SELECTIVE APPROACH TO SOLVING SYLLOGISM
|
|
- Diana Wilkerson
- 6 years ago
- Views:
Transcription
1 SELECTIVE APPROACH TO SOLVING SYLLOGISM While solving Syllogism questions, we encounter many weird Statements: Some Cows are Ugly, Some Lions are Vegetarian, Some Cats are not Dogs, Some Girls are Boys, and such. The people who are comfortable using Venn Diagrams waste not a second more making the quickest Diagram based upon the given Statements. Ironically, this is not the case for others. Some find these questions challenging, cumbersome and time consuming to the point that they skip these at the first sight. But worry not. Syllogism is a piece of cake! I ll show you how. Give me about 20 minutes. Diagram Selection The basic thing to remember about Syllogism is: One Statement tells many things and thus, many Diagrams are possible. For example, consider this basic Statement: Some A are not B. Now, according to this Statement, three Diagrams are possible. These are shown here. (1) (2) (3) 1st Diagram is similar to basic Diagram of Some A are B. 2nd Diagram is similar to basic Diagram of No A are B. 3rd Diagram is similar to basic Diagram of All B are A. But which Diagram to select for solving question? 1st or 2nd or 3rd? Confused?? Well, don t be. Pay attention now. Selection of the best Diagram follows a very simple concept. And that is: Circles in Diagram should Overlap as Minimum as Possible
2 Why Minimum? For the very basic reason: Minimum is the overlap, minimum will be the confusion. So, 1st, 2nd or 3rd, which Diagram is the best to select? Answer is: 2nd one!! Okay! There are three more basic Statements. Some A are B. All A are B. No A are B. For these Statements as well, we ll select the Diagram in which minimum overlap of the circle is there. Minimum Overlap Diagrams for these Statements are given here. Some A are B All A are B No A are B Note three things here. Making Diagrams Quickly 1. The Diagram of Some A are B is drawn as such. 2. In Diagram of All A are B, I ve touched the boundaries of circle A and B. This results in further minimization of overlap (I ll show you how). 3. In Diagram of No A are B, I ve drawn a line with cross between circles A and B. This way I pretty much remembers their relation without confusion. Now let s shed some more light upon Point no. 2 mentioned above. Let we have few Statements as: A. Some Headphones are Earphones. B. All Earphones are Telephones.
3 Now, I m making three different Diagrams based upon these two Statements. (1) (2) (3) Tell me which Diagram has the Minimum Overlap? 1st, 2nd or 3rd? Of course, the 2nd one!! This boundary touching approach further reduces the overlap of a combination of Statements, like: A. All Comedians are Funny. B. All Comedians are Actors. Notice the way Red portion didn t come in circles drawn by hand. A. Some Pots are Keys. B. Some Keys are Locks. C. All Keys are Rings. Notice the way I didn t overlap the P and L circles. A. All Employees are Owners. B. No Owner is a Wager. C. Some Employees are not Managers. D. All Managers are Gatekeepers. E. Some Wagers are Managers. Notice the way I ve drawn the E and M circles That s how we draw the Diagrams so that Circles should have a Minimum Overlap. Pick up a few Syllogism Statements and practice these Diagram making approaches.
4 Applying These Approaches One more thing remains, which is necessary to learn before you embark upon solving Syllogism questions. And that is: Checking the validity of Conclusions. Let s learn this as we go along solving this interesting example. Statements: Question 1 A. Some Banks are Shops. B. Some Shops are Markets. C. All Markets are Junk. I. Some Junk are Shops. II. Some Markets are Banks. III. No junk is a Bank. IV. No Junk being Banks is a possibility. The Best Diagram (Minimum Overlap) is shown here. Now pay attention! To check the validity of a Simple Conclusion (no Possibility), just try to refute (prove false) the Conclusion. This is how it is done. 1. See Conclusion I Some Junk are Shops. To check whether this Conclusion follows or not, we ll try to prove false this Conclusion. Conclusion says Some Junk are Shops. If we can prove No Junk are Shop is actually possible according to the given Statements, then this Conclusion would be refuted. In simple words: this Conclusion will not follow. Now, is No Junk are Shop possible? The Minimum Overlap Diagram says it s not possible. We cannot prove this Conclusion false. So, this Conclusion will follow in ALL THE CASES.
