Schools
 
Undergraduate
Maths
Papers
MATH101
 
Department

Search Maths/Stats: 
 
Advanced Search

Sample problem


The aircraft’s flightpath goes through coordinates (1,2,0) and (23,-19,3). The top of the hill is at (18,-13,2).
How close does the aircraft get to the top of the hill? Vectors make this an easy calculation.





J Willard Gibbs, 1839-1903, was a pioneer in vector analysis. His family lived in Connecticut and Gibbs became Professor of Mathematical Physics at Yale in 1871 — rather surprisingly before he had published any work! He made major contributions to thermodynamics, the electromagnetic theory of light and statistical mechanics.




Sample problem


In a certain city, commuters go to work by car or bus. A study shows that from each year to the next year 20% of car users change to travelling by bus, while 15% of bus users change to travelling by car. What percentage of commuters travel by car, once things have settled down?

MATH101 Supplementary Algebra 1

First Semester, Second Semester, 9 points

Introduction

This 9-point half-paper covers methods and applications of algebra. It consists of the algebra component of MATH 160. Note that to go on to MATH 170, you will need both MATH 101 and MATH 102 - or their equivalent, MATH 160.

Paper details

This algebra paper is the natural continuation of 7th Form Mathematics.

After a review of basic trigonometry, the paper focusses on three-dimensional vectors and their many uses (such as in geometry, computer graphics, surveying and even calculus). The vector representation of lines, planes and projections leads naturally to the discussion of linear systems of equations. The basic properties of matrices are studied together with some applications. Complex numbers and polynomials complete this section of the course.

Potential students

MATH 101 is taken only by students who need the algebra component (but not the calculus) of MATH 160. This situation may arise when a student has transferred from another university, or is looking for a 9-point paper, or has previously taken the calculus half.

Main topics

  • Vectors; linear and planar geometry and applications
  • Solving linear systems
  • Matrices and applications
  • Complex numbers
  • Polynomials and their roots

Prerequisites

None

Required texts

MATH 160 Algebra Outline Notes
(Available from the Print Shop.)

Useful references

Elementary Vector Algebra by A.M. MacBeath
Algebra, Geometry and Trigonometry by M.V. Sweet

Lecturers

First semester: Assoc Prof Peter Fenton, room 220
Second semester: Dr Florian Beyer, room 218

Lectures

Mon and Wed and every second Friday in both semesters.
  • First semester: one stream at 10 am
  • Second semester: one stream at 12 noon

Tutorials

Attendance at tutorials is voluntary. An open tutorial system operates where classes run for 8 hours per week, and students may attend as many as they need to and are able to.

Internal Assessment

There are ten marked assignments which make up your internal assessment mark.
Five computer Skills Tests together make up 33.3% of your final mark.

You can check your marks by clicking on the Resources link at the top of this page.

Terms Requirement

You have to fulfil the terms requirement in order to be allowed to sit the final exam. In this paper, to pass “terms” you need to gain at least 5/10 in each of the first four Skills Tests.

Exam format

The 90-minute final exam is answered in spaces provided on the question booklet. All questions should be attempted and the number of marks available for each question is indicated on the paper. There are usually from 15 to 20 questions.

Past exams are available for download from the MATH160 resource page.

Final mark

The final mark F is calculated from:
F = max { E, (3E + A)/4 } + T
where E (exam mark) is out of 66.7, A (internal assessment) is out of 66.7, T (test mark) is out of 33.3.

The “max” corresponds to plussage: if your internal assessment mark is greater than your exam mark then it is combined in the proportion shown. If it is less then it is ignored and the exam mark itself is used.

So your internal assessment can boost your exam mark with a 1/4 weighting if that helps you. Note that the test component definitely counts and so the tests should be regarded as compulsory.

Plagiarism

Students should make sure that all submitted work is their own. “Plagiarism is a form of dishonest practice. Plagiarism is defined as copying or paraphrasing another’s work and presenting it as one’s own” (University of Otago Calendar). In practice this means that plagiarism includes any attempt in any piece of submitted work (e.g. an assignment or test) to present as one’s own work the work of another (whether of another student or a published authority). Any student found to be responsible for plagiarism in any piece of work submitted for assessment shall be subject to the University’s dishonest practice regulations which may result in various penalties, including forfeiture of marks for the piece of work submitted, a zero grade for the paper, or in extreme cases exclusion from the University. The University of Otago reserves the right to use plagiarism detection tools.

While we strive to keep details as accurate and up-to-date as possible, information given here should be regarded as provisional. Individual lecturers will confirm teaching and assessment methods.