pretest must be completed by the deadline date listed at the top of this page.
     However, you may redo the pretest as many times as you like before the due date.
     Your best score counts, and it will be rescaled to 5 points maximum.
3. If you are having trouble with any of the problems listed above or on the pretest, make use of the help resources listed on the Help page.
4. Arrange with your proctor to take the online proctored Unit 10 Exam. Remember to bring identification, and remember that you will not be able to take the unit exam after the deadline date given at the top of this page. You may NOT use your book or notes on this exam.
   • Directions: Click on the link above, then choose Unit 10 Exam.
   • The proctored unit exam must be completed by the deadline date listed at the top of this page, and may be repeated under certain conditions. See the Detailed Schedule page for specific rules.

   Note: Remember that you can always go back and take practice exams on this unit after the deadline has passed. In particular, this will help you prepare for the midterm and final exams.

   • Directions: Click on the link above, then choose Unit 10 Practice Exam. After the deadline has passed, this exam will be available in practice mode.

Unit 10 Checklist

To finish Unit 10, make sure that you have completed the following items:

• Read the material listed in the Study Guidelines.
• Practice the problems listed in the Study Guidelines, and use any of the listed supplementary material to help you understand the concepts.
• Complete the online Unit Pretest (read the exam description first).
• Complete the online proctored Unit Exam.

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