Study Sheet for Test 1 Math 105 C Fall

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Study Sheet for Test 1 Math 105 C Fall Powered By Docstoc
					Study Sheet for Final Math 105       Spring 2009

Covered by Final: This study sheet, tests, homeworks, your notes and your book are
your primary study aids. The shaded sections of the study sheet are almost always
covered on the final exam. Calculators are allowed on the exam, but may not be
shared. You may use the calculator handouts or similar documentation if you do not
have a TI-83+. “Using the Stat Package on the TI-83 Plus” and “Row Operations Using
the TI-83+”. I will inspect all handouts during the exam. If your copy of a handout has
extensive notes, I will furnish you with a “clean” copy for the exam.
TEST 1
Text                                 Assigned to        Suggested problems
                                     turn in
1.1     FUNCTIONS: Definition        1.1A:              Explain the vertical line test
        of function. Vertical line   8,10,15,16,17      as it relates to the definition
        test. Example 7, p. 9.       1.1B: 28, 30,      of a function.
        Determining the domain       32, 34, 36, 38,
        and range of a function.     40
1.2     LINEAR FUNCTIONS:            1.2A: 4, 6, 8,     Final: domain
                                     12, 14,18, 20,
                                     24, 26, 32
1.3     LINEAR MODELS:               1.3A: 2, 4
                                     1.3B: 8, 14, 17,
                                     18, 24
2.1     SYSTEMS OF LINEAR                               We covered examples 1, 3,
        EQUATIONS: graphical                            4, 7 ,8, 10 in class
        method, graphical
        method using calculator,                        2.1: 1, 9, 11, 19, 25, 31, 35
        substitution method,
        elimination method.
        Equivalent systems, p.
        64.
        Dependent system,
        inconsistent system.
        Break-even point.
2.2     USING MATRICES TO            2.2A: 19, 21, 22   Final exam:
        SOLVE SYSTEMS OF             Two problems
        LINEAR EQUATIONS:            on worksheet
                                                        dependent systems
        Row operations, reduced                         Remember how to
        row echelon form                                label row operations
2.3     LINEAR SYSTEM                2.3A: 1, 10
        APPLICATIONS: As
        you know, this section is
        primarily using your
        ability to solve systems
        of equations to word
        problems.
Some sample problems from old tests. These problems do not cover the
entire range of the material covered on the test. They are primarily to show
you the format of the type of problems on the test.-
   1.     [13] Solve the following system of equations by substitution (no
          matrices):
                  2 y  2x  4
                  x  3 y  12
      2.     [14] Solve the following system of equations using elimination by
             addition (no matrices):
               2x + y = -7
               x + 3y = -1
      3.      [13] Use the Gauss-Jordan method for augmented matrices to solve
             the following system of equations:
               2x1 + 3x2 + 3x3 = 1
               x1 + 3x2 + x3 = 7
               2x1 + 3x2 + x3 = 1

CALCULATOR PROBLEMS
         1. [10] Solve the system of equations using the matrix operations on your
      calculator. Put calculator input in the appropriate column.
              5.1x + 9.5y = 53.3
              3.2x - 3.6y = -4.8

Test 2
Text                                   Assigned to     Suggested problems
                                       turn in
2.3        LINEAR SYSTEM               1, 10           1-19 (odds)
           APPLICATIONS: As
           you know, this section is
           primarily using your
           ability to solve systems
           of equations to word
           problems.
4.1        GRAPHING LINEAR             2,11, 12, 20,   1-40 (38-40 require more
           INEQUALITIES:               26, 27, 34      thought, but you can work
                                                       them.)
4.2        LINEAR                      9, 10, 24, 25   1-19 (odds), 21-27 (odds)
           PROGRAMMING: omit
           Integer Programming for
           now.
Two problems from recent tests:
  1. (a) Solve the system of inequalities graphically on the graph provided. Do
     not find corner points. Shade and
     identify the solution region neatly.
     Note the directions of the inequalities.
     3 y  3 x  60
     2 y  x  40
     y  2 x  40
    (b) Indicate whether the solution region is bounded or unbounded and
explain your answer.
2. An electronics company manufactures two types of personal computers, a
   standard model and a laptop model. The table below gives the relevant
   data for a single day.
                            Labor-hours per unit     Maximum labor-
          Department        Standard Laptop          hours available
                                                     per week
                                     80           40 2000
          Assembly
          Testing                  7           7 280

