TFCMATHS 92F : Foundation Mathematics 2


2024 Semester Two (1245) (15 POINTS)

Course Prescription

This mathematics course aims to use the skills learnt in TFCMATHS 91F to develop an understanding of functions in their tabular, algebraic and graphical representations. Prepares students for MATHS 102. Recommended preparation: TFCMATHS 91F or TFCMATHS 93F.

Course Overview

This second-semester course follows on from TFC Maths 91F. The course continues to focus on the development and understanding of higher mathematical skills and concepts. The aim is to provide a preparation for future study in Mathematics. In particular we aim to set a mathematical platform that includes:
  • Know accepted conventions of mathematical representations, including functional notation;
  • Experience graph sketching particularly of linear, quadratic, exponential and trigonometric functions, and software such as Desmos;
  • Ideas from certain early parts of discrete maths, such as probability, matrices, and combinatorics;
  • Continue to develop algebraic manipulative skills of factorizing , 
  • Understanding of fundamental angle geometry and trigonometry;
  • Explore sequence  behaviours, particularly arithmetic and geometric patterns;
  • Solve contextual problems by using the above themes.
On successful completion of this course (at least a C+ grade) students may apply to enter MATHS 102.

Course Requirements

Restriction: MATHS 92F

Capabilities Developed in this Course

Capability 1: People and Place
Capability 3: Knowledge and Practice
Capability 4: Critical Thinking
Capability 5: Solution Seeking
Capability 6: Communication
Capability 7: Collaboration
Capability 8: Ethics and Professionalism

Learning Outcomes

By the end of this course, students will be able to:
  1. Contribute to group collaborative tasks, to help provide a group solution to the activities. (Capability 1, 3, 4, 5, 6 and 7)
  2. Recognize and use various forms of function notation, write down and graph the inverses of functions and identify the domains and ranges of functions. (Capability 3, 5 and 6)
  3. Identify / model linear, quadratic, exponential, circle and trigonometric relationships with appropriate mathematical functions in mathematical and real world contexts, and then be able to interpret the various forms of these functions, and provide examples of applications. (Capability 3, 4, 5 and 6)
  4. Recognize a pattern and suggest appropriate formulae to describe it, then extend this to other situations. (Capability 3, 4, 5 and 6)
  5. Confidently estimate solutions to problems, and to reflect on what is a reasonable answer in the context. (Capability 3, 4, 5 and 6)
  6. Use relevant strategies and suitable technology to solve early discrete mathematics problems (e.g. matrices, introductory combinatorics). (Capability 3, 4, 5, 6 and 7)
  7. Be able to express mathematics in written form to communicate mathematical ideas and solutions to problems and contexts. (Capability 1, 3, 4, 5, 6 and 7)
  8. Be able to reflect critically on their own and on others' learning. (Capability 1, 3, 4, 5, 6 and 7)
  9. Be prepared to enter MATHS 102 in the following year. Note - Summer School is only suggested for well-prepared students, as is MATHS 108. (Capability 1, 3, 6 and 8)


Assessment Type Percentage Classification
Assignments 12% Individual Coursework
Group Work Collaborations 8% Group Coursework
Quizzes 10% Individual Coursework
Chapter Tests (2) and Mid Semester Test 30% Individual Coursework
Final Exam 40% Individual Coursework
Assessment Type Learning Outcome Addressed
1 2 3 4 5 6 7 8 9
Group Work Collaborations
Chapter Tests (2) and Mid Semester Test
Final Exam
Students must achieve a minimum mark of at least 35% on the final test in order to pass the course. 


Tuākana Science is a multi-faceted programme for Māori and Pacific students providing topic specific tutorials, one-on-one sessions, test and exam preparation and more. Explore your options at

Whanaungatanga and manaakitanga are fundamental principles of our Tuākana Mathematics programme which provides support for Māori and Pasifika students who are taking mathematics courses. The Tuākana Maths programme consists of workshops and drop-in times, and provides a space where Māori and Pasifika students are able to work alongside our Tuākana tutors and other Māori and Pasifika students who are studying mathematics.

