SAT Math MustKnow Facts & Formulas


 Eleanor Reeves
 3 years ago
 Views:
Transcription
1 SAT Mat MustKnow Facts & Formuas Numbers, Sequences, Factors Integers:..., 3, 2, 1, 0, 1, 2, 3,... Rationas: fractions, tat is, anyting expressabe as a ratio of integers Reas: integers pus rationas pus specia numbers suc as 2, 3 and π Order Of Operations: Aritmetic Sequences: PEMDAS (Parenteses / Exponents / Mutipy / Divide / Add / Subtract) eac term is equa to te previous term pus d Sequence: t 1, t 1 + d, t 1 + 2d,... Exampe: d = 4 and t 1 = 3 gives te sequence 3, 7, 11, 15,... Geometric Sequences: eac term is equa to te previous term times r Sequence: t 1, t 1 r, t 1 r 2,... Exampe: r = 2 and t 1 = 3 gives te sequence 3, 6, 12, 24,... Factors: te factors of a number divide into tat number witout a remainder Exampe: te factors of 52 are 1, 2, 4, 13, 26, and 52 Mutipes: te mutipes of a number are divisibe by tat number witout a remainder Exampe: te positive mutipes of 20 are 20, 40, 60, 80,... Percents: use te foowing formua to find part, woe, or percent part = percent 100 woe Exampe: 75% of 300 is wat? Sove x = (75/100) 300 to get 225 Exampe: 45 is wat percent of 60? Sove 45 = (x/100) 60 to get 75% Exampe: 30 is 20% of wat? Sove 30 = (20/100) x to get pg. 1
2 SAT Mat MustKnow Facts & Formuas Averages, Counting, Statistics, Probabiity average = sum of terms number of terms average speed = tota distance tota time Fundamenta Counting Principe: sum = average (number of terms) mode = vaue in te ist tat appears most often median = midde vaue in te ist (wic must be sorted) Exampe: median of {3, 10, 9, 27, 50} = 10 Exampe: median of {3, 9, 10, 27} = (9 + 10)/2 = 9.5 If an event can appen in N ways, and anoter, independent event can appen in M ways, ten bot events togeter can appen in N M ways. Probabiity: probabiity = number of desired outcomes number of tota outcomes Exampe: eac SAT mat mutipe coice question as five possibe answers, one of wic is te correct answer. If you guess te answer to a question competey at random, your probabiity of getting it rigt is 1/5 = 20%. Te probabiity of two different events A and B bot appening is P(A and B) = P(A) P(B), as ong as te events are independent (not mutuay excusive). Powers, Exponents, Roots x a x b = x a+b (x a ) b = x a b x 0 = 1 x a /x b = x a b (xy) a = x a y a xy = x y 1/x b = x b { ( 1) n +1, if n is even; = 1, if n is odd. pg. 2
3 Factoring, Soving SAT Mat MustKnow Facts & Formuas (x + a)(x + b) = x 2 + (b + a)x + ab FOIL a 2 b 2 = (a + b)(a b) Difference Of Squares a 2 + 2ab + b 2 = (a + b)(a + b) a 2 2ab + b 2 = (a b)(a b) To sove a quadratic suc as x 2 +bx+c = 0, first factor te eft side to get (x+a 1 )(x+a 2 ) = 0, ten set eac part in parenteses equa to zero. E.g., x 2 + 4x + 3 = (x + 3)(x + 1) = 0 so tat x = 3 or x = 1. To sove two inear equations in x and y: use te first equation to substitute for a variabe in te second. E.g., suppose x + y = 3 and 4x y = 2. Te first equation gives y = 3 x, so te second equation becomes 4x (3 x) = 2 5x 3 = 2 x = 1, y = 2. Functions A function is a rue to go from one number (x) to anoter number (y), usuay written y = f(x). For any given vaue of x, tere can ony be one corresponding vaue y. If y = kx for some number k (exampe: f(x) = 0.5 x), ten y is said to be directy proportiona to x. If y = k/x (exampe: f(x) = 5/x), ten y is said to be inversey proportiona to x. Absoute vaue: x = { +x, if x 0; x, if x < 0. Lines (Linear Functions) Consider te ine tat goes troug points A(x 1, y 1 ) and B(x 2, y 2 ). Distance from A to B: Midpoint of te segment AB: Sope of te ine: (x2 x 1 ) 2 + (y 2 y 1 ) 2 ( x1 + x 2 2, y ) 1 + y 2 2 y 2 y 1 = rise x 2 x 1 run pg. 3
