University of Florida - MAC - 1114

MAC 1114 - Trigonometry Fall 2009Instructor: Miriam Castillo-Gil E-mail: miriam22@u.edu Textbook: Precalculus. Calculators: Calculators will not be allowed during exams and quizzes unless otherwise announced. The use of the calculator at home is highly d

University of Florida - MAC - 1114

Name:MAC 1114 Test 109/20/2007SHOW ALL YOUR WORK. Answers without procedure will be graded zero.[2 points] I. Complete the values (like seen in class) on the following triangles.[8 points] II. Multiple Choice1.tan 90 = 02.csc( ) 43.4.TrueFal

University of Florida - MAC - 1114

Name: Version A MAC 1114 Test 1Recall that: s = r A= 12 r 2 = t v= s t v = r 09/24/2009[6 points] I. MULTIPLE CHOICE (True and false are half a point each) 1. 2. 3. 4. One revolution is equivalent to radians The reference angle of is the angle the termi

University of Florida - MAC - 1114

Name:Version AMAC 1114 Test 210/23/2007SHOW ALL YOUR WORK. Answers without procedure will be graded zero.[5 points] I. MULTIPLE CHOICE1. For y = 3 tan(2x + ), suppose A=amplitude, T =Period and2=phase shift. Then which of thefollowing holds.a)

University of Florida - MAC - 1114

Name: MAC 1114 Test 2 PART I10/22/2009 [6pt] 1. Sketch the graph of 3 csc( x + ). Remember to label, Amplitude, Period, Phase Shift and 3 3 Asymptotes![2pt] 2. Answer TRUE OR FALSE a. b. c. The range of sin1 x is [ , ] 22 cos1 (cos( ) = 2 2 sin(sin1 3

University of Florida - MAC - 1114

Name:MAC 1114 Test 311/29/2007SHOW ALL YOUR WORK. Answers without procedure will be graded zero.[5 pts] 1. Solve the following equation, nding the exact value of in radians, express as fractions of on the interval 0 < 2 .3 tan2 = 12. Solve each equ

University of Florida - MAC - 1114

Name:Version AMAC 1114 Test 203/06/2008[5 points] I. MULTIPLE CHOICE1. For y = 5 sin(2x + ), suppose AM =amplitude, T =Period and2=phase shift. Then which of thefollowing holds.a)AM = 5b)AM = 5c)AM = 5d)AM = 5e)AM = 5T = T =T =T =T

University of Florida - MATH - MAC1147

MAC 1147 (3067) - Quiz #1Name:For full credit, you must show all work and circle your nal answer.1Perform the operation below. Leave fractional answers in simplest form. (1 point)112+6232Simplify the radical expression below. (2 points)8a5b23

University of Florida - MATH - MAC1147

MAC 1147 (3067) - Quiz #1Name:KeyFor full credit, you must show all work and circle your nal answer.1Perform the operation below. Leave fractional answers in simplest form. (1 point)112+62311213413+421+=+===.6236666632Simplify t

University of Florida - MATH - MAC1147

MAC 1147 (3069) - Quiz #1Name:KeyFor full credit, you must show all work and circle your nal answer.1Perform the operation below. Leave fractional answers in simplest form. (1 point)412+5 3 15412125212 5 + 293+=+===.5 3 1515 15 1

University of Florida - MATH - MAC1147

MAC 1147 (4258) - Quiz #1Name:For full credit, you must show all work and circle your nal answer.1Perform the operation below. Leave fractional answers in simplest form. (1 point)132+2 10 52Simplify the radical expression below. (2 points)27x7

University of Florida - MATH - MAC1147

MAC 1147 (4258) - Quiz #1Name:KeyFor full credit, you must show all work and circle your nal answer.1Perform the operation below. Leave fractional answers in simplest form. (1 point)132+2 10 513253453+463+=+===.2 10 510 10 101

University of Florida - MATH - MAC1147

MAC 1147 (4258) - Quiz #2Name:For full credit, you must show all work and circle your nal answer.1Write the rational expression in simplest form.Hint: Dont forget to specify domain restrictions, if any. (1 point)9x2 + 9 x2x + 22Find all solutions

University of Florida - MATH - MAC1147

MAC 1147 (4258) - Quiz #2Name:KeyFor full credit, you must show all work and circle your nal answer.1Write the rational expression in simplest form.Hint: Dont forget to specify domain restrictions, if any. (1 point)9x2 + 9 x2x + 29x2 + 9 x9x(x +