5 2. See Conclusion II Some Markets are Banks To check whether this Conclusion follows or not, we ll try to prove false this Conclusion. Conclusion says Some Markets are Banks. If we can prove No Market are Bank is actually possible according to the given Statements, then this Conclusion would be refuted. In simple words: this Conclusion will not follow. Now, is No Market are Bank possible? The Minimum Overlap Diagram says it s possible. So, if No Market are Bank is possible, Some Markets are Banks will not follow. As simple as that. (You see, Minimum Overlap Diagram reduces so much work while checking the validity of the questions.) 3. See Conclusion III No Junk is a Bank. To check whether this Conclusion follows or not, we ll try to prove false this Conclusion. Conclusion says No Junk is a Bank. If we can prove that Some Junk are Bank is actually possible according to the given Statements, then this Conclusion would be refuted. In simple words: this Conclusion will not follow. Now, is Some Junk are Bank possible? Yes, it is possible. See the Diagram (Here, another Diagram is shown, but you can easily imagine this Diagram all in your head.) So, if Some Junk are Bank is possible, No Junk is a Bank will not follow. As simple as that. Now pay attention again! Validity checking of Possibility Conclusions runs different course. We tried to prove false the Simple Conclusions, but when it comes to Possibility Conclusions, we try to prove them true. 4. See Conclusion IV No Junk being Bank is a Possibility To check whether this Conclusion follows or not, we ll try to prove this Conclusion true. Conclusion asks, is No Junk are Bank Possible? Of course, it is possible.
6 Some Junk are Bank is possible and No Junk are Bank is also possible. So, this Conclusion follows. And doing all this, we ve solved this question. Full marks! You don t even have to remember this table to check the validity of Simple Conclusions. (If Counter-Conclusion is possible, Simple Conclusion will not follow.) Conclusion Counter-Conclusion 1. Some A are B No A are B 2. No A are B Some A are B 3. All A are B Some A are not B 4. Some A are not B All A are B Just note: 1. The Counter-Conclusion of Some A are B is No A are B while the Counter-Conclusion of No A are B is Some A are B. These are Counter-Pairs. 2. The Counter-Conclusion of All A are B is Some A are not B while the Counter-Conclusion of Some A are not B is All A are B. These are also Counter-Pairs. With practice only you ll learn that you don t need to counter check the Conclusion every time. Minimum Overlap Diagram does much of the work for you. Why? Because you cannot go more Minimum than that! Let s quickly solve some of the questions now. Statements: A. Some Questions are Answers. B. All Questions are Puzzles. C. No Puzzle is Problem. I. Some Puzzles are Answers. II. No Question is a Problem. Conclusion I? Follows! Conclusion II? Follows! Question 2
7 Question 3 Same Statements as of Question 2 I. All Problem being Answer is a Possibility. II. All Problem being Question is a Possibility. Conclusion I? Follows! Conclusion II? Doesn t Follows! Statements: A. No Second is Hour. B. Some Minutes are Time. C. All Hours are Minutes. Question 4 I. All Hours are Time. II. Some Minutes being Second is a Possibility. Conclusion I? Doesn t Follows! Conclusion II? Follows! (Just imagine) And that s all what is needed to solve Syllogism the quickest way! Practice as much as you can until you feel comfortable solving the questions using these methods. Thank You! All the very best!!
base 2 4 The EXPONENT tells you how many times to write the base as a factor. Evaluate the following expressions in standard notation.
