n - 1 PMT = 2) ( ) + ( ) + (9 1) A) 7,002,009 B) 70,002,009 C) 70,020,009 D) 700,020,009

Transcription

1 MGF 1107-Math for Liberal Arts II-Final Eam Stud Guide Spring 015 The final eam will consist of three parts: both a multiple choice and free response section allowing a scientific calculator, and a free response section that must be completed without the use of a calculator. The stud guide is divided into those three sections. A formula bank is given below. Be advised that not ever formula ou will need is given. Make sure ou have learned all formulas required to work the problems below that are not given in the bank. Formulas Given: A = P 1 + r n nt A = Pe rt Y = 1 + r n n - 1 PMT = P r n r n -nt Part I. Multiple Choice (Scientific Calculators Allowed) Epress the epanded form as a Hindu-Arabic numeral. 1) ( ) + ( 10 5 ) + (9 10 ) + ( ) + (3 10 ) + ( ) + (8 1) A) 8,98,368 B) 60 C) 6 D) 331,776 ) ( ) + ( 10 ) + (9 1) A) 7,00,009 B) 70,00,009 C) 70,00,009 D) 700,00,009 3) ( ) + ( ) + ( ) + ( ) + ( 10-8 ) + ( 10-9 ) A) B) C) D) Write the Bablonian numeral as a Hindu-Arabic numeral. ) A) 1083 B) 18 C) 11,53 D) 903 5) A) B) 3300 C),00,71 D),16,71 Convert the numeral to a numeral in base ten. 6) 305si A) 15 B) 3 C) 35 D) 75 7) BAEsiteen A) 7,8 B) 5,196 C) 560 D),00 1

2 Write the Egptian numeral as a Hindu-Arabic numeral using the table below. Hindu-Arabic Numeral Egptian Numeral Description 1 Staff 10 Heel bone 100 Spiral 1000 Lotus blossom 10,000 Pointing finger 100,000 Tadpole 1,000,000 Astonished person 8) A) 13,0 B) 13,0 C) 13, D) 13,0 9) A) 3,3 B),300,3 C),030,3 D),003,3 Write the Hindu-Arabic numeral as an Egptian numeral using the table above. 10) 3,57 A) B) C) D)

3 11) 1,35,0 A) B) C) D) Write the Roman numeral as a Hindu-Arabic numeral. 1) XIII A) 103 B) 53 C) 13 D) 30 13) MDCXXXI A) 1631 B) 1831 C) 1591 D) 15,131 Write the Hindu-Arabic numeral as a Roman numeral. 1) 139 A) CXXXVIIII B) CXXLVIIII C) CXXXIX D) CXXLIX 15) 758 A) IVDCCLVIII B) IVDCCLVIII C) VIDCCLVIII D) MMMMDCCLVIII Write the Ionic Greek numeral as a Hindu-Arabic numeral using the table below. Hindu-Arabic Ionic Greek Hindu-Arabic Ionic Greek Hindu-Arabic Ionic Greek Numeral Numeral Numeral Numeral Numeral Numeral 1 α 0 κ 00 σ β 30 λ 300 τ 3 γ 0 µ 00 υ δ 50 ν 500 φ 5 ε 60 ξ 600 χ 6 7 ζ ο π ψ ω 8 η 90 Q θ ι 100 ρ 16) ια A) 10 B) 1 C) 1 D) 11 3

4 17) φξβ A) 76 B) 57 C) 56 D) 67 Evaluate the function at the given values of the variable. 18) f() = a. f(-1) b. f(-7) A) 30, 130 B) 10, 50 C) -5, -65 D) -50, ) f() = a. f(-) b. f(6) A) 960, 860 B) 1, 5 C) -7, 101 D) 11, 135 The figure shows the percentage of the U.S. population, f(), made up of teachers as a function of time,, where is the number of ears after Use the graph to solve the problem. 0) Use the graph to estimate f(50). A) % B) 50% C) 1% D) 3% Provide an appropriate response. 1) The cost, in millions of dollars, for a compan to manufacture thousand automobiles is given b the function C() = Find the number of automobiles that must be produced to minimize cost. Cost to Manufacture Automobiles Number of Autos (thousands) A) thousand automobiles B) 8 thousand automobiles C) 0 thousand automobiles D) 6 thousand automobiles

5 Epress the fraction as a percent. ) 1 A).5% B) 5% C) 80% D) 31.3% 3) A) 6.15 % B) 16.5 % C) 1.63 % D) 61.5 % Write the decimal as a percent. ) A) 0.95% B) % C) 0.095% D) 0.76% 5) A) 100% B).% C) 00% D) 0.% Solve the problem. 6) What number is 88% of 90? A) 790 B) 79,00 C) 79 D) 79. 7) What number is % of 17? A) 3.7 B) 0.37 C) 37 D) 37. 8) 39.3 is 9 1 % of what number? A) 35.6 B) 3560 C) 356 D) 35,600 9) 0. is 8% of what number? A) 0.5 B) C) 0.05 D) ) What percent of 110 is 0.7? A) 0.37% B) 37% C) 370% D) 3.7% 31) 5.5 is what percent of 55? A) 9.5% B) 1.05% C) 10.53% D) 950% The principal P is borrowed at simple interest rate r for a period of time t. Find the simple interest owed for the use of the mone. Round answer to the nearest cent. 3) P = $6700 r =.5% t = 1 months A) $ B) $77.63 C) $ D) $ ) P = $180 r = % t = ears A) $1.0 B) $8.00 C) $7.0 D) $19.0 5