4 SAT Mat MustKnow Facts & Formuas Sopeintercept form: given te sope m and te yintercept b, ten te equation of te ine is y = mx + b. Parae ines ave equa sopes: m 1 = m 2. Perpendicuar ines ave negative reciproca sopes: m 1 m 2 = 1. a a b b a b b a a b m b a Intersecting Lines Parae Lines ( m) Intersecting ines: opposite anges are equa. Aso, eac pair of anges aong te same ine add to 180. In te figure above, a + b = 180. Parae ines: eigt anges are formed wen a ine crosses two parae ines. Te four big anges (a) are equa, and te four sma anges (b) are equa. Trianges Rigt trianges: c a b 30 2x x 3 60 x x 2 45 x 45 x a 2 + b 2 = c 2 Specia Rigt Trianges Note tat te above specia triange figures are given in te test booket, so you don t ave to memorize tem, but you soud be famiiar wit wat tey mean, especiay te first one, wic is caed te Pytagorean Teorem (a 2 + b 2 = c 2 ). A good exampe of a rigt triange is one wit a = 3, b = 4, and c = 5, aso caed a rigt triange. Note tat mutipes of tese numbers are aso rigt trianges. For exampe, if you mutipy tese numbers by 2, you get a = 6, b = 8, and c = 10 (6 8 10), wic is aso a rigt triange. Te Specia Rigt Trianges are needed ess often tan te Pytagorean Teorem. Here, x is used to mean any positive number, suc as 1, 1/2, etc. A typica exampe on te test: you are given a triange wit sides 2, 1, and 3 and are asked for te ange opposite te 3. Te figure sows tat tis ange is pg. 4
5 SAT Mat MustKnow Facts & Formuas A trianges: b Area = 1 2 b Te area formua above works for a trianges, not just rigt trianges. Anges on te inside of any triange add up to 180. Te engt of one side of any triange is aways ess tan te sum of te engts of te oter two sides. Oter important trianges: Equiatera: Tese trianges ave tree equa sides, and a tree anges are 60. Isoscees: Simiar: An isoscees triange as two equa sides. Te base anges (te ones opposite te two sides) are equa. A good exampe of an isoscees triange is te one on page 4 wit base anges of 45. Two or more trianges are simiar if tey ave te same sape. Te corresponding anges are equa, and te corresponding sides are in proportion. For exampe, te triange and te triange from before are simiar since teir sides are in a ratio of 2 to 1. Circes (, k) r r n Arc Sector Area = πr 2 Circumference = 2πr Fu circe = 360 (Optiona) Lengt Of Arc = (n /360 ) 2πr Area Of Sector = (n /360 ) πr 2 pg. 5
6 Rectanges And Friends SAT Mat MustKnow Facts & Formuas w Rectange Paraeogram (Optiona) (Square if = w) (Rombus if = w) Area = w Area = Te formua for te area of a rectange is given in te test booket, but it is very important to know, so you soud memorize it anyway. Soids w r w Rectanguar Soid Voume = w Rigt Cyinder Voume = πr 2 Note tat te above soids figures are given in te test booket, so you don t ave to memorize tem, but you soud be famiiar wit wat tey mean. pg. 6
SAT Math Facts & Formulas
Numbers, Sequences, Factors SAT Mat Facts & Formuas Integers:..., 3, 2, 1, 0, 1, 2, 3,... Reas: integers pus fractions, decimas, and irrationas ( 2, 3, π, etc.) Order Of Operations: Aritmetic Sequences:
More informationACT Math Facts & Formulas
Numbers, Sequences, Factors Integers:..., 3, 2, 1, 0, 1, 2, 3,... Rationals: fractions, tat is, anyting expressable as a ratio of integers Reals: integers plus rationals plus special numbers suc as
More informationSAT Subject Math Level 1 Facts & Formulas
Numbers, Sequences, Factors Integers:..., 3, 2, 1, 0, 1, 2, 3,... Reals: integers plus fractions, decimals, and irrationals ( 2, 3, π, etc.) Order Of Operations: Aritmetic Sequences: PEMDAS (Parenteses
More informationTopic 1: Pythagoras Theorem
Topic 1: Pytagoras Teorem Pytagoras Teorem states tat in a rigt anged triange: Te square of te ypotenuse is equa to te sum of te squares of te oter two sides Diagrammaticay: Hypotenuse a c () Oter sides
More informationA. V = lwh where l = 11, w = 8 and h = 2 = = 88 2 = 176 cm 3. b) Find the volume of the cube. =... m 3 = = cm 3
5. [Voume] Ski 5.1 rectanguar prism square prism cube Cacuating te voume of square and rectanguar prisms. engt widt eigt w engt widt eigt engt engt engt w MM5. 11 44 MM6.1 11 44 Q. Te parce is a rectanguar
More informationThis supplement is meant to be read after Venema s Section 9.2. Throughout this section, we assume all nine axioms of Euclidean geometry.