EXPONENTIALS Exponential is a number written with an exponent. The rules for exponents make computing with very large or very small numbers easier. Students will come across exponentials in geometric sequences
More informationHypothesis testing I. - In particular, we are talking about statistical hypotheses. [get everyone s finger length!] n =
Hypothesis testing I I. What is hypothesis testing? [Note we re temporarily bouncing around in the book a lot! Things will settle down again in a week or so] - Exactly what it says. We develop a hypothesis,
More informationMATH240: Linear Algebra Review for exam #1 6/10/2015 Page 1
MATH24: Linear Algebra Review for exam # 6//25 Page No review sheet can cover everything that is potentially fair game for an exam, but I tried to hit on all of the topics with these questions, as well
More informationGuide to Proofs on Sets
CS103 Winter 2019 Guide to Proofs on Sets Cynthia Lee Keith Schwarz I would argue that if you have a single guiding principle for how to mathematically reason about sets, it would be this one: All sets
More informationLesson 1.2 Position Time Graphs
Lesson 1.2 Position Time Graphs Be able to explain the motion represented in a position time graph Be able to calculate the avg. vel, x, and t for portions of a position time graph. Be able to draw a position
More informationSolving Quadratic & Higher Degree Equations
Chapter 9 Solving Quadratic & Higher Degree Equations Sec 1. Zero Product Property Back in the third grade students were taught when they multiplied a number by zero, the product would be zero. In algebra,
More information( )( b + c) = ab + ac, but it can also be ( )( a) = ba + ca. Let s use the distributive property on a couple of
Factoring Review for Algebra II The saddest thing about not doing well in Algebra II is that almost any math teacher can tell you going into it what s going to trip you up. One of the first things they
More informationPre-calculus is the stepping stone for Calculus. It s the final hurdle after all those years of
Chapter 1 Beginning at the Very Beginning: Pre-Pre-Calculus In This Chapter Brushing up on order of operations Solving equalities Graphing equalities and inequalities Finding distance, midpoint, and slope
More informationToss 1. Fig.1. 2 Heads 2 Tails Heads/Tails (H, H) (T, T) (H, T) Fig.2
1 Basic Probabilities The probabilities that we ll be learning about build from the set theory that we learned last class, only this time, the sets are specifically sets of events. What are events? Roughly,
More information{ }. The dots mean they continue in that pattern.
INTEGERS Integers are positive and negative whole numbers, that is they are;... 3, 2, 1,0,1,2,3... { }. The dots mean they continue in that pattern. Like all number sets, integers were invented to describe
More informationMath Fundamentals for Statistics I (Math 52) Unit 7: Connections (Graphs, Equations and Inequalities)
Math Fundamentals for Statistics I (Math 52) Unit 7: Connections (Graphs, Equations and Inequalities) By Scott Fallstrom and Brent Pickett The How and Whys Guys This work is licensed under a Creative Commons
More informationAnswers for Calculus Review (Extrema and Concavity)
Answers for Calculus Review 4.1-4.4 (Extrema and Concavity) 1. A critical number is a value of the independent variable (a/k/a x) in the domain of the function at which the derivative is zero or undefined.
More informationModule 1: Introduction to Functions
Haberman / Kling MTH 95 Section II: Functions, Inequalities, and the Absolute Value Module 1: Introduction to Functions A function is a special type of binary relation. So before we discuss what a function
More informationAlex s Guide to Word Problems and Linear Equations Following Glencoe Algebra 1
Alex s Guide to Word Problems and Linear Equations Following Glencoe Algebra 1 What is a linear equation? It sounds fancy, but linear equation means the same thing as a line. In other words, it s an equation
More informationChapter 15. Probability Rules! Copyright 2012, 2008, 2005 Pearson Education, Inc.
Chapter 15 Probability Rules! Copyright 2012, 2008, 2005 Pearson Education, Inc. The General Addition Rule When two events A and B are disjoint, we can use the addition rule for disjoint events from Chapter
More informationMath101, Sections 2 and 3, Spring 2008 Review Sheet for Exam #2:
Math101, Sections 2 and 3, Spring 2008 Review Sheet for Exam #2: 03 17 08 3 All about lines 3.1 The Rectangular Coordinate System Know how to plot points in the rectangular coordinate system. Know the
More informationUNDERSTANDING FUNCTIONS
Learning Centre UNDERSTANDING FUNCTIONS Function As a Machine A math function can be understood as a machine that takes an input and produces an output. Think about your CD Player as a machine that takes
More informationMath 5a Reading Assignments for Sections
Math 5a Reading Assignments for Sections 4.1 4.5 Due Dates for Reading Assignments Note: There will be a very short online reading quiz (WebWork) on each reading assignment due one hour before class on
More informationMI 4 Mathematical Induction Name. Mathematical Induction
Mathematical Induction It turns out that the most efficient solution to the Towers of Hanoi problem with n disks takes n 1 moves. If this isn t the formula you determined, make sure to check your data
More informationProbability and Independence Terri Bittner, Ph.D.
