PART 1 MULTIPLE CHOICE Circle the appropriate response to each of the questions below. Each question has a value of 1 point.


 Kelley Hood
 1 years ago
 Views:
Transcription
1 PART MULTIPLE CHOICE Circle the pproprite response to ech of the questions below. Ech question hs vlue of point.. If in sequence the second level difference is constnt, thn the sequence is:. rithmetic b. liner qudrtic d. cubic A first level difference indictes n rithmetic sequence. A second level difference indictes qudrtic sequence. A third level difference indictes cubic sequence. A sequence with common rtio between terms indictes geometric sequence.. The eqution of the xis of symmetry of the prbol represented by the function y x is :. x b. x y d. x 0 When the eqution is plced in trnsformtionl form, y + x, the vertex cn be tken from the horizontl trnsltion nd the verticl trnsltion, in this cse, (0,). The eqution of the xis of symmetry is lwys the xvlue of the vertex becuse the xis of symmetry will lwys be verticl line. Therefore, the eqution for the xis of symmetry ( verticl line) is x 0.. Given the eqution x , then x is equl to:. ± 4 b. ± 4 i 6. 9 d. no possible vlue To solve for the vlue of x, we need to use order of opertions in reverse to isolte the vrible. We would subtrct 48 from both sides to give x 48. Then we would squre root both sides, giving us x ± 48. Since you cnnot squre root negtive numbers, we re now deling with complex numbers (IMAGINARY!!!). We would need to simplify the root 48. The solution would give x ±4 i. 4. For the function y x + bx + c, the yintercept is lwys: b.. c c 4c d. 4 y x + bx + c When in the generl form, intercept., the vlue of c will lwys give you the y. If the eqution kx 4x + 0 hs two equl rel roots ( rel root), then the vlue of k is:. k 0 b. k > 0 k d. k > equl rel roots (or rel root) mens tht the discriminnt, b 4c ( 4) 4( )(), is equl to 0. We would plug in ech vlue s follows: k 0. We would then simplify the eqution to 6 8k 0 nd then solve for the vlue of k, which would be. 6. An Olympic diver dives from the high diving bord. The distnce, d, in meters, from the surfce of the wter vries with the time, t, in seconds, tht hve pssed since she left the bord, ccording to the eqution d t + t + 0. Wht is her mximum elevtion bove the wter during the dive? (round to the nerest unit).. meters b. 0 meters meters d. meters We lredy know the eqution nd we re being sked for the MAXIMUM height. I should ( ) immeditely think VERTEX. We find the x of the vertex, x vertex or0. 7. This is the time of the mximum height. To solve for the y, I plug in the vlue of t into the originl eqution d (0.7) + (0.7) + 0., round to the nerest unit, is meters Which of the following is the trnsformtionl form of the function y ( x ) +?
2 . ( y ( x ) b. y ) ( x ) d. ( y ) ( x ) y ( x ) I would use my formul sheet which tells me tht trnsformtionl form looks like this ( y k) ( x h). I would then strt to rerrnge the eqution given until it looks like trnsformtionl form. This would strt by subtrcting from both sides to give y ( x ) nd then I would divide both sides by to give ( ) ( x ) 8. Wht vlue of b mkes the expression x + bx + perfect squre? b. d. y. When I complete the squre, I will tke the vlue of b (ssuming tht the vlue of is lredy ) nd divide it by two, then squre it. I hve the finl vlue, so I need to work 6 6 bckwrds. I would squre root to give me, but then I would hve to multiply by, so I would end up with s my finl nswer. 9. The students t Est High School re plnning surprise prty for the principl. One student tells two other students who in turn tell two other people. These people ech tell two other people nd so on. Wht type of sequence is generted in this sitution?. cubic b. geometric qudrtic d. rithmetic One person would tell, then would tell more ech, et This would be sequence tht looks like {,, 4, 8, 6..} which hs common rtio of, therefore, it would be geometric becuse of wht we lredy discussed in question. 0. Which of the following is NOT geometric sequence? 9. {,,, } b. {4, 8,., } {0.8, 0.08, 0.008, } d. {,, 4, } For geometric sequence, there needs to be common rtio. In, the common rtio when I tke the rd term nd divide it by the nd nd the nd divided by the st is.. In b, the common rtio is 0.7. In c, the common rtio is 0.. However, in d, when I divide the rd term by the nd term I get 0.7 nd when I divide the nd term by the first term, I get twothirds ( ). There is no common rtio in d, therefore, it is NOT geometri
