3. If x and y are real numbers, what is the simplified radical form

Size: px
Start display at page:

Download "3. If x and y are real numbers, what is the simplified radical form"

Transcription

1 lgebra II Practice Test Objective:.a. Which is equivalet to ?. Which epressio is aother way to write 5 4? If ad y are real umbers, what is the simplified radical form of 5 y 5? 5 y y y 5 5 y 5 Objective.b 4. What is the simplified epressio of What is the simplified form of 5 5? ?

2 6. What is the sum of ad 5 7? 7. The area of a square is. What is the legth of a side of the square? Objective.a 8. Which epressio represets the quotiet? 4 z z 4 z z 4 4 z z 4 z z 4 9. Which epressio represets the quotiet? z 4 z 4z y y 8y 8 y 6 0. Which epressio represets the quotiet? y 8 y 8 y 4 y 4 y 4y ( y 4)

3 . rectagular prism has a volume of 8 4 ad a height of. Which epressio represets the area of the base of the prism? objective.b. What is the completely simplified equivalet of ?. Which epressio represets the result of this subtractio? What is the simplified equivalet of? 55 57

4 objective.b 5. Which epressio is equivalet to 4i? i i 64i 64i 6. circuit has a curret of (8 + 7i) amps, ad aother circuit has a curret of (5 i) amps. What is the differece betwee the currets of the two circuits? ( 4i) amps ( + 4i) amps ( 0i) amps ( + 0i) amps 7. Which epressio is equivalet to 6 4? 6 4 6i 6 i 6 i 8. What is the product of i ad 5 4i i 7i i 7i? 9. What is the completely simplified equivalet of 5 i 5 i 5 i 5 i 5 i? objective.a 0. What is the paret graph of the followig fuctio ad what trasformatios have take place o it: y? The paret graph is y, which is shifted uits up. The paret graph is y, which is shifted uits dow. The paret graph is y, which is shifted uits to the left. The paret graph is y, which is shifted uits to the right.

5 . What is the paret fuctio of this graph? f 4 f f 4 f objective.b, what is the value of f g. If f ( ) ad g( ) 4 7 7?. If f ( ) ad g( ) f g, what is the value of?

6 4. If f ( ) ad g( ), which graph correspods to the fuctio of fg? lie R lie S lie T lie U Objective.c 5. If f ( ) 7 ad g( ), what epressio represets ( f ( g( ))? If f g, how might f ad f ad g f ad g f ad g f ad g g be defied?

7 Objective.d 7. Which statemet is true for the fuctio f( ) 4? 4 is ot i the rage of the fuctio. 4 is ot i the domai of the fuctio. -4 is ot i the rage of the fuctio. -4 is ot i the domai of the fuctio. 8. What is the domai of the fuctio f : 0 : 5 :,4 :, 4 5 8? 9. Which itervals correctly defie the domai of f,4 ad 4,, 4 ad 4,, 4 ad 4,, 4 ad,? 4

8 0. omai: 0, Rage: y y the give costraits? Which graph correspods to. Which fuctio has the fewest domai restrictios for real umbers? f f f f Objective.e. What is the iverse of f f f f f?

9 . What is the iverse of the fuctio f f 4 4 f 4 f 4 f 4? 4. Which graph represets the iverse of f? 5. Which statemet about graphs ad their iverse is true? They are symmetric about y. They are symmetric about the origi. They are symmetric about the -ais. They are symmetric about the y-ais.

10 Objective.a 6. Profits, P, are equal to sales, S, mius epeses, E. If epeses are equal to travel, T, plus materials, M, which system of equatios models this situatio? P S E P S E E T M E T M P S E E T M P S E E T M 7. Tyroe wats to sped at most $0,000 o two televisios, R ad S. Each televisio must cost at least $,000, ad televisio R must cost at least twice as much as televisio S. Which system of iequalities models the amout of moey spet o each televisio? RS 0, 000 R S R,000 S,000 RS 0,000 S R R,000 S,000 RS 0,000 R S R,000 S,000 RS 0, 000 S R R,000 S, Meredith ivests $50,000 i her ew busiess. It costs the compay $0 to produce each uit, which is sold for $5. Let represet the cost ad R represet the reveue for uits. Which statemet is true about the graphs of the equatios 50,000 0 ad R 5? oth slopes are positive. oth slopes are egative. Oe slope is positive, ad the other is zero. oe slope is egative, ad the other is positive. Objective.b 9. Which quadrats cotai the solutios to this system of iequalities? y y 4 quadrats I ad IV quadrats II ad III quadrats III ad IV quadrats II, III, ad IV

11 40. What is the solutio to this system of equatios? y 5 0 y 4 0, y, y, y, y 4. The corers of a triagle are (,), (4,4), ad (6,). Which system of iequalities describes the iterior of the triagle? 4y y y8 y y4 y8 4y y4 y8 y y y8 Objective.c 4. What is the solutio set of this system of equatios? y 0 y 0,,,0,0,,,0, 0,,0,, 4. What is the solutio set of this system of equatios? y 7y 0,5, 5,,5, 5,8 5,8, 8,5 8,5, 8,8

12 44. What is the solutio set of this system of equatios? y y, 4,,4, 4,,4,4,, 4,4,,4 Objective.a 45. How may real roots does the fuctio give by the graph have? 0 real roots real root real roots 4 real roots 46. What umber is added to both sides of the equatio it by completig the square? to solve

13 47. What is the solutio of 5 0? Objective.b f? 48. What is the y-itercept of (0, -) (0, ) (-, 0) (, 0) 49. What are the coordiates at the miimum poit of (-, -) (-, ) (, -) (, ) 50. Which fuctio represets this graph? f 4? f 4 f 4 f 4 f 4

14 5. Which statemet best describes these two fuctios? f 6 g 5 They have o commo poits. They have the same -itercepts. The maimum of f() is the same as the miimum of g(). The maimum of g() is the same as the miimum of f(). 5. Which statemet best describes these two fuctios? f 4 g 7 The maimum of f() is less tha the miimum of g(). The miimum of f() is less tha the maimum of g(). The maimum of f() is greater tha the miimum of g(). The miimum of f() is greater tha the maimum of g(). Objective.c 5. The legth of a rectagular swimmig pool is 0 feet greater tha the width. The surface area of the pool is,500 square feet. What are the legth ad width of the pool? legth = 0 ft, width =0 ft legth = 50 ft, width =0 ft legth = 60 ft, width =40 ft legth = 50 ft, width =0 ft 54. The profit, P, (i dollars) for ce ar Retal is give by P 00 0., where is the umber of cars reted. How may cars have to be reted for the compay to maimize profits? 500 cars,000 cars,500 cars 5,000 cars 55. The reveue, R, at a bowig alley is give by the equatio R,400, where is the umber of frames bowled. 800 What is the maimum amout of reveue the bowlig alley ca geerate? $800 $,00 $,800 $,400