Probability and Independence Terri Bittner, Ph.D. The concept of independence is often confusing for students. This brief paper will cover the basics, and will explain the difference between independent
More informationDEVELOPING MATH INTUITION
C HAPTER 1 DEVELOPING MATH INTUITION Our initial exposure to an idea shapes our intuition. And our intuition impacts how much we enjoy a subject. What do I mean? Suppose we want to define a cat : Caveman
More informationRigid Body Equilibrium. Free Body Diagrams. Equations of Equilibrium
Rigid Body Equilibrium and the Equations of Equilibrium small boy swallowed some coins and was taken to a hospital. When his grandmother telephoned to ask how he was a nurse said 'No change yet'. Objectives
More informationAP Calculus. Derivatives.
1 AP Calculus Derivatives 2015 11 03 www.njctl.org 2 Table of Contents Rate of Change Slope of a Curve (Instantaneous ROC) Derivative Rules: Power, Constant, Sum/Difference Higher Order Derivatives Derivatives
More informationAlgebra. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.
This document was written and copyrighted by Paul Dawkins. Use of this document and its online version is governed by the Terms and Conditions of Use located at. The online version of this document is
More informationSystem of Linear Equation: with more than Two Equations and more than Two Unknowns
System of Linear Equation: with more than Two Equations and more than Two Unknowns Michigan Department of Education Standards for High School: Standard 1: Solve linear equations and inequalities including
More information{ }. The dots mean they continue in that pattern to both
INTEGERS Integers are positive and negative whole numbers, that is they are;... 3, 2, 1,0,1,2,3... { }. The dots mean they continue in that pattern to both positive and negative infinity. Before starting
More informationCalculus II. Calculus II tends to be a very difficult course for many students. There are many reasons for this.
Preface Here are my online notes for my Calculus II course that I teach here at Lamar University. Despite the fact that these are my class notes they should be accessible to anyone wanting to learn Calculus
More informationPhysics nd Air Table Experiment Conservation of Angular Momentum
Physics 141 2 nd Air Table Experiment Conservation of Angular Momentum Introduction In this experiment, you will investigate angular momentum, and learn something important about the conditions under which
More informationSection 20: Arrow Diagrams on the Integers
Section 0: Arrow Diagrams on the Integers Most of the material we have discussed so far concerns the idea and representations of functions. A function is a relationship between a set of inputs (the leave
More informationWhy Doesn t the Moon Hit us? In analysis of this question, we ll look at the following things: i. How do we get the acceleration due to gravity out
Why Doesn t the oon Hit us? In analysis of this question, we ll look at the following things: i. How do we get the acceleration due to gravity out of the equation for the force of gravity? ii. How does
More informationMGF 1106: Exam 1 Solutions
MGF 1106: Exam 1 Solutions 1. (15 points total) True or false? Explain your answer. a) A A B Solution: Drawn as a Venn diagram, the statement says: This is TRUE. The union of A with any set necessarily
More information9 UNITS OF MEASUREMENT
!119 9 UNITS OF MEASUREMENT There are many measurements that we must take into consideration when shooting long range: distance to the target, size of the target, elevation compensation, windage compensation,
More informationExtensions to the Logic of All x are y: Verbs, Relative Clauses, and Only
1/53 Extensions to the Logic of All x are y: Verbs, Relative Clauses, and Only Larry Moss Indiana University Nordic Logic School August 7-11, 2017 2/53 An example that we ll see a few times Consider the
More informationImplicit Differentiation and Related Rates
Math 31A Discussion Session Week 5 Notes February 2 and 4, 2016 This week we re going to learn how to find tangent lines to curves which aren t necessarily graphs of functions, using an approach called
More informationChapter 1: Functions. Section 1.1 Functions and Function Notation. Section 1.1 Functions and Function Notation 1
Section. Functions and Function Notation Chapter : Functions Section. Functions and Function Notation... Section. Domain and Range... Section. Rates of Change and Behavior of Graphs... 4 Section.4 Composition
More informationSeries, Parallel, and other Resistance
EELE 2310 Analysis Lecture 3 Equivalent s Series, Parallel, Delta-to-Wye, Voltage Divider and Current Divider Rules Dr Hala El-Khozondar Series, Parallel, and other Resistance Equivalent s ١ Overview Series,
More informationUnit 2 Linear Equations and Inequalities
Unit 2 Linear Equations and Inequalities Test Date: Name: By the end of this unit, you will be able to Use rate of change to solve problems Find the slope of a line Model real-world data with linear equations
More informationDIFFERENTIAL EQUATIONS
DIFFERENTIAL EQUATIONS Basic Concepts Paul Dawkins Table of Contents Preface... Basic Concepts... 1 Introduction... 1 Definitions... Direction Fields... 8 Final Thoughts...19 007 Paul Dawkins i http://tutorial.math.lamar.edu/terms.aspx
More informationChapter 2. Mathematical Reasoning. 2.1 Mathematical Models
Contents Mathematical Reasoning 3.1 Mathematical Models........................... 3. Mathematical Proof............................ 4..1 Structure of Proofs........................ 4.. Direct Method..........................