3 . Given the grph below, determine the generl form of the function WITHOUT using regression on your clcultor. [ points] I hve three points but I m not llowed to use regression. I need to strt with the trnsformtionl form becuse I know the vertex. ( y k) ( x h) nd plug in the vlues of my vertex to get ( y 6) ( x + ). Then I would substitute in one of the other two points nd solve for. (0 6) ( 6 + ) which simplifies to give ( 6) ( 4) nd then ( 6) 6so when I divide both sides by 6, I get. ( 6) ( x + ) I plug this bck into ( y 6) ( x + ) to get ( y 6) ( x + ). I then multiply both sides by  to get y nd then strt to simplify to get ( y 6) ( x + 4x + 4) nd then I get y 6 x 4x 4) nd then dd 6 to both sides to get y by itself, which is generl form. y x 4x +. Solve lgebriclly to find the exct roots of the following equtions. Simplify where possible. ) 6x [. points] + 6x 0 ( x + ) 0 0 x + 0 x 0 x 4 b) + 4 x x + [ points] ( x + ) 4( x) + ( x)( x + ) ( x)( x + ) ( x + ) + 4( x) 4 ( x)( x + ) x x x x x + x x + 8 4x 0 4x ± () + x + 6 ( 4) ± ± 8 + 4x + 4 4( 4)(6) x 4 x
4 . {, +k, 6k } is geometric sequence. ) Find the vlue of k [ points] 6 k + k + k (6 k)( ) ( + k)( + k) k k + 4k k k k + 4.k 9 + 4k ( k + 6)( k.) x. x 6 b) Find the eqution of the generl term [ points] There re two possible solutions for the sequence, therefore the sequences would be: {0.,., 4. } with common rtio of 7 so t n n (7) {0., 4, } with common rtio of 8 so t n n ( 8) 4. A footbll is kicked into the ir. The eqution h 4.9t + expresses the reltionship between the height, h, in meters nd time, t, in seconds. ) Determine the mximum height reched by the footbll. [ points] We lredy know the eqution nd we re being sked for the MAXIMUM height. I should ( 4.9) immeditely think VERTEX. We find the x of the vertex,. This is the time of the mximum height. To solve for the y, I plug in the vlue of t into the originl eqution h 4.9() + 9.8() x vertex The mximum height reched by the footbll ws.90m. b) For how long ws the bll t height of t lest meters bove ground? [ points] The yellow re indictes the time tht the bll would hve been t lest m in the ir. We would tke the two vlues.4 nd 0.7 nd find the difference seconds. The bll is t lest meters bove the ground for 0.86 seconds. 4.9t 0 4.9t + 4 ± ± (9.8) ( 4.9) ± 7.64 ± 4. 4( 4.9)( 4) x 0.7 x.4
5 . A piece of lnd in the shpe below hs to be fenced. If 600m of fencing re to be used, find the vlues of x nd y tht will produce mximum re. [ points] x + 8y 600 A y x 00 4y A y(00 4y) A 900y y A y + 900y The perimeter of the fencing used The formul of the fenced re The perimeter formul rerrnged to isolte x The re formul with substitution for x The re formul fter distributive property The re formul simplified We now hve the eqution nd we re being sked for the MAXIMUM re produced. I should immeditely think VERTEX. It is very importnt tht we understnd tht the formul is telling us the re bsed on the length of y. Yes, we re looking for the xvlue of the vertex, but tht is only telling us the length of y in this sitution. See the grph below. We find the x of the vertex, x vertex 40. 9m ( ). This is the length of y tht produces the mximum re. To solve for the length of x, I plug in this vlue into the eqution x 00 4y 00 4(40.9) 6. 6m. The vlues of x nd y tht would produce the mximum re would be 6.6m nd 40.9m.
Before we can begin Ch. 3 on Radicals, we need to be familiar with perfect squares, cubes, etc. Try and do as many as you can without a calculator!!!
Nme: Algebr II Honors PreChpter Homework Before we cn begin Ch on Rdicls, we need to be fmilir with perfect squres, cubes, etc Try nd do s mny s you cn without clcultor!!! n The nth root of n n Be ble
More informationLesson 1: Quadratic Equations
Lesson 1: Qudrtic Equtions Qudrtic Eqution: The qudrtic eqution in form is. In this section, we will review 4 methods of qudrtic equtions, nd when it is most to use ech method. 1. 3.. 4. Method 1: Fctoring
More informationARITHMETIC OPERATIONS. The real numbers have the following properties: a b c ab ac
REVIEW OF ALGEBRA Here we review the bsic rules nd procedures of lgebr tht you need to know in order to be successful in clculus. ARITHMETIC OPERATIONS The rel numbers hve the following properties: b b
More informationALevel Mathematics Transition Task (compulsory for all maths students and all further maths student)
ALevel Mthemtics Trnsition Tsk (compulsory for ll mths students nd ll further mths student) Due: st Lesson of the yer. Length:  hours work (depending on prior knowledge) This trnsition tsk provides revision
More informationUNIT 5 QUADRATIC FUNCTIONS Lesson 3: Creating Quadratic Equations in Two or More Variables Instruction
Lesson 3: Creting Qudrtic Equtions in Two or More Vriles Prerequisite Skills This lesson requires the use of the following skill: solving equtions with degree of Introduction 1 The formul for finding the
More informationapproaches as n becomes larger and larger. Since e > 1, the graph of the natural exponential function is as below
. Eponentil nd rithmic functions.1 Eponentil Functions A function of the form f() =, > 0, 1 is clled n eponentil function. Its domin is the set of ll rel f ( 1) numbers. For n eponentil function f we hve.