15 Objective Which best describes the graph of circle ellipse parabola hyperbola y? What is the equatio of a circle with ceter (-4, ) ad diameter 6? 4 ( y ) 6 4 ( y ) 6 4 ( y ) 9 y 4 ( ) Which statemet describes the equatio y 6 8? It is a vertical parabola. It is a vertical hyperbola. It is a horizotal parabola. It is a horizotal hyperbola. 59. What is the equatio of the give parabola? y y y y 6

16 60. What is the equatio of the graphed Hyperbola? y 4 4 y 4 4 y y What is the verte of the parabola y (-, -9) (, -9) (-9, -) (-9, ) 9? 6. What is the equatio of the ellipse whose ceter is at the origi, major ais has legth of 0 uits alog the -ais, ad mior ais has legth of 6 uits? y a b y 5 9 y 9 5 y 0 y 00 6

17 Objective.5a 6. Which fuctio is best represeted by the data i this table? f ( ) f( ) f ( ) f ( ) X 0 4 Y What are the horizotal asymptote ad y-itercept for the graph of this fuctio f( ) 7? symptote: y=7, Itercept: (0, 7) symptote: y=-7, Itercept: (0, 7) symptote: y=7, Itercept: (0, 8) symptote: y=-7, Itercept: (0, 8) 65. Which fuctio is best represeted by this graph? f f f f ( ) log ( ) log ( ) log ( ) ( ) log ( )

18 66. Which fuctio is best represeted by this graph? f ( ) f f( ) f( ) ( )

19 67. Which graph represets the fuctio f ( ) log( )? objective.5b 68. Which fuctio is the iverse of f ( ) log? f ( ) e f( ) f( ) 0 f( ) log log If, what is the value of?

20 70. Which equatio represets the solutio for i the formula 6? log 6 log log log 6 log log6 log log6 7. What is the value of log 0? 0 ½ 0 7. If log 80, what is the value of? If 4Log, what is the value of? Objective:.5c 74. If the loudess of fizz i a ca of soda pop is represeted by F 4log 0 5, where is represeted by the itesity of soud, how loud is the fizz if 0? 4 decibels 8 decibels 6 decibels decibels

21 75. The formula, r, gives the aual iterest rate, r, required for your moey to double i years. If it takes 8 years for your moey to double, what was the approimate aual iterest rate? % 4% 8% 8% 76. The populatio, P, of prairie dogs icreases accordig to the equatio P,50e rt, where t is the umber of years, ad r is the rate of growth. Which equatio solves for r? P l,50 r t t r P l,50,50 l P r t t r,50 l P 77. The mass of a radioactive sample is give by M ( t) M00 kt, where t is the time i years, M 0 is the iitial mass, ad k is a costat. If 400 grams of this material decays to 40 grams i 0 years, what is the value of k? Objective.6a 78. Which equatio has - ad as solutios?

22 79. Which of these is a root of f ( ) 4? Give that ad are factors of the polyomial, 7, what is the third factor? What is the solutio set of, 5, 5, 5, 5 0 0? 8. rectagular prism has a volume of 0 cubic iches. The legth of the prism is 5 iches, the width is (-) iches, ad the height is (+) iches. What are the width ad height of the prism? width: i., height: 8 i. width: 4 i., height: 6 i. width: 6 i., height: 4 i. width: 8 i., height: i. 8. What is divided by ?

23 Objective.6b 84. I which directio does the graph of the parabola up left right dow y ope? 85. What is the graph of the polyomial y?

24 86. Which fuctio is represeted by this graph? f ( ) f ( ) f ( ) f ( ) 87. Which statemet describes the characteristics of the graph 4 of f ( ) 5? The graph primarily icreases i the third quadrat ad icreases i the first quadrat.. The graph primarily decreases i the secod quadrat ad icreases i the first quadrat.. The graph primarily icreases i the third quadrat ad decreases i the fourth quadrat.. The graph primarily decreases i the secod quadrat ad decreases i the fourth quadrat. Objective.6c 88. What is the y-itercept of the graph of y 4?

25 89. What are the - ad y-itercepts of this graphed fuctio? -itercepts: (-, 0), (., 0), (7, 0); y-itercepts: (0, 8) -itercepts: (-0, 8); y-itercepts: (-, 0), (., 0), (7, 0) -itercepts: (, 0), (-., 0), (-7, 0); y-itercepts: (0, 8) -itercepts: (0, 8); y-itercepts: (, 0), (-., 0), (-7, 0) 90. What is the set of -itercepts of this graphed fuctio? {} {-, } {-, } {-,, }

26 9. What is the set of approimate y-values of the relative miimum ad maimum of this graphed fuctio? {} {-, } {-, } {-,, } 9. What are the properties of the poit (0, ) i this graphed fuctio? It is a relative miimum ad a -itercept. It is a relative maimum ad a -itercept. It is a relative miimum ad a y-itercept. It is a relative maimum ad a y-itercept.

27 Objective.6 9. The itesity, L, of light varies iversely with the square of the distace, r, from the source of the light. Give that k is the costat of proportioality, which equatio describes this relatioship? L kr k L r L k r L kr 94. compay is sellig a item ad determies that the profit from sellig the item for a price of dollars is give by the fuctio below. P( ) ( 6) 4 4 Which price will maimize the profit? $4 $ $6 $0 95. The path of a kicked soccer ball ca be modeled by the fuctio f ( ) 6, where is the horizotal distace (i meters) ad f( ) is the height (i meters). If the height is meters, what is the horizotal distace? 4 meters 6 meters meters 4 meters 96. ladscape desiger has to costruct a rectagular flower bed with a perimeter of 00 feet ad the maimum possible area. What is the area of the flower bed? 5 sq. ft 00 sq. ft 65 sq. ft,500 sq. ft Objective.7a 97. What is the value of i this ratioal equatio 4 5?

28 98. What is the solutio set of this ratioal equatio {6} {-} {, 6} {-, -6} 5 9? What is the value of i this ratioal equatio 4 4 5? What is the solutio set of this ratioal equatio? {-,-} {-, } {-, } {, } Objective.7b 0. What is the vertical asymptote of the graph of 4 4 f( ) 4?

29 0. What is the graph of the fuctio f( )?

30 0. Which fuctio is represeted by this graph? f( ) f( ) f( ) f( ) 04. How may vertical asymptotes does the graph of y 4 0 vertical asymptotes vertical asymptote vertical asymptotes 4 vertical asymptotes have?

