WTW 134 Study guide 2021 PDF

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Summary

Breakdown of themes for 2021 and some practice questions...

Description

University of Pretoria Department of Mathematics and Applied Mathematics

MATHEMATICS - WTW 134

COURSE COORDINATOR: Ms K Bothma Office in the Mathematics Building: 2-12 Telephone at work: 012 420 2374 email: [email protected]

CONTENTS Page  General Information

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Organisation of the course

... 2

Assessment

... 4

Marks and examinations

... 7

 Study Guide - Calculus Theme 1 - Functions and change

... 8

Theme 2 - Differentiation

... 13

Theme 3 - Exponential, logarithmic, trigonometric ... 16 and absolute value functions Theme 4 - Using the derivative

21

Theme 5 - Integration

... 23

Theme 6 - Using the definite integral

... 25

Theme 7 - Functions and economics

... 26

 Study Guide-Linear Algebra

... 27

WTW 134 2021 Study guide page 1 of 27

ORGANISATION OF THE WTW 134 COURSE - 2021 1.

ADMITTANCE

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You can only register for the module WTW 134 on the premise that you can attend all 4 weekly lectures with the same lecturer as well as one practical class. If you are a veterinary science student or medical science student (with MGW 112 as prerequisite) then you have to register for the module WTW 165, presented in the second semester. Please note that WTW 165 is not an anti-semester module for WTW 134. STAFF

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NAME

ROLE

OFFICE

TELEPHONE

Ms K Bothma

Couse coordinator, Lecturer Mathematics 2-12 012 420 2374

Mr P Shabangu Lecturer

Mathematics 1-44 012 420 2858

Ms A Verwey

Lecturer

Mathematics 2-29 012 420 2331

Dr B Yizengaw

Lecturer

Mathematics 1-21 012 420 5882

Ms S Mdayi

Technical assistant

Mathematics1-22

012 420 2713

EMAIL ADDRESS: [email protected] TEXTBOOK Calculus-APPLIED CALCULUS by Deborah Hughes-Hallett et al (SIXTH EDITION) The hard copy and an electronic version is available. Linear Algebra-Notes compiled by the lecturers of the department Please note that the study guide refers to page numbers and problem numbers in the prescribed textbook, the sixth edition of APPLIED CALCULUS. Lecturers are under no obligation to assist students with the problem numbers and page numbers in other editions of the textbook. ANNOUNCEMENTS All announcements are posted on ClickUP. It is the only mode of communication for module related matters and it is your responsibility as students to remain informed by frequently checking the announcements on ClickUP. ATTENDANCE The module will be presented online. Your attendance of online classes and activity on ClickUP will be monitored. It is important that you attend each lecture of your lecture group and the weekly practical class of your practical group. During lectures emphasis is placed on mathematical understanding and the lecturers demonstrate but also facilitate problem solving and the exposition of mathematical problems. During practical classes opportunities are created for students to resolve difficulties with understanding. CALCULATORS The calculator that you used in school is sufficient for WTW 134.

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CONSULTING HOURS You can consult with your lecturer by email and during office hours (from 8:00 to 17:00, Monday to Friday). Please note that lecturers will attempt to respond within two working days, but are not available for consultation outside office hours. 8. CONTACT TIME Contact time involves four lectures and one practical class per week, presented online. 9. PRACTICAL CLASSES It is compulsory to attend one practical class per week during the same time slot. The practical classes will commence on 29 March. An announcement about practical class allocation will be made on 17 March. Emails about practical class allocation will not be attended to if sent before 17 March. For a practical class you have to prepare the content (study units) covered during the lectures of the previous week (or weeks) by doing all the problems listed (per study unit) in the study guide. The purpose of the practical class is for students to resolve difficulties encountered during preparation. You can contact the staff member in charge of the practical class to specify problem numbers to be discussed during the practical class, but your attempts must be included as an attachment and emails must be sent at least 24 hours in advance. The weekly assessment is based on the scope of the practical class and the nature of the assessment is announced on Friday of the previous week. 10. STUDY HOURS Mathematics is a skill that you acquire through study and practice. A student has to devote about 11 hours study time per week to this module. The scheduled contact time is about 5.5 hours per week, which means that another 5.5 hours of your weekly study time should be devoted to this module. 11. EMAILS Emails are an essential mode of communication. All emails about administrative issues (practical group allocation, marks etc) must be sent to [email protected]. The email address of your lecturer will be made available during the first week of lectures and must be used for the purpose of consultation. Emails about administrative issues will not be attended to by lecturers. Please adhere to the principles of email etiquette and remain respectful in your communication with any staff member of the University of Pretoria. Emails that are disrespectful or motivated by an attempt to haggle for marks, will not be attended to. When the marks of a test or worksheet are made available, you have three days to query the marking by completing the relevant query form available on ClickUP. Any emails sent outside the time period of three days will be immediately deleted. Also note that an email can constitute a legally binding document.

