Qm 1 Course Manual 1013

8/11/2019 Qm 1 Course Manual 1013

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Quanti tative Methods 1

EBC1005 EBC1006 EBC1007

102BB 102BE 102BF

Cour se manual 2013/2014

More course-related information in Eleum,

our electronic learni ng envir onment!

http://eleum.unimaas.nl
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Contents

1 General Introduction to Quantitative Methods 1 3

1.1 Subjects and textbooks 41.1.1 Mathematics 4

1.1.2

Statistics 5

1.1.3 Computer skills 6

1.2 The teaching system 6

1.2.1 Lectures 6

1.2.2 Group meetings 7

1.3 Examination rules 7

1.3.1 Part 1: quizzes 8

1.3.2 Part 2: written test 8

1.3.3 Part 3: computer skills 8

1.3.4 Part 4: presence and participation requirements 8

1.3.5 Passing QM 1 91.3.6 Re-examination arrangements QM 1 9

1.3.7

Test strategy 10

1.4 Organization 11

1.5 The weekly cycle 11

1.5.1 Literature and lecture 111.5.2 Preparation 11

1.5.3 Project 11

1.5.4 Tutorial group meeting 11

1.5.5 Quizzes 11

1.5.6 The Thursday/Friday Recap lecture 11

1.6 Block schedule 12

2

Weekly Assignments 13

2.0 Week 0: what you should do before starting 13

2.1 Week 1 14

2.1.1 Statistics 14

2.1.2 Mathematics 14

2.2 Week 2 17

2.2.1 Statistics 17


2.3 Week 3 19

2.3.1 Statistics 19


2.4 Week 4 21

2.4.1 Statistics 21


2.5 Week 5 22

2.5.1 Statistics 22


2.6 Week 6 24

2.6.1 Statistics 24


2.7 Week 7 27

2.7.1 Statistics 27

2.7.2

Mathematics 27


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1

General I ntroduction to Quanti tative Methods 1

All students of International Business, Economics and Fiscal Economics at this school receive a basic

training in quantitative methods covering subjects from mathematics, statistics and computer skills.The majority of this training is given in the first year. This block, you will be participating in what we

call Quantitative Methods 1 (QM 1). It is followed by a second round of quantitative methods (QM 2)in period 4. In the second year, some additional subjects will be covered. The topics for the latter twocourses and the block-period for the third course depend on your choice regarding study and

specialization.

The prerequisites for Quantitative Methods 1 are high-school algebra and preferably somecalculus (Wiskunde A or Wiskunde B in the Netherlands, preferably Mathematik Leistungskursin Germany). The QM 1 program will repeat many topics that are familiar to students of the WiskundeA program. However, do not be deceived by the similarity in topics: we expect you to demonstrate adifferent mastery of quantitative knowledge than most high-school programs. We place moreemphasis on active knowledge, i.e. the capability to apply your knowledge to real-life situations, thanon the mere understanding of our methods. Given the diversity of the prior knowledge of our studentpopulation, the personal effort required from each one of you may differ considerably depending onyour background. It is therefore extremely important for you to keep up with the course in order to

benefit from it as much as possible.

In mathematics, we will repeat and extend your knowledge about functions and equations.Questions that play a role in this course are:

How to translate a given problem into a mathematical model. Most of these problemsare questions for a maximum or minimum value or for the significance of the problem

mathematically, the existence of a solution.

How to find maximum and minimum values for a function of one and two variables.

We will make use of derivatives and partial derivatives in order to formulate equationsand conditions for extreme values.

How to solve a system of equations, especially linear equations.

In statistics, we will focus on the following topics: Methods of data collection, and types of data.

Descriptive statistics: describing important characteristics of populations or samples bynumerical methods as the mean, median, mode (measures of central tendency) variance

and standard deviation (measures of spread) as well as by graphical methods, likehistograms, bar charts or Box-and-Whiskers displays.

Probability theory, as an introduction to random variables.

Discrete random variables and the most important discrete probability distribution: thebinomial distribution.

Continuous random variables and two continuous probability distributions: the uniformand the normal distribution.

Sampling distributions, as a first step to the topic that will dominate the QM statistics

agenda from now on: inferential statistics, or inductive reasoning. Understanding whylarge samples provide so much more information than small samples is an importantelement of this first step.

The construction of confidence intervals to estimate unknown population parametersand

Hypothesis testing in the simplest case of one population. This includes concepts as nulland alternative hypothesis, type I and type II errors as well as the p-value of ahypothesis test.

In computer ski ll s, we will endeavour to provide basic training in Microsoft Excel and itsstatistical add-in PHStat, leading up to more intensive use of the package in QM 2 as well as a numberof other subjects in later blocks. While we do not expect any previous experience with Microsoft

Excel, we require prior knowledge of the Microsoft Windows operating system, as well as theMicrosoft Word word processing package and other Microsoft Office applications. If you feel that youlack vital experience with these programs, we suggest that you familiarize yourself with both as soon


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as possible. Your local bookseller will be able to recommend a number of useful introductions if youfeel the need. Personally, we prefer the for dummies series of computer books *, but there are manyothers that are just as suitable.

All information in this manual as well as a lot of additional information can be found in our

electronic learning environment Eleum:http://eleum.unimaas.nl.Among the features you canfind online will be copies of old exams and announcements regarding your group and the entirecourse. It is our aim to update the site frequently, and we strongly advise you to check it regularly.Ideally, you should check the site daily, but minimally you should drop by at least once a week.

1.1 Subjects and textbooks

In QM 1, the study load of mathematics and statistics are equal: about 45% each (of 20 hours perweek). Computer skills will require the remaining 10%. These percentages are only an indication; yourreal workload may differ significantly depending on your specific background.

1.1.1 Mathematics

For QM 1, the textbook is Knut Sydster, Peter J. Hammond, & Arne

Strom (2012): Essential Mathematics for Economic Analysis, 4th

ed.

Harlow: Financial Times/Prentice Hall.[UM library code: SB QA 00.01].

The text is available at a reduced price and in combination with aMyMathLab Student Access Kit through StudyStore in a bundle with the

Statistics & Marketing texts.

Some additional background literature, for those that are interested:

Chiang, Alpha C.: Fundamental Methods of MathematicalEconomics, 3

rded. New York, 1984: McGrawHill. [SF QA 90AXX]

Haeussler, Ernest F. & Paul, Richard S.: Introduction to Mathematic Analysis, 10thed.

Upper Saddle River, 2002: Prentice Hall. [4thed.: SB QA 00.01]

Wisniewski, Mik: Introductory Mathematical Methods in Economics, 2nd

ed. London,1996: McGrawHill. [SB QA 90AXX]

In the mathematics part of QM 1 we will confine our attention to the mathematical subjects that

are necessary for economics as well as business administration students. Our starting point is theconcept of a function. We will survey specific types of functions that are widely used in economic

applications. Exponential and logarithmic functions for instance are ideal to describe growth andproportional effects. Functions can be seen as a bridgehead between empirical regularities andscientific explanations. They make up the core of every formal model and therefore play a central rolein the application of mathematics to economic problems. This explains our attention to functions and,as a natural continuation, our attention to the analysis of functions, i.e. the study of patterns and

characteristics of functions. A function describes the relation between variablesand an important wayto get a rough idea of the character of this relation is plotting the graphof the function. However, ifyou want to have more precise information, then a more profound study is necessary. We areespecially interested in the aspect of change in a (functional) relation. Observed or expected change iswhat triggers the actions of economic agents including all of us. Not only the sign and size of

changes matter, also the speed of change, or the length of time in which the change is completed. Inorder to measure that speed, we introduce the derivative of a function. Economic concepts like

marginality and elasticity are based on (rates of) change and thus on the derivative of a function.Besides, derivatives play a major role in the analysis of the functional form itself. They are most

useful in locating maxima and minima of functions also interesting characteristics for economicagents. Derivatives are found with the help of differential rules, i.e. rules for differentiating commonclasses of functions (such as exponential and logarithmic functions) and combinations (such as sumsand products).

So far what we understood by function was a relation between just two variables. The real worldis of course far too complex to be described and explained by such simple relationships. Most

*Respectively known as voordummies in Dutch, fr Dummies in german and pour les nuls in

French.
http://eleum.unimaas.nl/http://eleum.unimaas.nl/http://eleum.unimaas.nl/http://catalogue.pearsoned.co.uk/educator/product/Essential-Mathematics-for-Economic-Analysis/9780273760689.pagehttp://eleum.unimaas.nl/


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situations involve some form of dependence between more than two variables. We will therefore studyrelations between three (and more) variables, one being viewed as the dependent one and all othersbeing viewed as independent ones. If such a relationship relates every combination of values of theindependent variables to at most one value of the dependent variable, then that dependent variable is afunction of the independent variables. For the analysis of functions of several variables we will extendthe concept of derivative to that of partial derivative. Partial derivatives can be used for findingmaxima and minima of functions and for the determination of (partial) marginalities and elasticities.