More informationIntroduction. So, why did I even bother to write this?
Introduction This review was originally written for my Calculus I class, but it should be accessible to anyone needing a review in some basic algebra and trig topics. The review contains the occasional
More informationLesson 26: Characterization of Parallel Lines
Student Outcomes Students know that when a system of linear equations has no solution, i.e., no point of intersection of the lines, then the lines are parallel. Lesson Notes The discussion that begins
More informationConceptual Explanations: Simultaneous Equations Distance, rate, and time
Conceptual Explanations: Simultaneous Equations Distance, rate, and time If you travel 30 miles per hour for 4 hours, how far do you go? A little common sense will tell you that the answer is 120 miles.
More informationWEEK 1 THE BIBLE BIG IDEA WELCOME TIME DISCUSSION TIME TEACHING TIME PLAY TIME PRESCHOOL LESSON OUTLINE THIS WEEK AT A GLANCE
WEEK 1 PRESCHOOL LESSON OUTLINE BIG IDEA Jesus cares about us when we are sick. THE BIBLE Jesus Heals the Leper: Luke 5:12-15 THIS WEEK AT A GLANCE WELCOME TIME ACTIVITY Play-Doh Unbelievable Scenes ACTIVITY
More informationElectrostatics Level 1: Basic Charges
Electrostatics 2014 Level 1: Basic Charges The universe is made up of basic particles that combine and seperate to form all matter. These basic particles (as you learned in chemistry) consist of protons,
More informationAn Introduction to Proofs in Mathematics
An Introduction to Proofs in Mathematics The subject of mathematics is often regarded as a pinnacle in the achievement of human reasoning. The reason that mathematics is so highly regarded in the realm
More informationChapter Three. Deciphering the Code. Understanding Notation
Chapter Three Deciphering the Code Mathematics has its own vocabulary. In addition to words, mathematics uses its own notation, symbols that stand for more complicated ideas. Some of these elements are
More informationLesson 6-1: Relations and Functions
I ll bet you think numbers are pretty boring, don t you? I ll bet you think numbers have no life. For instance, numbers don t have relationships do they? And if you had no relationships, life would be
More informationMath 138: Introduction to solving systems of equations with matrices. The Concept of Balance for Systems of Equations
Math 138: Introduction to solving systems of equations with matrices. Pedagogy focus: Concept of equation balance, integer arithmetic, quadratic equations. The Concept of Balance for Systems of Equations
More informationAlgebra & Trig Review
Algebra & Trig Review 1 Algebra & Trig Review This review was originally written for my Calculus I class, but it should be accessible to anyone needing a review in some basic algebra and trig topics. The
More informationTo factor an expression means to write it as a product of factors instead of a sum of terms. The expression 3x
Factoring trinomials In general, we are factoring ax + bx + c where a, b, and c are real numbers. To factor an expression means to write it as a product of factors instead of a sum of terms. The expression
More informationFunctions & Function Notation
Functions & Function Notation What is a Function? The natural world is full of relationships between quantities that change. When we see these relationships, it is natural for us to ask If I know one quantity,
More information1 Intro. 2 Guest Visitor. 3 Rulers
The Equivalence Principle and Foundations of General Relativity K. Arthur Croker Department of Physics and Astronomy University of Hawaii at Manoa http://www.phys.hawaii.edu/~kcroker Abstract These are
More informationEngineering Notebook
Draft 12/2013 Engineering Notebook Here Comes the Sun: Engineering Insulated Homes Name: Prep Activity 1 Criteria and Constraints Woolly Mammoth Melt Your goal: to design an insulated transportation tank
More informationUniversity of Maryland Department of Physics
Spring 3 University of Maryland Department of Physics Laura Lising Physics 1 March 6, 3 Exam #1 nswer all questions on these sheets. Please write clearly and neatly: We can only give you credit for what
More informationSolving Quadratic & Higher Degree Equations
Chapter 9 Solving Quadratic & Higher Degree Equations Sec 1. Zero Product Property Back in the third grade students were taught when they multiplied a number by zero, the product would be zero. In algebra,
More informationBig-oh stuff. You should know this definition by heart and be able to give it,