31 0bjective.7c 05. What is the horizotal asymptote of this graph? 0 y 0.5 y Which statemet correctly describes the asymptotes of the graph of this ratioal fuctio? The vertical asymptote is asymptote. The vertical asymptote is asymptote. The horizotal asymptote is asymptote. The horizotal asymptote is asymptote., ad there is a egative slat y, ad there is a egative slat, ad there is a positive slat y, ad there is a positive slat

32 07. How may -itercepts does the graph of y What are the vertical ad horizotal asymptotes of 4, ad y y 4, ad 4, ad y y 4, ad have? 9 f( ) 6? Objective.7d 09. If the surface area of a closed cylider is 5 square iches, which equatio represets the height of the cylider i terms of r? S rh r 5 r h r 5 r h r h5 r h5 r 0. homeower stocked his pod with fish. The umber of fish, F, 9 t icreases accordig to the equatio, F, where t is the time i 0.05t years. What is the approimate umber of fish after 0 years? 49 fish 69 fish 8 fish 9 fish. The cost,, i thousads of dollars, to remove percet of the trash 450 left by a torado is modeled by the equatio 5. pproimately what percet of trash will be removed if 00 thousad dollars are spet? 4% 50% 59% 64%

33 Objective.a. Nacy made a scatter plot of how much moey she had left at the ed of each day of her vacatio. Which table best represets the data i her scatter plot? ay 4 5 Moey $00 $00 $00 $00 $00 ay 4 5 Moey $00 $00 $00 $400 $500 ay 4 5 Moey $500 $00 $00 $400 $00 ay 4 5 Moey $500 $400 $00 $00 $00

34 . Which set of data best represets the data o the scatter plot? Time Memory Time Memory Time Memory Time Memory

35 4. Which scatter plot best represets the lack of correlatio betwee shoe size ad hair legth?

36 objective.b 5. The test scores ad hours studied of 6 studets were put ito a scatter plot. If aother studet studies hours, what is the most likely test score based o this data? Which of these observatios would be cosistet with a epoetial model of populatio growth? The populatio started out large, decreased i size, the became large agai. The populatio is observed to icrease at a faster rate as time passes. The populatio is observed to icrease steadily over time. The populatio grew very quickly but the declied.

37 Objective.c 7. Which equatio most closely models the data i the scatter plot? y y y y 8. Which type of fuctio best models the data i this scatter plot? epoetial logarithmic quadratic liear

38 9. Studets i a sciece classroom perform a eperimet to fid the rate at which a hot liquid cools i a freezer. They plot the temperature over time ad obtai the followig graph. Which type of fuctio best models the data i this scatter plot? epoetial logarithmic quadratic liear 0. Which equatio most closely models the data i the scatter plot? y 4 6 y 6 y 6 y 5 6

39 . Which equatio best models the data i this scatter plot? y 5 y 0.5 y y Objective.. What is the th term i the sequece {,, 5, 7, }? 4 5 rithmetic Sequeces & Series th term : a a ( ) d Sum: s a a Geometric Sequeces & Series th term : a a r Sum: s a ( r ) ( r)

40 . What is the sum of the first 6 terms of the series ?,906 7,8 5,64,48 rithmetic Sequeces & Series th term : a a ( ) d Sum: s a a Geometric Sequeces & Series th term : a a r Sum: s a ( r ) ( r) 4. child puts $.00 ito a piggy bak. Oe week later, he puts $.5 i the bak. Two weeks later, he puts $.50 i the bak, ad so o. How much moey does he put i the bak o the 5 th week? $ 6.5 $7.00 $9.00 $00.00 rithmetic Sequeces & Series th term : a a ( ) d Sum: s a a Geometric Sequeces & Series th term : a a r Sum: s a ( r ) ( r)

41 5. What is the value of i the geometric sequece,,,,... 8? rithmetic Sequeces & Series th term : a a ( ) d -4-9 Sum: s a a Geometric Sequeces & Series th term : a a r Sum: s a ( r ) ( r) 6. Which formula could be used to fid the sum of a arithmetic series if the last term is ukow? rithmetic Sequeces & Series th term : a a ( ) d Sum: s a a Geometric Sequeces & Series th term : a a r Sum: s s a ( ) d s a ( ) d s a ( ) d s a ( ) d a ( r ) ( r)

42 7. I a arithmetic sequece begiig with 6 ad edig with 405, how may itegers are divisible by 9? 4 itegers 4 itegers 44 itegers 45 itegers rithmetic Sequeces & Series th term : a a ( ) d Sum: s a a Geometric Sequeces & Series th term : a a r Sum: s a ( r ) ( r) 8. How may terms are there i a geometric series if the first term is, the commo ratio is 4, ad the sum of the series is,0? 4 terms 5 terms 6 terms terms rithmetic Sequeces & Series th term : a a ( ) d Sum: s a a Geometric Sequeces & Series th term : a a r Sum: s a ( r ) ( r)

43 swers

MATH 083 Final Exam Review

MATH 083 Final Exam Review MATH 08 Fial Eam Review Completig the problems i this review will greatly prepare you for the fial eam Calculator use is ot required, but you are permitted to use a calculator durig the fial eam period

More information

2-3 The Remainder and Factor Theorems

2-3 The Remainder and Factor Theorems - The Remaider ad Factor Theorems Factor each polyomial completely usig the give factor ad log divisio 1 x + x x 60; x + So, x + x x 60 = (x + )(x x 15) Factorig the quadratic expressio yields x + x x

More information

NATIONAL SENIOR CERTIFICATE GRADE 12

NATIONAL SENIOR CERTIFICATE GRADE 12 NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P EXEMPLAR 04 MARKS: 50 TIME: 3 hours This questio paper cosists of 8 pages ad iformatio sheet. Please tur over Mathematics/P DBE/04 NSC Grade Eemplar INSTRUCTIONS

More information

FOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS GRADE 10

FOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS GRADE 10 FOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS GRADE 10 [C] Commuicatio Measuremet A1. Solve problems that ivolve liear measuremet, usig: SI ad imperial uits of measure estimatio strategies measuremet strategies.

