Calculus & Linear Algebra I (MATH1051)

Course overview

Vectors, linear independence, scalar product. Matrices, simultaneous equations, determinants, vector product, eigenvalues, eigenvectors, applications. Equation of straight line and plane. Extreme value theorem, maxima and; minima. Sequences, series, Taylor series, L'Hopital's rules. Techniques of integration, numerical methods, volumes of revolution.

MATH1051 provides an important foundation in calculus and linear algebra that will prove useful for further studies in pure and applied sciences, engineering, finance or further mathematics pursuits.

The calculus component extends high school concepts. We investigate optimisation techniques, limits and L'Hopital's rule, as well as standard techniques of integration and volumes of revolution. Another important topic is the study of sequences and series (infinite sums). This extends to Taylor series which are an important tool used throughout the sciences. Numerical integration techniques will be developed.

Linear algebra is the study of vectors and matrices and is extensively used to model systems of interacting elements. For example, matrix methods are common in structural engineering and matrix algebra is necessary for computer graphics. This course covers vectors, linear independence and scalar product which are tools to manipulate vectors. The course continues with matrices, simultaneous equations and determinants. An important component of the study concerns eigenvalues and eigenvectors which model resonant frequencies in dynamical systems.

Any questions relating to administrative matters should be sent to ﾠmath1051@uq.edu.au

In the School of Mathematics and Physics we are committed to creating an inclusive and empowering learning environment for all students. We value and respect the diverse range of experiences our students bring to their education, and we believe that this diversity is essential for fostering a rich culture of knowledge sharing and meaningful exploration. We hold both students and staff accountable for actively contributing to the establishment of a respectful and supportive learning environment.

Bullying, harassment, and discrimination in any form are strictly against our principles and againstﾠUQ Policy, and will not be tolerated. We have developed a suite of resourcesﾠ to assist you in recognising, reporting, and addressing such behaviour. If you have any concerns about your experience in this course, we encourage you to tell a member of the course teaching team, or alternatively contact an SMP Classroom Inclusivity Champion (see Blackboard for contact details). Our Inclusivity Champions are here to listen, to understand your concerns, and to explore potential actions that can be taken to resolve them. Your well-being and a positive learning atmosphere are of utmost importance to us.

Course requirements

Assumed background

Students should have at least a Grade C in Queensland Specialist Mathematics (formerly Mathematics C) , passed MATH1050, or have an equivalent qualification. 

It is possible to take MATH1051 and MATH1052 in the same semester. In this case, you should have achieved a grade B or higher in Queensland Year 12 Specialist Mathematics (or equivalent) or obtained a credit or better in MATH1050. Note that MATH1052 assumes knowledge of MATH1051. 

Students should be familiar with the following.

• Algebra: Factoring polynomials, expansion and simplification of algebraic expressions, functions, trigonometric functions and identities, logarithms and the exponential function
• Calculus: Limits, continuity, the derivative, finding simple maxima and minima, integrals. (These topics will be quickly reviewed)
• Vectors: Complex numbers, vectors in 2D & 3D space, addition of vectors, angles between vectors, 2x2 matrices and their inverses. (These topics will be quickly reviewed)

Students who have trouble because of gaps in their background should work through the review material from the course Blackboard site and discuss their difficulties in the First-Year Learning Centre. In particular, students with Grade C in Queensland Specialist Mathematics (formerly Mathematics C) or a grade 4 in MATH1050, or who are repeating the course are encouraged to contact the course coordinator to register for a support learning programme.

Prerequisites

You'll need to complete the following courses before enrolling in this one:

MATH1050 or a grade of C or higher in Queensland Year 12 Specialist Mathematics (Units 3 and 4) (or equivalent).

Incompatible

You can't enrol in this course if you've already completed the following:

MATH1071, MATH7051 (co-taught).

Restrictions

Semester 1 external offering restricted to students enrolled in Enhanced Studies Program (program code 1014).

Jointly taught details

This course is jointly-taught with:

• Another instance of the same course

MATH1051 In-person mode

Course contact

Course staff

Timetable

The timetable for this course is available on the UQ Public Timetable.

Additional timetable information

Students are required to ensure that they are properly enrolled in and actively participate in the following teaching components:

• Three lectures per week, each of two hours’ duration.