More informationPreSession Review. Part 1: Basic Algebra; Linear Functions and Graphs
PreSession Review Prt 1: Bsic Algebr; Liner Functions nd Grphs A. Generl Review nd Introduction to Algebr Hierrchy of Arithmetic Opertions Opertions in ny expression re performed in the following order:
More informationIdentify graphs of linear inequalities on a number line.
COMPETENCY 1.0 KNOWLEDGE OF ALGEBRA SKILL 1.1 Identify grphs of liner inequlities on number line.  When grphing firstdegree eqution, solve for the vrible. The grph of this solution will be single point
More informationCH 9 INTRO TO EQUATIONS
CH 9 INTRO TO EQUATIONS INTRODUCTION I m thinking of number. If I dd 10 to the number, the result is 5. Wht number ws I thinking of? R emember this question from Chpter 1? Now we re redy to formlize the
More information20 MATHEMATICS POLYNOMIALS
0 MATHEMATICS POLYNOMIALS.1 Introduction In Clss IX, you hve studied polynomils in one vrible nd their degrees. Recll tht if p(x) is polynomil in x, the highest power of x in p(x) is clled the degree of
More informationMath Sequences and Series RETest Worksheet. Short Answer
Mth 0 Nme: Sequences nd Series RETest Worksheet Short Answer Use n infinite geometric series to express 353 s frction [ mrk, ll steps must be shown] The popultion of community ws 3 000 t the beginning
More informationList all of the possible rational roots of each equation. Then find all solutions (both real and imaginary) of the equation. 1.
Mth Anlysis CP WS 4.X Section 4.4.4 Review Complete ech question without the use of grphing clcultor.. Compre the mening of the words: roots, zeros nd fctors.. Determine whether  is root of 0. Show
More informationI. Equations of a Circle a. At the origin center= r= b. Standard from: center= r=
11.: Circle & Ellipse I cn Write the eqution of circle given specific informtion Grph circle in coordinte plne. Grph n ellipse nd determine ll criticl informtion. Write the eqution of n ellipse from rel
More informationMORE FUNCTION GRAPHING; OPTIMIZATION. (Last edited October 28, 2013 at 11:09pm.)
MORE FUNCTION GRAPHING; OPTIMIZATION FRI, OCT 25, 203 (Lst edited October 28, 203 t :09pm.) Exercise. Let n be n rbitrry positive integer. Give n exmple of function with exctly n verticl symptotes. Give
More informationThe semester B examination for Algebra 2 will consist of two parts. Part 1 will be selected response. Part 2 will be short answer.
ALGEBRA B Semester Em Review The semester B emintion for Algebr will consist of two prts. Prt will be selected response. Prt will be short nswer. Students m use clcultor. If clcultor is used to find points
More informationAlgebra Readiness PLACEMENT 1 Fraction Basics 2 Percent Basics 3. Algebra Basics 9. CRS Algebra 1
Algebr Rediness PLACEMENT Frction Bsics Percent Bsics Algebr Bsics CRS Algebr CRS  Algebr Comprehensive PrePost Assessment CRS  Algebr Comprehensive Midterm Assessment Algebr Bsics CRS  Algebr QuikPiks
More informationChapters Five Notes SN AA U1C5
Chpters Five Notes SN AA U1C5 Nme Period Section 5: Fctoring Qudrtic Epressions When you took lger, you lerned tht the first thing involved in fctoring is to mke sure to fctor out ny numers or vriles
More informationThe semester B examination for Algebra 2 will consist of two parts. Part 1 will be selected response. Part 2 will be short answer. is a real number.