University of Florida - MATH - MAC1147

MAC 1147 (3069) - Quiz #3Name:KeyFor full credit, you must show all work and circle your nal answer.1Rewrite the expression using negative exponents. (1 point)2x2(x + 1) 32x(x + 1)2= (2 x)(x + 1)2/3 .Identify all x or y intercepts and graph t

University of Florida - MATH - MAC1147

MAC 1147 (3067) - Quiz #5Name:For full credit, you must show all work and circle your nal answer.1Use long division OR synthetic division to divide. (1.5 points)(2x3 + 14x2 20x + 7) (x + 6)Make sure to write your answer out after performing the long

University of Florida - MATH - MAC1147

MAC 1147 (3067) - Quiz #5Name:KeyFor full credit, you must show all work and circle your nal answer.1Use long division OR synthetic division to divide. (1.5 points)2x2x+6(2x3 + 14x2 20x + 7) (x + 6)+ 2x 322x3 + 14x2 20x 2x3 12x2+72x2 20x 2x2

University of Florida - MATH - MAC1147

MAC 1147 (3069) - Quiz #5Name:For full credit, you must show all work and circle your nal answer.1Use long division OR synthetic division to divide. (1.5 points)(3x3 16x2 72) (x 6)Make sure to write your answer out after performing the long division

University of Florida - MATH - MAC1147

MAC 1147 (3069) - Quiz #5Name:KeyFor full credit, you must show all work and circle your nal answer.1Use long division OR synthetic division to divide. (1.5 points)(3x3 16x2 72) (x 6)3x2 + 2x + 12x63x3 16x2 3x3 + 18x2 722x2 2x2 + 12x312x 72

University of Florida - MATH - MAC1147

MAC 1147 (4258) - Quiz #5Name:For full credit, you must show all work and circle your nal answer.1Use long division OR synthetic division to divide. (1.5 points)(9x3 16x 18x2 + 32) (x 2)Make sure to write your answer out after performing the long di

University of Florida - MATH - MAC1147

MAC 1147 (4258) - Quiz #5Name:KeyFor full credit, you must show all work and circle your nal answer.1Use long division OR synthetic division to divide. (1.5 points)(9x3 16x 18x2 + 32) (x 2)9x2x2 169x3 18x2 16x + 32 9x3 + 18x29 16x + 3216x 32

University of Florida - MATH - MAC1147

MAC 1147 - Quiz #6 PracticeName:For full credit, you must show all work and circle your nal answer.1The interest rate for a bank account is 7.5%. Find the annual percentage yield if interest is compounded:(2 points)(a) Weekly(b) Continuously[Note:

University of Florida - MATH - MAC1147

MAC 1147 - Quiz #7 PracticeName:KeyFor full credit, you must show all work and circle your nal answer.1The interest rate for a bank account is 7.5%. Find the annual percentage yield if interest is compounded:(2 points)(a) Weekly(b) Continuously[N

University of Florida - MATH - MAC1147

MAC 1147 (3067) - Quiz #8Name:For full credit, you must show all work and circle your nal answer.1(1 point) In each group of two statements, circle the one that is always true.tan(t) = tan(t)tan(t) = tan(t)2csc(t) = csc(t)csc(t) = csc(t)1(2 poi

University of Florida - MATH - MAC1147

MAC 1147 (3069) - Quiz #8Name:For full credit, you must show all work and circle your nal answer.1(1 point) In each group of two statements, circle the one that is always true.sec(t) = sec(t)sec(t) = sec(t)2csc(t) = csc(t)csc(t) = csc(t)tan(t) =

University of Florida - MATH - MAC1147

MAC 1147 (3069) - Quiz #8Name:KeyFor full credit, you must show all work and circle your nal answer.1(1 point) In each group of two statements, circle the one that is always true.sec(t) = sec(t)sec(t) = sec(t)csc(t) = csc(t)csc(t) = csc(t)sec(t)

University of Florida - MATH - MAC1147

MAC 1147 (4258) - Quiz #8Name:For full credit, you must show all work and circle your nal answer.1(1 point) In each group of two statements, circle the one that is always true.cos(t) = cos(t)cos(t) = cos(t)2sin(t) = sin(t)sin(t) = sin(t)(2 point

University of Florida - MATH - MAC1147

MAC 1147 (4258) - Quiz #8Name:KeyFor full credit, you must show all work and circle your nal answer.1(1 point) In each group of two statements, circle the one that is always true.cos(t) = cos(t)cos(t) = cos(t)sin(t) = sin(t)sin(t) = sin(t)cos(t)

University of Florida - MATH - MAC1147

MAC 1147 LECTURE OUTLINEYou should read the textbook sections covered in each days lecture beforeclass. After each lecture, review your notes and the text to make sure youunderstand the main ideas to prior to working the exercises.If you have question