  Students may follow lectures in any of the following ways:

• face-to-face lectures or online via Zoom (preferred!)
• pre-recordings on UQ Extend, 
• lecture recordings (usually available soon after the lecture)

• Two applied classes (APP) per week, each of two hours’ duration.
• Internal students are expected to attend the on-campus applied classes.
• External students will participate in the applied classes online via Zoom.

Lectures and applied classes will begin in Week 1.

The Support Learning Tutorial (SLT) is optional. This class is highly recommended for: 

• Students who are repeating MATH1051.
• Students who obtained a Grade 4 in MATH1050.
• Students who obtained a grade C  for Queensland Specialist Mathematics (or equivalent).
• Students who are returning to maths studies after a significant period.
• Check Blackboard for further information about the SLT. 

There are no classes scheduled on Public Holidays. Alternate arrangements will be communicated via Blackboard

Aims and outcomes

The aim of this course is to provide students with an introduction to and a solid basis for further study in mathematics, in particular mathematical analysis. Students will be introduced to a number of new mathematical concepts, and will be presented with theory and practical examples. The course also aims to help students develop an appropriate level of mathematical rigour needed in presenting mathematical arguments and solutions.

Learning outcomes

After successfully completing this course you should be able to:

Assessment

Assessment summary

A hurdle is an assessment requirement that must be satisfied in order to receive a specific grade for the course. Check the assessment details for more information about hurdle requirements.

Assessment details

Applied Class Exercise

• Identity Verified
• Team or group-based

Mode

Written

Category

Participation/ Student contribution, Quiz

Weight

10%

Due date

-Week 1: 3/12/2025

-Week 2: both submissions are due 15/12/2025

-Week 3: 22/12/2025

-Week 4: 5/01/2026

-Week 5: both submissions are due 12/01/2026

-Week 6: 19/01/2026

-Week 7: both submissions are due 27/01/2026

Other conditions

Time limited.

See the conditions definitions

Task description

Submission guidelines

You will submit the quiz through blackboard.

Deferral or extension

You cannot defer or apply for an extension for this assessment.

If you are absent from an Applied Class due to medical reasons, you may apply for an exemption from that Applied Class Exercise. If your application is approved, your overall mark will be reweighted based on the Applied Classes you attend. For example, if you are granted an exemption from one Applied Class, your overall mark will be calculated from your best 7 out of 9 marks.

There are NO extensions for the Applied Class Exercise. If you are unable to attend your Applied Class, you must email math1051@uq.edu.au within 5 calendar days of your Applied class and provide appropriate supporting evidence (e.g., medical certificate).

Please note that you must attend at least one Applied Class to be eligible to receive marks for this assessment item.

Competency Tests

• Hurdle
• Identity Verified

Mode

Written

Category

Examination

Weight

30% split evenly across two competency tests

Due date

17/12/2025

14/01/2026

The applied classes on Wednesday run from 2:00 p.m. to 4:00 p.m.

The competency test will start at 2:45 pm

Other conditions

Time limited, Secure.

See the conditions definitions

Task description

Hurdle requirements

Exam details

Submission guidelines

Deferral or extension

You cannot defer or apply for an extension for this assessment.

You cannot defer or apply for an extension for this assessment.

If there are extenuating circumstances for why you have missed Competency Test 1 or 2, please email math1051@uq.edu.au. You will need to do this within 5 calendar days of the test and include evidence (e.g., medical certificate). You must attend at least one competency test in order to receive marks for this assessment item.  

Assignment

Mode

Written

Category

Tutorial/ Problem Set

Weight

15%

Due date

16/01/2026 2:00 pm

Task description

Submission guidelines

The assignment will be submitted electronically.

Deferral or extension

You may be able to apply for an extension.

The maximum extension allowed is 7 days. Extensions are given in multiples of 24 hours.

Solutions for assessment item/s will be released 7 days after the assessment is due and as such, an extension after 7 days will not be possible.

 See ADDITIONAL ASSESSMENT INFORMATION for the extension and deferred examination information relating to this assessment item.

Late submission

A penalty of 10% of the maximum possible mark will be deducted per 24 hours from time submission is due for up to 7 days. After 7 days, you will receive a mark of 0.

End of Semester Exam

• Hurdle
• Identity Verified
• In-person

Mode

Written

Category

Examination

Weight

45%

Due date

End of Semester Exam Period

7/02/2026 - 14/02/2026

Other conditions

Time limited, Secure.