Relations between more than two variables may be very complicated. However, if therelations are linear, then we may use other tools to analyze them. For example, during the last week ofthe course we will present a technique, Gaussian Elimination, to solve systems of linear equations.The principle is easy: solving by simplification and substitution.

Prerequisite mathematical knowledge (what you should know before starting the QM 1 course)

Chapters 1 and 2, as well as sections 3.1 and 4.14.6 of Sydster & Hammond.Minimally, you should have mastered the contents of the first two chapters. Furthermore, you

are supposed to know the concepts contained in sections 4.14.6 of Sydster & Hammond. Althoughthese sections are contained in the 1

stweek of this course, we will only scratch the surface of these

subjects.If you feel that your understanding of the above-mentioned concepts is lacking, and you missed

the math summer course that took place in the months June to August, we recommend that youpractice some of the materials we have created for that summer course. In MyMathLab, within thesection HomeWork, you will not only find seven different HomeWork lessons for all seven weeks ofQM1, but also 50 HomeWork lessons prepared for the summer course. All of these HomeWorklessons carry names like SC Ch 13.1: Functions: Notation, so start their name with the abbreviation

SC of SummerCourse. Please go through these 50 lessons, and practice several items from each ofthem. If you already master the items, you will discover that you can do them in no more than a couple

of minutes. If you do not master them, you will need some more time, but that will pay out: thismaterial is essential to be able to grasp the QM1 coverage (students of the summer course whosuccessfully completed all items of all 50 lessons, took on average 13.5 hours to do so, so it is lesstime-consuming as you may think).

1.1.2

Statistics

Statistics can be divided into two sub-disciplines: descriptive statistics and inductive statistics.Descriptive statisticsaims to describe, summarize and display possibly large sets of data, such as a

census or population count, in a way that facilitates communication. Examples are tables and figureslike bar plots and line graphs, characteristic numbers such as averages or proportions, and the use ofsome functional relation, like a time trend, to describe patterns in a large data set. These examplesinvolve two kinds of instruments: (i) graphical means of display that are relatively easy to grasp, and(ii) numerical summaries of the data which reduce any number of observations to a small number ofitems. Descriptive statistics typically treat the data as if it were a complete set of records on thephenomenon or group we are interested in, which is called the population in statistical jargon; itsambition is to display and summarize the data set as such.

However, it is rarely the case that we have complete records. This is where inductive statisticstakes over. Inductive statistics deals explicitly with partial, often relatively smallsamples,drawn fromlarger populations which are impossible or too costly to observe in their entirety. From the samplesone endeavours to learn about the populations. Induction (as opposed to deduction) means just that: tosqueeze information concerning the general whole out of information on a particular part. Its aim, in a

word, is generalization. What we are really interested in is the general population and we only studythe sample as a way to learn more about the underlying population. Naturally, a good deal ofuncertainty is unavoidable in the process. That is why induction, unlike deduction, cannot generateexact and rigorous knowledge. Even when our statistical inference looks very conclusive, we have toremember that the conclusion is subject to the possibility of error.

Inductive statistics (also called inferential statistics) dominates descriptive statistics, thoughmaybe more in terms of its level of complexity and technicity than in terms of daily practice. The last

three weeks of this block as well as the entire QM 2 course are devoted to it. The first four weeks ofthis block prepare the necessary ground. First of all, we pay some attention to the concepts andmethods of descriptive statistics. Secondly, and somewhat paradoxically, we study probability theory,


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the application of deductive reasoning to chance and randomness. This is a sub-discipline ofmathematics and, in a sense, the mirror image of inductive statistics. It deals with the hypotheticalsituation where we know all about the population and want to predict the likely features of randomsamples drawn from it. Some knowledge of the rules of probability theory is indispensable as astepping-stone to understand the rather more subtle rules of inductive statistics.

The subject matter of this block corresponds to a large extent to chapters 1-5, 7-13 of the Sharpe

et. al. textbook which is the prescribed literature for both QM 1 and QM 2: Sharpe, Norean R., De Veaux, Richard D., &

Velleman, Paul F. (2012): Business Statistics, 2nd

ed.

New York: Pearson Education International.

Sharpe et. al. is available through StudyStore in abundle with a license of:

MyStatLab Student Access Ki t.

(The most economic way to buy this textbook, is in awrapping together with the Math and Marketing texts.)

As you understand from above specification, the delivery of mathematics and statistics in this

block will be of somewhat experimental nature: it will be your first e-learning block. An importantlearning tool is the MyLabsoftware, an electronic learning environment that allows you to prepareyour tutorial sessions by solving math and statistics problems and receiving digital feedback in caseyou make errors, or opposite, are able to find the correct solution in one straight way.

1.1.3 Computer skills

The computer skills section of this block serves several purposes. The most important is to familiarize

you with Microsofts Excel spreadsheet package, which is widely used in later blocks, organizationsand businesses, and the so-called Excel add-in PHSTAT (or DDXL), a dedicated tool for solvingstatistical problems. (The textbook suggests another tool, XLSTAT, but last year, we encounteredmajor problems with installing this add-in, and abandoned it. If you are more successful in installing,feel free to use it, or any other add-in: they all do the same kind of statistical calculations. We will

focus our support on Excel itself, and PHSTAT.). In the first two weeks, two lectures aim to providean overview of the programs functions moving from knowledge required for beginners to advancedknowledge required to tackle mathematical or statistical problems in Excel. We offer group sessions inall weeks that allow you to get vital experience in applying these techniques. Furthermore, thecomputer skills sessions are also used to test whether you have developed an adequate understandingof the most important concepts. In weeks 2, 4 and 6, you will work on three so-called Excelassignments. These have the status of required assignments: you have to send in a satisfactory

solution, in order to get a pass for computer skills.Finally, students will need to take computer tests of their knowledge in mathematics and

statistics in weeks 1, 3, 5, and 7. These tests not only serve as an indication of your strengths andweaknesses, they also allow you to obtain bonus points that will be added to your exam. Furtherinformation regarding the MyStatLab system, including login and usage instructions, will be made

available during the first lecture of the block, and the Eleum site.Part of computing is the use of calculators. In this course, only one, specific calculator is

allowed in exam and quizzes: the Casio FX-82MS or Casio FX-85MS. StudyStore does sell the

proper machine.

1.2 The teaching system

1.2.1 Lectures

During the blocks QM 1 and QM 2, lectures will be given every Monday. There will be a one-hourlecture in mathematics and a one-hour lecture in statistics. The aim of these lectures is to give a surveyof the subject material of that week. Since one hour is short, that survey will focus on the mostdifficult parts of each weeks topic instead of covering all topics.Lectures will be most effective if you

read the relevant chapters in the textbooks in advance: this way, you have the necessary backgroundknowledge to follow the explanations and examples provided in the lecture.
http://vig-fp.prenhall.com/bigcovers/0321728114.jpghttp://vig-fp.prenhall.com/bigcovers/0321716094.jpg


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At the end of the week, on Thursday or Friday (depending on your study), a second lecture willbe held. In the first weeks, part of that lecture is devoted to computer skills, whilst the main focus willbe on problems that came up during the group meetings. Furthermore, the weeks most tediousassignments will be elaborated in more detail than is possible during the group meetings.

1.2.2 Group meetings

On Tuesdays or Wednesdays (depending on your study) we will hold tutorial group meetings. The

meetings last for two hours (divided equally between mathematics and statistics), during which theweekly assignments are discussed. The assignments can be found in Chapter2of this manual.

As for most business and economics subjects, the tutorial group of 12 to 14 students is thecentral working unit in QM 1. There are, however, some differences between the QM courses andother courses. The main difference is that the teams work on explicitly given problems (theassignments). Hence, there is no PBL-like preparatory discussion and brainstorming. The teammembers have to solve the assignments individually before the meeting, where they are then discussedby all. During the discussion, solutions will be compared and evaluated, and difficulties encounteredby individual members may be discussed and clarified. Another difference concerns the role played bythe tutor. This role is more active in QM than is typical for business or economics subjects. Togetherwith the team the tutor examines the solutions of the assignments and indicates which are correct andwhich are incorrect or incomplete. If necessary, i.e. if the team is unable to find a solution, the tutor

will provide help.In the mathematics part of the tutorial group meetings, we will discuss the so-called selected

exercises listed, per week, in Chapter 2 of this block book. It is absolutely imperative that you preparethese exercises before every meeting of the tutorial group, even though short answers are providedeither at the end of the textbook (odd numbered exercises) or in this block book (even numberedexercises). For those who like and/or need even more practice: the book contains a host of other

exercises, and the solutions/answers to the odd numbered exercises are all given at the end of thebook, whilst more elaborate versions of the answers will be provided through Eleum.