7.

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ASSESSMENT 1.

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SOLUTIONS TO PROBLEMS You have to show all steps and use the correct mathematical notation to explain your answer by means of a coherent and mathematically precise solution. Since this is an applied mathematics module most problems constitute ’word problems’ of which the final answer is a sentence with units included. INSTRUCTIONS The examination and test instructions of the University of Pretoria must always be adhered to for al assessments. SEMESTER TESTS Assessment of this module includes two semester tests. The date, time and scope will be published on ClickUP. A student with special assessment needs (e.g. extra time) must contact the course coordinator well in advance of every test and examination. Note that there are no sick tests but only one special test that must be written if one of the semester tests was missed. If you miss both semester tests, you do not have exam entrance for WTW 134. SPECIAL TEST If you missed one of the semester tests (with a valid reason for your absence), then you must write the special test. No student will be allowed to write the special test to improve his/her marks. The test is scheduled near the end of the semester and the date is only made available after the second semester test. The scope is the combined scopes of the first and second semester tests. WEEKLY ASSESSMENT An assessment is scheduled each week of which the scope and nature are announced on Friday of the previous week. An assessment can take the form of a ClickUP test or assignment. TECHNICAL ISSUES WITH WEEKLY ASSESSMENT It is the responsibility of the student to ensure that your immediate environment, computer and computer settings allow for the successful completion of a ClickUP test or assignment. Technical issues (e.g. a power failure) might impede the process of completing a ClickUP test or assignment, but a ClickUP test or assignment will not be reopened in the case of technical problems. The formula used for calculating the weekly assessment marks at the end of the semester will make provision for technical problems with one of the ClickUP tests or assignments. CLICKUP TESTS You cannot use a cell phone or a tablet to complete a ClickUP test. With a ClickUP test there is a time limit, you are allowed only one opportunity and you cannot backtrack to a question once you have answered it. These settings are to protect students from being logged out of a test.

WTW 134 2021 Study guide page 4 of 27

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9.

CLICKUP ASSIGNMENTS You have to use a PDF scanner e.g. CamScanner to submit your assignments. All the pages must be upright and in focus. Pages that are not upright and in focus cannot be marked. Your pages must be submitted in the correct order and your student card displayed in the top right corner of every page. Submitted assignments must be directly accessible and cannot be submitted via online platforms for which the student’s permission is required. If you are not successful at submitting an assignment via ClickUP then you can mail the assignment to [email protected]. If you submit an assignment by email you have to provide proof of your ClickUP submission not being successful and your email must be in the prescribed format (see ClickUP announcement). A student will be penalised for mailing an assignment that was also submitted via ClickUP. ABSENCE FROM TESTS Absence from a test, assignment or semester test must be reported to the course coordinator within three days of the date of the assessment. Failure to contact the course coordinator within three days will result in a zero mark. You are granted an absence with valid reason (code "999") if you submit a sick note or affidavit within three days of missing the test or worksheet. The following sick notes are accepted: Sick notes issued by a medical doctor registered at the Health Professions Council of South Africa (HPCSA) or by an advanced practice nurse (a registered nurse with a postgraduate qualification) as determined by the South African Nursing Council who has a BHCF practice number, provided that the diagnosis falls only within their specific field of specialisation. An affidavit will only be accepted if supported by substantiating documentation, e.g. case report or criminal charge with case number obtained from a police station, valid medical certificate for injuries, a death certificate for a funeral, etc. Please note that submission of fraudulent sick notes and affidavits is a criminal offense, which will lead to disciplinary action and may result in dismissal. The same regulation holds for fraudulent emails. You can only be granted an absence with valid reason for a maximum of two assessments. A sick note, affidavit or email cannot exempt you from another assessment if you have already been granted an absence with valid reason for two assessments. Missing more than two assessments will result in a zero mark for all the other missed assessments. Note that this regulation does not apply to semester tests.