More information

MATHEMATICS P1 COMMON TEST JUNE 2014 NATIONAL SENIOR CERTIFICATE GRADE 12

MATHEMATICS P1 COMMON TEST JUNE 2014 NATIONAL SENIOR CERTIFICATE GRADE 12 Mathematics/P1 1 Jue 014 Commo Test MATHEMATICS P1 COMMON TEST JUNE 014 NATIONAL SENIOR CERTIFICATE GRADE 1 Marks: 15 Time: ½ hours N.B: This questio paper cosists of 7 pages ad 1 iformatio sheet. Please

More information

Chapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions

Chapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions Chapter 5 Uit Aual Amout ad Gradiet Fuctios IET 350 Egieerig Ecoomics Learig Objectives Chapter 5 Upo completio of this chapter you should uderstad: Calculatig future values from aual amouts. Calculatig

More information

NATIONAL SENIOR CERTIFICATE GRADE 11

NATIONAL SENIOR CERTIFICATE GRADE 11 NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P NOVEMBER 007 MARKS: 50 TIME: 3 hours This questio paper cosists of 9 pages, diagram sheet ad a -page formula sheet. Please tur over Mathematics/P DoE/November

More information

Algebra Vocabulary List (Definitions for Middle School Teachers)

Algebra Vocabulary List (Definitions for Middle School Teachers) Algebra Vocabulary List (Defiitios for Middle School Teachers) A Absolute Value Fuctio The absolute value of a real umber x, x is xifx 0 x = xifx < 0 http://www.math.tamu.edu/~stecher/171/f02/absolutevaluefuctio.pdf

More information

Listing terms of a finite sequence List all of the terms of each finite sequence. a) a n n 2 for 1 n 5 1 b) a n for 1 n 4 n 2

Listing terms of a finite sequence List all of the terms of each finite sequence. a) a n n 2 for 1 n 5 1 b) a n for 1 n 4 n 2 74 (4 ) Chapter 4 Sequeces ad Series 4. SEQUENCES I this sectio Defiitio Fidig a Formula for the th Term The word sequece is a familiar word. We may speak of a sequece of evets or say that somethig is

More information

Chapter 9: Correlation and Regression: Solutions

Chapter 9: Correlation and Regression: Solutions Chapter 9: Correlatio ad Regressio: Solutios 9.1 Correlatio I this sectio, we aim to aswer the questio: Is there a relatioship betwee A ad B? Is there a relatioship betwee the umber of emploee traiig hours

More information

Equation of a line. Line in coordinate geometry. Slope-intercept form ( 斜 截 式 ) Intercept form ( 截 距 式 ) Point-slope form ( 點 斜 式 )

Equation of a line. Line in coordinate geometry. Slope-intercept form ( 斜 截 式 ) Intercept form ( 截 距 式 ) Point-slope form ( 點 斜 式 ) Chapter : Liear Equatios Chapter Liear Equatios Lie i coordiate geometr I Cartesia coordiate sstems ( 卡 笛 兒 坐 標 系 統 ), a lie ca be represeted b a liear equatio, i.e., a polomial with degree. But before

More information

4.1 Sigma Notation and Riemann Sums

4.1 Sigma Notation and Riemann Sums 0 the itegral. Sigma Notatio ad Riema Sums Oe strategy for calculatig the area of a regio is to cut the regio ito simple shapes, calculate the area of each simple shape, ad the add these smaller areas

More information

.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth

.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth Questio 1: What is a ordiary auity? Let s look at a ordiary auity that is certai ad simple. By this, we mea a auity over a fixed term whose paymet period matches the iterest coversio period. Additioally,

More information

I. Why is there a time value to money (TVM)?

I. Why is there a time value to money (TVM)? Itroductio to the Time Value of Moey Lecture Outlie I. Why is there the cocept of time value? II. Sigle cash flows over multiple periods III. Groups of cash flows IV. Warigs o doig time value calculatios

More information

Trigonometric Form of a Complex Number. The Complex Plane. axis. ( 2, 1) or 2 i FIGURE 6.44. The absolute value of the complex number z a bi is

Trigonometric Form of a Complex Number. The Complex Plane. axis. ( 2, 1) or 2 i FIGURE 6.44. The absolute value of the complex number z a bi is 0_0605.qxd /5/05 0:45 AM Page 470 470 Chapter 6 Additioal Topics i Trigoometry 6.5 Trigoometric Form of a Complex Number What you should lear Plot complex umbers i the complex plae ad fid absolute values

More information

Lesson 17 Pearson s Correlation Coefficient

Lesson 17 Pearson s Correlation Coefficient Outlie Measures of Relatioships Pearso s Correlatio Coefficiet (r) -types of data -scatter plots -measure of directio -measure of stregth Computatio -covariatio of X ad Y -uique variatio i X ad Y -measurig

More information

Math 114- Intermediate Algebra Integral Exponents & Fractional Exponents (10 )

Math 114- Intermediate Algebra Integral Exponents & Fractional Exponents (10 ) Math 4 Math 4- Itermediate Algebra Itegral Epoets & Fractioal Epoets (0 ) Epoetial Fuctios Epoetial Fuctios ad Graphs I. Epoetial Fuctios The fuctio f ( ) a, where is a real umber, a 0, ad a, is called

More information

Learning objectives. Duc K. Nguyen - Corporate Finance 21/10/2014

Learning objectives. Duc K. Nguyen - Corporate Finance 21/10/2014 1 Lecture 3 Time Value of Moey ad Project Valuatio The timelie Three rules of time travels NPV of a stream of cash flows Perpetuities, auities ad other special cases Learig objectives 2 Uderstad the time-value

More information

Confidence Intervals for One Mean

Confidence Intervals for One Mean Chapter 420 Cofidece Itervals for Oe Mea Itroductio This routie calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) at a stated cofidece level for a

More information

Soving Recurrence Relations

Soving Recurrence Relations Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree

More information

CHAPTER 3 THE TIME VALUE OF MONEY

CHAPTER 3 THE TIME VALUE OF MONEY CHAPTER 3 THE TIME VALUE OF MONEY OVERVIEW A dollar i the had today is worth more tha a dollar to be received i the future because, if you had it ow, you could ivest that dollar ad ear iterest. Of all

More information

NATIONAL SENIOR CERTIFICATE GRADE 11

NATIONAL SENIOR CERTIFICATE GRADE 11 NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P EXEMPLAR 007 MARKS: 50 TIME: 3 hours This questio paper cosists of pages, 4 diagram sheets ad a -page formula sheet. Please tur over Mathematics/P DoE/Exemplar

More information

SAMPLE QUESTIONS FOR FINAL EXAM. (1) (2) (3) (4) Find the following using the definition of the Riemann integral: (2x + 1)dx

SAMPLE QUESTIONS FOR FINAL EXAM. (1) (2) (3) (4) Find the following using the definition of the Riemann integral: (2x + 1)dx SAMPLE QUESTIONS FOR FINAL EXAM REAL ANALYSIS I FALL 006 3 4 Fid the followig usig the defiitio of the Riema itegral: a 0 x + dx 3 Cosider the partitio P x 0 3, x 3 +, x 3 +,......, x 3 3 + 3 of the iterval

More information

Confidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the.

Confidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the. Cofidece Itervals A cofidece iterval is a iterval whose purpose is to estimate a parameter (a umber that could, i theory, be calculated from the populatio, if measuremets were available for the whole populatio).

More information

Normal Distribution.