Both math and statistics sessions contain two separate sets of exercises: the Homework tasks,and the Tutorial Group tasks. In statistics, these two types of tasks are mirrored, making use of thepairing of even and uneven exercises in the textbook: for every uneven numbered exercise in the

textbook, included in the homework section, there is an even numbered exercise covering exactly thesame topic, included in the tutorial group section as discussion task. For math, there is not such strongtie between individual homework and selected exercises, but still is true that mastery of homeworktasks is the first step to be able to do the group, selected exercises.

So therefore:Homeworktasks prepare the group tasks. Homework tasks are best done in MyMathLaband

MyStatLab. The tools provide you with immediate feedback, give help when needed, collect all typesof tools that can help solving the task, and, not unimportant, you can even achieve some additionalbonus when you do so (they can recover half of the bonus lost in the quizzes by consistently usingMyMathLab and MyStatLab in preparing the homework tasks).

Group tasks to finish the learning cycle in the tutorial group: the Discussion tasks forstatistics, the Selected exercisesfor math.

There will be two additional tutorial sessions in weeks 5 and 7 (Thursdays or Fridays,depending on your study). A sample exam is available in the back of this blockbook, that may be

placed on the agenda of those second meetings. Answer keys to the sample exam will be posted inEleum, after the tutorial sessions have taken place.

1.3

Examination rul es

Your assessment in QM 1 consists offour parts:1. Three math & statistics quizzes that take place during the block and that allow you to

earn 8 bonus points.2. A final written test for mathematics and statistics, consisting of 40 multiple-choice

questions and leading to your test score.3.

The computer-skills part, which leads to the mark pass or fail.4. Presence and participation requirements.


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1.3.1 Part 1: quizzes

In the computer skills sessions of weeks 3, 5, and 7, electronic quizzes in MyMathLab and MyStatLabwill be taken that allow you to earn 8 bonus points. The first two quizzes, one for math and one forstatistics, will be taken in week 3 and are rewarded with one bonus points each. In week 5, the secondquiz for statistics and for math are rewarded with 1.5 bonus points each. In week 7, the last quiz for

statistics and math are again rewarded with 1.5 bonus points each. In total, a maximum of 8 bonuspoints may be scored. Some further bonus can be achieved for both mathematics and statistics bysystematically preparing for the tutorial sessions using the MyMathLab and MyStatLab tools: that willbring you (in case of full preparation) half of the bonus score lost in all quizzes. Total bonus will beadded to your exam score to obtain your final mark. So quizzes, MyMathLab and MyStatLab are abonus in the purest sense of the word: you do not lose if you do not participate, or if you performbadly. However, any points you score may be added to your exam score and will therefore improveyour final grade! That is why we strongly recommend that you participate: experience shows that for alarge share of our students, the bonus points make the difference between passing and failing thiscourse.

Important: bonus points are valid within the current academic year only. That includes the resit.But if you fail both QM1 first sit and resit this year, your bonus points are void. However, you will beable to try and earn bonus points again next year.

1.3.2

Part 2: written test

The written QM tests consist of 20 multiple-choice questions on mathematics (numbered 1 to 20) and20 multiple-choice questions on statistics (numbered 21 to 40). Your test score will be based on thenumber of questions you answer correctly out of the 40 multiple-choice questions. There is oneconstraint: you must score at least 9 correct answers for each of the two subjects.

It is sensible to practice old exams in order to gain experience with multiple-choice tests and inorder to determine any weaknesses in your knowledge. You can download old exams from Eleum.

Moreover, we have arranged that the final exam of last year, printed in the last pages of this manual,can be covered in the extra tutorial sessions of weeks 5, 7.

1.3.3 Part 3: computer skills

Computer skills in QM 1 is tested by preparing the student project, on which you will be working forseveral weeks. This student project consists of a statistical analysis of a large data set: your firstempirical research. In order to make up a data set for every student that is worthwhile investigating,we split the project in two parts: in weeks 1-6, you collect your own data, and in weeks 6-7, you will

perform a statistical analysis of these data. Collecting data is done in several ways, but the mostimportant part is filling several questionnaires. All questionnaires refer to one topic: you own way ofstudying. Once you have filled these questionnaires, we will provide you with data: your own data,and data summarizing the characteristics of all students. (Everything will be completely anonymous,of course!) After receiving your data, you can start doing your empirical research. The report of thisresearch, to be sent in at the end of the examinations week, describes the outcomes of your research.

Computer skills is marked pass or fail. To achieve a pass, you need:1. to send in all questionnaires, in order to build up a personal data set;

2.

to do the two entry tests in week 1, and the two Excel assignments in weeks 2 & 4;3. make a satisfactory Student Project.

All questionnaires will be taken through the Eleum. Additional information, such asrequirements for the student project report, will be made available via Eleum. With regard to thequestionnaires: since you need to do a proper statistical analysis of your own data, you will benefitfrom sending in true, that is real, scores. Fancy data, or even somewhat inaccurate data, will generallycontain all kinds of inconsistencies that make any statistical analysis really awkward. Questionnairedata will, beyond serving the student projects, be used in anonymous format to improve QM1education, and in educational research.

1.3.4 Part 4: presence and participation requirements

As in most other blocks, you are required to attend and actively participate in at least 75% of thetutorial group meetings. In QM 1, we have 9 meetings, so you can miss at most 2 (physically, ormentally, or both).


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Active participation is a subjective criterion, and the tutor is responsible for the evaluation ofthis part of your grade. However, the most important ingredient of active participation is not yourbehaviour during the group meeting, but your preparation before the group meeting, which is easy toassess in a relatively objective way. In a typical meeting, most of the time one of the students is at theboard explaining to other students how to solve a particular assignment. You wont be able to do sowithout having prepared the meeting and without having solved the required assignments at home.Maybe your solution is not the best one, or even incorrect. That does not make you unprepared: as

long as you can explain how you got there, you and other students can probably learn more fromunsuccessful attempts than from correct solutions. However, if you do not have any solution or dohave a solution but are not capable of explaining how you got there, the tutor will regard you asunprepared and will mark your participation as insufficient.

The fulfilment of both the presence and the participation requirement is necessary to beexempted from the block assignment.

1.3.5 Passing QM 1

You must fulfil three conditions to pass the QM 1 block:

1. The mark pass for computer skills.2. A final score (test score + bonus points) of at least 27 points.3. A minimum score of 9 correct answers (each) in both the math and the statistics

subsections of the final exam.4. A pass for presence and participation requirements (or in case you fail the requirement,

a pass for the block assignment that makes it up).

Your final score (test score + any activated bonus points) is then translated to a grade on a scale from 1to 10 as follows:

Correct answers

F inal grade

Min score 9 Min score 8

010 1 111, 12 1 113, 14 2 115, 16 2 2

17, 18 3 219, 20 3 321, 22 4 323, 24 4 425, 26 5 427 5 5

28, 29 6 530 6 531, 32 7 533 7 534, 35 8 5

36 8 5

37, 38 939 940 10

A grade of 5 or higher is sufficient.

1.3.6 Re-examination arrangements QM 1

As stipulated in the examination rules, there is asecond chance(a.k.a. resit) for each QM exam. Resits

always take place at the end of the block period following the first test. For instance, the resit for QM1 comes at the end of block 2. According to examination rules,you cannot participate the resit if yougot a passing mark already in the first sit.

Your final score after the resit will be calculated as your highest test score (first test or resit)

including the bonus points you earned during the block. Remember that your final score will only betranslated into a grade if you fulfilled the computer skills requirement as well. (However, there is no


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required chronological order in which you have to complete the requirements. Your final graderemains on hold until everything else has been completed.)

The resit for computer skills in QM 1 consists of making an individual version of the studentproject report and hand it in as a resit.

1.3.7 Test strategy

The mathematics and statistics tests consist of multiple-choice questions (with four alternative answer

choices). No books or notes of any kind may be used. Tables, a list of important formulas, scrap paper,and answer forms will be provided together with the test itself. You will need a pencil and you may

use a pocket calculator of the type Casio FX-82MS or Casio FX-85MS (no other calculators will

be allowed). The use of a pocket computer or a mobile phone during the exam is strictly forbiddenand will be considered as fraudulent. (For further information, cf. the examination rules.) Note that theexam wardens may bring detection equipment to bear to be on the safe side, it is best not to bringappliances that are prohibited.