The semester B emintion for Algebr will consist of two prts. Prt will be selected response. Prt will be short nswer. Students m use clcultor. If clcultor is used to find points on grph, the pproprite clcultor
More informationTHE DISCRIMINANT & ITS APPLICATIONS
THE DISCRIMINANT & ITS APPLICATIONS The discriminnt ( Δ ) is the epression tht is locted under the squre root sign in the qudrtic formul i.e. Δ b c. For emple: Given +, Δ () ( )() The discriminnt is used
More informationPHYS Summer Professor Caillault Homework Solutions. Chapter 2
PHYS 1111  Summer 2007  Professor Cillult Homework Solutions Chpter 2 5. Picture the Problem: The runner moves long the ovl trck. Strtegy: The distnce is the totl length of trvel, nd the displcement
More information4 7x =250; 5 3x =500; Read section 3.3, 3.4 Announcements: Bell Ringer: Use your calculator to solve
Dte: 3/14/13 Objective: SWBAT pply properties of exponentil functions nd will pply properties of rithms. Bell Ringer: Use your clcultor to solve 4 7x =250; 5 3x =500; HW Requests: Properties of Log Equtions
More informationThe Quadratic Formula
LESSON 7.4 EXAMPLE A Solution The Qudrtic Formul Although you cn lwys use grph of qudrtic function to pproximte the xintercepts, you re often not ble to find exct solutions. This lesson will develop procedure
More information7.2 The Definite Integral
7.2 The Definite Integrl the definite integrl In the previous section, it ws found tht if function f is continuous nd nonnegtive, then the re under the grph of f on [, b] is given by F (b) F (), where
More informationSOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 2014
SOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 014 Mrk Scheme: Ech prt of Question 1 is worth four mrks which re wrded solely for the correct nswer.
More informationRead section 3.3, 3.4 Announcements:
Dte: 3/1/13 Objective: SWBAT pply properties of exponentil functions nd will pply properties of rithms. Bell Ringer: 1. f x = 3x 6, find the inverse, f 1 x., Using your grphing clcultor, Grph 1. f x,f
More informationSummary Information and Formulae MTH109 College Algebra
Generl Formuls Summry Informtion nd Formule MTH109 College Algebr Temperture: F = 9 5 C + 32 nd C = 5 ( 9 F 32 ) F = degrees Fhrenheit C = degrees Celsius Simple Interest: I = Pr t I = Interest erned (chrged)
More informationPolynomials and Division Theory
Higher Checklist (Unit ) Higher Checklist (Unit ) Polynomils nd Division Theory Skill Achieved? Know tht polynomil (expression) is of the form: n x + n x n + n x n + + n x + x + 0 where the i R re the
More informationMATH 144: Business Calculus Final Review
MATH 144: Business Clculus Finl Review 1 Skills 1. Clculte severl limits. 2. Find verticl nd horizontl symptotes for given rtionl function. 3. Clculte derivtive by definition. 4. Clculte severl derivtives
More informationSUMMER KNOWHOW STUDY AND LEARNING CENTRE
SUMMER KNOWHOW STUDY AND LEARNING CENTRE Indices & Logrithms 2 Contents Indices.2 Frctionl Indices.4 Logrithms 6 Exponentil equtions. Simplifying Surds 13 Opertions on Surds..16 Scientific Nottion..18
More informationLinear Inequalities. Work Sheet 1
Work Sheet 1 Liner Inequlities RentHep, cr rentl compny,chrges $ 15 per week plus $ 0.0 per mile to rent one of their crs. Suppose you re limited y how much money you cn spend for the week : You cn spend
More informationFUNCTIONS: Grade 11. or y = ax 2 +bx + c or y = a(x x1)(x x2) a y
FUNCTIONS: Grde 11 The prbol: ( p) q or = +b + c or = ( 1)( ) The hperbol: p q The eponentil function: b p q Importnt fetures: intercept : Let = 0 intercept : Let = 0 Turning points (Where pplicble)
More informationAQA Further Pure 1. Complex Numbers. Section 1: Introduction to Complex Numbers. The number system
Complex Numbers Section 1: Introduction to Complex Numbers Notes nd Exmples These notes contin subsections on The number system Adding nd subtrcting complex numbers Multiplying complex numbers Complex
More informationPrecalculus Spring 2017
Preclculus Spring 2017 Exm 3 Summry (Section 4.1 through 5.2, nd 9.4) Section P.5 Find domins of lgebric expressions Simplify rtionl expressions Add, subtrct, multiply, & divide rtionl expressions Simplify
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: How to identify the leding coefficients nd degrees of polynomils How to dd nd subtrct polynomils How to multiply polynomils
More informationUnit #9 : Definite Integral Properties; Fundamental Theorem of Calculus
Unit #9 : Definite Integrl Properties; Fundmentl Theorem of Clculus Gols: Identify properties of definite integrls Define odd nd even functions, nd reltionship to integrl vlues Introduce the Fundmentl
More informationDuality # Second iteration for HW problem. Recall our LP example problem we have been working on, in equality form, is given below.