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10. QUERIES CONCERNING MARKING

It is the responsibility of the student to access ClickUP frequently (more than once a week) in order to be informed about the availability of marks and the relevant time period for submitting queries. All queries concerning the marking of an assessment (test or assignment) must be submitted by completing and submitting (to [email protected]) the relevant query form (see ClickUP) within three days after the marks become available. A schedule will be made available (and frequently updated) on ClickUP to inform students of the dates of assesments, the dates of the publication of marks and the due dates for queries. Queries that are submitted outside the allowed time period of three days (see schedule on ClickUP) will not be attended to. 11. FILE YOUR TESTS You must file all the marked tests and assignments in case it is needed as evidence when semester marks are calculated. 12. DISCIPLINARY CASES It is the policy of the department to refer every incident in which there is a suspicion of dishonesty or other irregularity to the Disciplinary Committee of the University. 13. DECLARATION OF AUTHENTICITY You will have to complete a declaration of authenticity for every test and/or assignment.

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MARKS AND EXAMINATIONS 1.

2.

CHECK YOUR MARKS The marks of tests, assignments and semester tests are published on clickUP after the marking process has been completed for all students. You have three days after the publication of the marks to report mistakes and/or omissions by completing the relevant query form. No late alterations or additions will be made after three days (see schedule on ClickUP). PRELIMINARY MARK The preliminary mark is calculated as follows: Semester tests 70% Weekly assessments

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30%

ADMISSION TO THE EXAMINATION Students will not write a formal examination. Instead you will complete a final assignment on the examination date determined by the faculty. You may complete the exam assignment if you  attended all the practical classes  completed all the weekly assessments  completed two semester tests or a semester test and the special test and  have a preliminary mark of at least 40%. FINAL MARK The final mark is calculated as follows: Preliminary mark 75% Exam assignment 25% To pass this course a minimum of 50% is required for the final mark. SUPPLEMENTARY EXAMINATION In cases where a final mark between 40% and 49% has been obtained, a student will not have the opportunity to write a supplementary exam. A student will qualify to complete a supplementary assignment on the supplementary examination date scheduled by the faculty, if the student could not complete the exam assignment on the examination date scheduled by the faculty in each of the following cases:  The student submitted proof of absence with valid reason within three days of the examination date  The student submitted proof (well in advance) of the examination date clashing with other modules  The student’s submission of the examination assignment failed and proof of the failed submission was provided within three days of the examination date. Special assignments are not arranged for students who are unable to complete the supplementary assignment at the time scheduled by the faculty. SUMMER SCHOOL In cases where a final mark between 40% and 49% has been obtained, a student will qualify to attend a summer school, scheduled in January of 2022.