Mat 444/445 Geometry for Teacers Summer 2008 Supplement : Similar Triangles Tis supplement is meant to be read after Venema s Section 9.2. Trougout tis section, we assume all nine axioms of uclidean geometry.
More informationTrapezoid Rule. y 2. y L
Trapezoid Rule and Simpson s Rule c 2002, 2008, 200 Donald Kreider and Dwigt Lar Trapezoid Rule Many applications of calculus involve definite integrals. If we can find an antiderivative for te integrand,
More informationArea of Trapezoids. Find the area of the trapezoid. 7 m. 11 m. 2 Use the Area of a Trapezoid. Find the value of b 2
Page 1 of. Area of Trapezoids Goal Find te area of trapezoids. Recall tat te parallel sides of a trapezoid are called te bases of te trapezoid, wit lengts denoted by and. base, eigt Key Words trapezoid
More informationDivide and Conquer Approach
Divide and Conquer Approac Deiverabes Divide and Conquer Paradigm nteger Mutipication Strassen Matrix Mutipication Cosest Pair of points nfinite Wa Probem 6/7/01 8:58 PM Copyrigt @ gdeepak.com Divide and
More informationThe EOQ Inventory Formula
Te EOQ Inventory Formula James M. Cargal Matematics Department Troy University Montgomery Campus A basic problem for businesses and manufacturers is, wen ordering supplies, to determine wat quantity of
More informationACTIVITY: Deriving the Area Formula of a Trapezoid
4.3 Areas of Trapezoids a trapezoid? How can you derive a formula for te area of ACTIVITY: Deriving te Area Formula of a Trapezoid Work wit a partner. Use a piece of centimeter grid paper. a. Draw any
More informationInstantaneous Rate of Change:
Instantaneous Rate of Cange: Last section we discovered tat te average rate of cange in F(x) can also be interpreted as te slope of a scant line. Te average rate of cange involves te cange in F(x) over
More informationSAT Subject Math Level 2 Facts & Formulas
Numbers, Sequences, Factors Integers:..., 3, 2, 1, 0, 1, 2, 3,... Reals: integers plus fractions, decimals, and irrationals ( 2, 3, π, etc.) Order Of Operations: Arithmetic Sequences: PEMDAS (Parentheses
More informationTangent Lines and Rates of Change
Tangent Lines and Rates of Cange 922005 Given a function y = f(x), ow do you find te slope of te tangent line to te grap at te point P(a, f(a))? (I m tinking of te tangent line as a line tat just skims
More information7.6 Complex Fractions
Section 7.6 Comple Fractions 695 7.6 Comple Fractions In tis section we learn ow to simplify wat are called comple fractions, an eample of wic follows. 2 + 3 Note tat bot te numerator and denominator are
More informationCompute the derivative by definition: The four step procedure
Compute te derivative by definition: Te four step procedure Given a function f(x), te definition of f (x), te derivative of f(x), is lim 0 f(x + ) f(x), provided te limit exists Te derivative function
More information2 Limits and Derivatives
2 Limits and Derivatives 2.7 Tangent Lines, Velocity, and Derivatives A tangent line to a circle is a line tat intersects te circle at exactly one point. We would like to take tis idea of tangent line
More informationMath: Fundamentals 100
Math: Fundamentas 100 Wecome to the Tooing University. This course is designed to be used in conjunction with the onine version of this cass. The onine version can be found at http://www.tooingu.com. We
More informationSolution Derivations for Capa #7
Solution Derivations for Capa #7 1) Consider te beavior of te circuit, wen various values increase or decrease. (Select Iincreases, Ddecreases, If te first is I and te rest D, enter IDDDD). A) If R1
More information22.1 Finding the area of plane figures
. Finding te area of plane figures a cm a cm rea of a square = Lengt of a side Lengt of a side = (Lengt of a side) b cm a cm rea of a rectangle = Lengt readt b cm a cm rea of a triangle = a cm b cm = ab