Normal Distribution. Normal Distributio www.icrf.l Normal distributio I probability theory, the ormal or Gaussia distributio, is a cotiuous probability distributio that is ofte used as a first approimatio to describe realvalued

More information

1 Correlation and Regression Analysis

1 Correlation and Regression Analysis 1 Correlatio ad Regressio Aalysis I this sectio we will be ivestigatig the relatioship betwee two cotiuous variable, such as height ad weight, the cocetratio of a ijected drug ad heart rate, or the cosumptio

More information

CHAPTER 11 Financial mathematics

CHAPTER 11 Financial mathematics CHAPTER 11 Fiacial mathematics I this chapter you will: Calculate iterest usig the simple iterest formula ( ) Use the simple iterest formula to calculate the pricipal (P) Use the simple iterest formula

More information

Approximating Area under a curve with rectangles. To find the area under a curve we approximate the area using rectangles and then use limits to find

Approximating Area under a curve with rectangles. To find the area under a curve we approximate the area using rectangles and then use limits to find 1.8 Approximatig Area uder a curve with rectagles 1.6 To fid the area uder a curve we approximate the area usig rectagles ad the use limits to fid 1.4 the area. Example 1 Suppose we wat to estimate 1.

More information

7.1 Finding Rational Solutions of Polynomial Equations

7.1 Finding Rational Solutions of Polynomial Equations 4 Locker LESSON 7. Fidig Ratioal Solutios of Polyomial Equatios Name Class Date 7. Fidig Ratioal Solutios of Polyomial Equatios Essetial Questio: How do you fid the ratioal roots of a polyomial equatio?

More information

5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized?

5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized? 5.4 Amortizatio Questio 1: How do you fid the preset value of a auity? Questio 2: How is a loa amortized? Questio 3: How do you make a amortizatio table? Oe of the most commo fiacial istrumets a perso

More information

AP Calculus AB 2006 Scoring Guidelines Form B

AP Calculus AB 2006 Scoring Guidelines Form B AP Calculus AB 6 Scorig Guidelies Form B The College Board: Coectig Studets to College Success The College Board is a ot-for-profit membership associatio whose missio is to coect studets to college success

More information

SEQUENCES AND SERIES CHAPTER

SEQUENCES AND SERIES CHAPTER CHAPTER SEQUENCES AND SERIES Whe the Grat family purchased a computer for $,200 o a istallmet pla, they agreed to pay $00 each moth util the cost of the computer plus iterest had bee paid The iterest each

More information

SEQUENCES AND SERIES

SEQUENCES AND SERIES Chapter 9 SEQUENCES AND SERIES Natural umbers are the product of huma spirit. DEDEKIND 9.1 Itroductio I mathematics, the word, sequece is used i much the same way as it is i ordiary Eglish. Whe we say

More information

GCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number.

GCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number. GCSE STATISTICS You should kow: 1) How to draw a frequecy diagram: e.g. NUMBER TALLY FREQUENCY 1 3 5 ) How to draw a bar chart, a pictogram, ad a pie chart. 3) How to use averages: a) Mea - add up all

More information

3.1 Measures of Central Tendency. Introduction 5/28/2013. Data Description. Outline. Objectives. Objectives. Traditional Statistics Average

3.1 Measures of Central Tendency. Introduction 5/28/2013. Data Description. Outline. Objectives. Objectives. Traditional Statistics Average 5/8/013 C H 3A P T E R Outlie 3 1 Measures of Cetral Tedecy 3 Measures of Variatio 3 3 3 Measuresof Positio 3 4 Exploratory Data Aalysis Copyright 013 The McGraw Hill Compaies, Ic. C H 3A P T E R Objectives

More information

Vladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT

Vladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT Keywords: project maagemet, resource allocatio, etwork plaig Vladimir N Burkov, Dmitri A Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT The paper deals with the problems of resource allocatio betwee

More information

7. Sample Covariance and Correlation

7. Sample Covariance and Correlation 1 of 8 7/16/2009 6:06 AM Virtual Laboratories > 6. Radom Samples > 1 2 3 4 5 6 7 7. Sample Covariace ad Correlatio The Bivariate Model Suppose agai that we have a basic radom experimet, ad that X ad Y

More information

CS103X: Discrete Structures Homework 4 Solutions

CS103X: Discrete Structures Homework 4 Solutions CS103X: Discrete Structures Homewor 4 Solutios Due February 22, 2008 Exercise 1 10 poits. Silico Valley questios: a How may possible six-figure salaries i whole dollar amouts are there that cotai at least

More information

Limits, Continuity and derivatives (Stewart Ch. 2) say: the limit of f(x) equals L

Limits, Continuity and derivatives (Stewart Ch. 2) say: the limit of f(x) equals L Limits, Cotiuity ad derivatives (Stewart Ch. 2) f(x) = L say: the it of f(x) equals L as x approaches a The values of f(x) ca be as close to L as we like by takig x sufficietly close to a, but x a. If

More information

Lecture 13. Lecturer: Jonathan Kelner Scribe: Jonathan Pines (2009)

Lecture 13. Lecturer: Jonathan Kelner Scribe: Jonathan Pines (2009) 18.409 A Algorithmist s Toolkit October 27, 2009 Lecture 13 Lecturer: Joatha Keler Scribe: Joatha Pies (2009) 1 Outlie Last time, we proved the Bru-Mikowski iequality for boxes. Today we ll go over the

More information

The second difference is the sequence of differences of the first difference sequence, 2

The second difference is the sequence of differences of the first difference sequence, 2 Differece Equatios I differetial equatios, you look for a fuctio that satisfies ad equatio ivolvig derivatives. I differece equatios, istead of a fuctio of a cotiuous variable (such as time), we look for

More information

Measures of Central Tendency

Measures of Central Tendency Measures of Cetral Tedecy A studet s grade will be determied by exam grades ( each exam couts twice ad there are three exams, HW average (couts oce, fial exam ( couts three times. Fid the average if the

More information

Basic Elements of Arithmetic Sequences and Series

Basic Elements of Arithmetic Sequences and Series MA40S PRE-CALCULUS UNIT G GEOMETRIC SEQUENCES CLASS NOTES (COMPLETED NO NEED TO COPY NOTES FROM OVERHEAD) Basic Elemets of Arithmetic Sequeces ad Series Objective: To establish basic elemets of arithmetic

More information

FM4 CREDIT AND BORROWING

FM4 CREDIT AND BORROWING FM4 CREDIT AND BORROWING Whe you purchase big ticket items such as cars, boats, televisios ad the like, retailers ad fiacial istitutios have various terms ad coditios that are implemeted for the cosumer

More information

1 Computing the Standard Deviation of Sample Means

1 Computing the Standard Deviation of Sample Means Computig the Stadard Deviatio of Sample Meas Quality cotrol charts are based o sample meas ot o idividual values withi a sample. A sample is a group of items, which are cosidered all together for our aalysis.