Dulity #. Second itertion for HW problem Recll our LP emple problem we hve been working on, in equlity form, is given below.,,,, 8 m F which, when written in slightly different form, is 8 F Recll tht we
More informationEach term is formed by adding a constant to the previous term. Geometric progression
Chpter 4 Mthemticl Progressions PROGRESSION AND SEQUENCE Sequence A sequence is succession of numbers ech of which is formed ccording to definite lw tht is the sme throughout the sequence. Arithmetic Progression
More informationDate Lesson Text TOPIC Homework. Solving for Obtuse Angles QUIZ ( ) More Trig Word Problems QUIZ ( )
UNIT 5 TRIGONOMETRI RTIOS Dte Lesson Text TOPI Homework pr. 4 5.1 (48) Trigonometry Review WS 5.1 # 3 5, 9 11, (1, 13)doso pr. 6 5. (49) Relted ngles omplete lesson shell & WS 5. pr. 30 5.3 (50) 5.3 5.4
More informationUnit #10 De+inite Integration & The Fundamental Theorem Of Calculus
Unit # De+inite Integrtion & The Fundmentl Theorem Of Clculus. Find the re of the shded region ove nd explin the mening of your nswer. (squres re y units) ) The grph to the right is f(x) = x + 8x )Use
More informationA sequence is a list of numbers in a specific order. A series is a sum of the terms of a sequence.
Core Module Revision Sheet The C exm is hour 30 minutes long nd is in two sections. Section A (36 mrks) 8 0 short questions worth no more thn 5 mrks ech. Section B (36 mrks) 3 questions worth mrks ech.
More informationBridging the gap: GCSE AS Level
Bridging the gp: GCSE AS Level CONTENTS Chpter Removing rckets pge Chpter Liner equtions Chpter Simultneous equtions 8 Chpter Fctors 0 Chpter Chnge the suject of the formul Chpter 6 Solving qudrtic equtions
More information( ) Same as above but m = f x = f x  symmetric to yaxis. find where f ( x) Relative: Find where f ( x) x a + lim exists ( lim f exists.
AP Clculus Finl Review Sheet solutions When you see the words This is wht you think of doing Find the zeros Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor Find
More informationChapter 1: Fundamentals
Chpter 1: Fundmentls 1.1 Rel Numbers Types of Rel Numbers: Nturl Numbers: {1, 2, 3,...}; These re the counting numbers. Integers: {... 3, 2, 1, 0, 1, 2, 3,...}; These re ll the nturl numbers, their negtives,
More informationHow do we solve these things, especially when they get complicated? How do we know when a system has a solution, and when is it unique?
XII. LINEAR ALGEBRA: SOLVING SYSTEMS OF EQUATIONS Tody we re going to tlk bout solving systems of liner equtions. These re problems tht give couple of equtions with couple of unknowns, like: 6 2 3 7 4
More informationUNIT 1 FUNCTIONS AND THEIR INVERSES Lesson 1.4: Logarithmic Functions as Inverses Instruction
Lesson : Logrithmic Functions s Inverses Prerequisite Skills This lesson requires the use of the following skills: determining the dependent nd independent vribles in n exponentil function bsed on dt from
More informationJackson 2.7 Homework Problem Solution Dr. Christopher S. Baird University of Massachusetts Lowell
Jckson.7 Homework Problem Solution Dr. Christopher S. Bird University of Msschusetts Lowell PROBLEM: Consider potentil problem in the hlfspce defined by, with Dirichlet boundry conditions on the plne
More informationEquations, expressions and formulae
Get strted 2 Equtions, epressions nd formule This unit will help you to work with equtions, epressions nd formule. AO1 Fluency check 1 Work out 2 b 2 c 7 2 d 7 2 2 Simplify by collecting like terms. b
More informationCHAPTER 9. Rational Numbers, Real Numbers, and Algebra
CHAPTER 9 Rtionl Numbers, Rel Numbers, nd Algebr Problem. A mn s boyhood lsted 1 6 of his life, he then plyed soccer for 1 12 of his life, nd he mrried fter 1 8 more of his life. A dughter ws born 9 yers
More informationEquations and Inequalities
Equtions nd Inequlities Equtions nd Inequlities Curriculum Redy ACMNA: 4, 5, 6, 7, 40 www.mthletics.com Equtions EQUATIONS & Inequlities & INEQUALITIES Sometimes just writing vribles or pronumerls in
More informationQuotient Rule: am a n = am n (a 0) Negative Exponents: a n = 1 (a 0) an Power Rules: (a m ) n = a m n (ab) m = a m b m
Formuls nd Concepts MAT 099: Intermedite Algebr repring for Tests: The formuls nd concepts here m not be inclusive. You should first tke our prctice test with no notes or help to see wht mteril ou re comfortble