More informationDerivatives Math 120 Calculus I D Joyce, Fall 2013
Derivatives Mat 20 Calculus I D Joyce, Fall 203 Since we ave a good understanding of its, we can develop derivatives very quickly. Recall tat we defined te derivative f x of a function f at x to be te
More informationLecture 10: What is a Function, definition, piecewise defined functions, difference quotient, domain of a function
Lecture 10: Wat is a Function, definition, piecewise defined functions, difference quotient, domain of a function A function arises wen one quantity depends on anoter. Many everyday relationsips between
More informationDiscovering Area Formulas of Quadrilaterals by Using Composite Figures
Activity: Format: Ojectives: Related 009 SOL(s): Materials: Time Required: Directions: Discovering Area Formulas of Quadrilaterals y Using Composite Figures Small group or Large Group Participants will
More information1.6. Analyse Optimum Volume and Surface Area. Maximum Volume for a Given Surface Area. Example 1. Solution
1.6 Analyse Optimum Volume and Surface Area Estimation and oter informal metods of optimizing measures suc as surface area and volume often lead to reasonable solutions suc as te design of te tent in tis
More informationMath WarmUp for Exam 1 Name: Solutions
Disclaimer: Tese review problems do not represent te exact questions tat will appear te exam. Tis is just a warmup to elp you begin studying. It is your responsibility to review te omework problems, webwork
More informationMath Test Sections. The College Board: Expanding College Opportunity
Taking te SAT I: Reasoning Test Mat Test Sections Te materials in tese files are intended for individual use by students getting ready to take an SAT Program test; permission for any oter use must be sougt
More informationSection 3.3. Differentiation of Polynomials and Rational Functions. Difference Equations to Differential Equations
Difference Equations to Differential Equations Section 3.3 Differentiation of Polynomials an Rational Functions In tis section we begin te task of iscovering rules for ifferentiating various classes of
More informationExam 2 Review. . You need to be able to interpret what you get to answer various questions.
Exam Review Exam covers 1.6,.1.3, 1.5, 4.14., and 5.15.3. You sould know ow to do all te omework problems from tese sections and you sould practice your understanding on several old exams in te exam
More informationSurface Areas of Prisms and Cylinders
12.2 TEXAS ESSENTIAL KNOWLEDGE AND SKILLS G.10.B G.11.C Surface Areas of Prisms and Cylinders Essential Question How can you find te surface area of a prism or a cylinder? Recall tat te surface area of
More informationComputer Science and Engineering, UCSD October 7, 1999 GoldreicLevin Teorem Autor: Bellare Te GoldreicLevin Teorem 1 Te problem We æx a an integer n for te lengt of te strings involved. If a is an nbit
More informationResearch on the Antiperspective Correction Algorithm of QR Barcode
Researc on te Antiperspective Correction Algoritm of QR Barcode Jianua Li, YiWen Wang, YiJun Wang,Yi Cen, Guoceng Wang Key Laboratory of Electronic Tin Films and Integrated Devices University of Electronic
More informationAlgebra 1 Chapter 3 Vocabulary. equivalent  Equations with the same solutions as the original equation are called.
Chapter 3 Vocabulary equivalent  Equations with the same solutions as the original equation are called. formula  An algebraic equation that relates two or more reallife quantities. unit rate  A rate
More informationMath 113 HW #5 Solutions
Mat 3 HW #5 Solutions. Exercise.5.6. Suppose f is continuous on [, 5] and te only solutions of te equation f(x) = 6 are x = and x =. If f() = 8, explain wy f(3) > 6. Answer: Suppose we ad tat f(3) 6. Ten
More informationCan a LumpSum Transfer Make Everyone Enjoy the Gains. from Free Trade?