Big-oh stuff Definition. if asked. You should know this definition by heart and be able to give it, Let f and g both be functions from R + to R +. Then f is O(g) (pronounced big-oh ) if and only if there
More informationSection 2.5 Linear Inequalities
Section 2.5 Linear Inequalities WORDS OF COMPARISON Recently, you worked with applications (word problems) in which you were required to write and solve an equation. Sometimes you needed to translate sentences
More informationGrade 7/8 Math Circles November 14/15/16, Estimation
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Introduction Grade 7/8 Math Circles November 14/15/16, 2017 Estimation Centre for Education in Mathematics and Computing If you ever find yourself without
More informationChapter 1: January 26 January 30
Chapter : January 26 January 30 Section.7: Inequalities As a diagnostic quiz, I want you to go through the first ten problems of the Chapter Test on page 32. These will test your knowledge of Sections.
More informationWhat is proof? Lesson 1
What is proof? Lesson The topic for this Math Explorer Club is mathematical proof. In this post we will go over what was covered in the first session. The word proof is a normal English word that you might
More informationSTA Why Sampling? Module 6 The Sampling Distributions. Module Objectives
STA 2023 Module 6 The Sampling Distributions Module Objectives In this module, we will learn the following: 1. Define sampling error and explain the need for sampling distributions. 2. Recognize that sampling
More informationRemember that all physical quantities are measured in units. The unit of force is called the newton (N), where 1 N = (1 kg)(1 m/s 2 ).
Force as an Interaction 1.1 Observe and Represent a) Pick up a tennis ball and hold it in your hand. Now pick up a bowling ball and hold it. Do you feel the difference? How can you describe what you feel
More informationSolving Quadratic & Higher Degree Equations
Chapter 7 Solving Quadratic & Higher Degree Equations Sec 1. Zero Product Property Back in the third grade students were taught when they multiplied a number by zero, the product would be zero. In algebra,
More informationThe Witch Who Was Frightened of Halloween.
The Witch Who Was Frightened of Halloween http://storynory.com/2007/10/14/the-witch-who-was-frightenedof-halloween/ As every kid knows, Halloween is both spooky and sweet. It s spooky because there are
More informationMA 1128: Lecture 08 03/02/2018. Linear Equations from Graphs And Linear Inequalities
MA 1128: Lecture 08 03/02/2018 Linear Equations from Graphs And Linear Inequalities Linear Equations from Graphs Given a line, we would like to be able to come up with an equation for it. I ll go over
More informationGetting Started with Communications Engineering
1 Linear algebra is the algebra of linear equations: the term linear being used in the same sense as in linear functions, such as: which is the equation of a straight line. y ax c (0.1) Of course, if we
More informationPolynomials; Add/Subtract
Chapter 7 Polynomials Polynomials; Add/Subtract Polynomials sounds tough enough. But, if you look at it close enough you ll notice that students have worked with polynomial expressions such as 6x 2 + 5x
More informationPart I Electrostatics. 1: Charge and Coulomb s Law July 6, 2008
Part I Electrostatics 1: Charge and Coulomb s Law July 6, 2008 1.1 What is Electric Charge? 1.1.1 History Before 1600CE, very little was known about electric properties of materials, or anything to do
More informationHow to Work an Older Storm
How to Work an Older Storm How to Work an Older Storm We know what it s like to be out knocking doors 11 months after the latest hailstorm. The buzz has worn off and people seem to have forgotten how destructive
More informationTalk Science Professional Development
Talk Science Professional Development Transcript for Grade 5 Scientist Case: The Water to Ice Investigations 1. The Water to Ice Investigations Through the Eyes of a Scientist We met Dr. Hugh Gallagher
More informationMath 101 Review of SOME Topics
Math 101 Review of SOME Topics Spring 007 Mehmet Haluk Şengün May 16, 007 1 BASICS 1.1 Fractions I know you all learned all this years ago, but I will still go over it... Take a fraction, say 7. You can
More informationChapter 1 Review of Equations and Inequalities
Chapter 1 Review of Equations and Inequalities Part I Review of Basic Equations Recall that an equation is an expression with an equal sign in the middle. Also recall that, if a question asks you to solve
More informationChapter 18. Sampling Distribution Models. Copyright 2010, 2007, 2004 Pearson Education, Inc.