In multiple-choice testing, you are meant to form a judgment on every single question, and tomark the best answer in each case. Your test score is simply the number of correctly marked answers.

That is why it is never a good idea to leave a question unanswered. Tactically speaking, it is bestalways to select one (and only one) answer, even if you have to make a guess. Furthermore, there is

always exactly onecorrect answer. Should you indicate more than one answer for the same question,then all your answers to that question will be ignored. Therefore it would be wise to use a pencil tomark your answers; this way, you will be able to change your answer if you change your mind.

It is useful to reflect upon the multiple-choice situation. A number of answers (usually four) isproposed for each question. Of these answers, one and one only is correct. The others are called

distracters: they are incorrect but correspond to possible and maybe even attractive mistakes. It isvery pleasant when your reasoning and/or calculation leads you immediately to one of the proposedanswers. But be careful: test writers have some experience in accounting for all sorts of popularmistakes. The wrong answers are not totally innocent. You may have found the correct answer, butyou may also have been attracted by a more or less subtle distracter. This happens often when astudent attempts to reason backwards from the answers to the question, which is why you are advisednot to do so. Reasoning forward and thinking twice is no luxury!

When the answers are numerical it may well happen that your solution corresponds to none ofthe proposed answers. What next? Re-do your reasoning and your calculation. Most probably youhave made an error that was not anticipated by the test designer. It is indeed not feasible to foresee allpossible reasoning mistakes, and even less practicable to simulate all possible calculation errors. Lookat the up side: this helps you to eliminate all sorts of non-essential mistakes, including calculationerrors, before you select an answer. Ready-made answers are not only a convenience (for students andgraders alike); they are also a sort of sieve for many errors. Use it as such by subjecting your ownsolution to this verification. If you dont find your solution among the proposed answers, dont gostraight for a guess. Rather, try to find and correct the mistake.

Another quandary you may find yourself in, especially with non-numerical questions, is whenmore than one answer look correct to you. Again, dont go straight for a guess. Exclude carefully asmany alternatives as possible, this will improve your odds. Look for the differences between the

remaining answers, there the knot must be. Reason forward: how would you have expressed ityourself? Again, you are more likely to be tempted by a subtle distracter if you are trying to reasonbackward from the answers. So avoid that!

In the end, if you really cannot identify a single answer as the only correct one, choose and markone answer that, to the best of your insight, is at least as good as all the others.A few final tips

In the textbooks exercises and problems are arranged by chapter and even by section. In the tests thisis obviously not the case. That is why tests are more difficult than weekly assignments, even if the

questions are quite comparable. The aim of your study must be to master the subject matter as a whole,so that you can find your way in it and so that you see the connections between its various parts.Otherwise your knowledge will be of no help to solve the business or economic problems you will

encounter later in your career.

We provide real tests from previous years in Eleum, and one in the back of this blockbook.These tests are representative of the way you will be tested in and of the level of difficulty you mayexpect. They are good material for practice provided you really simulate the circumstances of a test:


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11

answer all questions in one go, time yourself and do not use any books or notes until you havefinished the exam. Study associations provide exam training for all that are interested during the lastweeks of each block.

1.4 Organization

Three lecturers are working in block QM 1, one each for mathematics, statistics, & recap, with one of

the lecturers serving as the contact person for general problems (the coordinator). Each of the lecturerscan be contacted with problems and comments regarding his subject.Statistics & Coordinator Dirk Tempelaar [email protected]

Mathematics Stan van Hoesel [email protected] Lutz Krebs [email protected]

1.5

The weekly cycle

In the following we provide a suggestion on how to structure your weekly learning activities in orderto help you benefit as much as possible from this course. However, since learning styles andbackground knowledge differ greatly between individuals, this schedule should only be considered asan indication.

1.5.1

Literature and lectureWe strongly recommend that you turn to the weekly literature before the Monday lecture. The lectureis not a summary of the literature; instead it focuses only on the some key concepts. If you have not

had a first look at the literature before the lecture, you may not be able to follow the deliberations andthey will certainly not be as useful. Also, it is often beneficial to go back to the literature to reread theproblematic sections after the lecture in order to deepen your understanding of them.

1.5.2 Preparation

Once you feel confident with the weekly topics, it is time to put your knowledge to practice bypreparing the selected exercises for mathematics and the homework tasks for statistics. Remember thatyou are not per se required to find the perfect solution. If you get stuck with any particular problem, be

sure to verbalize your difficulties and bring them to the group meeting for discussion.

1.5.3

Project

The project consists of two parts: gathering data, by answering several questionnaires early in theblock, and analysing these data, and their relationship to data of other students, in weeks 6-7. The typeof data analysis expected from you, and the Excel commands you need for them, are described in theExcel appendices of the several chapters. The computing skills session in week 6 is reserved for it.

1.5.4 Tutorial group meeting

Here, you will have the opportunity to discuss any difficulties you may have had with your fellowgroup members and your tutor. This is the best time to ask any questions! While you will be evaluatedfor your participation (and your presence), this should not keep you from speaking up about anyproblems. On the contrary: you and your fellow students can learn more from a discussion of

challenging issues than from a simple presentation of correct answers. As indicated, group meetingsneed to be prepared, as a kind of individual prediscussion of the relevant tasks. For Math and Stats, itis solving the Homework tasks, preferably in the MyLab learning environments.

1.5.5 Quizzes

Three times during the block, quizzes will be offered as a self-assessment measure and as a way toscore bonus points. The quizzes are not obligatory and you may skip the meetings during which they

are administered. Quizzes allow you to check whether you have fully understood the subjects of theprevious weeks, and the bonus points you score will be added to your exam score to raise your grade.

1.5.6 The Thursday/Friday Recap lecture

Finally, the weekly cycle is concluded with a final lecture, during which the most challenging items ofthe week will be discussed again. Topics on the agenda are to a great extent determined by students:you can send in proposals for difficulties to be tackled in the Recap lecture.
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]


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1.6 Bl ock schedule

Week Mathematics Statistics Computer Skil ls

1Sections 4.14.10Definition of a function, graph of a

function, linear and quadratic functions,general polynomials and rational

functions, power functions, exponentialand logarithmic functions

Chapter 1Statistics and Variation

Chapter 2Data

Chapter 3Surveys and Sampling

CS group session:Math & Stats entry tests

Recap Lecture

Project

Questionnaire 1 to be handed in theweekend (+entry tests)

2Sections 5.15.5Manipulating graphs and the inversefunction, graph of an equation, graph of

a function, piecewise defined functions,distance, equation of a circle, ellipses,hyperbola

Chapter 4Displaying and DescribingCategorical Data

CS Group sessionFirst Excel assignment

Recap Lecture

ProjectQuestionnaire 2 to be handed in theweekend (+ Excel assignment)

3Sections 6.16.9Introduction to differential calculus,rules for differentiation, a.o. the chain

rule and higher derivatives

Chapter 5Displaying and DescribingQuantitative Data

CS Group session

First Quiz for Mathematics and

Statistics, taken in MML/MSL

Recap LectureProjectQuestionnaire 3 to be handed in

4Sections 6.106.11

Derivatives of exponential andlogarithmic functionsSections 7.17.4Implicit differentiation, derivative of

inverse, approximationSection 7.7

Elasticity

Chapter 7

Randomness and ProbabilityChapter 8Random Variables and ProbabilityModels l

CS Group session

Second Excel assignment

Recap Lecture

Project

Questionnaire 4 to be handed in the

weekend (+ Excel assignment)

5

Sections 8.18.3

First-derivative test formaximum/minimum and economic

examples

Section 8.4 until The mean-valuetheorem

Extreme-value theorem

Sections 8.58.7Further economic examples, second-derivative test, inflection points

Chapter 9

The Normal Distribution

Chapter 10

Sampling Distributions

CS Group session

Second Quiz for Mathematics andStatistics, taken in MML/MSL

Recap Lecture

Project

Questionnaire 5 to be handed in.

6Sections 11.111.3Dependent and independent variables,Cobb-Douglas functions, domain of afunction of two variables, partial

derivatives of a function of twovariables, higher order partial

derivatives, graph of a function of twovariables, level curves, isoquants of a

production function, geometricinterpretation of partial derivatives

Sections 11.711.8Marginal products, complementarity ofinput factors, Partial elasticitys

Chapter 11Confidence Intervals forProportionsChapter 12

Confidence Intervals for Means

CS Group sessionStudent Project

Recap Lecture

ProjectQuestionnaire 6 to be handed in theweekend

7 Section 13.113.5Unconstrained optimization, stationarypoints, first and second order conditionsfor an optimum, convexity/concavity of

a function of two variables, local

optima, saddle points, economicapplications: discriminating monopolist,linear regression, extreme value theorem

Chapter 13

Testing Hypotheses

CS Group session

Third Quiz for Mathematics and


Recap Lecture

Hand in your project at latest

October, Sunday 20 through

Eleum


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2 Weekl y Assignments

2.0

Week 0: what you should do before star ting

It is wise to prepare your personal computer/laptop for studying QM before week 1 starts, since you

will find such personal computing environment to be crucial in the next seven weeks.