Can a LumpSum Transfer Make Everyone Enjoy te Gains from Free Trade? Yasukazu Icino Department of Economics, Konan University June 30, 2010 Abstract I examine lumpsum transfer rules to redistribute te
More information3 Ans. 1 of my $30. 3 on. 1 on ice cream and the rest on 2011 MATHCOUNTS STATE COMPETITION SPRINT ROUND
0 MATHCOUNTS STATE COMPETITION SPRINT ROUND. boy scouts are accompanied by scout leaders. Eac person needs bottles of water per day and te trip is day. + = 5 people 5 = 5 bottles Ans.. Cammie as pennies,
More informationProjective Geometry. Projective Geometry
Euclidean versus Euclidean geometry describes sapes as tey are Properties of objects tat are uncanged by rigid motions» Lengts» Angles» Parallelism Projective geometry describes objects as tey appear Lengts,
More informationDetermine the perimeter of a triangle using algebra Find the area of a triangle using the formula
Student Name: Date: Contact Person Name: Pone Number: Lesson 0 Perimeter, Area, and Similarity of Triangles Objectives Determine te perimeter of a triangle using algebra Find te area of a triangle using
More informationGeometric Stratification of Accounting Data
Stratification of Accounting Data Patricia Gunning * Jane Mary Horgan ** William Yancey *** Abstract: We suggest a new procedure for defining te boundaries of te strata in igly skewed populations, usual
More informationVerifying Numerical Convergence Rates
1 Order of accuracy Verifying Numerical Convergence Rates We consider a numerical approximation of an exact value u. Te approximation depends on a small parameter, suc as te grid size or time step, and
More informationMth 95 Module 2 Spring 2014
Mth 95 Module Spring 014 Section 5.3 Polynomials and Polynomial Functions Vocabulary of Polynomials A term is a number, a variable, or a product of numbers and variables raised to powers. Terms in an expression
More informationSYMMETRY AND PRACTICAL GEOMETRY NCERT
MTHEMTIS UNIT 9 SYMMETRY N RTIL GEOMETRY () Main oncepts and Resuts figure is said to have ine symmetry, if by foding the figure aong a ine, the eft and right parts of it coincide exacty. The ine is caed
More informationFinite Difference Approximations
Capter Finite Difference Approximations Our goal is to approximate solutions to differential equations, i.e., to find a function (or some discrete approximation to tis function) tat satisfies a given relationsip
More information1 Derivatives of Piecewise Defined Functions
MATH 1010E University Matematics Lecture Notes (week 4) Martin Li 1 Derivatives of Piecewise Define Functions For piecewise efine functions, we often ave to be very careful in computing te erivatives.
More informationCollege Planning Using Cash Value Life Insurance
College Planning Using Cas Value Life Insurance CAUTION: Te advisor is urged to be extremely cautious of anoter college funding veicle wic provides a guaranteed return of premium immediately if funded
More informationFunctions and Equations
Centre for Education in Mathematics and Computing Euclid eworkshop # Functions and Equations c 014 UNIVERSITY OF WATERLOO Euclid eworkshop # TOOLKIT Parabolas The quadratic f(x) = ax + bx + c (with a,b,c
More informationUnderstanding the Derivative Backward and Forward by Dave Slomer
Understanding te Derivative Backward and Forward by Dave Slomer Slopes of lines are important, giving average rates of cange. Slopes of curves are even more important, giving instantaneous rates of cange.
More informationf(x) f(a) x a Our intuition tells us that the slope of the tangent line to the curve at the point P is m P Q =
Lecture 6 : Derivatives and Rates of Cange In tis section we return to te problem of finding te equation of a tangent line to a curve, y f(x) If P (a, f(a)) is a point on te curve y f(x) and Q(x, f(x))
More informationDistances in random graphs with infinite mean degrees
Distances in random graps wit infinite mean degrees Henri van den Esker, Remco van der Hofstad, Gerard Hoogiemstra and Dmitri Znamenski April 26, 2005 Abstract We study random graps wit an i.i.d. degree
More informationDifferential Calculus: Differentiation (First Principles, Rules) and Sketching Graphs (Grade 12)
OpenStaxCNX moule: m39313 1 Differential Calculus: Differentiation (First Principles, Rules) an Sketcing Graps (Grae 12) Free Hig Scool Science Texts Project Tis work is prouce by OpenStaxCNX an license
More informationAn inquiry into the multiplier process in ISLM model
An inquiry into te multiplier process in ISLM model Autor: Li ziran Address: Li ziran, Room 409, Building 38#, Peing University, Beijing 00.87,PRC. Pone: (86) 0062763074 Internet Address: jefferson@water.pu.edu.cn
More informationACT Math Flash Cards. PowerScore. Order of Operations. SAT Preparation. Live Online ACT Course. Full Length ACT Course. How to Study Math Flash Cards
PowerScore ACT Math Flash Cards Formulas, definitions, and concepts for success on the ACT Mathematics Test How to Study Math Flash Cards Review each card, and remove any formulas that you already know.