WTW 134 2021 Study guide page 7 of 27

THEME 1 - FUNCTIONS AND CHANGE Unit 1.1 What is a function? Source

Textbook, pp 2 - 5 and p 21

Objectives On completing this unit you should be able to 1. describe a function, the domain of a function and the range of a function. 2. interpret function values. 3. calculate or estimate function values (using a formula, a table or a graph). 4. calculate the vertical and horizontal intercept(s) of a function. 5. describe an increasing function on a interval and a decreasing function on an interval. 6. describe an function that is concave up on an interval and a function that is concave down on an interval. The definitions are on p 21 in the textbook, but we use the definitions in the lecture notes. 7. use a graph to find the interval(s) on which a function is increasing or decreasing or concave up or concave down. Problems for the practical class Problems for Section 1.1 (p 5), numbers 10 to 14, 16 to 20 and 25. Problems for Section 1.3 (p 25), numbers 1 to 5 and 7. Unit 1.2 Types of functions Source

Lecture notes

Objectives On completing this unit you should be able to 1. give the name and the general formula of the six types of functions. 2. sketch the graphs of the functions without calculating function values. 3. represent the domain and range of the functions. Problems for the practical class 1. Give the name of the function and sketch the function without using a table of values. Label the axes and indicate the horizontal and vertical intercepts, if any. Use the graph to represent the domain and range of each function using interval notation. i b  3a  6 ii a  4b  12 iii P  0. 21 t iv m  2. 1 n v

y  e x

vi

ix

a  b 4

x

xiii P 

7

t

v  log0.5 z

w  v5 xiv x  14 y

vii P  lnt xi

v  w 7

xv l  m 5

WTW 134 2021 Study guide page 8 of 27

viii b  a 6 xii

m

4

xvi y  7

n

2.

Use a graph to solve the inequality. Hint: If you have to solve the inequality x 5  1, graph y  x 5 and y  1, solve the equality x 5  1 and then use the graph to determine the final answer. i

x5  1

iv x 2  2x  8  0 3.

4. 5.

ii x 3  8

iii x 2  x  6  0

v 2x  0

vi

0. 5x  0

Use graphs to solve the inequality below. Hint: Find the point(s) of intersection of the two graphs and sketch both graphs. i x2  x ii x 3  x Consider the graphs of polynomial functions given below In each graph fx  a n x n  a n1 x n1  . . . a 1 x  a 0 , is represented on a large viewing window so that you cannot see the turning points, horizontal intercepts or vertical intercepts. Give the sign of the leading term of each polynomial.

i

ii

iii

iv

Unit 1.3 New functions from old functions Source

Textbook, pp 66 - 69

Objectives On completing this unit you should be able to 1. identify and use a composite function. 2. sketch the graph of a function obtained from an old function through a vertical shift (y  fx  c) or through a horizontal shift (y  fx  c). 3. sketch the graph of a function obtained from an old function by multiplying the function with a constant (y  cfx). 4. sketch the graph of a function obtained from an old function by reflecting the graph about the x axis (y  fx or by reflecting the graph about the y axis (y  fx. 5. determine the domain of a composite function and represent the domain using set notation and in interval notation.

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Remarks 1. Omit Example 5 on p 62. 2. When you have to solve a quadratic inequality in this course, use a graph. 3. You have to memorize the formula for the roots of the quadratic polynomial b  b 2  4ac . fx  ax 2  bx  c, ax 2  bx  c  0  x  2a Problems for the practical class Problems for Section 1.8 (p 63), numbers 3, 9, 11, 31 (hint for number 31, the average number of leaves is equal to the product of the number of branches and the number of leaves per branch) , 53, 55 and 56. Extra problems for the practical class 1. Write down the functions fx and gx if i fgx  ln x ii fgx  ln x . Your answer cannot be a composite function or the function y  x 1 . 2. Write down functions ft, gt and ht if hgft  1  t 2 Your answer cannot be a composite function or the function y  x 3. Consider the functions f 1 x  ln x, f 2 x  ln x  1, f 3 x  lnx  1, f 4 x   ln x and f 5 x  lnx Sketch the functions and give the domain and range of each function. You do not have to indicate the horizontal and/or vertical intercepts but use a dotted line to indicate horizontal and vertical shifts. 4. If fx  e x sketch the following graphs and write down the domain and range of the function. You do not have to write down the horizontal and/or vertical intercepts but use a dotted line to indicate horizon...