Skip to main content
Unit outline_

MATH1111: Introduction to Calculus

Semester 1, 2023 [Normal day] - Camperdown/Darlington, Sydney

This unit is an introduction to the calculus of one variable. Topics covered include elementary functions, differentiation, basic integration techniques and coordinate geometry in three dimensions. Applications in science and engineering are emphasised.

Unit details and rules

Academic unit Mathematics and Statistics Academic Operations
Credit points 6
MATH1011 or MATH1901 or MATH1906 or MATH1001 or HSC Mathematics Extension 1 or HSC Mathematics Extension 2 or ENVX1001 or MATH1021 or MATH1921 or MATH1931
Assumed knowledge

Knowledge of algebra and trigonometry equivalent to NSW Year 10

Available to study abroad and exchange students


Teaching staff

Coordinator Ayesha Sohail,
Lecturer(s) Ayesha Sohail,
Type Description Weight Due Length
Supervised exam
Final exam
Exam testing techniques and reasoning skills
50% Formal exam period 2 hours
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9
Small test Online homework 1
See Canvas
4% Week 04
Due date: 17 Mar 2023 at 23:59

Closing date: 27 Mar 2023
Outcomes assessed: LO1 LO4 LO3 LO2
Small test Online homework 2
See Canvas
4% Week 06
Due date: 31 Mar 2023 at 23:59

Closing date: 11 Apr 2023
Outcomes assessed: LO1 LO6 LO5 LO4 LO3 LO2
Assignment Assignment 1
Calculations and explanations
10% Week 07
Due date: 05 Apr 2023 at 23:59

Closing date: 17 Apr 2023
6-8 pages (as a guide)
Outcomes assessed: LO1 LO2 LO3 LO4 LO5
Small test Online homework 3
See Canvas
4% Week 08
Due date: 21 Apr 2023 at 23:59

Closing date: 02 May 2023
Outcomes assessed: LO1 LO7 LO6
Small test Online homework 4
See Canvas
4% Week 10
Due date: 05 May 2023 at 23:59

Closing date: 15 May 2023
Outcomes assessed: LO1 LO7 LO6
Assignment Assignment 2
Calculations and explanations
10% Week 11
Due date: 10 May 2023 at 23:59

Closing date: 20 May 2023
6-8 pages (as a guide)
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7
Small test Online homework 5
See Canvas
4% Week 12
Due date: 19 May 2023 at 23:59

Closing date: 29 May 2023
Outcomes assessed: LO1 LO9 LO8 LO7
Assignment Assignment 3
Calculations and explanations
10% Week 13
Due date: 24 May 2023 at 23:59

Closing date: 03 Jun 2023
6-8 pages (as a guide)
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9

Assessment summary

Below are brief assessment details. Further information can be found in the Canvas site for this unit.

  • Assignments: There are three assignments, which must be submitted electronically, as PDF files only via Canvas, by the deadline. Note that your assignment will not be marked if it is illegible or if it is submitted sideways or upside down. It is your responsibility to check that your assignment has been submitted correctly. A mark of zero will be awarded for all submissions more than 10 days past the original due date. Further extensions past this time will not be permitted.
  • Online homework: A series of online homework exercises have been set using the online MOOC Introduction to Calculus available from Coursera. These exercises are self-paced and allow multiple attempts, so that a diligent student may be able to progressively master all of them.

  • Final Exam: The final exam for this unit is compulsory and must be attempted. Failure to attempt the final exam will result in an AF grade for the course. Further details will be published on Canvas at a further date. If a second replacement exam is required, this exam may be delivered via an alternative assessment method, such as a viva voce (oral exam). The alternative assessment will meet the same learning outcomes as the original exam. The format of the alternative assessment will be determined by the unit coordinator.

Assessment criteria

Result name Mark range Description
High distinction  85 -100 Representing complete or close to complete mastery of the material.
Distinction 75 – 84 Representing excellence, but substantially less than complete mastery.
Credit 65 – 74 Representing a creditable performance that goes beyond routine knowledge and understanding, but less than
Pass 50 – 64 Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and
concepts in the course.
Fail 0 – 49 When you don’t meet the learning outcomes of the unit to a satisfactory standard.


For more information see guide to grades.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

  • Deduction of 5% of the maximum mark for each calendar day after the due date.
  • After ten calendar days late, a mark of zero will be awarded.

Academic integrity

The Current Student website  provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.  