More informationWhat are the place values to the left of the decimal point and their associated powers of ten?
The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything
More informationSOLVING RIGHT TRIANGLES
PYTHAGOREAN THEOREM SOLVING RIGHT TRIANGLES An triangle tat as a rigt angle is called a RIGHT c TRIANGLE. Te two sides tat form te rigt angle, a and b, a are called LEGS, and te side opposite (tat is,
More informationPressure. Pressure. Atmospheric pressure. Conceptual example 1: Blood pressure. Pressure is force per unit area:
Pressure Pressure is force per unit area: F P = A Pressure Te direction of te force exerted on an object by a fluid is toward te object and perpendicular to its surface. At a microscopic level, te force
More informationCHAPTER 7. Di erentiation
CHAPTER 7 Di erentiation 1. Te Derivative at a Point Definition 7.1. Let f be a function defined on a neigborood of x 0. f is di erentiable at x 0, if te following it exists: f 0 fx 0 + ) fx 0 ) x 0 )=.
More informationVolumes of Pyramids and Cones. Use the Pythagorean Theorem to find the value of the variable. h 2 m. 1.5 m 12 in. 8 in. 2.5 m
5 Wat You ll Learn To find te volume of a pramid To find te volume of a cone... And W To find te volume of a structure in te sape of a pramid, as in Eample Volumes of Pramids and Cones Ceck Skills You
More informationMath 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.
Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used
More informationSAT Math Facts & Formulas Review Quiz
Test your knowledge of SAT math facts, formulas, and vocabulary with the following quiz. Some questions are more challenging, just like a few of the questions that you ll encounter on the SAT; these questions
More informationChapter 7 Numerical Differentiation and Integration
45 We ave a abit in writing articles publised in scientiþc journals to make te work as Þnised as possible, to cover up all te tracks, to not worry about te blind alleys or describe ow you ad te wrong idea
More informationMATHEMATICS FOR ENGINEERING DIFFERENTIATION TUTORIAL 1  BASIC DIFFERENTIATION
MATHEMATICS FOR ENGINEERING DIFFERENTIATION TUTORIAL 1  BASIC DIFFERENTIATION Tis tutorial is essential prerequisite material for anyone stuing mecanical engineering. Tis tutorial uses te principle of
More informationNew Vocabulary volume
. Plan Objectives To find te volume of a prism To find te volume of a cylinder Examples Finding Volume of a Rectangular Prism Finding Volume of a Triangular Prism 3 Finding Volume of a Cylinder Finding
More informationM(0) = 1 M(1) = 2 M(h) = M(h 1) + M(h 2) + 1 (h > 1)
Insertion and Deletion in VL Trees Submitted in Partial Fulfillment of te Requirements for Dr. Eric Kaltofen s 66621: nalysis of lgoritms by Robert McCloskey December 14, 1984 1 ackground ccording to Knut
More informationDifferentiable Functions
Capter 8 Differentiable Functions A differentiable function is a function tat can be approximated locally by a linear function. 8.. Te derivative Definition 8.. Suppose tat f : (a, b) R and a < c < b.
More informationArea of a Parallelogram
Area of a Parallelogram Focus on After tis lesson, you will be able to... φ develop te φ formula for te area of a parallelogram calculate te area of a parallelogram One of te sapes a marcing band can make
More information1.3 Polynomials and Factoring
1.3 Polynomials and Factoring Polynomials Constant: a number, such as 5 or 27 Variable: a letter or symbol that represents a value. Term: a constant, variable, or the product or a constant and variable.
More informationMATH 65 NOTEBOOK CERTIFICATIONS
MATH 65 NOTEBOOK CERTIFICATIONS Review Material from Math 60 2.5 4.3 4.4a Chapter #8: Systems of Linear Equations 8.1 8.2 8.3 Chapter #5: Exponents and Polynomials 5.1 5.2a 5.2b 5.3 5.4 5.5 5.6a 5.7a 1
More information( ) FACTORING. x In this polynomial the only variable in common to all is x.