More informationStudent Session Topic: Particle Motion
Student Session Topic: Prticle Motion Prticle motion nd similr problems re on the AP Clculus exms lmost every yer. The prticle my be prticle, person, cr, etc. The position, velocity or ccelertion my be
More information10. AREAS BETWEEN CURVES
. AREAS BETWEEN CURVES.. Ares etween curves So res ove the xxis re positive nd res elow re negtive, right? Wrong! We lied! Well, when you first lern out integrtion it s convenient fiction tht s true in
More informationMath 1102: Calculus I (Math/Sci majors) MWF 3pm, Fulton Hall 230 Homework 2 solutions
Mth 1102: Clculus I (Mth/Sci mjors) MWF 3pm, Fulton Hll 230 Homework 2 solutions Plese write netly, nd show ll work. Cution: An nswer with no work is wrong! Do the following problems from Chpter III: 6,
More informationfractions Let s Learn to
5 simple lgebric frctions corne lens pupil retin Norml vision light focused on the retin concve lens Shortsightedness (myopi) light focused in front of the retin Corrected myopi light focused on the retin
More informationPolynomial Approximations for the Natural Logarithm and Arctangent Functions. Math 230
Polynomil Approimtions for the Nturl Logrithm nd Arctngent Functions Mth 23 You recll from first semester clculus how one cn use the derivtive to find n eqution for the tngent line to function t given
More informationExam 1 Solutions (1) C, D, A, B (2) C, A, D, B (3) C, B, D, A (4) A, C, D, B (5) D, C, A, B
PHY 249, Fll 216 Exm 1 Solutions nswer 1 is correct for ll problems. 1. Two uniformly chrged spheres, nd B, re plced t lrge distnce from ech other, with their centers on the x xis. The chrge on sphere
More informationSample pages. 9:04 Equations with grouping symbols
Equtions 9 Contents I know the nswer is here somewhere! 9:01 Inverse opertions 9:0 Solving equtions Fun spot 9:0 Why did the tooth get dressed up? 9:0 Equtions with pronumerls on both sides GeoGebr ctivity
More information1 ELEMENTARY ALGEBRA and GEOMETRY READINESS DIAGNOSTIC TEST PRACTICE
ELEMENTARY ALGEBRA nd GEOMETRY READINESS DIAGNOSTIC TEST PRACTICE Directions: Study the exmples, work the prolems, then check your nswers t the end of ech topic. If you don t get the nswer given, check
More informationFinal Exam Study Guide
Finl Exm Study Guide Includes. Integrls & Antiderivtive Rules 2. Definite Integrls (Integrls with bounds) 3. Are Between Two Curves  Region Bounded by Two Curves 4. Consumer nd Producer Surplus. USubstitution.
More informationPhysics 121 Sample Common Exam 1 NOTE: ANSWERS ARE ON PAGE 8. Instructions:
Physics 121 Smple Common Exm 1 NOTE: ANSWERS ARE ON PAGE 8 Nme (Print): 4 Digit ID: Section: Instructions: Answer ll questions. uestions 1 through 16 re multiple choice questions worth 5 points ech. You
More informationMarkscheme May 2016 Mathematics Standard level Paper 1
M6/5/MATME/SP/ENG/TZ/XX/M Mrkscheme My 06 Mthemtics Stndrd level Pper 7 pges M6/5/MATME/SP/ENG/TZ/XX/M This mrkscheme is the property of the Interntionl Bcclurete nd must not be reproduced or distributed
More informationWe divide the interval [a, b] into subintervals of equal length x = b a n
Arc Length Given curve C defined by function f(x), we wnt to find the length of this curve between nd b. We do this by using process similr to wht we did in defining the Riemnn Sum of definite integrl:
More informationSect 10.2 Trigonometric Ratios
86 Sect 0. Trigonometric Rtios Objective : Understnding djcent, Hypotenuse, nd Opposite sides of n cute ngle in right tringle. In right tringle, the otenuse is lwys the longest side; it is the side opposite
More informationMath 113 Exam 1Review
Mth 113 Exm 1Review September 26, 2016 Exm 1 covers 6.17.3 in the textbook. It is dvisble to lso review the mteril from 5.3 nd 5.5 s this will be helpful in solving some of the problems. 6.1 Are Between
More informationSection 6: Area, Volume, and Average Value
Chpter The Integrl Applied Clculus Section 6: Are, Volume, nd Averge Vlue Are We hve lredy used integrls to find the re etween the grph of function nd the horizontl xis. Integrls cn lso e used to find
More informationSection 5.1 #7, 10, 16, 21, 25; Section 5.2 #8, 9, 15, 20, 27, 30; Section 5.3 #4, 6, 9, 13, 16, 28, 31; Section 5.4 #7, 18, 21, 23, 25, 29, 40
