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Mathematics for General Studies

by: Angelita Ledner

Mathematics for General Studies MATH 1010

Angelita Ledner
GPA 3.8

Matthew Duncan

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Matthew Duncan
Class Notes
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This 21 page Class Notes was uploaded by Angelita Ledner on Wednesday September 23, 2015. The Class Notes belongs to MATH 1010 at Middle Tennessee State University taught by Matthew Duncan in Fall. Since its upload, it has received 150 views. For similar materials see /class/212987/math-1010-middle-tennessee-state-university in Mathematics (M) at Middle Tennessee State University.


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Date Created: 09/23/15
SYLLABUS MATH 1010K Fall 2010 TRANSITIONAL COLLEGE ALGEBRA Instructor Mr Matthew Duncan phone 898 7859 office Office SAG 106A email mduncanmtsuedu Office Hours Monday 1200 1245 Tuesday 200 545 Wednesday 1215 1245 Thursday 200 545 Friday 1215 1245 Text and Materials Mathematical Ideas 11th edition by Miller Heeren and Hornsby A TI 8384 or TI8384 plus graphing calculator is also required IT89 TI92 and QWERTY keypad calculators are not allowed Please be advised that all instruction for calculator use will be based on the TI 8384 or TI8384 plus Computer Access MyMathLab is a required component of this course You will need internet access either at home or you may use the computers in SAG 202 wwwcoursecompasscom COURSE ID duncan Attendance Policy Attendance Policy Attendance is required at every class and roll will be taken daily An absence is any day that you are not in class regardless of the reason Tardiness and early departures will also be counted and three of them count as one absence Attendance records will be submitted at midterm and finals for nancial aid purposes More than 3 absences will result in an automatic F All homework assignments will be due at 1159 PM CST the night before the exam on that material ie Assignments that will be covered on Test 1 will be due the night before Test 1 Academic Misconduct Plagiarism cheating and other forms of academic dishonesty or facilitating any such act will not be tolerated Academic misconduct is a disciplinary offense and this instructor will punish such offenses to the highest degree allowed by the university A grade of quotFquot Will be assigned for the exercise or examination for the rst offense If there is a second offense a grade of quotFquot Will be assigned for the course Purpose The purpose of this course is to introduce the student to a wide variety of mathematical perspectives The course is designed to expand the student s appreciation of how mathematics applies to quantitative problems that originate in many fields and to provide opportunities to solve some of these problems The student will learn the process of problem solving An introduction to logic will provide tools of deductive reasoning that are essential to not only mathematics but also to other subjects and to daily life The student will encounter numeration systems in particular the binary system and its relation to computing devices Advanced topics in geometry will include such ideas as right triangle trigonometry graph theory fractals and projective and nonEuclidean geometry The formulas of nancial mathematics will be derived and applied to problems of annuity amortization and interest Probability and statistics will be introduced The student will be required to communicate the results of hisher mathematical work in forms such as write ups of solutions of selected problems and projects and oral presentations involving the use of technology such as graphing calculators MS Excel LOGO or The Geometer s Sketchpad Learning Outcomes Upon completion of this course the student will have the abilities to 1 Use inductive reasoning to generate hypotheses from identi able mathematical patterns and use logical operators in applications of deductive reasoning Apply processes of problem solving including Polya s method in various mathematical connotations 3 Make conversions between the binary and decimal numeration systems and show in uences of earlier numeration systems Distinguish between Euclidean and nonEuclidean geometries and apply Euclidean postulates in solving geometrical problems Exercise financial management formulas in the consumer