Excel

You will need to use it a lot in several courses of the first year. Convince yourself that it isavailable on your private pc, preferably Excel 2010, and preferably the English version! Excelcommands in the English, Dutch and German versions of Excel are really different, so you willfind it troublesome to work with different language versions at different places. Realize that in theLibrary, and in the SBE, all software is English based. (One can achieve student licenses for theOffice 2010 product, to which Excel belongs, athttps://www.surfspot.nl/.)

Excel add-ins Analysis Toolpak and Analysis Toolpak-VBA

These additional statistical features of Excel are part of Excel itself, but need to be activated. Youdo so by opening Excel; in the File-menu, select Options; click Add-Inns, and in the Manage box,select Excel Add-Inn, and click Go; in the Add-Ins available box, check Analysis Toolpak and

Analysis Toolpak-VBA, and click OK. As a result, you will find a new group called Data Analysisin the Data ribbon.

Additional statistical add-ins: PHSTAT, DDXL, XLSTAT,

Since Excel is a very all round program, you will experience that it has limitations in some moreapplications. Dedicated statistical add-ins offer help in these cases. There are many around, andmost have very similar capabilities. One that comes with the textbook is XLSTAT (but, asindicated, we found it not easy to install). Two other add-ins are available through Eleum, togetherwith installation instructions: PHSTAT and DDXL (last one is not compatible with Applecomputers). But you may have your own favourite. Please install one on your own computer to beready to do any statistical analysis.

MyMathLabGlobal & MyStatLabThe publisher of the math, statistics and marketing textbooks, Pearson, has created one registrationsite for all three MyLabs:www.pearsoned.co.uk/maastrichtsbe .Preferably, please register throughthat site, and ignore the next two bullet points, which refer to the situation of separate registrationto all three MyLabs. Please prepare your MyLab accounts in time, so that you are ready to start inweek 1 (or before using the summer course materials to refresh your math mastery).

MyStatLab

Your textbook should come with a so-called MyMathLabGlobal Student Access Kit. To prepareyour account, you need your access code, which is in the card in your book, and the course code:

tempelaar01647, with internet access athttp://www.mystatlab.com/.Choose Buy now or

use your Access Code to register and establish a Login Name and Password. MyMathLabGlobal

Your textbook should come with a so-called MyMathLabGlobal Student Access Kit. To prepareyour account, you need your access code, which is in the card in your book, and the course code:

XL00-B1HG-501Z-6T24, with internet access athttp://global.mymathlabglobal.com/.

Before starting with the course Quantitative Methods 1, we have run the SBE Math Summer Course in

which about 200 of you have participated. The summer course refreshes material from high schoolprograms, mainly the junior phase of high school (first three years). It is our experience that many

students lack essential knowledge and skills in basic algebraic operations as solving quadraticequations, calculating the ratio of numbers, manipulating with logs and exponentials. In the sameMyMathLab tool as we will use the next seven weeks, the participants of the summer course practiced

these basic algebraic skills. If you missed the summer course but better had not missed it: the materialsare still available in MML, as 50 HomeWork lessons all labelled SC*****. So better give them a try to

be fully prepared.
https://www.surfspot.nl/https://www.surfspot.nl/https://www.surfspot.nl/http://www.pearsoned.co.uk/maastrichtsbehttp://www.pearsoned.co.uk/maastrichtsbehttp://www.pearsoned.co.uk/maastrichtsbehttp://www.mystatlab.com/http://www.mystatlab.com/http://www.mystatlab.com/http://global.mymathlabglobal.com/http://global.mymathlabglobal.com/http://global.mymathlabglobal.com/http://global.mymathlabglobal.com/http://global.mymathlabglobal.com/http://global.mymathlabglobal.com/http://www.mystatlab.com/http://www.pearsoned.co.uk/maastrichtsbehttps://www.surfspot.nl/


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2.1 Week 1

Mathematics Statistics Computer Skil ls

Sections 4.14.10

Definition of a function, graph of afunction, linear and quadratic functions,

general polynomials and rationalfunctions, power functions, exponential

and logarithmic functions

Chapter 1

Statistics and Variation

Chapter 2Data

Chapter 3Surveys and Sampling

CS group session:

Math & Stats entry test

Recap Lecture

ProjectQuestionnaire 1 to be handed in the

weekend (+entry tests)

2.1.1 Statistics

Literature: Sharpe et. al. Ch. 1, 2, & 3

Homeworktasks (solve outside group, preferably in MyStatLab, and check your answers):

Chapter 2: exercises 1, 3, 5, 10, 20, 27, 29, 31, & 33;

Chapter 3: exercises 1, 2, 3, 6, 7, 8, 9, 11, 13, 14, 15, 16, 17, 19, 23, 35, 39, & 49.

Discussiontasks (for discussion in tutorial group meeting, no preparation needed):

Chapter 2: exercises 2, 4, 6, 13, 24, 28, 32, & 34;

Chapter 3: exercises 4, 5, 10, 12, 20, 24, 33, 41, & 46.

2.1.2

Mathematics

Homeworktasks in MyMathLab on the subjects:

Chapter 4:

- Sections 4.1 - 4.10 (quick rehearsal): definition of a function, graph of a function, linear and

quadratic functions, general polynomials and rational functions, power functions, exponential

and logarithmic functions.

Selected exercisesfor tutorial group session:

Section 4.2: Problem 14Section 4.4: Problem 7

Section 4.6: Problem 7

Section 4.8: Problems 1 and 4


Section 4.10: Problems 3(a)(b)(c), 4 and 7

Review problems 10 and 18

Extra exercise


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Extra exercises

(A) Application

McDonalds faces a weekly demand for hamburgers depending on the price. One franchisee

collected the following two observations concerning this dependency: if the price is p= 3.00 euros,

then the demand turns out to beq= 50 hamburgers and at a price of p= 1.50 euros demand is q=

125.Assume that price and demand have a linear relation, and that each week, the franchisee can

always produce and sell exactly the demanded quantity. Besides, the franchisee has to take account of

fixed costs to the amount of 100 euros per week and so-called variable costs to the amount of 0.60

euros per hat. Suppose, that the company has 50 operating weeks per year.

(a) Determine the revenueR(q)and the profit W(q)in euros per week as functions of q.

(b) At which qdoes the weekly profit attain its maximum? What is this profit? What is the yearly

profit?

Assume that the manufacturer wants to extend his factory as soon as possible. At this moment,January 1, 2006, the necessary investment for the desired extension would amount to 4000 euros, and

the manufacturer can only reserve half of one year profit at that moment. However, the costs of the

extension will rise at 2% per year. On the other hand the reserved amount is saved on an account with

a yearly interest of 9%.

(c) In which year can the restaurant be extended?

(d) Assume that the government puts an environmental tax on the paper-wraps around

hamburgers to the amount of 0.04 euros per hamburger. How does this change the situation?

(B) xexfy )( . For which value ofxisf(x) = 10? For which value ofxisf(x) = y?

Sketch in one picture the graphs of xexf )( ,g(x)= lnxand h(x) = x.

In general: whetherf(x) = ycan be solved w.r.t.xdepends onfandy.

When can this solution x be considered as a function ofy?

(C) Determine the slope of the lines throughPand Qin the following cases:

P Q

(2,3) (2.1, 3.2)

(2,3) )3,2( yx

(x,y) (a,b)

),( 11 yx ),( 22 yx

Only linear functions have an equal slope at each point in the domain.

Let xxxC 2101)( be the cost function of a firm producing quantityxof some product. Sketch

the graph of Cand estimate the slope of the tangent line at the point of the graph withx = 3. The same

forx = 6.

Determine the additional cost at a production quantityx = 4compared tox = 3. The same forx

= 3.5,x = 3.2,x = 3.1(compared to x = 3). Try to get a feeling for what happens if we take xever

closer to 3, in the graph as wel as in the formula and the numerical results.