Mth B Prof. Audrey Terrs HW # Solutions by Alex Eustis Due Tuesdy, Oct. 9 Section 5. #7,, 6,, 5; Section 5. #8, 9, 5,, 7, 3; Section 5.3 #4, 6, 9, 3, 6, 8, 3; Section 5.4 #7, 8,, 3, 5, 9, 4 5..7 Since
More informationI do slope intercept form With my shades on MartinGay, Developmental Mathematics
AATA Dte: 1//1 SWBAT simplify rdicls. Do Now: ACT Prep HW Requests: Pg 49 #1745 odds Continue Vocb sheet In Clss: Complete Skills Prctice WS HW: Complete Worksheets For Wednesdy stmped pges Bring stmped
More informationSummer Work Packet for MPH Math Classes
Summer Work Pcket for MPH Mth Clsses Students going into Preclculus AC Sept. 018 Nme: This pcket is designed to help students sty current with their mth skills. Ech mth clss expects certin level of number
More informationProblem Set 9. Figure 1: Diagram. This picture is a rough sketch of the 4 parabolas that give us the area that we need to find. The equations are:
(x + y ) = y + (x + y ) = x + Problem Set 9 Discussion: Nov., Nov. 8, Nov. (on probbility nd binomil coefficients) The nme fter the problem is the designted writer of the solution of tht problem. (No one
More informationHIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 3 UNIT (ADDITIONAL) AND 3/4 UNIT (COMMON) Time allowed Two hours (Plus 5 minutes reading time)
HIGHER SCHOOL CERTIFICATE EXAMINATION 998 MATHEMATICS 3 UNIT (ADDITIONAL) AND 3/4 UNIT (COMMON) Time llowed Two hours (Plus 5 minutes reding time) DIRECTIONS TO CANDIDATES Attempt ALL questions ALL questions
More informationSection 3.2: Negative Exponents
Section 3.2: Negtive Exponents Objective: Simplify expressions with negtive exponents using the properties of exponents. There re few specil exponent properties tht del with exponents tht re not positive.
More informationReview Factoring Polynomials:
Chpter 4 Mth 0 Review Fctoring Polynomils:. GCF e. A) 5 5 A) 4 + 9. Difference of Squres b = ( + b)( b) e. A) 9 6 B) C) 98y. Trinomils e. A) + 5 4 B) + C) + 5 + Solving Polynomils:. A) ( 5)( ) = 0 B) 4
More informationThe Fundamental Theorem of Calculus, Particle Motion, and Average Value
The Fundmentl Theorem of Clculus, Prticle Motion, nd Averge Vlue b Three Things to Alwys Keep In Mind: (1) v( dt p( b) p( ), where v( represents the velocity nd p( represents the position. b (2) v ( dt
More information( ) as a fraction. Determine location of the highest
AB Clculus Exm Review Sheet  Solutions A. Preclculus Type prolems A1 A2 A3 A4 A5 A6 A7 This is wht you think of doing Find the zeros of f ( x). Set function equl to 0. Fctor or use qudrtic eqution if
More informationReversing the Chain Rule. As we have seen from the Second Fundamental Theorem ( 4.3), the easiest way to evaluate an integral b
Mth 32 Substitution Method Stewrt 4.5 Reversing the Chin Rule. As we hve seen from the Second Fundmentl Theorem ( 4.3), the esiest wy to evlute n integrl b f(x) dx is to find n ntiderivtive, the indefinite
More informationPHYSICS 211 MIDTERM I 21 April 2004
PHYSICS MIDERM I April 004 Exm is closed book, closed notes. Use only your formul sheet. Write ll work nd nswers in exm booklets. he bcks of pges will not be grded unless you so request on the front of
More information4.4 Areas, Integrals and Antiderivatives
. res, integrls nd ntiderivtives 333. Ares, Integrls nd Antiderivtives This section explores properties of functions defined s res nd exmines some connections mong res, integrls nd ntiderivtives. In order
More informationAB Calculus Review Sheet
AB Clculus Review Sheet Legend: A Preclculus, B Limits, C Differentil Clculus, D Applictions of Differentil Clculus, E Integrl Clculus, F Applictions of Integrl Clculus, G Prticle Motion nd Rtes This is
More informationSAINT IGNATIUS COLLEGE
SAINT IGNATIUS COLLEGE Directions to Students Tril Higher School Certificte 0 MATHEMATICS Reding Time : 5 minutes Totl Mrks 00 Working Time : hours Write using blue or blck pen. (sketches in pencil). This
More informationLoudoun Valley High School Calculus Summertime Fun Packet
Loudoun Vlley High School Clculus Summertime Fun Pcket We HIGHLY recommend tht you go through this pcket nd mke sure tht you know how to do everything in it. Prctice the problems tht you do NOT remember!