mathematics topics of installment loans credit card usage home buying and investment opportunities Illustrate and prove set relationships using Venn diagrams and carry out combined set operations 7 Generate descriptive statistics from given data sets and nd probabilities of given events 8 Determine if given networks are Euler circuits or have Hamiltonian cycles 9 Sort figures into topologically equivalent classes 10Conduct an individual andor group project as assigned by instructor and prepare a report on the project 11Use appropriate technology such as a graphing calculator an MS Excel spreadsheet or Geometer s Sketchpad software in related mathematical applications N 4 U1 0391 Topical Outline This course will include material from Chapters 14 9 14 of the required text along with a selection of applications and independent presentations Topics included in the course consist of o Problem solving and communication of mathematics o Sets and Logic Geometry and right triangle trigonometry Counting and Probability Introductory Statistics The Mathematics of Personal Financial Management Requirements In order to accomplish the objectives of this course the learner is expected to o Attend class lectures Participate in class activities Read and study class assignments Solve assigned problem sets Complete tests quizzes etc Complete an individual assignment or project Complete a comprehensive final exam Testing and Grading Procedures Unit Tests 70 There will be 4 Unit Tests that are 100 points each and a class presentation worth 100 points Missed tests will be made up at a future date set by instructor Homework 10 This is computed as an average of online homework grades and quizzes Final exam 20 The final exam is comprehensive It is mandatory and will be given during the scheduled time for the Final Exam Section K classes cannot be passed without the completion of the final exam Evaluation Means of evaluation is at instructor s discretion There will be a required comprehensive final exam for this course that will count 20 of the grade Grading Student assessment will be at instructor s discretion A student must earn a grade of D or better to successfully complete the course The plusminus grade scale will not be used in this course Students may not drop or withdraw from this course unless they withdraw from all University courses or obtain special permission from the chair of the University Studies Department go to PH 202 for information Grading Scale A 90100 B 8089 C 7079 D 6069 Exam Name MULTIPLE CHOICE Choose the one alternative that best completes the statement or answers the question Decide whether the argument is an eannple of inductive or deductive reasoning 1 Every coach knows his sport well John Madden is a football coach Therefore John Madden knows football well A lnductive 2 All US Presidents have come from the original 48 states Therefore no US President can be from Alaska A Deductive Use the method of successive differences to determine the next term in the sequence 3 14 20 31 47 68 A 98 B 89 4 10 22 82 190 346 B 598 List the elements in the set 5 X l x is a whole number between 1 and 5 A 1234 B 234 Find nA for the set 6 A 2 4 6 810 A nA 4 B nA 2 7 A 4 4 5 5 8 8 A M 10 B M 3 Tell whether the statement is true or false 8 6 E 12 18 24 30 36 A True 9 2 612 0 2 612 A True Write true or false for the following statement Let A 3 5 7 9 11 13 B 3 5 9 11 C 5 9 13 10 9 C A True B Deductive B Inductive C 2 3 4 5 B False B False B False D ll34 5 4 n a mu 7 mm HM 121371EIH1213 A Nenher a Bath and g C A m 2 7 3173nA2 A g a Nenher C A man numbu nf mbmx nflh 11 6 E A 7 a 3 C s Snlv u ptnbkm 1A L15 3 passue sums n he sec m n A D C a m n m D m n m n n m n m m n Lin 1h dzmmlx in 3911 m Let u c mm 1 15 A A a n c A My WrYr 2 E qrwry 16AnEuC Aqsuw C qr Yr W Y 2 E qr 5 W Y pm A cmg mpmm I A Z 9 1D E 1A 4 Fmd A X a A 12 1A 91n 1D1A B121A 12A 91A 9 A m M 1UA C M 2 1A 9 1A In A 12 A 9 A 1a D 12 M 9 A D qr Y z D qr Y z Writ A ducrip nn nf nu xhadzd ng39nn un39ngth xymbnll A B c u n 7 WV 1 nudnd 1839 u ABnA aAra CE7A DAnE 19Le u1zsA5s7Ht A36K was c1s7K u 393 V d 5 6 B 25 Snlv 1h mum A mu 3 sun Writ mga m m 3911 xmumm c ADD D sun a She dues mteam 1255 um me D She Earl39s thesameasme 13 7 a True 23 p A q 23 A False B True Let p represent a true statement while 11 and r represent false statements Find the truth value of the compound statement 24 