6 The principal P is borrowed at simple interest rate r for a period of time t. Find the loan's future value (the total amount due at time t). Round answer to the nearest cent. 3) P = $160 r = 8% t = 3 ears A) $18.00 B) $ C) $198.0 D) $ ) P = $300 r = 7.5% t = 8 months A) $7.00 B) $31.50 C) $ D) $315.8 Solve the problem. 36) A passbook savings account has a rate of 6.1%. Find the effective annual ield if the interest is compounded semiannuall. A) 6.1% B) 6.% C) 6.3% D) 6% 37) A passbook savings account has a rate of 6%. Find the effective annual ield if the interest is compounded quarterl. A) 6.% B) 6.1% C) 6.3% D) 6% 38) Find the accumulated value of an investment of $7000 at 7% compounded continuousl for 6 ears. A) $10, B) $ C) $10, D) $10, ) Find the accumulated value of an investment of $8000 at 9% compounded continuousl for 6 ears. A) $13,16.80 B) $1,30.00 C) $13,78.05 D) $13, ) How much mone should be deposited toda in an account that earns 10% compounded semiannuall so that it will accumulate to $1000 in 1 ears? A) $ B) $ C) $35.10 D) $ ) James and Susan wish to have $10,000 available for their wedding in ears. How much mone should the set aside now at 6% compounded monthl in order to reach their financial goal? A) $10, B) $ C) $ D) $

7 Which of the following is a possible representation for the graph with the given edges. ) QR, RS, RT, and SS A) B) Q R Q T S R T S C) Q D) None of these R T S The graph models the football schedule for 5 area high schools. The vertices represent the teams and each game plaed is represented as an edge between two teams. Use the information in the graph to answer the question. 3) How man games are scheduled for West? A) 5 B) 7 C) D) 6 7

8 Use the weighted graph shown to answer the question. ) Find the weight of edge CE. A) B) C) 1 D) 1 5) Find the total weight of the circuit A, B, F, G, D, E, C, A. A) 111 B) 110 C) 87 D) 17 Determine if the graph must have Hamilton circuits. If so, determine the number of such circuits. 6) A) No B) Yes, 7 C) Yes, 500 D) Yes, 70 7) A) Yes, 70 B) Yes, 6 C) Yes, 500 D) No Determine the number of Hamilton circuits in a complete graph with the given number of vertices. 8) 6 A) 500 B) 10 C) cannot be determined D) 70 8

9 9) 15 A) 15! B) cannot be determined C) 16! D) 1! Find a spanning tree for the connected graph. 50) A) B) C) D) 51) A) B) C) D) 9

10 Part II. Free Response (Scientific Calculators Allowed) Work MUST be shown for credit in this section. Write the Hindu-Arabic numeral in epanded form. 5) ) 80,005,00 Use the table below to write the Maan numeral as a Hindu-Arabic numeral. 5) 55) Convert the base ten numeral to a numeral in the given base. 56),87 to base eight 57) 15 to base three Add in the indicated base. 58) 8765nine +586nine 10

11 59) 6Asiteen +593siteen Subtract in the indicated base. 60) 56eight - 36 eight 61) 653seven - 15seven Multipl in the indicated base. 6) 3si 5si 63) 3four 13four Divide in the indicated base. 6) 3four 10four 65) five 11five Calculate the slope of the line passing through the given points. If the slope is undefined, so state. Then indicate whether the line rises, falls, is horizontal, or is vertical. 66) (9, 6), (8, 9) 67) (1, 8), (1, 6) 11

12 In the following problem: a. Put the equation in slope-intercept form. b. Identif the slope and -intercept. c. Graph the line. 68) + = ) = Graph the line. 70) =

13 71) = Solve b the method of our choice. 7) - 5 = 7 - = 1 73) + = = -31 7) 3 + = = 0 Graph the linear inequalit. 75)

14 76) < First, create a scatter plot for the data in the table. Then, use the shape of the scatter plot given to determine if the data are best modeled b a linear function, an eponential function, a logarithmic function, or a quadratic function. 77) ) Solve the problem. 79) The price of a home is $60,000. The bank requires a 0% down pament and one point at the time of closing. The cost of the home is financed with a 15-ear fied-rate mortgage at 7%. a. Find the required down pament. b. Find the amount of the mortgage. c. How much must be paid for the one point at closing? d. Find the total cost of interest over 15 ears, to the nearest dollar. 1