More informationReview of Calculus, cont d
Jim Lmbers MAT 460 Fll Semester 200910 Lecture 3 Notes These notes correspond to Section 1.1 in the text. Review of Clculus, cont d Riemnn Sums nd the Definite Integrl There re mny cses in which some
More informationImproper Integrals. Type I Improper Integrals How do we evaluate an integral such as
Improper Integrls Two different types of integrls cn qulify s improper. The first type of improper integrl (which we will refer to s Type I) involves evluting n integrl over n infinite region. In the grph
More informationInClass Problems 2 and 3: Projectile Motion Solutions. InClass Problem 2: Throwing a Stone Down a Hill
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Deprtment of Physics Physics 8T Fll Term 4 InClss Problems nd 3: Projectile Motion Solutions We would like ech group to pply the problem solving strtegy with the
More informationCBE 291b  Computation And Optimization For Engineers
The University of Western Ontrio Fculty of Engineering Science Deprtment of Chemicl nd Biochemicl Engineering CBE 9b  Computtion And Optimiztion For Engineers Mtlb Project Introduction Prof. A. Jutn Jn
More information( ) where f ( x ) is a. AB Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x).
AB Clculus Exm Review Sheet A. Preclculus Type prolems A1 Find the zeros of f ( x). This is wht you think of doing A2 A3 Find the intersection of f ( x) nd g( x). Show tht f ( x) is even. A4 Show tht f
More informationMath 113 Exam 2 Practice
Mth 3 Exm Prctice Februry 8, 03 Exm will cover 7.4, 7.5, 7.7, 7.8, 8.3 nd 8.5. Plese note tht integrtion skills lerned in erlier sections will still be needed for the mteril in 7.5, 7.8 nd chpter 8. This
More informationSections 1.3, 7.1, and 9.2: Properties of Exponents and Radical Notation
Sections., 7., nd 9.: Properties of Eponents nd Rdicl Nottion Let p nd q be rtionl numbers. For ll rel numbers nd b for which the epressions re rel numbers, the following properties hold. i = + p q p q
More informationApplications of Bernoulli s theorem. Lecture  7
Applictions of Bernoulli s theorem Lecture  7 Prcticl Applictions of Bernoulli s Theorem The Bernoulli eqution cn be pplied to gret mny situtions not just the pipe flow we hve been considering up to now.
More information1. Extend QR downwards to meet the xaxis at U(6, 0). y
In the digrm, two stright lines re to be drwn through so tht the lines divide the figure OPQRST into pieces of equl re Find the sum of the slopes of the lines R(6, ) S(, ) T(, 0) Determine ll liner functions
More informationName Solutions to Test 3 November 8, 2017
Nme Solutions to Test 3 November 8, 07 This test consists of three prts. Plese note tht in prts II nd III, you cn skip one question of those offered. Some possibly useful formuls cn be found below. Brrier
More informationSection 6.1 Definite Integral
Section 6.1 Definite Integrl Suppose we wnt to find the re of region tht is not so nicely shped. For exmple, consider the function shown elow. The re elow the curve nd ove the x xis cnnot e determined
More informationBelievethatyoucandoitandyouar. Mathematics. ngascannotdoonlynotyetbelieve thatyoucandoitandyouarehalfw. Algebra
Believethtoucndoitndour ehlfwtherethereisnosuchthi Mthemtics ngscnnotdoonlnotetbelieve thtoucndoitndourehlfw Alger therethereisnosuchthingsc nnotdoonlnotetbelievethto Stge 6 ucndoitndourehlfwther S Cooper
More informationand that at t = 0 the object is at position 5. Find the position of the object at t = 2.
7.2 The Fundmentl Theorem of Clculus 49 re mny, mny problems tht pper much different on the surfce but tht turn out to be the sme s these problems, in the sense tht when we try to pproimte solutions we
More informationConsolidation Worksheet
Cmbridge Essentils Mthemtics Core 8 NConsolidtion Worksheet N Consolidtion Worksheet Work these out. 8 b 7 + 0 c 6 + 7 5 Use the number line to help. 2 Remember + 2 2 +2 2 2 + 2 Adding negtive number is
More information71: Zero and Negative Exponents
7: Zero nd Negtive Exponents Objective: To siplify expressions involving zero nd negtive exponents Wr Up:.. ( ).. 7.. Investigting Zero nd Negtive Exponents: Coplete the tble. Write nonintegers s frctions
More informationSuppose we want to find the area under the parabola and above the x axis, between the lines x = 2 and x = 2.
Mth 43 Section 6. Section 6.: Definite Integrl Suppose we wnt to find the re of region tht is not so nicely shped. For exmple, consider the function shown elow. The re elow the curve nd ove the x xis cnnot
More informationProperties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives
Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums  1 Riemnn
More informationIMPORTANT. Read these directions carefully:
Physics 208: Electricity nd Mgnetism Finl Exm, Secs. 506 510. 7 My. 2004 Instructor: Dr. George R. Welch, 415 EngineeringPhysics, 8457737 Print your nme netly: Lst nme: First nme: Sign your nme: Plese
More information