P A q v r 24 A True B False Construct a truth table for the statement 25 r A s 25 A r s r A s B r s r A s T T F T T T T F F T F F F T F F T F F F F F F T C r s r A s D r s r A s T T F T T F T F T T F F F T T F T F F F T F F T 26 s V p V s 26 As p sVst Bs p sVst T T T T T T T F T T F F F T T F T T F F T F F T Cs p sVst Ds p sVst T T F T T F T F T T F F F T T F T T F F T F F T 27 r q 27 AM q rq Br q rq Cr q rq Dr q rq T T T T T T T T F T T F T F T T F F T F F T F T F T F F T T F T T F T T F F F F F T F F T F F T SHORT ANSWER Write the word or phrase that best completes each statement or answers the question Draw a circuit representing the following statement as it is given Simplify if possible 28 P A r V q V p 28 MULTIPLE CHOICE wms ms cnnvuxz invuxt m cnnlnpnxiliv nf ms mmmm u xsqusnsa 19 m pass n pa Camspasuvs A m dun tparty mde pass a m dan tpassl wun t party c m party msnx passed D n 1 party m pass Dzlmnin whethuth ugumsnm valid at invalid u n read A Valid 3 Invalid A The squxrrels are scun39ymg a Squxrxels du nutsmn y dunng The day c The squxrrels are mt scun39ymg D Squxnels du nut scurry at mgm Snlv ms squnim 33 my z 3y r A A 16 Em C HE D 8 Snlv ms mum anh 39eeze m get The desxred szmngmv A 125 Mars 3 16 7ht2rs c 251nm D Z htsrs Snlv ms squnim 5 15 3A AEIIZ a3 c83 D 3 Snlv ms mum 35 Fmd ms mssng xsngm m The smdarh angl s s 9 Ex CgtltIZ DxA Ax16 31 Solve and gra h 36 18x 12 gt 62x 2 36 A 4 w l1 l0 399 I8 I7 6 5 I 3 2 1 0 1 2 3 B w 4 quot 39 39 39 39 11 10 9 8 7 6 5 4 3 2 1 0 1 2 3 C 4 w 39 39 11 10 9 8 7 6 5 34 3 2 1 0 1 2 3 D 0 w 39 7 6 5 4 3 2 1 6 1 2 3 4 5 6 7 Solve the inequality then graph the solution 37 4ltgtlt1lt2 37 I I I I I I I I I I I I I I I I I I I I I9 109876543210 1 2 3 4 5 6 7 8 910 AHLW l 1o9s7554321312 3 4 5 5 7 s 910 B15 39 1098765432l012 3 4395 5 7 8 910 C51 ma 1 109 8 7 5 3 4 3 2 1 0 D33 quot39 1098765432101234 5 6 7 8 910 Use a combination of rules for exponents to simplify Write answers with only positive exponents Assume that all variables represent nonzero real nanbers 38 2x52x33 38 2 2 2 C 2 1 A 22 90 B D X X3 X19 2 10X19 Factor completely 39 x2 30x 225 A x 152 B x 15x 15 40 1222 7z 12 A 122 4z 3 B 32 44z 3 41 25x2 36 A 5x 62 C 5x 65x 6 Solve the equation by using the quadratic formula Give only r 42 7x2 10x 2 A miJ11 B 5 4739139 43p23p 90 1 Find the slope of the line through the points 44 6 8 and 9 9 A 3 B B 3 i 345 g 15 Graph the following line 45 Through 0 5 m C x 152 C 12z 4z 12 B 5x 62 D 25x 1x 36 eal number solutions 015 55 14 D Prime D 32 44z 3 455 w 35 9 Lab 39 40 41 42 43 44 45 Write the slope intercept form of the equation for the line passing through the given pair of points 46 5 3 and 1 6 9 33 2 44 9 33 2 44 Ay7 ZXT By7 7x7 yizxT Dy77x7 Write an equation in slope intercept form of a line satisfying the set of conditions 47 Through 8 4 perpendicular to 4X 5y 12 4 4 8 12 5 5 Ay7 x By7 X Cyizx6 Dy7 ZX6 Find the domain and range 48 2 4 51 7 4 5 8 9 9 A D 5 2 9 7 5 R 8 2 9 4 2 B D 9 7 4 5 2 R 5 8 2 2 9 C D 5 8 2 2 9 R 9 7 4 5 2 D D 8 2 9 4 2 R 5 2 9 7 5 46 47 48 Assume thanks graph extsnds mde mtsly mum end 1 3 3 M5 57 w c mu w my 5 57 a my 3 Rpm mop 3 12935571 E o dag a c 32 C c 59 a ZLSyd3 C 45Uyd3 Find 1 mm mg mun gm my 53 A m 7 A 233 a 151 7 C m 7 Find 3911 exact VII of th func nn magnum 1h dmnmimlnx if nncunry 5 can 15w mm Snlv u rig triangn 5Aa191 9 D AA515 E375 b31A CA n1 a5n1 b1s 99 EA5U1 E399b DA n1 E3 DAZ D 3375de D m 3 143 3 Dyi 15 31 55 A 33 b 564 C 90 A B 57 a 868 c 1036 C B 57 a 366 c 672 B B 33 a 473 c 366 D B 33 a 868 c 473 Solve the problem 56 At a lumber comp any shelves are sold in 3 types of wood 3 different widths and 5 different lengths How many different types of shelves could be ordered A 45 B 30 C 27 D 11 57 A baseball manager has 10 players of the same ability How many 9 player starting lineups can he create A 3628800 B 362880 C 90 D 10 58 Given a group of 8 women and 11 men how many different ways are there of choosing one man and one woman for a committee A 19 B 361 C 88 D 342 59 Four married couples have reserved eight seats in a row at the theater starting at an aisle seat In how many ways can they arrange themselves if there are no restrictions on the seating arrangement A 16777216 B 8 C 5040 D 40 320 60 A baseball manager has 10 players of the same ability How many different 9 player starting lineups can he create A 90 B 10 C 3628800 D 362880 61 A