study guide summer 2013

8/13/2019 Study Guide Summer 2013

1/7

1

DEPARTMENT OF MATHEMATICS

Mathematics Two Study Guide

SUMMER SEMESTER 2013

MATHS 102(15 Points)

Welcome to Mathematics at the University of Auckland. We are delighted that you havechosen to study this subject, and hope to further capture your interest so that you willcontinue to be part of our mathematical community in the years ahead. Mathematically welive in exciting times: new applications, new research questions, new ways of studying thisoldest of subjects.

COURSE DESCRIPTIONThis course focuses on the mathematics that leads up to, and includes, calculus. We wish to engageyou in active participation in problems involving real life contexts. The content is organised around

the key idea of a function, and examines different kinds of functions and their characteristics. Weaim to build your confidence and enjoyment in mathematics, as well as preparing you for furtherstudy. In response to modern developments in our field, we emphasise mathematical modelling. Wewill also make full use of computer technology and web access.

Recommended Preparation: The course is intended for those students who have achieved at least 18credits in Mathematics at NCEA Level 2 and fewer than 12 credits in Calculus or Statistics at

NCEA Level 3 (or equivalent). If you are unsure whether you are in the correct course, please comeand talk to us.

Restrictions: MATHS 102 may not be taken with any other mathematics course except MATHS190, nor can it be taken after having previously passed any other mathematics course exceptMATHS 101/101G or MATHS 190/109G.If you pass MATHS 102, the next course would normally be MATHS 108. An A- pass grade or

better in MATHS102 is the prerequisite for progressing to MATHS 150.

LEARNING OUTCOMESA student who successfully completes this course will:

recognise and use various forms of function notation, and be able to write down and graph theinverses of functions, and identify the domain and range of functions;

be able to identify, model and interpret the algebraic or graphical forms of polynomial,exponential, logarithmic, and cyclic relationships in both mathematical and real world contexts;

be able to relate rational functions with their graphs, identifying asymptotes and intercepts; be able to use algebra to solve equations, including problems involving trigonometry; be able to perform arithmetic on complex numbers; be able to find the derivative and integral of polynomial, power, exponential, logarithmic, and

trigonometric functions, including the use of product, quotient and chain rules; understand the relationship between integration and differentiation; be able to identify when a derivative is an appropriate mathematical model, and use it to solve

optimisation problems; know when and how to use technology appropriately for mathematical problems in this course; know several strategies for approaching problems with no obvious solution method; have the ability to communicate mathematical ideas and problem solutions orally and in writing.

A student who has taken this course can also expect to have developed mathematical habits of

logical thinking, persistence, problem-solving, modelling, proving, conjecturing, symbolism,abstraction and generalisation.


2/7

2

LECTURERS

Bill Barton (Coordinator) [email protected] Room 505 Building 303 Ext 88779Office hours: Daily 2-4pm (except first week)

Judy Paterson [email protected] Room 502 Building 303 Ext 88603Office hours: Daily 2-4pm (first week only)

ASSESSMENTYour final grade will be based on a combination of coursework and a 2 hour final examination. Youmust participate in coursework if you wish to pass the course.

Total coursework mark 40%

2 Semester tests 10% 5% for each of two 30min multichoice tests3 Written assignments 15% 5% for each assignmentFive Online Skills Quizzes 5% 1% eachFive Collaborative Tutorials 10% 2% each

End of semester exam (2 hours) 60%

Semester TestsThese will be held during lectures, one in the middle of the course and one at the end of the course.

No calculators will be permitted.

Written Assignments (also see later description) Place your assignment in the MATHS 102 hand-in box in the ground floor (foyer) of the ScienceCentre Building 303 (Maths/Physics).

Due Dates (by 4pm)Assign. 1: Tue 22 nd Jan Assign. 2: Tue 29 th Jan Assign. 3: Thu 7 th Feb

Skills Quizzes (also see later description) NO EXTENSIONS WILL BE GIVEN.

These will be completed on Cecil as shown in the MATHS 102 calendar schedule at the end of thisstudy guide. They will be available to do from 8am on the day shown on the calendar schedule,until 12pm on the evening on which the quiz is due.