Chapter 18 Sampling Distribution Models Copyright 2010, 2007, 2004 Pearson Education, Inc. Normal Model When we talk about one data value and the Normal model we used the notation: N(μ, σ) Copyright 2010,
More informationAlgebra Exam. Solutions and Grading Guide
Algebra Exam Solutions and Grading Guide You should use this grading guide to carefully grade your own exam, trying to be as objective as possible about what score the TAs would give your responses. Full
More informationCOLLEGE ALGEBRA. Paul Dawkins
COLLEGE ALGEBRA Paul Dawkins Table of Contents Preface... iii Outline... iv Preliminaries... 7 Introduction... 7 Integer Exponents... 8 Rational Exponents...5 Radicals... Polynomials...30 Factoring Polynomials...36
More informationEgyptian Fractions: Part I
Egyptian Fractions: Part I Prepared by: Eli Jaffe October 8, 2017 1 Cutting Cakes 1. Imagine you are a teacher. Your class of 10 students is on a field trip to the bakery. At the end of the tour, the baker
More informationUnit 7 Graphs and Graphing Utilities - Classwork
A. Graphing Equations Unit 7 Graphs and Graphing Utilities - Classwork Our first job is being able to graph equations. We have done some graphing in trigonometry but now need a general method of seeing
More informationHere Comes the Sun: Engineering Insulated Homes. Name:
Engineering Notebook Here Comes the Sun: Engineering Insulated Homes Name: Prep Activity 1 Criteria and Constraints Woolly Mammoth Melt Your goal is to design an insulated transportation tank that will
More informationPartial Solutions to Homework 2
Partial Solutions to Homework. Carefully depict some of the indi erence curves for the following utility functions. In each case, check whether the preferences are monotonic and whether preferences are
More informationMath 31 Lesson Plan. Day 2: Sets; Binary Operations. Elizabeth Gillaspy. September 23, 2011
Math 31 Lesson Plan Day 2: Sets; Binary Operations Elizabeth Gillaspy September 23, 2011 Supplies needed: 30 worksheets. Scratch paper? Sign in sheet Goals for myself: Tell them what you re going to tell
More informationSolving with Absolute Value
Solving with Absolute Value Who knew two little lines could cause so much trouble? Ask someone to solve the equation 3x 2 = 7 and they ll say No problem! Add just two little lines, and ask them to solve
More informationQuadratic Equations Part I
Quadratic Equations Part I Before proceeding with this section we should note that the topic of solving quadratic equations will be covered in two sections. This is done for the benefit of those viewing
More informationSTA Module 4 Probability Concepts. Rev.F08 1
STA 2023 Module 4 Probability Concepts Rev.F08 1 Learning Objectives Upon completing this module, you should be able to: 1. Compute probabilities for experiments having equally likely outcomes. 2. Interpret
More informationCHM 105 & 106 MO1 UNIT TWO, LECTURE THREE 1 IN OUR PREVIOUS LECTURE WE TALKED ABOUT USING CHEMICAL EQUATIONS TO SHOW THE
CHM 105 & 106 MO1 UNIT TWO, LECTURE THREE 1 CHM 105/106 Program 10: Unit 2 Lecture 3 IN OUR PREVIOUS LECTURE WE TALKED ABOUT USING CHEMICAL EQUATIONS TO SHOW THE LAW OF MASS AND THE LAW OF CONSERVATION
More informationChild sexual abuse is a serious crime that is why you must listen while the Touching Rules are being explained.