University of Florida - MATH - MAC1147

University of Florida - MATH - MAC1147

FinalExamReviewforMAC1147Spring2009PartI:2pointseach1. True/False:If231isapolynomialofdegree4.a. TRUEb. FALSE1when2. If isinverselyproportionalto and4,then2a. TRUEb. FALSE,3. |2112a.1|2_.1b.4. Howmanysolutionsdoestheequationtan 4

University of Florida - MATH - MAC1147

Final Exam Review KEY for MAC1147 Spring 20091.2.3.4.5.FALSEFALSEBAC6.7.8.9.10.DBBBC11.12.13.14.15.BADCB, Ooops. There is a typo, it should be a 5 in the denominator by .16.17.18.19.20.EABCC21.22.23.24.25.AB

University of Florida - MATH - MAC1147

MAC 1147 LECTURE OUTLINEYou should read the textbook sections covered in each days lecture beforeclass. After each lecture, review your notes and the text to make sure youunderstand the main ideas to prior to working the exercises.If you have question

University of Florida - MATH - MAC1147

Lecture 2: Section A.2Exponents and RadicalsInteger ExponentsDef. Ifthenis a real number andis a positive integer,=where is the base andis the exponent or power.ex. (3)4 = 34 =(2)3 = 23 =NOTE:1) Zero exponent: If= 0, then2) Negative expon

University of Florida - MATH - MAC1147

Lecture 5: Section A.5Solving EquationsDef. An equation in is a statement that twoalgebraic expressions are equal.To solve an equation is to nd all values ofwhich the equation is true.forSuch values of are solutions (or roots, zeros)of the equatio

University of Florida - MATH - MAC1147

Lecture 8, part I: Section 1.3Linear Equations in Two VariablesDef. The equation++ = 0 is the generalform of a linear equation in two variables.The slopeofis dened by the formula=( x2 , y 2 )( x1 , y 1 )Slope as a Rate of ChangeFor line ,is

University of Florida - MATH - MAC1147

Lecture 11: Section 1.8Combinations of FunctionsAlgebra of FunctionsLet and be two functions with domains. We dene some new functions:NameDenitionandDomainex. Given ( ) =function3and ( ) =and its domain.. Find theex. If ( ) =and ( ) =func

University of Florida - MATH - MAC1147

Lecture 12: Section 1.9Inverse FunctionsDef. If a function is a set of ordered pairs ( , ),then inverse relation of is the set of orderedpairs ( , ).ex. Find the inverse relation of the following functions. Is the inverse a function?1): cfw_(2, 2),

University of Florida - MATH - MAC1147

Lecture 15: Section 2.4Complex NumbersConsider the equation2= 1.Def. The imaginary unit, , is the number suchthat2= 1 or= 1Power of1=5=2= 13=4=61 ==7=8=Therefore, every integer power of can be written as, 1, , 1.In general, d

University of Florida - MATH - MAC1147

Lecture 16, Part I: Section 2.5Zeros of Polynomial FunctionsLinear Factorization TheoremEvery polynomial function ( ) of degree > 0 canbe factored into linear factors (not necessarilydistinct) of the form( )=where1, 2, . . . ,(1 )(2) ()are co

University of Florida - MATH - MAC1147

Lecture 17: Section 2.6Rational FunctionsHoles and Vertical AsymptotesThe graph of a rational function ( ) =hole at=if()has a()1. both ( ) and ( ) have the common factor( ), and2. the simplied denominator DOES NOT havethe factor ( ).NOTE: To

University of Florida - MATH - MAC1147

Lecture 18: Section 2.7Nonlinear InequalitiesTo Solve a Polynomial Inequality1. Write the inequality with 0 on the right hand sideto obtain one of the following:( )>0( )0( )<0( )02. Find all real zeros of the polynomial ( ). Thesezeros are the c

University of Florida - MATH - MAC1147

Lecture 21: Section 3.2Logarithmic FunctionsRecall the graph of exponential function ( ) => 1:,(0,1)Since ( ) is one-to-one, it has an inverse function.Def. The logarithmic function with base ,where > 0 and = 1 is written ( ) = log andis dened by

University of Florida - MATH - MAC1147

Lecture 23: Section 3.4Exponential and Logarithmic EquationsTwo basic strategies for solving exponential orlogarithmic equations:1. One-to-One Properties=logif and only if= logif and only if2. Inverse Propertieslog=log=ex. Solve for :1) 2