Final ExaminationThe examination is 2 hours long. The date and time of the exam will be confirmed later in thecourse. An information sheet on the exam will be available on Cecil once the semester starts. In theevent of problems at the time of the exam, contact Student Health and Counselling. Moreinformation is available on the examinations website: http://www.auckland.ac.nz/exams

EXPECTATIONS

Pre-requisite KnowledgeStudents taking this course are expected to have a working knowledge of the basic elements of Year11 and Year 12 Mathematics. Assumed knowledge for each module is stated in the Course Book.The Cecil skills quizzes will test students on pre-requisite knowledge. Students who experiencedifficulties with this knowledge are expected to spend some time learning it outside of lectures,using the sources of help suggested at the start of each module in the supplementary course notes.

Course-loadA semester course at The University of Auckland is assumed to require at least 10 hours per weekof student time. In MATHS 102, the normal pattern of student study each week is expected to be:

3 hours lectures 1 hour tutorial 3 hours lecture preparation/revision 3 hours assignments/quizzes/test preparation.


3/7


4/7

4

Students having problems with earlier knowledge are referred to the Student Learning Centre (KateEdgar Commons), or to school mathematics texts. A suitable reference and source of exercises isDavid Bartons Gamma Mathematics Level 11 , available from Abacus Educational Book Supply.

WORKING TOGETHER & CHEATINGThe University of Auckland will not tolerate cheating, or assisting others to cheat, and views

cheating in coursework as a serious academic offence. The work that a student submits for gradingmust be the student's own work, reflecting his or her learning. You are encouraged to discuss problems with one another and to work together on assignments, but you must not copy another person's assignment. Any cases of suspected cheating will be referred to the course coordinator.Marks for the assignment may be deducted, or in serious or repeat cases, the student may be deletedfrom the course, or referred to the university for other possible disciplinary action.

Generally the following are acceptable forms of collaboration: Getting help in understanding from staff and tutors. Discussing assignments and methods of solution with other students.

Unacceptable forms of collaboration ("cheating") include:

Copying all or part of another student's assignment, or allowing someone else to doall or part of your assignment for you.

Allowing another student to copy all or part of your assignment, or doing all or part ofan assignment for somebody else. This is treated as seriously as copying anotherstudent's assignment.

If you are in any doubt about the permissible degree of collaboration, then please discuss it with astaff member. For complete information about the universitys policy on cheating, see Guidelines:Conduct of Coursework on the university website.

TECHNOLOGY

CalculatorsWe strongly recommend that students obtain a graphics calculator for this course, but should younot wish to purchase a graphics calculator, you MUST have at least a scientific calculator withtrigonometric, exponential, and logarithmic functions.

Graphics calculators will be used by some lecturers in their teaching, and are supported bysupplementary material located on Cecil. You can use a graphics calculator in all assignments, thetest, and the examination. Graphics calculators will really help your mathematics learning inMATHS 102 and beyond, and although some other courses may not permit them in exams, they canstill be used in assignments etc. Any model graphics calculator may be used (e.g. Casio, TI, Sharp).

ComputersThe mathematics department is progressively introducing the use of Matlab in all its courses.However, MATHS 102 will continue to use the graphing package AUTOGRAPH . It is available onthe computers in the Mathematics Undergraduate Computer Laboratory. There will be a tutorial oncomputer graphing (see course calendar).

WRITTEN ASSIGNMENT INFORMATIONYou will have 3 assessed written assignments, to be handed by 4pm on the dates shown earlier.Assignment Four is not marked, it is provided to help you prepare for exams, by covering the topicsafter assignment 3. Model answers will be provided for all four assignments.

Each written assignment will be marked out of 50, reduced to a mark out of 10. Bonus marks are

sometimes awarded for exceptional work (up to a maximum of 10/10).Starting work on the night before your assignment is due is not a good idea! The presentation ofyour assignment solutions is important. Markers cannot be expected to 'hunt' for your solutions.


5/7

5

Solutions should be numbered and all necessary working clearly shown. In other words do not penalise yourself through handing in hastily done work that cannot be easily read.

Use the special blue cover sheet for mathematics available from the SRC. Put your name, coursenumber, assignment number, and tutorial group on the front page, and Student ID on the back.

COLLABORATIVE ASSIGNMENTS INFORMATION:Discussion is important in the process of mathematics learning. Being able to communicate yourunderstanding is an important aspect of mathematical knowledge. In this course you will be givenan opportunity to develop these skills. A collaborative assignment task is an activity in which agroup of students (usually three) attempt to solve a mathematics problem together. The solution issubmitted as a joint effort and all three students will gain the same mark. You do not have to workwith the same students every time. The assessment is in two equal parts:

Oral in which tutors will assess the extent of the collaboration of the group members in the problemsolving process and the understanding that the whole group has of the problem and its solution.