Child sexual abuse is a serious crime that is why you must listen while the Touching Rules are being explained. Touching Rule 1: It is never all right for someone older or more powerful than you to touch
More informationboth spooky witches wizards fair rather odd
As every kid knows, Halloween is both spooky and sweet. It s spooky because there are witches and wizards about, and it s sweet because children go in search of treats. This story is about a little girl
More informationFractions. Warm up galleryitem. If I eat the two pizza slices shown, how much of the pizza did I eat?
Fractions Warm up 2017-01-09 20.04.33.galleryitem If I eat the two pizza slices shown, how much of the pizza did I eat? When my family gets a Papa Murphy s pizza, I cut it like this for people who like
More informationMITOCW MIT8_01F16_w02s05v06_360p
MITOCW MIT8_01F16_w02s05v06_360p One of our classic problems to analyze using Newton's second law is the motion of two blocks with a rope that's wrapped around a pulley. So imagine we have a pulley, P,
More informationAP Calculus AB Summer Assignment
AP Calculus AB Summer Assignment Name: When you come back to school, it is my epectation that you will have this packet completed. You will be way behind at the beginning of the year if you haven t attempted
More informationc 2007 Je rey A. Miron
Review of Calculus Tools. c 007 Je rey A. Miron Outline 1. Derivatives. Optimization 3. Partial Derivatives. Optimization again 5. Optimization subject to constraints 1 Derivatives The basic tool we need
More informationGuide to Proofs on Discrete Structures
CS103 Handout 17 Spring 2018 Guide to Proofs on Discrete Structures In Problem Set One, you got practice with the art of proofwriting in general (as applied to numbers, sets, puzzles, etc.) Problem Set
More informationLearning From Data Lecture 14 Three Learning Principles
Learning From Data Lecture 14 Three Learning Principles Occam s Razor Sampling Bias Data Snooping M. Magdon-Ismail CSCI 4100/6100 recap: Validation and Cross Validation Validation Cross Validation D (N)
More informationDesigning geared 3D twisty puzzles (on the example of Gear Pyraminx) Timur Evbatyrov, Jan 2012
Designing geared 3D twisty puzzles (on the example of Gear Pyraminx) Timur Evbatyrov, Jan 2012 Introduction In this tutorial I ll demonstrate you my own method of designing geared 3D twisty puzzles on
More informationDay 1: Over + Over Again
Welcome to Morning Math! The current time is... huh, that s not right. Day 1: Over + Over Again Welcome to PCMI! We know you ll learn a great deal of mathematics here maybe some new tricks, maybe some
More informationName: Block: Unit 2 Inequalities
Name: Block: Unit 2 Inequalities 2.1 Graphing and Writing Inequalities 2.2 Solving by Adding and Subtracting 2.3 Solving by Multiplying and Dividing 2.4 Solving Two Step and Multi Step Inequalities 2.5
More informationASTRO 114 Lecture Okay. We re now gonna continue discussing and conclude discussing the entire
ASTRO 114 Lecture 55 1 Okay. We re now gonna continue discussing and conclude discussing the entire universe. So today we re gonna learn about everything, everything that we know of. There s still a lot
More information2.7 Implicit Differentiation and Related Rates Math 125
.7 IMPLICIT DIFFERENTIATION AND RELATED RATES Implicit and Explicit Functions Suppose your boss says, I have had it with your incompetence. You ve screwed up everything we ve ever given you to do! The
More informationRead the selection and choose the best answer to each question. Then fill in the answer on your answer document. Lights Out
Read the selection and choose the best answer to each question. Then fill in the answer on your answer document. Characters DEXTER: Younger brother LEO: Older brother Lights Out 1 [Night. A boys bedroom
More informationUnit 1: Equilibrium and Center of Mass
Unit 1: Equilibrium and Center of Mass FORCES What is a force? Forces are a result of the interaction between two objects. They push things, pull things, keep things together, pull things apart. It s really
More informationINTRODUCING NEWTON TO SECONDARY SCHOOL STUDENTS
INTRODUCING NEWTON TO SECONDARY SCHOOL STUDENTS K. P. Mohanan and Tara Mohanan This write-up is a draft that could serve as a starting point for a project. The goal of the project is to design learning
More information