More information

Time Value of Money. First some technical stuff. HP10B II users

Time Value of Money. First some technical stuff. HP10B II users Time Value of Moey Basis for the course Power of compoud iterest $3,600 each year ito a 401(k) pla yields $2,390,000 i 40 years First some techical stuff You will use your fiacial calculator i every sigle

More information

NEW HIGH PERFORMANCE COMPUTATIONAL METHODS FOR MORTGAGES AND ANNUITIES. Yuri Shestopaloff,

NEW HIGH PERFORMANCE COMPUTATIONAL METHODS FOR MORTGAGES AND ANNUITIES. Yuri Shestopaloff, NEW HIGH PERFORMNCE COMPUTTIONL METHODS FOR MORTGGES ND NNUITIES Yuri Shestopaloff, Geerally, mortgage ad auity equatios do ot have aalytical solutios for ukow iterest rate, which has to be foud usig umerical

More information

Running Time ( 3.1) Analysis of Algorithms. Experimental Studies ( 3.1.1) Limitations of Experiments. Pseudocode ( 3.1.2) Theoretical Analysis

Running Time ( 3.1) Analysis of Algorithms. Experimental Studies ( 3.1.1) Limitations of Experiments. Pseudocode ( 3.1.2) Theoretical Analysis Ruig Time ( 3.) Aalysis of Algorithms Iput Algorithm Output A algorithm is a step-by-step procedure for solvig a problem i a fiite amout of time. Most algorithms trasform iput objects ito output objects.

More information

Measures of Spread and Boxplots Discrete Math, Section 9.4

Measures of Spread and Boxplots Discrete Math, Section 9.4 Measures of Spread ad Boxplots Discrete Math, Sectio 9.4 We start with a example: Example 1: Comparig Mea ad Media Compute the mea ad media of each data set: S 1 = {4, 6, 8, 10, 1, 14, 16} S = {4, 7, 9,

More information

S. Tanny MAT 344 Spring 1999. be the minimum number of moves required.

S. Tanny MAT 344 Spring 1999. be the minimum number of moves required. S. Tay MAT 344 Sprig 999 Recurrece Relatios Tower of Haoi Let T be the miimum umber of moves required. T 0 = 0, T = 7 Iitial Coditios * T = T + $ T is a sequece (f. o itegers). Solve for T? * is a recurrece,

More information

Present Value Factor To bring one dollar in the future back to present, one uses the Present Value Factor (PVF): Concept 9: Present Value

Present Value Factor To bring one dollar in the future back to present, one uses the Present Value Factor (PVF): Concept 9: Present Value Cocept 9: Preset Value Is the value of a dollar received today the same as received a year from today? A dollar today is worth more tha a dollar tomorrow because of iflatio, opportuity cost, ad risk Brigig

More information

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,

More information

Bond Valuation I. What is a bond? Cash Flows of A Typical Bond. Bond Valuation. Coupon Rate and Current Yield. Cash Flows of A Typical Bond

Bond Valuation I. What is a bond? Cash Flows of A Typical Bond. Bond Valuation. Coupon Rate and Current Yield. Cash Flows of A Typical Bond What is a bod? Bod Valuatio I Bod is a I.O.U. Bod is a borrowig agreemet Bod issuers borrow moey from bod holders Bod is a fixed-icome security that typically pays periodic coupo paymets, ad a pricipal

More information

Department of Computer Science, University of Otago

Department of Computer Science, University of Otago Departmet of Computer Sciece, Uiversity of Otago Techical Report OUCS-2006-09 Permutatios Cotaiig May Patters Authors: M.H. Albert Departmet of Computer Sciece, Uiversity of Otago Micah Colema, Rya Fly

More information

Gregory Carey, 1998 Linear Transformations & Composites - 1. Linear Transformations and Linear Composites

Gregory Carey, 1998 Linear Transformations & Composites - 1. Linear Transformations and Linear Composites Gregory Carey, 1998 Liear Trasformatios & Composites - 1 Liear Trasformatios ad Liear Composites I Liear Trasformatios of Variables Meas ad Stadard Deviatios of Liear Trasformatios A liear trasformatio

More information

M06/5/MATME/SP2/ENG/TZ2/XX MATHEMATICS STANDARD LEVEL PAPER 2. Thursday 4 May 2006 (morning) 1 hour 30 minutes INSTRUCTIONS TO CANDIDATES

M06/5/MATME/SP2/ENG/TZ2/XX MATHEMATICS STANDARD LEVEL PAPER 2. Thursday 4 May 2006 (morning) 1 hour 30 minutes INSTRUCTIONS TO CANDIDATES IB MATHEMATICS STANDARD LEVEL PAPER 2 DIPLOMA PROGRAMME PROGRAMME DU DIPLÔME DU BI PROGRAMA DEL DIPLOMA DEL BI 22067304 Thursday 4 May 2006 (morig) 1 hour 30 miutes INSTRUCTIONS TO CANDIDATES Do ot ope

More information

Sequences and Series

Sequences and Series CHAPTER 9 Sequeces ad Series 9.. Covergece: Defiitio ad Examples Sequeces The purpose of this chapter is to itroduce a particular way of geeratig algorithms for fidig the values of fuctios defied by their

More information

CHAPTER 7: Central Limit Theorem: CLT for Averages (Means)

CHAPTER 7: Central Limit Theorem: CLT for Averages (Means) CHAPTER 7: Cetral Limit Theorem: CLT for Averages (Meas) X = the umber obtaied whe rollig oe six sided die oce. If we roll a six sided die oce, the mea of the probability distributio is X P(X = x) Simulatio:

More information

WHEN IS THE (CO)SINE OF A RATIONAL ANGLE EQUAL TO A RATIONAL NUMBER?

WHEN IS THE (CO)SINE OF A RATIONAL ANGLE EQUAL TO A RATIONAL NUMBER? WHEN IS THE (CO)SINE OF A RATIONAL ANGLE EQUAL TO A RATIONAL NUMBER? JÖRG JAHNEL 1. My Motivatio Some Sort of a Itroductio Last term I tought Topological Groups at the Göttige Georg August Uiversity. This

More information

5: Introduction to Estimation

5: Introduction to Estimation 5: Itroductio to Estimatio Cotets Acroyms ad symbols... 1 Statistical iferece... Estimatig µ with cofidece... 3 Samplig distributio of the mea... 3 Cofidece Iterval for μ whe σ is kow before had... 4 Sample

More information

Convexity, Inequalities, and Norms

Convexity, Inequalities, and Norms Covexity, Iequalities, ad Norms Covex Fuctios You are probably familiar with the otio of cocavity of fuctios. Give a twicedifferetiable fuctio ϕ: R R, We say that ϕ is covex (or cocave up) if ϕ (x) 0 for