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Remark concerning Plotting Graphs

Most graphs, that will be considered, can easily be sketched by hand. However, if you are

familiar with a graphic calculator, then you could use it, of course. Besides, you may use computer

programs for plotting graphs. If you are used to work with Microsoft's EXCEL for example, then you

may try to plot the graphs with it, although this way is rather cumbersome. Another program, that

simulates a graphic calculator on a computer, is TI-Interactive!, edited by Texas Instruments and easy

to use. A free 30 days trial version can be found on the site

http://education.ti.com/product/software/tii/down/download.html

A better option is probably a really free program, called GraphCalc, which can be found at the

site www.graphcalc.com : go to the download page and choose version 3.1b for regular users.

Although it is very easy to use, it has an extensive help function. If you want to plot for example the

function

1

12)(

x

xf

you simply click on the sheet labelled Graph 1 and choose under the menu 2D Graph the

option Equations .... Once you have done that you can e.g. tick the box y3 and type 1/x^2-1 in thecorresponding display. After (optionally) adjusting the Range&Precision you can click on OK and

graphcalc will plot the graph for you. The result looks as follows.
http://education.ti.com/product/software/tii/down/download.htmlhttp://education.ti.com/product/software/tii/down/download.htmlhttp://www.graphcalc.com/http://www.graphcalc.com/http://www.graphcalc.com/http://education.ti.com/product/software/tii/down/download.html


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2.2 Week 2


Sections 5.15.5

Manipulating graphs and the inverse

function, graph of an equation, graph ofa function, piecewise defined functions,

distance, equation of a circle, ellipses,hyperbola

Chapter 4

Displaying and Describing Categorical

Data

Group session

First Excel Assignment

Recap Lecture


weekend (+ Excel assignment if not yet)

2.2.1 Statistics

Literature: Sharpe et. al. Ch. 4


Chapter 4: exercises 1, 3, 5, 7, 9, 15, 19, 23, 29, 31, 36, 47, 51, & 53;


Chapter 4: exercises 16, 18, 27, 28, 30, 32, 41, 50, & 54.

2.2.2 Mathematics


Chapter 5:

- Sections 5.1-5.3: manipulating graphs and the inverse function.- Section 5.4: graph of an equation, graph of a function, piecewise defined functions.

- Section 5.5: distance, equation of a circle, ellipses, hyperbola.






Section 5.5: Problems 2, 4 and 5(a)

Review problems Chapter 5: 10Extra exercises


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Extra exercises

(A) Application

In inventory management the central problem is to find the optimal order strategy. As an

example, we consider an inventory model for a VW car dealer selling only Golf.

In order to get a model, that can be analysed mathematically in a rather simple way, we assume

the following:- Cars are sold at a constant rate over the year. For example: if demand is 100 per year and a

year has 250 working-days, then each 2.5 working-days a car is sold.

- Ordering takes place in equal quantities qequally distributed over the year.

- Ordered cars arrive at the moment that the inventory is depleted.

- The total demand during one year is constant equal toD.

- The cost for keeping in stock one car for a whole year is equal to a fixed percentage Rof the

value of the car.

- The value of a car is W.

- The cost per order for the car dealer isB.

Try to find the optimal order strategy. You may start with a numerical example: take e.g. D = 50, R =

4%, W = 25000 and B = 250. Choose an obvious variable, e.g. the order quantity qand express thetotal cost-function as a function of q. Make use of the graph of the total cost-function in order to get

an idea where the optimal value could be found. Think about how to use derivatives to determine the

optimal order quantity.

(B) Consider the function .96)( 23 xxxxf

Sketch in one picture the graphs of f, fandf, wherefis the derivative of f. What can you

from the graph of ffor the behaviour offand from the graphs offandffor the behaviour off?


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2.3 Week 3


Sections 6.16.9

Introduction to differential calculus,

rules for differentiation, a.o. the chainrule and higher derivatives

Chapter 5

Displaying and Describing Quantitative

Data

Group session

First Quiz for Mathematics and


Recap Lecture

Project

Questionnaire 3 to be handed in theweekend

2.3.1 Statistics



Chapter 5: exercises 1, 3, 5, 7, 9, 11, 15, 18, 19, 22, 27, 33, 35, 41, 49, 51, 68, & 71;


Chapter 5: exercises 10, 13, 17, 26, 34, 36, 42, 48, 50, 53, 54, 58, 73, 75, & 76.

2.3.2 Mathematics


Chapter 6:- Sections 6.1-6.6: introduction to differential calculus.Remark concerning Section 6.3: in order

to understand the meaning of , and read Section 3.4 pages 61 to 63 until Solving

Equations.

- Sections 6.7-6.9: rules for differentiation, a.o. the chain rule, and higher derivatives.





Section 6.4: Problem 1Section 6.5: Problems 3 and 5


Section 6.7: Problems 3(b)(c)(g)(h), and 9(a)(b)


Section 6.9: Problems 3(a)(c)(d) and 6

Extra exercise


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Extra exercise

Application: Logistic growth

The growth of customer satisfaction or the sales of a new product on a market is often

graphically similar to an S-shaped curve. Such a curve can very well be described by a so-called

logistic function, this is a function Vof time tof the following form:

rtAe

KtV

1

)(

whereK, A and rare positive constants. If tbecomes bigger and bigger (approaches infinity), then

V(t)will approachK, the so-calledsaturationlevel. Shortly:

.)(lim KtVt

Suppose for example that we consider a dealer of Airbus. V(t)is the number of A380 jumbos,

sold per week, tmonths after the introduction on time t = 0. Suppose further, that the weekly sales at t= 0are equal to 2 machines and after 2 months 6 machines. Let the saturation level be 12 machines

per week.

(a) Determine for this example te values of K, A and r.

(b) At which time weekly sales will be exactly 9 machines?

(c) Show, using the derivative, that sales are an increasing function of t.

(d) Can you find the moment where the sales have the fastest growth?

(e) Sketch the graph of the function.

(f) Answer the questions (c) and (d) for the general function as given in formula (*).

Answers to selected, even-numbered exercises

Section 6.2:

Problem 2: (a) ,26)(' xxf (b) .12 xy

Problem 4: )(

1)()()(

11

)()(hxx

h

hxx

h

h

hxx

hx

hxx

x

h

xhx

h

xfhxf

Section 6.6:

Problem 4: (a) r8 , (b) (c) 2/725

A .

Section 6.7:

Problem 8: f increasing in ],1,( in , and in

).,32(

Section 6.8:

Problem 2: (a) ,)1(15/ 43312 ttdtdY (b) .)(/

1

acbtAabdtdK

Section 6.9:

Problem 6: .)12(3 2/5

t

,)14(

)1)(1(3)('

22

xx

xxxf )32,1[


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2.4 Week 4


Sections 6.106.11

Derivatives of exponential andlogarithmic functionsSections 7.17.4Implicit differentiation, derivative of

inverse, approximationSection 7.7Elasticity

Chapter 7

Randomness and ProbabilityChapter 8Random Variables and ProbabilityModels l

Group session

Second Excel Assignment

Recap Lecture


weekend (+ Excel assignment if not yet)

2.4.1 Statistics

Literature: Sharpe et. al. Ch. 7, 8


Chapter 7: exercises 1, 3, 5, 7, 9, 11, 19, 23, 25, 33, 39, 57, & 59;

Chapter 8: exercises 1, 2, 3, 5, 9, 13, 14, 15, 16, 17, 21, 33, 37, 41, 46, 49, & 55;


Chapter 7: exercises 2, 4, 6, 8, 10, 12, 16, 17, 20, 36, 38, 50, & 60;

Chapter 8: exercises 4, 8, 10, 19, 20, 34, 38, 42, 45, & 56.

2.4.2 Mathematics


Chapter 6:

- Sections 6.10 and 6.11: derivatives of exponential and logarithmic functions.

Chapter 7:

- Section 7.1: implicit differentiation of functions of one variable, first and second derivatives.

- Section 7.3: differentiating the inverse function.

- Section 7.4: linear approximation.- Section 7.7: elasticity.




Review Problems for Chapter 6: 15(b)(c)

Section7.1: Problems 3(a) and 6(b)(c)Section7.3: Problem 1

Section7.4: Problem 3Section 7.7: Problems 4(b)(c) and 6


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2.5 Week 5


Sections 8.18.3

First-derivative test for

maximum/minimum and economic

examplesSection 8.4 until The mean-valuetheorem

Extreme-value theorem

Sections 8.58.7Further economic examples, second-derivative test, inflection points

Chapter 9

The Normal Distribution

Chapter 10Sampling Distributions

Group session

Second Quiz for Mathematics and


Recap Lecture

Project

Questionnaire 5 to be handed in the

weekend

This week, we will have 2 tutorial sessions: one Tuesday/Wednesday, one Thursday/Friday! In the

back of this blockbook, an old exam is included; it may be attractive to devote some time (this week

and in week 7) to discuss it, to get acquainted with the way of testing.