student is told to work any 8 out of 10 questions on an exam ln how many different ways can he complete the exam The correctness of his answers has no bearing A 16 B 45 C 100000000 D 90 62 The library is to be given 5 books as a gift The books will be selected from a list of21 titles If each book selected must have a different title how many possible selections are there A 20349 B 4257578514e17 C 5109094217e19 D 2441880 63 If a single card is drawn from a standard 52 card deck in how many ways could it be a diamond or a face card A 21 ways B 25 ways C 13 ways D 22 ways 64 If subsets are formed using only digits from the set 1 2 3 4 how many subsets can be formed with at least two digits A 16 subsets B 11 subsets C 6 subsets D 5 subsets 65 If you toss six fair coins in how many ways can you obtain at least two heads A 58 ways B 57 ways C 63 ways D 64 ways 55 65 Find the probability 66 A bag contains 9 red marbles 8 blue marbles and 6 green marbles What is the probability that a randomly selected marble is blue 8 6 8 9 A 3 OE 13 67 Two fair 6 sided dice are rolled What is the probability the sum of the two numbers on the dice is 3 1 1 17 A 3 B 2 C E D E 68 When two balanced dice are rolled there are 36 possible outcomes What is the probability that the sum of the numbers on the dice is 6 or 10 2 4 4 A a B a C 3 D g 69 A fair die is rolled What is the probability of rolling a3 or a5 1 1 1 A 2 B a C 3 D E Find the indicated probability 70 A bag contains5 red marbles 4 blue marbles and 1 green marble If a marble is selected at random what is the probability that it is not blue A B 6 C 13 71 A fair die is rolled Find the probability that the number obtained is not greater than 4 A B C D Find the probability 72 If you are dealt two cards successively with replacement of the first from a standard 52 card deck find the probability of getting a heart on the first card and a diamond on the second 1 1 A 169 B E C 204 D 204 73 In one town 29 of all voters are Democrats If two voters are randomly selected for a survey find the probability that they are both Democrats 84 B 0290 C 0580 D 0081 Use the general multiplication rule to find the indicated probability 74 You are dealt two cards successively without replacement from a shuffled deck of 52 playing cards Find the probability that both cards are black 1 13 A B a 25 25 2652 C E D 102 69 71 72 73 74 cards Fmd the pmbabmtythanhe rst card 15 o m and the secund card 15 o queen 13 A 1 A m We 9 13 Cnnnmd en mum mph to we dun 75 Mr bum me o oepuyueempxoyeee uses m e graph ueow ore themes 23 m5 AZ 3m 27 A a C u 23A7 ZBZAU 2232A27 23A7 ms 3mm 33m 5 A25 mm mm m 5 3 A3 A3 5 3 o o A studentev A About szetuoems B About aetuoems c About 125 students D About 32 students Findth man nfth m nf am 7a 12 85113 AHZS am c9 mm Find the man at the g39vm zquzncy dixh39ibu nn 7 mm czA3 Dz7z Find the median 80 3 5 19 24 38 38 45 25 81 29 31 29 32 32 29 34 31 39 35 35 33 28 35 29 24 19 31 3131 A 32 Find the median for the given frequency distribution Find the mode or modes 83 20 34 46 34 49 34 49 8 A3 B 31 B 46 Find the range for the set of data given 84 6 16 A 1 85 11311 Value Frequency A 49 B5 B 24 C 35 C 49 C 23 Find the standard deviation Round to one more place than the data 86 19 14 17 6 5 14 14 16 15 A 47 87 Age yr 14 15 16 Frequency 33 40 32 33 B 17 C 45 C 168 80 D 38 81 D 3085 82 D 30 83 D 34 84 D 16 85 D 22 86 D 51 87 D 08 Use Chebyshev39s theorem to solve the problem 88 Find the least possible fraction of numbers in a data set lying within 5 standard deviations of the 88 mean 1 24 1 4 NE 3 C D 89 In a certain distribution of numbers the mean is 50 and the standard deviation is 6 What can yOL 89 say about the fraction ofnumbers that lie between 32 and 68 A at least B at most C at most D at least Solve the problem 90 Elizabeth and Angela skate for their college speed skating team In the last race Elizabeth skated 90 the 500 meter race in 60 seconds The average for this race is 65 seconds with a standard deviation of 40 seconds Angela skated the 1000 meter race in 132 seconds The average for this race is 140 seconds with a standard deviation of 100 seconds Find the z score for each skater Relatively speaking which skater had the faster time A 12 08 Elizabeth B 12 08 Angela C 50 80 Angela D 50 80 Elizabeth At one high school the mean time for running the 100 yard dash is 152 seconds with a standard