FACTORING Factoring is similar to breaking up a number into its multiples. For example, 10=5*. The multiples are 5 and. In a polynomial it is the same way, however, the procedure is somewhat more complicated
More informationStrategic trading in a dynamic noisy market. Dimitri Vayanos
LSE Researc Online Article (refereed) Strategic trading in a dynamic noisy market Dimitri Vayanos LSE as developed LSE Researc Online so tat users may access researc output of te Scool. Copyrigt and Moral
More information3. Power of a Product: Separate letters, distribute to the exponents and the bases
Chapter 5 : Polynomials and Polynomial Functions 5.1 Properties of Exponents Rules: 1. Product of Powers: Add the exponents, base stays the same 2. Power of Power: Multiply exponents, bases stay the same
More informationPractical Geometry. construction of a Line ParaLLeL to a given Line through a Point not on it
12 ractica Geometry introduction In the previous cass, you have earnt to construct a circe of given radius, a ine segment of given ength, a copy of a ine segment, a perpendicuar ine to a given ine at a
More informationAlgebra I Vocabulary Cards
Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression
More informationMATH 095, College Prep Mathematics: Unit Coverage Prealgebra topics (arithmetic skills) offered through BSE (Basic Skills Education)
MATH 095, College Prep Mathematics: Unit Coverage Prealgebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,
More informationPerimeter, Area and Volume of Regular Shapes
Perimeter, Area and Volume of Regular Sapes Perimeter of Regular Polygons Perimeter means te total lengt of all sides, or distance around te edge of a polygon. For a polygon wit straigt sides tis is te
More information2.28 EDGE Program. Introduction
Introduction Te Economic Diversification and Growt Enterprises Act became effective on 1 January 1995. Te creation of tis Act was to encourage new businesses to start or expand in Newfoundland and Labrador.
More informationAreas and Centroids. Nothing. Straight Horizontal line. Straight Sloping Line. Parabola. Cubic
Constructing Sear and Moment Diagrams Areas and Centroids Curve Equation Sape Centroid (From Fat End of Figure) Area Noting Noting a x 0 Straigt Horizontal line /2 Straigt Sloping Line /3 /2 Paraola /4
More informationWhat is Advanced Corporate Finance? What is finance? What is Corporate Finance? Deciding how to optimally manage a firm s assets and liabilities.
Wat is? Spring 2008 Note: Slides are on te web Wat is finance? Deciding ow to optimally manage a firm s assets and liabilities. Managing te costs and benefits associated wit te timing of cas in and outflows
More informationOptimal Pricing Strategy for Second Degree Price Discrimination
Optimal Pricing Strategy for Second Degree Price Discrimination Alex O Brien May 5, 2005 Abstract Second Degree price discrimination is a coupon strategy tat allows all consumers access to te coupon. Purcases
More information1.3 Algebraic Expressions
1.3 Algebraic Expressions A polynomial is an expression of the form: a n x n + a n 1 x n 1 +... + a 2 x 2 + a 1 x + a 0 The numbers a 1, a 2,..., a n are called coefficients. Each of the separate parts,
More informationProof of the Power Rule for Positive Integer Powers
Te Power Rule A function of te form f (x) = x r, were r is any real number, is a power function. From our previous work we know tat x x 2 x x x x 3 3 x x In te first two cases, te power r is a positive
More informationCharacterization and Uniqueness of Equilibrium in Competitive Insurance
Caracterization and Uniqueness of Equiibrium in Competitive Insurance Vitor Farina Luz June 16, 2015 First draft: September 14t, 2012 Tis paper provides a compete caracterization of equiibria in a gameteoretic
More informationComparing Alternative Reimbursement Methods in a Model of Public Health Insurance
Comparing Aternative Reimbursement Metods in a Mode of Pubic Heat Insurance Francesca Barigozzi y First version: October 1998 Tis version: June 2000 Abstract I compare inkind reimbursement and reimbursement
More informationHEXAGON FLOWERS CUTTING OUT 1 COVERING THE FLOWERS 2
YOU WILL NEED Small scraps of fabric to cover fourteen exagons (includes enoug for front and back) Ribbon 6½in lengt Fourteen paper exagon templates (I used a size, but any would be fine, as long as you
More informationMoore Catholic High School Math Department COLLEGE PREP AND MATH CONCEPTS
Moore Catholic High School Math Department COLLEGE PREP AND MATH CONCEPTS The following is a list of terms and properties which are necessary for success in Math Concepts and College Prep math. You will
