MATHS 108 : General Mathematics 1
Science
2025 Semester Two (1255) (15 POINTS)
Course Prescription
Course Overview
This course is intended for students from commerce and the social sciences, who have studied Mathematics at a Year 13 level. It is also suitable for students interested in studying Physics or Mathematics, who don't have the recommended entry requirements for MATHS 120 and 130. MATHS 108 covers selected topics in algebra and calculus and their applications, including: linear functions, linear equations and matrices; functions, equations and inequalities; limits and continuity; differential calculus of one and two variables; integral calculus of one variable. After successfully completing MATHS 108 students will be well prepared for further courses in mathematics, such as MATHS 208 or Maths 120/130, depending on the grade received.
Capabilities Developed in this Course
| Capability 3: | Knowledge and Practice |
| Capability 4: | Critical Thinking |
| Capability 5: | Solution Seeking |
| Capability 6: | Communication |
| Capability 7: | Collaboration |
Learning Outcomes
- Display mastery of the algebra concepts covered. (Capability 3, 4 and 5)
- Solve problems involving functions and/or calculus. (Capability 3, 4 and 5)
- Apply the mathematical techniques covered to solve real life problems. (Capability 3, 4 and 5)
- Communicate mathematics, both verbally and in writing. (Capability 3 and 6)
- Engage in group discussions and critical interactions. (Capability 3, 6 and 7)
Assessments
| Assessment Type | Percentage | Classification |
|---|---|---|
| Assignments | 25% | Individual Coursework |
| Tutorials | 5% | Individual Coursework |
| Mid-semester assessment | 20% | Individual Test |
| Final Exam | 50% | Individual Examination |
| 4 types | 100% |
| Assessment Type | Learning Outcome Addressed | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||||||
| Assignments | ||||||||||
| Tutorials | ||||||||||
| Mid-semester assessment | ||||||||||
| Final Exam | ||||||||||
As well as requiring an overall mark of at least 50%, a mark of at least 35% in the exam is required to pass the course.
Key Topics
- Operations with sets: union, intersection and exclusion.
- Functions: their definition, domains, codomains, range, and compositions. Various types of functions will be examined, limit of a function and computational techniques will be introduced.
- Continuity with be introduced and techniques to determine continuity discussed.
- Vectors: operations with vectors, vector equations of lines, and planes, the computation of intersections, orthogonality and parallelism, and angle between 2 vectors. The cross product of two vectors will be introduced and developed.
- Introduction to matrix arithmetic. Linear algebra: using matrices to analyse systems of linear equations. Elementary row operations will be used as a tool for producing equivalent matrices, inverse matrices, and determinants. Determinants, invertibility and their link will be explored.
- Differential calculus of one and two variables: Differentiation as a limit, differentiation rules, tests using the first and second derivatives, relative extrema, concavity and points of inflection, graphing.
- Integral calculus of one variable: Indefinite integral, the antiderivative, rules of integration including the u-substitution and integration by parts, definite integration.
- Differential calculus of two variables: Defining a function of 2 variables, level curves, the partial derivative, tangent planes to a surface.
Special Requirements
The mid-semester test will run in the evening outside of normal hours. This is usually in the fifth week of semester and from 6:25 - 7:30pm.
Tuākana
Workload Expectations
This course is a standard 15-point course and students are expected to spend 10 hours per week involved in each 15-point course that they are enrolled in. For each week of this course, you can expect 3 hours of lectures, a 1-hour tutorial, 3 hours of reading and thinking about the content and 3 hours of work on assignments and/or test preparation.
Delivery Mode
Campus Experience
Attendance is required at scheduled activities including tutorials to receive credit for components of the course.
Lectures will be available as recordings. Other learning activities including tutorials will not be available as recordings.
The course will not include live online events.
Attendance on campus is required for the test/exam.
The activities for the course are scheduled as a standard weekly timetable.
Learning Resources
Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).
Please remember that the recording of any class on a personal device requires the permission of the instructor.
- MATHS 108 Coursebook
- Poole, D. (2015). Linear Algebra, A Modern Introduction 4th Edition. CENGAGE Learning, Nelson Education Ltd, Canada. This is an optional text
- Stewart, J. (2012). Calculus Early Transcendentals, Seventh Edition, International Metric Version. Brooks/Cole CENGAGE Learning, Nelson Education Ltd, Canada. This is an optional text
Student Feedback
During the course Class Representatives in each class can take feedback to the staff responsible for the course and staff-student consultative committees.
At the end of the course students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback.
Your feedback helps to improve the course and its delivery for all students.
No major changes are likely for next year but slight tweaks are always made thanks to feedback from students.
Academic Integrity
The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework, tests and examinations as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. A student's assessed work may be reviewed against electronic source material using computerised detection mechanisms. Upon reasonable request, students may be required to provide an electronic version of their work for computerised review.
Class Representatives
Class representatives are students tasked with representing student issues to departments, faculties, and the wider university. If you have a complaint about this course, please contact your class rep who will know how to raise it in the right channels. See your departmental noticeboard for contact details for your class reps.
Copyright
The content and delivery of content in this course are protected by copyright. Material belonging to others may have been used in this course and copied by and solely for the educational purposes of the University under license.
You may copy the course content for the purposes of private study or research, but you may not upload onto any third party site, make a further copy or sell, alter or further reproduce or distribute any part of the course content to another person.
Inclusive Learning
All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.
Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website http://disability.auckland.ac.nz
Special Circumstances
If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.
If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page https://www.auckland.ac.nz/en/students/academic-information/exams-and-final-results/during-exams/aegrotat-and-compassionate-consideration.html.
This should be done as soon as possible and no later than seven days after the affected test or exam date.
Learning Continuity
In the event of an unexpected disruption we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and your assessment is fair, and not compromised. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator, and if disruption occurs you should refer to the University Website for information about how to proceed.
The delivery mode may change depending on COVID restrictions. Any changes will be communicated through Canvas.
Student Charter and Responsibilities
The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter https://www.auckland.ac.nz/en/students/forms-policies-and-guidelines/student-policies-and-guidelines/student-charter.html.
Disclaimer
Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.
In this course you may be asked to submit your coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. The final decision on the completion mode for a test or examination, and remote invigilation arrangements where applicable, will be advised to students at least 10 days prior to the scheduled date of the assessment, or in the case of an examination when the examination timetable is published.