See the conditions definitions

Task description

Hurdle requirements

Exam details

Submission guidelines

Deferral or extension

You may be able to defer this exam.

See ADDITIONAL ASSESSMENT INFORMATION for the extension and deferred examination information relating to this assessment item.

Course grading

Full criteria for each grade is available in the Assessment Procedure.

Additional course grading information

HURDLE REQUIREMENTS

If you do not either:ﾠ

ﾠ ﾠ ﾠ (i)ﾠ pass both competency testsﾠand Section A of the end-of-semester exam; OR

ﾠ ﾠ ﾠ (ii)ﾠ receive at least 40% of the available marksﾠfor Calculusﾠin Section B of the end-of-semester exam, AND 40% of the marks for Linear Algebra in Section B of the end-of-semester exam.

Then the maximum grade you can obtain is 3.

COMPETENCY TESTS 

Each competency test is Pass/Fail. There will be 20 questions. All questions carry equal marks. The Pass threshold is 80%.

SECTION A OF THE END-OF-SEMESTER EXAM

Part A of the exam is Pass/Fail. A student who passes Part A earns all 20 marks. A student who fails

Part A earns 0 marks.

The Pass threshold is 65%.

Supplementary assessment

Supplementary assessment is available for this course.

Should you fail a course with a grade of 3, you may be eligible for supplementary assessment. Refer to my.UQ for information on supplementary assessment and how to apply. 

Supplementary assessment provides an additional opportunity to demonstrate you have achieved all the required learning outcomes for a course.  

If you apply and are granted supplementary assessment, the type of supplementary assessment set will consider which learning outcome(s) have not been met.  

Supplementary assessment in this course will be a 2-hour examination similar in style to the end-of-semester examination. To receive a passing grade of 3S4, you must obtain a mark of 50% or more on the supplementary assessment. 

Additional assessment information

Artificial Intelligence

To pass this course, students will be required to demonstrate a detailed understanding of course material together with a range of associated skills independent of Artificial Intelligence (AI) and Machine Translation (MT) tools.

For assessment tasks that are completed in-person (including examinations) termed “secure assessment”, the use of generative Artificial Intelligence (AI) or Machine Translation (MT) tools will not be permitted unless otherwise advised. Any attempted use of AI or MT may constitute student misconduct under the Student Code of Conduct.

 Other non-secure assessment tasks (such as assignments) are designed to help you develop your understanding and skills, and to prepare you for secure assessment. You are thus generally encouraged to complete such assessment without the use of AI/MT, unless explicitly advised to the contrary in the assessment item. In any event, if you choose to use such tools, then you must clearly reference any such use within your submitted work. A failure to reference AI or MT use may constitute student misconduct under the Student Code of Conduct.

Applications for Extensions to Assessment Due Dates

Extension requests are submitted online via my.UQ – applying for an extension. Extension requests received in any other way will not be approved. Additional details associated with extension requests, including acceptable and unacceptable reasons, may be found at my.UQ.

Please note:

• Requests for an extension to an assessment due date must be submitted through your my.UQ portal and you must provide documentation of your circumstances, as soon as it becomes evident that an extension is needed. Your application must be submitted on or before the assessment item's due date and time.
• Applications for extension can take time to be processed so you should continue to work on your assessment item while awaiting a decision. We recommend that you submit any completed work by the due date, and this will be marked if your application is not approved. Should your application be approved, then you will be able to resubmit by the agreed revised due date.
• If an extension is approved, you will be notified via your my.UQ portal and the new date and time for submission provided. It is important that you check the revised date as it may differ from the date that you requested.
• If the basis of the application is a medical condition, applications should be accompanied by a medical certificate dated prior to the assignment due date. If you are unable to provide documentation to support your application by the due date and time you must still submit your application on time and attach a written statement (Word document) outlining why you cannot provide the documentation. You must then upload the documentation to the portal within 24 hours.
• If an extension is being sought on the basis of exceptional circumstances, it must be accompanied by supporting documentation (eg. Statutory declaration).
• For extensions based on a SAP you may be granted a maximum of 7 days (if no earlier maximum date applies). See the Extension or Deferral availability section of each assessment for details. Your SAP is all that is required as documentation to support your application. However, additional extension requests for the assessment item will require the submission of additional supporting documentation e.g., a medical certificate. All extension requests must be received by the assessment due date and time.
• Students may be asked to submit evidence of work completed to date. Lack of adequate progress on your assessment item may result in an extension being denied.
• If you have been ill or unable to attend class for more than 14 days, you are advised to carefully consider whether you are capable of successfully completing your courses this semester. You might be eligible to withdraw without academic penalty - seek advice from the Faculty that administers your program.
• There are no provisions for exemption from an assessment item within UQ rules. If you are unable to submit an assessment piece then, under special circumstances, you may be granted an exemption, but may be required to submit alternative assessment to ensure all learning outcomes are met.