deviation of 09 seconds The times are very closely approximated by anormal curve Find the percent of times that are 91 Greater than 161 seconds 91 A 155 B 2 C 16 D 135 A company installs 5000 light bulbs The lifetimes of the lightbulbs are approximately normally distributed with a mean of 500 hours and a standard deviation of 100 hours Find the approximate number of bulbs that can be expected to last the indicated amount of time 92 Less than 500 hours 92 A 2500 B 3000 C 2400 D 1000 93 At least 500 hours 93 A 2500 B 1000 C 2400 D 5000 Solve the problem 94 Scores on a test are approximately normally distributed with a mean of 70 and a standard deviation 94 of 9 The teacher wants to give A39s to the top 10 of students What is the bottom cutoff for an A grade Round your answer to the nearest whole number 13 82 C 80 D 90 Find the indicated probability or percentage for the normally distributed variable 95 A machine produces bolts with a mean diameter of 030 inches and a standard deviation of 95 001 inches The diameters are approximately normally distributed What is the probability that a randomly selected bolt will have a diameter greater than 032 inches A 0977 B 0023 C 0477 D 0046 Find the simple interest The rate is an annual rate unless otherwise noted Assume 365 days in a year and 30 days pe th 96 1400 at 6 for 1 year 96 A 840 B 840 C 233 D 84 Use the compound interest formula to compute the future value of the investment 97 15000 at 8 compounded annually for 12 years 97 A 2820000 B 3497458 C 3777255 D 2940000 98 900 at 5 compounded quarterly for 6 years 98 A 96964 B 120609 C 117000 D 121262 Find the effective annual interest rate for the given nominal annual interest rate Round your answers to the nearest 001 99 4 compounded semiannually 99 A 406 B 404 C 400 D 407 100 6 compounded quarterly 100 A 617 B 600 C 609 D 614 Solve the problem 101 Joe is buying some kitchen equipment for his new apartment The total cost is 3400 and he places a 101 down payment of 340 There is add on interest of9 What is the total amount to be repaid if he takes 3 years to pay for the purchase A 388620 B 8568000 C 333540 D None of the above is correct Find the nance charge on the open end charge account Asqune interest is calculated on the unpaid balance of the account 102 Unpaid Balance Monthly Interest Rate 102 48110 139 A 514 B 428 C 802 D 669 Find the unpaid balance at the end of the month for the Open end Charge Account 103 Unp aid Balance 103 at Beginning Finance Month of Month Charge Purchases Returns Panent Mar 84670 17840 1497 10500 Monthly interest rate is 13 on the unpaid balance A 93111 B 91614 C 94608 D 6944 Find the APR true annual interest rate to the nearest half percent for the following loan 104 Amount Financed 1200 104 Finance Charge 90 Number of Monthly Payments 12 A 125 B 135 C 13 D 12 Find the APR true annual interest rate to the nearest half percent for the following 105 Amount financed 5800 105 Monthly payment 26897 Number of payments 24 A 12 B 95 C 105 D 14 Solve the problem 106 An item is purchased for 800 with a down payment of 50 There is a finance charge of30 Find 106 the monthly payment if 10 payments are made A 78 8 75 C 83 D None of the above is correct Use the actuarial method to find the mount of unearned interest for the loan paid in full before the due date 107 Regular Monthly Payment 42777 107 APR 12 Remaining Number of Scheduled Payments After Payoff 36 A 261239 B 321640 C 164991 D 252047 Use the actuarial method to find the payoff mount for the loan paid in full before its due date 108 Regular Monthly Payment 45134 108 APR 12 Remaining Payments After Payoff 36 A 1495876 B 1330595 C 1404023 D 1394325 Use the actuarial method to find the mount of unearned interest for the loan paid in full before the due date 109 Regular Monthly Payment 23524 109 APR 10 Remaining Number of Scheduled Payments After Payoff 6 A 4211 B 4031 C 7339 D 12821 Use the actuarial method to find the payoff amount for the loan paid in full before its due date 110 Regular Monthly Payment 20849 110 APR 10 Remaining Payments After Payoff 6 A 134580 B 139438 C 142211 D 142370 Answer Key Testname FINAL REVIEW 1010 F10 27 D 23 The skatean ampli es m p A rVq Testname FINAL REVIEW 1010 F10 Answer Key DCDACDADADCCBCAACDCBADBBCCACDABADBADCBBBDDCCABBDAC 9M uwmmmw wwwwmwww mmwwmnmmMWmmmmmMwwwwm 18


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