More information

PSYCHOLOGICAL STATISTICS

PSYCHOLOGICAL STATISTICS UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION B Sc. Cousellig Psychology (0 Adm.) IV SEMESTER COMPLEMENTARY COURSE PSYCHOLOGICAL STATISTICS QUESTION BANK. Iferetial statistics is the brach of statistics

More information

Recursion and Recurrences

Recursion and Recurrences Chapter 5 Recursio ad Recurreces 5.1 Growth Rates of Solutios to Recurreces Divide ad Coquer Algorithms Oe of the most basic ad powerful algorithmic techiques is divide ad coquer. Cosider, for example,

More information

Taking DCOP to the Real World: Efficient Complete Solutions for Distributed Multi-Event Scheduling

Taking DCOP to the Real World: Efficient Complete Solutions for Distributed Multi-Event Scheduling Taig DCOP to the Real World: Efficiet Complete Solutios for Distributed Multi-Evet Schedulig Rajiv T. Maheswara, Milid Tambe, Emma Bowrig, Joatha P. Pearce, ad Pradeep araatham Uiversity of Souther Califoria

More information

Simple Annuities Present Value.

Simple Annuities Present Value. Simple Auities Preset Value. OBJECTIVES (i) To uderstad the uderlyig priciple of a preset value auity. (ii) To use a CASIO CFX-9850GB PLUS to efficietly compute values associated with preset value auities.

More information

Chapter 7: Confidence Interval and Sample Size

Chapter 7: Confidence Interval and Sample Size Chapter 7: Cofidece Iterval ad Sample Size Learig Objectives Upo successful completio of Chapter 7, you will be able to: Fid the cofidece iterval for the mea, proportio, ad variace. Determie the miimum

More information

FIBONACCI NUMBERS: AN APPLICATION OF LINEAR ALGEBRA. 1. Powers of a matrix

FIBONACCI NUMBERS: AN APPLICATION OF LINEAR ALGEBRA. 1. Powers of a matrix FIBONACCI NUMBERS: AN APPLICATION OF LINEAR ALGEBRA. Powers of a matrix We begi with a propositio which illustrates the usefuless of the diagoalizatio. Recall that a square matrix A is diogaalizable if

More information

BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets

BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets BENEIT-CST ANALYSIS iacial ad Ecoomic Appraisal usig Spreadsheets Ch. 2: Ivestmet Appraisal - Priciples Harry Campbell & Richard Brow School of Ecoomics The Uiversity of Queeslad Review of basic cocepts

More information

Chapter 6: Variance, the law of large numbers and the Monte-Carlo method

Chapter 6: Variance, the law of large numbers and the Monte-Carlo method Chapter 6: Variace, the law of large umbers ad the Mote-Carlo method Expected value, variace, ad Chebyshev iequality. If X is a radom variable recall that the expected value of X, E[X] is the average value

More information

THE ARITHMETIC OF INTEGERS. - multiplication, exponentiation, division, addition, and subtraction

THE ARITHMETIC OF INTEGERS. - multiplication, exponentiation, division, addition, and subtraction THE ARITHMETIC OF INTEGERS - multiplicatio, expoetiatio, divisio, additio, ad subtractio What to do ad what ot to do. THE INTEGERS Recall that a iteger is oe of the whole umbers, which may be either positive,

More information

Modified Line Search Method for Global Optimization

Modified Line Search Method for Global Optimization Modified Lie Search Method for Global Optimizatio Cria Grosa ad Ajith Abraham Ceter of Excellece for Quatifiable Quality of Service Norwegia Uiversity of Sciece ad Techology Trodheim, Norway {cria, ajith}@q2s.tu.o

More information

AP Calculus BC 2003 Scoring Guidelines Form B

AP Calculus BC 2003 Scoring Guidelines Form B AP Calculus BC Scorig Guidelies Form B The materials icluded i these files are iteded for use by AP teachers for course ad exam preparatio; permissio for ay other use must be sought from the Advaced Placemet

More information

Solving Logarithms and Exponential Equations

Solving Logarithms and Exponential Equations Solvig Logarithms ad Epoetial Equatios Logarithmic Equatios There are two major ideas required whe solvig Logarithmic Equatios. The first is the Defiitio of a Logarithm. You may recall from a earlier topic:

More information

GCE Further Mathematics (6360) Further Pure Unit 2 (MFP2) Textbook. Version: 1.4

GCE Further Mathematics (6360) Further Pure Unit 2 (MFP2) Textbook. Version: 1.4 GCE Further Mathematics (660) Further Pure Uit (MFP) Tetbook Versio: 4 MFP Tetbook A-level Further Mathematics 660 Further Pure : Cotets Chapter : Comple umbers 4 Itroductio 5 The geeral comple umber 5

More information

University of California, Los Angeles Department of Statistics. Distributions related to the normal distribution

University of California, Los Angeles Department of Statistics. Distributions related to the normal distribution Uiversity of Califoria, Los Ageles Departmet of Statistics Statistics 100B Istructor: Nicolas Christou Three importat distributios: Distributios related to the ormal distributio Chi-square (χ ) distributio.

More information

Divide and Conquer. Maximum/minimum. Integer Multiplication. CS125 Lecture 4 Fall 2015

Divide and Conquer. Maximum/minimum. Integer Multiplication. CS125 Lecture 4 Fall 2015 CS125 Lecture 4 Fall 2015 Divide ad Coquer We have see oe geeral paradigm for fidig algorithms: the greedy approach. We ow cosider aother geeral paradigm, kow as divide ad coquer. We have already see a

More information

Partial Di erential Equations

Partial Di erential Equations Partial Di eretial Equatios Partial Di eretial Equatios Much of moder sciece, egieerig, ad mathematics is based o the study of partial di eretial equatios, where a partial di eretial equatio is a equatio

More information

Time Value of Money, NPV and IRR equation solving with the TI-86

Time Value of Money, NPV and IRR equation solving with the TI-86 Time Value of Moey NPV ad IRR Equatio Solvig with the TI-86 (may work with TI-85) (similar process works with TI-83, TI-83 Plus ad may work with TI-82) Time Value of Moey, NPV ad IRR equatio solvig with

More information

1. C. The formula for the confidence interval for a population mean is: x t, which was

1. C. The formula for the confidence interval for a population mean is: x t, which was s 1. C. The formula for the cofidece iterval for a populatio mea is: x t, which was based o the sample Mea. So, x is guarateed to be i the iterval you form.. D. Use the rule : p-value

More information

Example 2 Find the square root of 0. The only square root of 0 is 0 (since 0 is not positive or negative, so those choices don t exist here).