         Profit per unit           $65       $45
(a) Using linear programming, determine how many standard models and
   how many laptops should be manufactured in order to maximize weekly
   profit? Show your work: define your variables, give the objective
   function, the constraints and all work leading to the optimal solution.
   The next page is available for your work.
(b) What is the maximum daily profit?
Test 3
Text   Text topics (page           Assigned to   Suggested problems
       number)                     turn in
1.2,   Review linear functions
1.3    and linear models
5.1    Degree of polynomial        2, 3, 9, 14   All types of problems, pp.
       (282); quadratic                          299-307
       function (283);
       parabola; vertex (284)—
       the formula gives only
       the x coordinate—
       remember to find the y
       coordinate of the vertex;
       Examples 1 and 2
5.2    Cubic function (311);       5, 6, 8       Problems 1-20, pp. 323-329
       Concavity (311);
       inflection points (311);
       quartic functions (318)
5.3    Exponential function        10, 16        Problems 1-20, pp. 343-344
       (331); horizontal
       asymptote (333); Table
       5.14 (333); Properties of
       exponents (334);
       Example 2 (335)
5.4    Logarithmic function      22, 26, 28          Problems 1-46, pp. 357-359.
       (348); common log and                         Be able to answer
       natural log (349);                            problem 47, p. 359.
       logarithmic and
       exponential function
       relationship (352); rules
       of logarithms (353);
       change of base formula
       (353)
5.5    Know the steps for        Worksheet           Problems 11-15, pp. 372-
       selecting a model; Table                      373.
       5.26, (361); Table 5.29                       For Final: be able
       (365)
                                                     to look at
                                                     scatterplot and
                                                     decide on
                                                     possible models.

Test 4
Text   Text topics (page            Assigned to      Suggested problems
       number)                      turn in
6.1    Solving exponential          1, 3, 9          Calculator problems: 21-25
       equations.                                    Problem 27
       Know how to use the
       information in the two
       boxes beginning on p.
       384 and on p. 387.
6.2    Simple and compound          11,12,19,27,33
       interest. Simple interest,
       p. 393; Compound
       interest, p. 395; APY, p.
       396; Continuous
       compounding, p. 399
6.3    Future value of an                            Assigned, but not to turn in:
       increasing annuity.                           3, 9, 17, 29, 33
       Be able to use all                            FV problems on TVM
       formulae.                                     handout.
6.4    Present value of a                            Assigned, but not to turn in:
       decreasing annuity.                           3, 9, 15, 23, 31, 33
       Be able to use all                            FV problems on TVM
       formulae.                                     handout.
Sample questions from Test 4
1. Bob buys a new house which costs $100,000. Bob makes a down payment of 20% of
the cost and finances the balance. If the loan is to be amortized over 15 years at an
interest rate of 5% compounded monthly, what will be the value of the monthly payment?
2. Bob wants to start a savings account so that he will have a balance of $10,000 dollars
in 10 years. If the bank account pays 4.8% interest compound semi-annually, how much
should Bob invest in the account?
3. How much must you invest each month into an account earning 4 percent interest
compounded monthly if you want the account balance to be at least $10,000 after three
years?
4. (a) [10 points] Find the amount in an account three years after a single deposit of
$800 (principal) is invested at annual simple interest rate of 7.5%.
 (b) [10] Find the amount in an account after three years when $800 invested at annual
nominal rate of 7.5% compounded monthly.
(c) [2] Why is your answer in part (b) larger than your answer in part (a)?
5. [12] In order to accumulate enough money to make a down payment on a house, a
couple deposits $200 per month into an account paying 5% compounded monthly. If
payments are made at the end of each period, how much money will be in the account in
4 years?
6. Some friends tell you that they paid $5000 as a down payment on a new house and
will pay $600 per month for 30 years. The annual interest rate is 7.2% compounded
monthly. (a) [12] What was the selling price of the house? (b) [4] What is the total
interest they will pay in 30 years?