Applications to defer an exam

In certain circumstances you can apply to take a deferred examination for in-semester and end-of-semester exams. You'll need to demonstrate through supporting documentation how unavoidable circumstances prevented you from sitting your exam. If you can’t, you can apply for a one-off discretionary deferred exam.

Deferred Exam requests are submitted online via mySi-net. Requests received in any other way will not be approved. Additional details associated with deferred examinations, including acceptable and unacceptable reasons may be found at my.UQ.

Please note:

• Applications can be submitted no later than 5 calendar days after the date of the original exam.
• There are no provisions to defer a deferred exam. You need to be available to sit your deferred examination.
• Your deferred examination request(s) must have a status of "submitted" in mySI-net to be assessed.
• All applications for deferred in-semester examinations are assessed by the relevant school. Applications for deferred end-of-semester examinations are assessed by the Academic Services Division.
• You’ll receive an email to your student email account when the status of your application is updated.
• If you have a medical condition, mental health condition or disability and require alternative arrangements for your deferred exam you’ll need to complete the online alternative exam arrangements through my.UQ. This is in addition to your deferred examinations request. You need to submit this request on the same day as your request for a deferred exam or supplementary assessment. Contact Student Services if you need assistance completing your alternative exam arrangements request.

Noteﾠ the requirements to achieve a passing grade (4,5,6 or 7) in the course. In summary,

(1)ﾠIf you do not receive a total score for the course of at least 50%, then you will fail MATH1051.

(2) If you do not either:ﾠ

ﾠ ﾠ ﾠ (i)ﾠ Pass both competency tests and Section A of the final exam; OR

ﾠ ﾠ ﾠ (ii)ﾠ Receive at least 40% of the available marksﾠfor Calculusﾠin Section B of the final examﾠ AND ﾠ40% of the marks for Linear Algebra in Section B of the final exam,

then you will fail MATH1051.

Learning resources

You'll need the following resources to successfully complete the course. We've indicated below if you need a personal copy of the reading materials or your own item.

Library resources

Library resources are available on the UQ Library website.

Additional learning resources information

As well as the textbooks and workbook, students will have:

• Problem sheets
• Assignment
• Applied class exercises
• Online Quizzes
• Practice problems for the final exam.
• Past Exam papers with worked solutions.

Completion of these itemsﾠwill have a direct benefit to your learning.

Additional learning material will be posted on Blackboard. It is, therefore, very important that students regularly check Blackboard.

The MATHS FIRST YEAR LEARNING CENTRE at St Lucia holds support tutorials on Tuesdays and Wednesdaysﾠfrom 2-4 p.m, beginning the firstﾠweek of the semester. The support sessions will be both online (via Zoom) and face-to-face. Appointments are not necessary for the Maths Learning Centre. Simply turn up with your questions.

The MATH1051 SUPPORT LEARNING TUTORIAL PROGRAM (SLT) is a regularﾠsupport programﾠaimed at students with gaps in their background skills.

This class is highly recommended for the following group of students:

• Students who are repeating MATH1051.
• Students who obtained a Grade 4 in MATH1050.
• Students with a grade C or lower in Queensland Specialist Maths (or equivalent).
• Students who are returning to math studies after a significant period

Please refer to the course Blackboard page for the schedule of these SLT sessions.

Learning activities

The learning activities for this course are outlined below. Learn more about the learning outcomes that apply to this course.

Policies and procedures

University policies and procedures apply to all aspects of student life. As a UQ student, you must comply with University-wide and program-specific requirements, including the:

• Student Code of Conduct Policy
• Student Integrity and Misconduct Policy and Procedure
• Assessment Procedure
• Examinations Procedure
• Reasonable Adjustments for Students Policy and Procedure
• AI for Assessment Guide

Learn more about UQ policies on my.UQ and the Policy and Procedure Library.