2.5.1 Statistics



Chapter 9: exercises 2, 3, 7, 9, 11, 13, 15, 17, 19, 21, 25, 27, 31, 33, 37, 43, 45, & 52;

Chapter 10: exercises 1, 3, 5, 7, 9, 12, 13, 25, 29, 37, 43, & 49;



Chapter 10: exercises 2, 4, 6, 8, 11, 14, 16, 19, 23, 41, 42, & 44.

2.5.2 Mathematics


Chapter 8:

- Sections 8.1-8.3: first-derivative test for maximum/minimum and economic examples.

- Section 8.4 until The mean-value theorem:extreme-value theorem.

- Sections 8.5-8.7: further economic examples, second-derivative test, inflection points.






Section 8.6: Problems 2, 4 and 6

Section 8.7: Problems 4 and 6Review Problems: 2 and 7

Extra exercises


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Guidelines for reading

1. In lines 8-9 of Example 1 (Section 8.5, page 274) the claim is that has a maximum value.

This is a consequence of Theorem 8.4.1 on page 268.

2. Page 276, line 5: this is again a consequence of Theorem 8.4.1.

Extra exercises

(A) Problem 10 in Section 8.2.

(B) Application

A farmer uses land (K) and labour (L) to produce wheat (Q), according to the production

function .),( 32

3

1

LKLKQQ

Note that this is a function of two variables. Such functions will be studied next week but for

the moment we hope that you understand what is meant. For instance, if the farmer uses 8 units of

land (K = 8)and 27 units of labour (L = 27)then he produces

18278)27,8( 32

3

1

QQ units of wheat.

The farmer wishes to maximize the produced amount of wheat by investing in an appropriate

mix of land and labour. The cost of land is 2 per unit and the cost of labour is 1 per unit. The farmer

wants to invest a total amount of 4. How much land and how much labour should the farmer use, and

how much wheat will he produce? We will solve this problem in a number of ways, using the

techniques of Chapter 8.

(a) Although there are two variables to be decided upon, the whole problem can be formulated as

a maximization problem with only one variable, namely L or K. Show this: determine the

function to be maximized, including its domain.(b) Solve the problem of part (a) by only using information provided by the first derivative.

(c) Solve the problem of part (a) by also using the second derivative.

(d) Solve the problem of part (a) by using Theorem 8.2.2.


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2.6 Week 6


Sections 11.111.3

Dependent and independent variables,Cobb-Douglas functions, domain of afunction of two variables, partialderivatives of a function of two

variables, higher order partialderivatives, graph of a function of twovariables, level curves, isoquants of aproduction function, geometricinterpretation of partial derivatives

Sections 11.711.8

Marginal products, complementarity ofinput factors, partial elasticities.

Chapter 11

Confidence Intervals for ProportionsChapter 12Confidence Intervals for Means

Group session

Student Project

Recap Lecture


weekend

2.6.1 Statistics




Chapter 12: exercises 1, 3, 5, 7, 9, 11, 17, 21, 29, & 35;


Chapter 11: exercises 2, 4, 8, 10, 18, 19, 20, & 54;

Chapter 12: exercises 2, 4, 6, 8, 10, 12, 20, 22, 26, & 40.

2.6.2 Mathematics


Chapter 11:

- Section 11.1: dependent and independent variables, Cobb-Douglas functions, domain of a

function of two variables.

- Section 11.2: partial derivatives of a function of two variables, higher order partial derivatives.

- Section 11.3: graph of a function of two variables, level curves, isoquants of a production

function, geometric interpretation of partial derivatives.

- Section 11.7: marginal products, complementarity of input factors.

- Section 11.8:partial elasticitys.



Section 11.2: Problems 4(a)(c)(d)(f) and 6




Review problems Chapter 11: 3, 7(a)(c) and 13(b)(d)Extra exercise


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- Section 11.1. If you want to get some intuition of what a partial derivative actually represents,

read Example 4 on page 371 carefully.

- Section 11.2 The part on the formal definition of partial derivatives on pages 375 and 376 is

optional, except the boxed remarks numbered (6).

- For basically all functionsfyou will encounter the next few years it holds that

.22

xy

f

yx

f

This is usually a convenient double check for any errors in your calculations of second order

derivatives.

- If you want to get a feeling for 2D and 3D plots of functions or equations of one or two

variables you are of course allowed to use your graphical calculator if you have one, or a

computer program like GraphCalc. See the remark in week 1 about the use of this program for

graphs of functions of 1 variable. For 2 variable functions plotting a graph is equally easy. Just

go to the window 3D Graph and enter a function ofxandy, in the Equations ... submenu of 3D

Graph. For example, if you want to plot ,),( 22 yxyxf then after entering the function and

adjusting some options you may find the following picture:

- Sections 11.7 and 11.8. In these sections you'll encounter partial derivatives of functions of

more than two variables. The only thing you have to remember for these cases is that

everything you learned for two variables translates directly to higher dimensions as well. So,

for example the partial derivativey

f

of a function yzxzyxzyxf 232),,( toycan simply

be computed by considering x andzas constants and taking the derivative to yas usual. The

result is .13),,( 22

zyxzyx

y

f


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26

Extra exercise

Consider a company that produces gadgets (G) using the production factors blood (B), sweat (S)

and tears (T) according to the production function

G(B,S,T)=BS + BT + ST.

1. What happens if the input (B,S,T)of production factors doubles? What if it increases with a

factor t> 0 from (B,S,T)to (tB,tS,tT)?

2. Compute the marginal productsSB GG ',' and .'TG

3. Compute the corresponding elasticitys GElGEl SB , and .GElT

4. Compute ).1,1,1(GElS How can you interpret the value of this partial elasticity?

5. Compute G(1,1,1)and G(1,1.03,1). How can you connect these values to the elasticity you

found in (4)?

6. Show that the sum of the elasticitys you computed in (3) equals 2 (which happens to be the

exponent of the increase of production you found in (1). This result is due to Leonhard Euler

(1707 - 1783)).


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27

2.7 Week 7


Section 13.1 13.5Unconstrained optimization, stationary

points, first and second orderconditions for an optimum,

convexity/concavity of a function oftwo variables, local optima, saddle

points, economic applications:discriminating monopolist, linearregression, extreme value theorem

Chapter 13

Testing Hypotheses

Group session

Third Quiz for Mathematics and


Recap Lecture

ProjectHand in your project at latestOctober, Sunday 20 through Eleum,

Safe Assignment

This week, we will have 2 tutorial sessions: one Tuesday/Wednesday, one Thursday/Friday! In the

back of this blockbook, an old exam is included; it may be attractive to devote some time to discuss it,

to get acquainted with the way of testing.

2.7.1

Statistics



Chapter 13: exercises 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 41, 43, 47, 48, 55 & 71.


Chapter 13: exercises 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 42, 44, 46, 56, 70 & 72.

2.7.2 Mathematics


Chapter 13:

- Sections 13.1 and 13.2: unconstrained optimization, stationary points, first and second order

conditions for an optimum, convexity/concavity of a function of two variables.

- Section 13.3: local optima, saddle points.

- Section 13.4: economic applications: discriminating monopolist, linear regression.

- Section 13.5: Extreme-value theorem, optimization of a differentiable function over a compactdomain.



Section 13.2: Problems 2, 3, 5 and 8


Section 13.4: Problems 2(a)(b) and 5

Section 13.5: Problems 2 en 6

Review problems Chapter 13: 4(a)(b), 7, 9 and 10

Extra exercise


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28


1. The proof on page 465 in section 13.3 concerning the second-order derivative test is optional.

(It is a good test for your intuition though to see if you can understand the arguments used in

the proof.)

2. Skip Example 4 in section 13.4. Though linear regression is a very useful example of the

optimization techniques you just learned, it has not yet been treated in the statistics part of thiscourse.

3. Notice that, like with the theory from Sections 13.1 and 13.2, and in contrast with the second-ordertechniques from Section 13.3, the extreme value theorem enables you to findglobalextrema instead oflocal ones.


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Quantitative Methods I, EBC1005/1006/1007, 2012/2013, first sit Mathematics part, version A

1. What is the inverse of the function() for ?a) () ( ) ( )b)() c)

() d) ()

2. What is the domain of the function() ?a) b) but c) d) or

3.