More informationME422 Mechanical Control Systems Modeling Fluid Systems
Cal Poly San Luis Obispo Mecanical Engineering ME422 Mecanical Control Systems Modeling Fluid Systems Owen/Ridgely, last update Mar 2003 Te dynamic euations for fluid flow are very similar to te dynamic
More information1. Use calculus to derive the formula for the area of a parallelogram of base b and height. y f(x)=mx+b
Area and Volume Problems. Use calculus to derive te formula for te area of a parallelogram of base b and eigt. y f(x)=mxb b g(x)=mx Te area of te parallelogram is given by te integral of te dierence of
More informationLinear Equations Review
Linear Equations Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The yintercept of the line y = 4x 7 is a. 7 c. 4 b. 4 d. 7 2. What is the yintercept
More informationThe Derivative as a Function
Section 2.2 Te Derivative as a Function 200 Kiryl Tsiscanka Te Derivative as a Function DEFINITION: Te derivative of a function f at a number a, denoted by f (a), is if tis limit exists. f (a) f(a+) f(a)
More informationAverage and Instantaneous Rates of Change: The Derivative
9.3 verage and Instantaneous Rates of Cange: Te Derivative 609 OBJECTIVES 9.3 To define and find average rates of cange To define te derivative as a rate of cange To use te definition of derivative to
More informationFor Sale By Owner Program. We can help with our for sale by owner kit that includes:
Dawn Coen Broker/Owner For Sale By Owner Program If you want to sell your ome By Owner wy not:: For Sale Dawn Coen Broker/Owner YOUR NAME YOUR PHONE # Look as professional as possible Be totally prepared
More informationShell and Tube Heat Exchanger
Sell and Tube Heat Excanger MECH595 Introduction to Heat Transfer Professor M. Zenouzi Prepared by: Andrew Demedeiros, Ryan Ferguson, Bradford Powers November 19, 2009 1 Abstract 2 Contents Discussion
More informationRecall from last time: Events are recorded by local observers with synchronized clocks. Event 1 (firecracker explodes) occurs at x=x =0 and t=t =0
1/27 Day 5: Questions? Time Dilation engt Contraction PH3 Modern Pysics P11 I sometimes ask myself ow it came about tat I was te one to deelop te teory of relatiity. Te reason, I tink, is tat a normal
More informationNSM100 Introduction to Algebra Chapter 5 Notes Factoring
Section 5.1 Greatest Common Factor (GCF) and Factoring by Grouping Greatest Common Factor for a polynomial is the largest monomial that divides (is a factor of) each term of the polynomial. GCF is the
More informationName: Period: 9/28 10/7
Nae: Period: 9/ 0/ LINES & TRANSVERSALS ) I can define, identify and iustrate te foowing ters Transversa Corresponding anges Aternate exterior anges. Aternate interior anges Sae side interior anges Dates,
More informationModuMath Algebra Lessons
ModuMath Algebra Lessons Program Title 1 Getting Acquainted With Algebra 2 Order of Operations 3 Adding & Subtracting Algebraic Expressions 4 Multiplying Polynomials 5 Laws of Algebra 6 Solving Equations
More informationTRADING AWAY WIDE BRANDS FOR CHEAP BRANDS. Swati Dhingra London School of Economics and CEP. Online Appendix
TRADING AWAY WIDE BRANDS FOR CHEAP BRANDS Swati Dingra London Scool of Economics and CEP Online Appendix APPENDIX A. THEORETICAL & EMPIRICAL RESULTS A.1. CES and Logit Preferences: Invariance of Innovation
More informationFactoring Trinomials: The ac Method
6.7 Factoring Trinomials: The ac Method 6.7 OBJECTIVES 1. Use the ac test to determine whether a trinomial is factorable over the integers 2. Use the results of the ac test to factor a trinomial 3. For
More informationRemember that the information below is always provided on the formula sheet at the start of your exam paper
Maths GCSE Linear HIGHER Things to Remember Remember that the information below is always provided on the formula sheet at the start of your exam paper In addition to these formulae, you also need to learn
More informationArea Formulas with Applications
Formulas wit Applications Ojective To review and use formulas for perimeter, circumference, and area. www.everydaymatonline.com epresentations etoolkit Algoritms Practice EM Facts Worksop Game Family Letters
More informationLagrange Interpolation is a method of fitting an equation to a set of points that functions well when there are few points given.
Polynomials (Ch.1) Study Guide by BS, JL, AZ, CC, SH, HL Lagrange Interpolation is a method of fitting an equation to a set of points that functions well when there are few points given. Sasha s method
More information