Example 2 Find the square root of 0. The only square root of 0 is 0 (since 0 is not positive or negative, so those choices don t exist here). BEGINNING ALGEBRA Roots ad Radicals (revised summer, 00 Olso) Packet to Supplemet the Curret Textbook - Part Review of Square Roots & Irratioals (This portio ca be ay time before Part ad should mostly

More information

Example Consider the following set of data, showing the number of times a sample of 5 students check their per day:

Example Consider the following set of data, showing the number of times a sample of 5 students check their  per day: Sectio 82: Measures of cetral tedecy Whe thikig about questios such as: how may calories do I eat per day? or how much time do I sped talkig per day?, we quickly realize that the aswer will vary from day

More information

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008 I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces

More information

3. Covariance and Correlation

3. Covariance and Correlation Virtual Laboratories > 3. Expected Value > 1 2 3 4 5 6 3. Covariace ad Correlatio Recall that by takig the expected value of various trasformatios of a radom variable, we ca measure may iterestig characteristics

More information

Trading the randomness - Designing an optimal trading strategy under a drifted random walk price model

Trading the randomness - Designing an optimal trading strategy under a drifted random walk price model Tradig the radomess - Desigig a optimal tradig strategy uder a drifted radom walk price model Yuao Wu Math 20 Project Paper Professor Zachary Hamaker Abstract: I this paper the author iteds to explore

More information

Building Blocks Problem Related to Harmonic Series

Building Blocks Problem Related to Harmonic Series TMME, vol3, o, p.76 Buildig Blocks Problem Related to Harmoic Series Yutaka Nishiyama Osaka Uiversity of Ecoomics, Japa Abstract: I this discussio I give a eplaatio of the divergece ad covergece of ifiite

More information

MMQ Problems Solutions with Calculators. Managerial Finance

MMQ Problems Solutions with Calculators. Managerial Finance MMQ Problems Solutios with Calculators Maagerial Fiace 2008 Adrew Hall. MMQ Solutios With Calculators. Page 1 MMQ 1: Suppose Newma s spi lads o the prize of $100 to be collected i exactly 2 years, but

More information

Math C067 Sampling Distributions

Math C067 Sampling Distributions Math C067 Samplig Distributios Sample Mea ad Sample Proportio Richard Beigel Some time betwee April 16, 2007 ad April 16, 2007 Examples of Samplig A pollster may try to estimate the proportio of voters

More information

CDs Bought at a Bank verses CD s Bought from a Brokerage. Floyd Vest

CDs Bought at a Bank verses CD s Bought from a Brokerage. Floyd Vest CDs Bought at a Bak verses CD s Bought from a Brokerage Floyd Vest CDs bought at a bak. CD stads for Certificate of Deposit with the CD origiatig i a FDIC isured bak so that the CD is isured by the Uited

More information

A Resource for Free-standing Mathematics Qualifications Working with %

A Resource for Free-standing Mathematics Qualifications Working with % Ca you aswer these questios? A savigs accout gives % iterest per aum.. If 000 is ivested i this accout, how much will be i the accout at the ed of years? A ew car costs 16 000 ad its value falls by 1%

More information

MEI Structured Mathematics. Module Summary Sheets. Statistics 2 (Version B: reference to new book)

MEI Structured Mathematics. Module Summary Sheets. Statistics 2 (Version B: reference to new book) MEI Mathematics i Educatio ad Idustry MEI Structured Mathematics Module Summary Sheets Statistics (Versio B: referece to ew book) Topic : The Poisso Distributio Topic : The Normal Distributio Topic 3:

More information

hp calculators HP 12C Statistics - average and standard deviation Average and standard deviation concepts HP12C average and standard deviation

hp calculators HP 12C Statistics - average and standard deviation Average and standard deviation concepts HP12C average and standard deviation HP 1C Statistics - average ad stadard deviatio Average ad stadard deviatio cocepts HP1C average ad stadard deviatio Practice calculatig averages ad stadard deviatios with oe or two variables HP 1C Statistics

More information

Math 113 HW #11 Solutions

Math 113 HW #11 Solutions Math 3 HW # Solutios 5. 4. (a) Estimate the area uder the graph of f(x) = x from x = to x = 4 usig four approximatig rectagles ad right edpoits. Sketch the graph ad the rectagles. Is your estimate a uderestimate

More information

Your organization has a Class B IP address of 166.144.0.0 Before you implement subnetting, the Network ID and Host ID are divided as follows:

Your organization has a Class B IP address of 166.144.0.0 Before you implement subnetting, the Network ID and Host ID are divided as follows: Subettig Subettig is used to subdivide a sigle class of etwork i to multiple smaller etworks. Example: Your orgaizatio has a Class B IP address of 166.144.0.0 Before you implemet subettig, the Network

More information

Output Analysis (2, Chapters 10 &11 Law)

Output Analysis (2, Chapters 10 &11 Law) B. Maddah ENMG 6 Simulatio 05/0/07 Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should

More information

Escola Federal de Engenharia de Itajubá

Escola Federal de Engenharia de Itajubá Escola Federal de Egeharia de Itajubá Departameto de Egeharia Mecâica Pós-Graduação em Egeharia Mecâica MPF04 ANÁLISE DE SINAIS E AQUISÇÃO DE DADOS SINAIS E SISTEMAS Trabalho 02 (MATLAB) Prof. Dr. José

More information

INVESTMENT PERFORMANCE COUNCIL (IPC)

INVESTMENT PERFORMANCE COUNCIL (IPC) INVESTMENT PEFOMANCE COUNCIL (IPC) INVITATION TO COMMENT: Global Ivestmet Performace Stadards (GIPS ) Guidace Statemet o Calculatio Methodology The Associatio for Ivestmet Maagemet ad esearch (AIM) seeks

More information

Chapter 5: Inner Product Spaces

Chapter 5: Inner Product Spaces Chapter 5: Ier Product Spaces Chapter 5: Ier Product Spaces SECION A Itroductio to Ier Product Spaces By the ed of this sectio you will be able to uderstad what is meat by a ier product space give examples

More information

where: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return

where: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return EVALUATING ALTERNATIVE CAPITAL INVESTMENT PROGRAMS By Ke D. Duft, Extesio Ecoomist I the March 98 issue of this publicatio we reviewed the procedure by which a capital ivestmet project was assessed. The

More information

Overview. Learning Objectives. Point Estimate. Estimation. Estimating the Value of a Parameter Using Confidence Intervals

Overview. Learning Objectives. Point Estimate. Estimation. Estimating the Value of a Parameter Using Confidence Intervals Overview Estimatig the Value of a Parameter Usig Cofidece Itervals We apply the results about the sample mea the problem of estimatio Estimatio is the process of usig sample data estimate the value of

More information

Terminology for Bonds and Loans

Terminology for Bonds and Loans ³ ² ± Termiology for Bods ad Loas Pricipal give to borrower whe loa is made Simple loa: pricipal plus iterest repaid at oe date Fixed-paymet loa: series of (ofte equal) repaymets Bod is issued at some

More information