The average price of a book is 25 euros at a certain bookstore, and it increases exponentially with 6%during every year. When is the average price going to reach 35 euros?

a) in less than 4 years

b) between 4 and 5 years

c) between 5 and 6 yearsd) more than 6 years

4. What is the derivative of() ?a)

b)

c) ( )

d)

5. The function() isa) decreasing and convex on the interval [0,4]

b) increasing and convex on the interval [0,4]c) decreasing and concave on the interval [0,4]

d) increasing and concave on the interval [0,4]

6. What is the elasticity

()of the function

() ()at

?

a)

1.5b) 2

c) 0

d) -2.5

7. The level curves of the function( ) area) parabolas

b) straight lines with slope -2

c) circles with center (-1,0)d) circles with center (1,0)


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8. What is the slope of the tangent line to the curve () at the point ?a) -3

b) 4

c)

0d)

9. The function( ) ( )hasa) 3 stationary points

b) 2 stationary points

c) 1 stationary pointd)

no stationary points

10.Which ()minimizes( ) given ?a) and b)

and c) and d) none of the above

11.The second order partial derivative

( )of the function( ) isa) b)

c)

d)

12.What are the inflection points of the function () a) b) and c) d) and

13.The function() () , where , hasa) 2 local maximum points

b) 1 local minimum point and no local maximum point

c)

1 local maximum point and no local minimum pointd)

1 local maximum point and 1 local minimum point

14. Consider the function() . For which case below is it true that has amaximum at ?

a) and b) and c) and d) and


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15.Consider a differentiable function()for positive values of . Let ()denote the elasticity of. Nowlet () (). What do you know about the elasticity ()of ?

a) () () b) () ()c)

() ()d) () () 16.Consider the equation ( )( ) . Suppose that the point (2,6) is on the curve

corresponding to this equation. What is the speed of increase of at this point?a) b) c) -2

d) -1

17.The function

()

()is defined for every

a) and b) and c) d)

18.Consider the function( ) . Which is true?a) The point (3,2) is on the level curve( ) andhas a stationary point on this level curve.b) The point (3,2) is not on the level curve( ) andhas a stationary point on this level

curve.

c) The point (3,2) is on the level curve( ) andhas no stationary point on this level curve.d)

The point (3,2) is not on the level curve( ) andhas no stationary point on this levelcurve.19.Consider the function( ) . Which case below describes all points ()for which the

equality

( )

( )holds?a) or b) or c) d) .

20.

A manager has to distribute 20 tasks to 2 machines. If he sends jobs to the first machine and jobs to thesecond machine, then his utility is . Each job has to be sent to exactly one of the machines.What is the optimal choice of the manager if he wants to maximize the utility?

a) and b) and c) and d) none of the above.


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Quantitative Methods I, EBC1005/1006/1007, 2012/2013, first sit Statistics part, version A

21. Which of the following is the best description of a systematic random sample?

A) A sample chosen in such a way that every possible sample of a given size has an equal chance to be the

sample.

B) After a population is separated into distinct groups, one or more of these groups are randomly selected

in their entirety to be the sample.

C) Select a sample in such a way that the proportion of some variables thought to impact the response is

approximately the same in the sample as in the population.

D) A value is randomly selected from an ordered list and then every nthvalue in the list after that first

value is selected for the sample.

22.A local park district is planning to build a recreation center. The park

district conducted a poll to find out the types of physical activities the local

population would be interested in. The poll was based on telephone

responses from 1013 randomly selected adults. The table shows the

percentages of people who expressed interest in various activities.Whichof the following displays is/are appropriate for these data? (More than one

display may be appropriate.)

A) I B) II C) I, II D) I, II, III

23. Three statistics classes (50 students each) took the same test. Shown below are histograms of the scores

for the classes. Use the histograms to answer which class had the highest mean score.

A) Class 1

B) Class 2C) Class 3

D) Classes 1 & 3


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24. Most US college-bound students take either the SAT (Scholastic Assessment Test) or the ACT (which

originally stood for American College Testing). Scores on both the ACT and the SAT are approximately

normally distributed. ACT scores have a mean of about 21 with a standard deviation of about 5. SAT

scores have a mean of about 508 with a standard deviation of about 110. Nicole takes the ACT and gets a

score of 24. Luis takes the SAT. What score would Luis have to have on the SAT to have the same

standardized score (z-score) as Nicole's standardized score on the ACT?

A) 548 B) 560 C) 574 D) 583

25. Each of the histograms below is of 15 integers from 1 through 5. The horizontal and vertical scales are

the same for each graph. Which graph has the smalleststandard deviation?

A) a. B) b. C) c. D) d.

26. Which of the following statements is true for two events, each with probability greater than 0?

A) If the events are mutually exclusive, they must be independent.

B) If the events are independent, they must be mutually exclusive.

C) If the events are not mutually exclusive, they must be independent.

D) If the events are mutually exclusive, they cannot be independent.

27. Given P(A) = 0.60, P(B) = 0.30, and P(A|B) = 0.50. Find P(A B).A) .40 B) .72 C) .75 D) .90

28. A group of volunteers for a clinical trial consists of 74 women and 77 men. 19 of the women and 21 of

the men have high blood pressure. Are high blood pressure and gender independent? Choose the best

explanation.

A) Yes; P(Highblood pressure and Male) = P(High blood pressure) P(Male).B) Yes; P(High blood pressure| Female) = 0.257; P(High blood pressure| Male) = 0.257; These are equal.

C) No; P(High blood pressure and Male) = 0.139; P(High blood pressure and Female) = 0.126; These are not

equal.D) No; P(High blood pressure) = 0.265; P(High blood pressure| Female) = 0.257; These are not equal .

29. You play a game that involves rolling a die. You either win

or lose1 depending on what number comes up on the die. Ifthe number is even, you lose1, and if it is odd, youwin1. However, the die is weighted and has the following probability distribution for the various faces.

Given that you win rather than lose, what is the probability that you rolled a "5"?

A) .10 B) .22 C) .33 D) .45


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30. A fair die is to be rolled 8 times. What is the probability of getting at least one 4?

A) B) (

) (

)

()

C) () (

)

()

() (

)

()

() (

)

()

D) () (

)

()

31. Based on the Normal model for yearly snowfall in cm in a certain town N(57, 8), how many cmsof

snow would represent the 80th percentile approximately?A) 64.5 cm B) 63.7 cm C) 63.3 cm D) 61.7 cm

32. For a Normal model, we know = 1250, and 35% of the distribution is below 1200. What is ?

A) 110 B) 120 C) 130 D) 140

33.A volunteer for a mayoral candidate's campaign periodically conducts polls to estimate the proportion

of people in the city who are planning to vote for this candidate in the upcoming election. Two weeks

before the election, the volunteer plans to double the sample size in the polls. The main purpose of this is

to:A) reduce nonresponse bias. B) reduce bias due to the interviewer effect.

C) decrease the variability in the population.

D) decrease the standard deviation of the sampling distribution of the sample proportion.

34. A sample is chosen randomly from a population that was strongly skewed to the right. Describe the

sampling distribution model for the sample mean if the sample size is small.

A) Skewed right, center at , standard deviation /nB) Skewed right, center at , standard deviation (/n)

C) Symmetric, center at , standard deviation /nD) Symmetric, center at , standard deviation (/n).

35. The real estate industry claims that it is the best and most effective system to market residential real

estate. A survey of randomly selected home sellers in Southern Limburg found that a 95% confidence

interval for the proportion of homes that are sold by a real estate agent is 69% to 75%. Interpret the

interval in this context.

A) 95% of all random samples of home sellers in Southern Limburg will show that between 69% and 75%

of homes are sold by a real estate agent.

B) We are 95% confident that between 69% and 75% of homes in this survey are sold by a real estate

agent.

C) We are 95% confident, based on this sample, that between 69% and 75% of all homes in Southern

Limburg are sold by a real estate agent.

D) If you sell a home, you have a 72% 3% chance of using a real estate agent.

36. The real estate industry claims that it is the best and most effective system to market residential real

estate. A survey of randomly selected home sellers in Southern Limburg found that a 95% confidence

interval for the proportion of homes that are sold by a real estate agent is 69% to 75%. Explain what "95%

confidence" means in this context.


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A) About 95% of all random samples of home sellers in Southern Limburg will produce a confidence

interval that contains the true proportion of homes sold by a real estate agent.

B) About 95% of all random samples of home sellers in Southern Limburg will find that between 66%

and 78% of homes are sold by a real estate agent.

C) There is a 95% chance that the true proportion of home sellers in Southern Limburg who sell their

home with a real estate agent is between 66% and 78%.

D) 95% of home sellers in Southern Limburg will sell their home with a real estate agent between 66% and

78% of the time.

37. How tall is your average statistics classmate? To determine this, you measure the height of a random

sample of 15 of your 100 fellow students, finding a mean height of 168 cm an

Qm 1 Course Manual 1013

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