Key Topics

  1. Geometry/Trigonometry , including angles on parallel lines, right-angled trigonometry, cosine and area rules, and straightforward graphs of trigonometric functions;
  2. Linear Relations, including gradients, distances, parallel and perpendicular forms, points of intersection, and early Graph Theory; 
  3. Introduce Discrete Mathematics, through Probability ideas, Combinatorics, and Matrices (incl. inverses of 2x2 matrices and their uses in equations);
  4. Functions, with notation, domain and range, inverses, and quadratic, exponential and trigonometric functions, and their graphs;
  5. Sequences, through Arithmetic and Geometric Progressions, and introducing Sigma notation, and Surds.

Special Requirements

  • Expect full attendance and participation in lectures.
  • Each aspect of course work is compulsory.
  • The Mid-Semester Test will run either in an evening outside of normal hours, or on two consecutive days, in class sessions. This is usually held in the sixth week of semester, according to availability of venues. Any updates will be shown in the schedule provided in Week One.

Workload Expectations

This course is a standard 15-point course. Students are expected to spend from 10 to 12 hours per week involved in each 15-point course that they are enrolled in. For each week of this course, you can expect 4 hours of lectures, a 1-hour tutorial and 5 hours of reading and working on homework exercises, assignments, and weekly e-quizzes; in some weeks, preparation for tests and the Final Examination should also be expected.

Delivery Mode

Campus Experience

  • Tertiary Foundation Certificate students are expected to attend and participate on Campus and are therefore not remote students. Attendance is required at scheduled activities, including classes and tutorials (such as, Group Work Collaborative tasks which 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 including tutorials.
  • Attendance on campus is required for the tests and the Group Work Collaborations.                                                                      
  • The Quizzes may be submitted electronically on Canvas - the best eight out of ten will count toward the final mark.
  • The activities for the course are scheduled as a standard weekly timetable delivery.

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.

  • Course books (usually Part A and Part B) distributed in Weeks One and Six respectively;
  • Standard scientific calculator (available in UBS);
  • Ruler for measuring and graphing;
  • Squared paper for graphing;

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.

The Part B course book was released earlier this Semester in both write-on hard copy form and on Canvas as an online resource.

Using the document camera meant that what we write can be recorded, except for addressing another person's queries if they are elsewhere in the room. So being in classes is still the most valuable kind of learning since it is responsive and flexible.

There is more in 92F than in 91F, and the pace sometimes catches people out. Most of the material is new (e.g. Trig, Functions, Matrices, Combinatorics, Sequence types), however, everything is usually covered by the start of Week 12. There is a domino effect if you miss a step or a session along the way. 

 It is essential you ask us if something does not make sense to you - we can often reword it so that you have a better grasp of it. Also, if you need to revise/check your understanding along the way, go to the rear of each chapter where there is usually a Skill Check with answers.

 A few more exercises on combinatorics have been included. But do read the notes before the exercises since the worked examples try to assist your thinking here.  

Students who started in Semester Two were a bit behind, so the first Friday session in the semester was designed to catch you up with some of the previous semester's concepts. Covering ideas such as factorizing quadratics, solving equations, and logarithms was useful preparation, but you also needed to practise these, so a resource for you will be created before we run this course again.

Academic Integrity

The 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 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. This requirement also applies to sources on the internet. A student's assessed work may be reviewed for potential plagiarism or other forms of academic misconduct, using computerised detection mechanisms.

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.

TFC administrators try to organize this early in the semester.


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

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

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 course assessment continues to meet the principles of the University’s assessment policy. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator/director, 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


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 students may be asked to submit 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. In exceptional circumstances changes to elements of this course may be necessary at short notice. Students enrolled in this course will be informed of any such changes and the reasons for them, as soon as possible, through Canvas.

Published on 31/10/2023 10:54 a.m.