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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?

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posted: | 5/19/2009 |

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