Written in which the groups written solution will be handed in and marked in the usual way.

SKILLS QUIZZES:These will consist of 5 on -line quizzes each comprising 10 questions and worth 1% towards yourcourse-work mark. They may be attempted on Cecil anytime during the scheduled week, as long asthey are completed by 12pm on the Sunday before it is due (see Schedule p. 8). You may have up tothree attempts for each test, with your best mark being counted. The questions are chosen to you'reyour knowledge of the preliminary skills required for each module (see the Module notes in theSupplementary Course Notes for more details). Quiz One will cover Module O and Module 1.

DELNADELNA is The University of Aucklands English Language testing programme. Information on the

programme can be found at: http://www.delna.auckland.ac.nz/ DELNA: Diagnoses your academic En glish language ability. Does not cost you anything. Directs you to the best language support for you. Does not exclude you from the courses you are enrolled in. Does not appear on your academic record.

The Department of Mathematics requires ALL first year students to undertake DELNA screening.This is a half-hour web-based test. Individual results are given only to you, although the departmentgets a summary of the class results. Arrangements for sitting the test will be made through theCourse Coordinator, who will advertise times and places where the screening can take place.

ENGLISH LANGUAGE ASSISTANCE & OTHER SUPPORTThere are several services provided by the university and by the Department of Mathematics.ELSAC the English Language Assistance Centre at Web site http://www.elsac.auckland.ac.nz/ isa computer-laboratory based service, it is free and open 7 days a week. Tutors are available to help.There are also some credit-bearing English language courses (ESOL 100/101/102).

GETTING FURTHER HELPThe Department of Mathematics offers special tutorial support for Maori and Pasifika students(contact Ru Nicholson, Extn 87856, or Beth McNab: [email protected] .) Please go tothe Mathematics Tuakana Website:http://www.math.auckland.ac.nz/uoa/home/for/maori-and-pacific-students

For assistance with the material covered in the course: Ask questions in class Ask about the material in the Friday tutorial.
mailto:[email protected]:[email protected]:[email protected]:[email protected]


6/7


7/7

7

MATHS 102 COURSE OUTLINE

(The course structure was changed for 2012, but the Coursebook has not yet been revised. Brackets after thetopic or lectures refer to the relevant module ( Mod ) & pages ( pp) in the Coursebook).

INTRODUCTORY MODULE 1: Mathematical modelling and functions. (2 lectures, Mod 0, pp. 7-15 )

Welcome to Maths 102: Thinking and Reasoning Mathematically Mathematical Models and Functions, and Domain

MODULE 2: (8 lectures) Polynomial functions Linear Functions ( Mod 1, pp. 16-18 ) Quadratic Functions ( Mod 1, pp. 24 -30 ) Solutions to Quadratic Equations The Quadratic Formula Number Sets and Inequalities ( Mod 1, pp. 20-21 ) Complex Numbers ( Mod 4, pp. 99-101 )

Simultaneous Equations & Matrices ( Mod 1, p. 19; Mod 4, pp. 102-106 ) (Assignment 1) Cubic & Higher Order Polynomial Functions ( Mod 1, pp. 31-32 )

MODULE 3: (10 lectures) Other Functions: Rational, Exponential, Logarithmic & Trigonometric Rational Functions (2 lectures, Mod 2, pp.36-39 ) Exponential Functions (2 lectures, Mod 2, pp.40-42 ) Logarithmic Functions ( Mod 2, pp. 43-45 ) Logarithms & Exponents (Assignment 2 & Test 1) Radians & Circular functions ( Mod 4, pp. 78-89 ) Trigonometric Relationships & Graphs Modelling Waves Piecewise Functions, Domain, Range & Inverse ( Mod 2, pp.45; 50-52 )

MODULE 4 (10 lectures) Gradient Functions - Differential Calculus Rates ( Mod 3, pp. 53-70 )) The Gradient of a Function The Derivative Function (Assignment 3) Differentiation Optimisation

Higher Derivatives Exponential & Logarithmic Functions Differentiation of trigonometric functions ( Mod 4, pp. 96-98 ) Product & Quotient Functions ( Mod 3, pp. 73-76 ) Composite Functions (The Chain Rule)

MODULE 5: (4 lectures) Area Functions - Integral Calculus (Coursebook Module 5, pp. 11-122) Area Under a Curve Indefinite Integration Definite Integration Applications of Integration (1-2 lectures) (Test 2)

study guide summer 2013

Documents