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

WK Topic Learning activity Learning outcomes
Week 01 Number systems, equations, and the Theorem of Pythagoras. The real number line, inequalities and intervals. Lecture (3 hr) LO1 LO2
Week 02 Coordinate geometry in the real plane, lines, and curves. Quadratics and polynomials. Lecture and tutorial (5 hr) LO1 LO2 LO3
Week 03 Functions, their graphs, and operations on functions. Inverse functions and review of trigonometry. Lecture and tutorial (5 hr) LO1 LO3 LO4 LO5
Week 04 Exponential functions, logarithms, exponential growth and decay. Introduction to hy- perbolic functions.* Lecture and tutorial (5 hr) LO1 LO3 LO4 LO5
Week 05 Introduction to coordinate geometry in space. Spheres and paraboloids.* Planes, sur- faces, level curves, peaks, troughs and saddles.* Lecture and tutorial (5 hr) LO1 LO3 LO4 LO5
Week 06 Limits, tangent lines, speed, and acceleration. Derivatives and simple properties. Lecture and tutorial (5 hr) LO6
Week 07 Leibniz notation and common derivatives. Differentials and applications. Lecture and tutorial (5 hr) LO6 LO7
Week 08 Product, Quotient and Chain Rules. Lecture and tutorial (5 hr) LO6 LO7
Week 09 Applications of 1st and 2nd derivatives. Optimisation. Limits, asymptotes and curve sketching. Lecture and tutorial (5 hr) LO1 LO6 LO7
Week 10 Areas under curves. Relationship between velocity and distance. Definite integrals and simple properties. Lecture and tutorial (5 hr) LO1 LO7 LO8
Week 11 Antidifferentiation and the Fundamental Theorem of Calculus. Indefinite integrals. Lecture and tutorial (5 hr) LO1 LO7 LO8
Week 12 Antidifferentiation and the Fundamental Theorem of Calculus. Indefinite integrals. Lecture and tutorial (5 hr) LO1 LO7 LO8
Week 13 Introduction to improper integrals.* Introduction to calculus of curves and surfaces in space.* Revision. Lecture and tutorial (5 hr) LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9

Attendance and class requirements

  • Lecture attendance: You are expected to attend lectures. If you do not attend lectures you should at least follow the lecture recordings available through Canvas.

  • Tutorial attendance: Tutorials (two per week) start in Week 2. You should attend the tutorial given on your personal timetable. Attendance at tutorials will be recorded. Your attendance will not be recorded unless you attend the tutorial in which you are enrolled. While there is no penalty if 80% attendance is not met we strongly recommend you attend tutorials regularly to keep up with the material and to engage with the tutorial questions. Since there is no assessment associated with the tutorials do not submit an application for Special Consideration or Special Arrangements for missed tutorials.


Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

At the completion of this unit, you should be able to:

  • LO1. Apply mathematical logic and rigour to solving problems, and express mathematical ideas coherently in written and oral form;
  • LO2. Demonstrate fluency in manipulating real numbers, their symbolic representations, operations, and solve associated algebraic equations and inequalities;
  • LO3. Develop fluency with lines, coordinate geometry in two dimensions, the notion of a function, its natural domain, range and graph;
  • LO4. Become conversant with elementary functions, including trigonometric, exponential, logarithmic and hyperbolic functions and be able to apply them to real phenomena and to yield solutions of associated equations;
  • LO5. Perform operations on functions and be able to invert functions where appropriate;
  • LO6. Understand the definitions of a derivative, definite and indefinite integral and be able to apply the definitions to elementary functions;
  • LO7. Develop fluency in rules of differentiation, such as the product, quotient and chain rules, and use them to differentiate complicated functions;
  • LO8. Understand and apply the Fundamental Theorem of Calculus; and develop fluency in techniques of integration, such as integration by substitution, the method of partial fractions and integration by parts;
  • LO9. Develop some fluency with coordinate geometry in three dimensions, planes, surfaces, ellipsoids, paraboloids, level curves and qualitative features such as peaks, troughs and saddle points.

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1 Depth of disciplinary expertise

Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.

GQ2 Critical thinking and problem solving

Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.

GQ3 Oral and written communication

Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.

GQ4 Information and digital literacy

Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.

GQ5 Inventiveness

Generating novel ideas and solutions.

GQ6 Cultural competence

Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.

GQ7 Interdisciplinary effectiveness

Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.

GQ8 Integrated professional, ethical, and personal identity

An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.

GQ9 Influence

Engaging others in a process, idea or vision.

Outcome map

Learning outcomes Graduate qualities

This section outlines changes made to this unit following staff and student reviews.

No changes have been made since this unit was last offered.
  • Lectures: Lectures are face-to-face and streamed live with online access from Canvas.
  • Tutorials: You should attend two tutorials per week, starting in Week 2, as shown on your personal timetable. One tutorial will be on Monday or Tuesday, and the second tutorial will be on Wednesday or Thursday. 
  • Tutorial sheets: The tutorial exercise sheets will be available from the MATH1111 webpage. Solutions to tutorial exercises for any given week will normally be posted later that week or early the following week.
  • Ed Discussion forum:


The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

To help you understand common terms that we use at the University, we offer an online glossary.