University of Florida - MATH - MAC1147

Lecture 24: Section 3.5Exponential and Logarithmic ModelsFour common types of mathematical models involving exponential functions and logarithmic functions:1. Exponential growth model:where== amount at time= amount at time 0= relative growth rate,

University of Florida - MATH - MAC1147

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University of Florida - MATH - MAC1147

Lecture 30: Section 4.7Inverse Trigonometric FunctionsThe Inverse Sine Function11Lets restrict the domain to the interval , .22Then = sin is one-to-one.Def. The inverse sine function is dened by= sin1if and only ifwith domain [1, 1] and range ,

University of Florida - MATH - MAC1147

MAC 2311LECTURE OUTLINE and HOMEWORK EXERCISESStewart: Calculus, Early Transcendentals, 6th editionYou should read the textbook sections covered in each dayslecture before class. After each lecture, review your notes andthe text section to make sure

University of Florida - MATH - MAC1147

Disclaimer:This PDF file is a scanned copy of a sample of pages fromMr. Mahoneys MAC1147 10th Period Lecture.The file cannot be printed but may be viewed. Thepurpose of this file is to allow students to reviewcertain pages that had a lot of detail fi

University of Florida - MATH - MAC1147

Disclaimer:This PDF file is a scanned copy of a sample of pages fromMr. Mahoneys MAC1147 10th Period Lecture.The file cannot be printed but may be viewed. Thepurpose of this file is to allow students to reviewcertain pages that had a lot of detail fi

University of Florida - MATH - MAC1147

Disclaimer:This PDF file is a scanned copy of a sample of pages fromMr. Mahoneys MAC1147 10th Period Lecture.The file cannot be printed but may be viewed. Thepurpose of this file is to allow students to reviewcertain pages that had a lot of detail fi

University of Florida - MATH - MAC1147

Disclaimer:This PDF file is a scanned copy of a sample of pages fromMr. Mahoneys MAC1147 10th Period Lecture.The file cannot be printed but may be viewed. Thepurpose of this file is to allow students to reviewcertain pages that had a lot of detail fi

University of Florida - MATH - MAC1147

MAC1147: Quiz #1 Solutions09/01/20091. LetAA = 0, , 0.67,12, 5, ,3(3)2.State which elements ofare(3)2 = 3)(a) whole numbers; (0,(b) integers; (0, -5,(3)2 = 3)10.67, -5, ,3(,2)(c) rational numbers; (0,(d) irrational numbers.(3)2 = 3)

University of Florida - MATH - MAC1147

MAC1147: Quiz #209/08/2009In the top-right corner of a clean sheet of paper, write your name, UFID,and section number. Please use a pen with blue or black ink. When you arenished, FOLD your paper in half lengthwise and write your name on theback.1.

University of Florida - MATH - MAC1147

MAC1147: Quiz #309/15/2009In the top-right corner of a clean sheet of paper, write your name, UFID,and section number. Please use a pen with blue or black ink. When you arenished, FOLD your paper in half lengthwise and write your name on theback.1.

University of Florida - MATH - MAC1147

MAC1147: Quiz #409/22/2009In the top-right corner of a clean sheet of paper, write your name, UFID,and section number. Please use a pen with blue or black ink. When you arenished, FOLD your paper in half lengthwise and write your name on theback.1.

University of Florida - MATH - MAC1147

MAC1147: Quiz #509/29/2009In the top-right corner of a clean sheet of paper, write your name, UFID,and section number. Please use a pen with blue or black ink. When you arenished, FOLD your paper in half lengthwise and write your name on theback.1a

University of Florida - MATH - MAC1147

MAC1147: Quiz #610/06/2009In the top-right corner of a clean sheet of paper, write your name, UFID,and section number. Please use a pen with blue or black ink. When you arenished, FOLD your paper in half lengthwise and write your name on theback.1.

University of Florida - MATH - MAC1147

MAC1147: Quiz #710/20/2009In the top-right corner of a clean sheet of paper, write your name, UFID, and sectionnumber. Please use a pen with blue or black ink. When you are nished, FOLD your paperin half lengthwise and write your name on the back.1.

University of Florida - MATH - MAC1147

MAC1147: Quiz #810/27/2009In the top-right corner of a clean sheet of paper, write your name, UFID,and section number. Please use a pen with blue or black ink. When you arenished, FOLD your paper in half lengthwise and write your name on theback.1.

University of Florida - MATH - MAC1147

MAC1147: Quiz #911/3/2009In the top-right corner of a clean sheet of paper, write your name, UFID, and sectionnumber. Please use a pen with blue or black ink. When you are nished, FOLD your paperin half lengthwise and write your name on the back.1. F