15 80) The cost of a home on a particular island is $1,000,000. The bank requires a 15% down pament and three points at the time of closing. The cost of the home is financed with a 30-ear fied rate at 8%. a. Find the required down pament b. Find the amount of the mortgage c. Find the amount that must be paid for the three points at closing d. Find the monthl pament e. Find the total cost of interest over 30 ears. Use the preference table to answer the question. 81) Diners at the Rive Gauche restaurant answer a questionnaire about their favorite course in a French meal. The choices are: Appetizer (A), Entree (E), and Dessert (D). Their votes are summarized in the following table. Number of Votes First choice E D A D Second choice A A D E Third choice D E E A Which course is selected as the most favorite using the pluralit method? 8) Four students are running for president of their residence hall: Debra (D), Farah (F), Jorge (J), and Hillar (H). The votes of their fellow students are summarized in the following preference table. Number of Votes First choice D F J F H Second choice F J F J J Third choice H H H D D Fourth choice J D D H F Who is declared the new president using the pluralit method? 83) Diners at the Rive Gauche restaurant answer a questionnaire about their favorite course in a French meal. The choices are: Appetizer (A), Entree (E), and Dessert (D). Their votes are summarized in the following table. Number of Votes First choice E D A D Second choice A A D E Third choice D E E A Which course is selected as the most favorite using the Borda count method? 15

16 8) Four students are running for president of their dormitor: Debra (D), Farah (F), Jorge (J), and Hillar (H). The votes of their fellow students are summarized in the following preference table. Number of Votes First choice D F J F H Second choice F J F J J Third choice H H H D D Fourth choice J D D H F Who is declared the new president using the Borda count method? Use Euler's theorem to determine whether the graph has an Euler path (but not an Euler circuit), Euler circuit, or neither. Make sure ou can eplain WHY! 85) The graph has 10 even vertices and no odd vertices. 86) The graph has 5 even vertices and three odd vertices. 87) The graph has 53 even vertices and two odd vertices. Use Kruskal's algorithm to find the minimum spanning tree for the weighted graph. Give the total weight of the minimum spanning tree. 88) Solve the problem. 89) A corporate campus plans to run computer network cable between buildings. Use Krustal's algorithm to find the minimum spanning tree that allows the network to connect all the buildings. How much cable is needed? 16

17 Part III. Number Theor (NO Calculators Allowed). Work MUST be shown for credit in this section. Perform the indicated operation(s). Where possible, reduce the answer to lowest terms. 90) ) ) ) Perform the indicated operation. Simplif the answer when possible. 9) ) Rationalize the denominator. 96) 5 97) 1 18 Write the first si terms of the arithmetic sequence with the first term, a1, and common difference, d. 98) a1 = 17; d = -5 99) a1 =.9, d = 0.5 Write the first si terms of the geometric sequence with first term, a1, and common ratio, r. 100) a1 = -7; r = 101) a1 = 1 3, r = 1 Use the order of operations to simplif the epression. 10) (-0) 103)

18 10) - [7 - ( - 7)] + (3-5) 3 18

19 Answer Ke Testname: MGF 1107 FINAL EXAM REVIEW 1) A ) D 3) A ) C 5) D 6) D 7) A 8) D 9) C 10) C 11) B 1) C 13) A 1) C 15) A 16) D 17) C 18) B 19) B 0) D 1) A ) B 3) B ) A 5) C 6) D 7) A 8) B 9) A 30) B 31) D 3) D 33) A 3) C 35) B 36) B 37) B 38) D 39) C 0) D 1) B ) C 3) A ) D 5) B 6) A 7) A 8) B 9) D 19 50) A 51) C 5) ( ) + (1 10 ) + ( ) + (9 1) 53) ( ) + ( 10 7 ) + ( ) + ( ) + ( 0 10 ) + ( ) + ( 0 10 ) + ( ) + ( 1 ) 5) ) 5,366 56) 5,7 eight 57) 111three 58) 1570nine 59) BDDsiteen 60) 36eight 61) 66seven 6) 30si 63) 10four 6) 30four 65) 13five 66) - 3, falls 67) undefined, is vertical 68) a. = - 1 b. slope = - 1, -intercept = 0 c (0, 0)

20 Answer Ke Testname: MGF 1107 FINAL EXAM REVIEW 69) a. = b. slope = - 3 8, -intercept = 3 7) {(, ) 3 + = 10} 75) 10 c (0, 3) -5 70) ) ) ) quadratic function ) {(7, 0)} 73) {(7, 9)} 0

21 Answer Ke Testname: MGF 1107 FINAL EXAM REVIEW 97) ) eponential function 98) 17, 1, 7,, -3, -8 99).9, 5., 5.9, 6., 6.9, ) -7, -1, -8, -56, -11, - 101) 1 3, 1 6, 1 1, 1, 1 8, ) 9 103) 11 10) 79) a. down pament: $5,000 b. amount of mortgage: $08,000 c. points paid at closing: $080 d. total cost of interest over 15 ears: $336,51 80) a. $150,000; b. $850,000; c. $5,500; d. $637; e. $1,395,30 81) Entree 8) Farah 83) Appetizer 8) Farah 85) Euler circuit 86) neither 87) Euler path 88) ) 56 feet 90) ) 9 9) ) ) 7 95) ) 5 5 1