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).ﾠ This extends to Taylor series which are an important tool used throughout the sciences.ﾠﾠ

Linear algebra is the study of vectors and matrices and is extensively used to modelﾠsystems 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 (adding the course, dropping the course, assignment extensions, special accommodations, etc) should be sent to math1051@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 crucial 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,ﾠand will not be tolerated. We have developed aﾠsuite of resourcesﾠto 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), MATH7501

Restrictions

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

Course contact

Course staff

Timetable

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

Additional timetable information

All classes will be conducted on campus for students enrolled in in-person mode and online for students enrolled in external mode. Consult your personal timetable for times and locations. Relevant Zoom links for external students will be provided on Blackboard. Students are expected to attend these sessions in person (in-person) or online (external) unless they have a valid reason for being unable to attend (such as illness). Alternative arrangements will be advised on Blackboard should the campus be closed for any reason.

You may follow lectures in any of the following ways:

• pre-recordings on UQ Extend,ﾠ
• lecture recordings (usually available a few hours after the lecture)

During public holidays there will be no applied classes or lectures. Student's whose applied class occurs on a public holiday may attend any other regularly scheduled applied class that week (provided there is space) and additional applied classes will be added during these weeks to facilitate students attending alternative applied class times. Makeup lectures may be scheduled, or cancelled at the discretion of the instructor, depending on how well the class is progressing through the material.

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 Exercises

• Identity Verified

Mode

Written

Category

Tutorial/ Problem Set

Weight

15%

Due date

Applied class assessments are due each week from week 2 – week 13 except for weeks an assignment is due 2/03/2026 - 29/05/2026

Other conditions

Secure.

See the conditions definitions

Task description

Submission guidelines

Assessment is completed within the scheduled time and turned in online at the end of the applied class.

Deferral or extension

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

If you are unable to attend your scheduled applied class, you are expected to watch the full recording and complete the online assessment by 5.00pm Friday.  Note that you can miss up to two applied class assessments without penalty, to allow for illness or other exceptional circumstances.   

If you are unable to attend more than two applied classes’ assessments, please email math1051@uq.edu.au to explain your circumstances, including an explanation of why you are/were unable to watch the recording at any point during the same week. You will need to do this within 5 calendar days of your applied class, and include appropriate evidence (e.g., medical certificate) covering the week for which you are seeking an exemption. If approved, you will be given an exemption from that assessment, and your remaining marks will be reweighted. For example, with one exemption, your mark will be based on your best 7 out of 9 marks. You can receive at most two exemptions during the semester. 

Late submission

You will receive a mark of 0 if this assessment is submitted late.

Assessment is completed within the scheduled class time and turned in online at the end of the applied class. There are no late submissions as assessments are completed in class. Instead, students will drop the lowest 2 applied class assessment scores to account for absences due to illness or exceptional circumstances.

2 Assignments

Mode

Written

Category

Tutorial/ Problem Set

Weight

15%

Due date

27/03/2026 5:00 pm

15/05/2026 5:00 pm

Task description

Submission guidelines

Follow the submission instructions on the course Blackboard site.

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 are released 7 days after the assignment is due to provide students with the necessary feedback they need to study for examinations. Therefore, extensions beyond 7 calendar days are not possible.

See ADDITIONAL ASSESSMENT INFORMATION for extension/deferral 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.

Solutions for assignments will be released 7 days after the assessment is due and as such, late submission after 7 days from the original time submission is due will not be possible, regardless of approved extensions.

In-Semester Exam

• Hurdle
• In-person

Mode

Written

Category

Examination

Weight

20%

Due date

In-semester Saturday

27/03/2026 - 3/05/2026

The possible dates for the in-semester exam have been updated as of Friday, February 20th.

This semester, in‑semester exams will be held on:

• Friday 27 March, Saturday 28 March and Sunday 29 March (Week 5)
• Friday 17 April, Saturday 18 April and Sunday 19 April (Week 7)
• Saturday 2 May (Week 9)

Exams may be scheduled at any time within these periods:

• Fridays: 5:00pm or 7:15pm
• Saturday and Sundays: between 8:00am and 7:15pm

The first exam of the weekend will commence at 8:00am, and the final session will begin at 7:15pm.

 You need to keep these days and times free until the in-semester timetable has been released.

Other conditions

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.

End of Semester Exam

• Hurdle
• Identity Verified

Mode

Written

Category

Examination

Weight

50%

Due date

End of Semester Exam Period

6/06/2026 - 20/06/2026

Other conditions

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 extension/deferral information relating to this assessment item.

Course grading

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

Additional course grading information

IMPORTANT

Noteﾠ the requirements to achieve a passing grade (4,5,6 or 7). 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 eitherﾠ

(i) receive at least 70% of the sum of the marks available for Section A of the in-semester exam and Section A of the final exam, OR

(ii) receive at least 50% of the marks available on the final exam.ﾠ

then you will fail MATH1051.ﾠ

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

You are responsible for checking that the various assessments' marks have been correctly entered.ﾠIf you feel an error has been made in assessing your work or have not received your mark, make a private post to the Ed discussion board, and the right person will follow up with you.ﾠ

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.

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
• Assignments
• Applied Class exercises
• Online Quizzes
• Practice problems for the in-semester exam and end of semester exam.
• Past exam papers with worked solutions.

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

Additional learning material will be posted on Blackboard. Itﾠis therefore very important that students regularly checkﾠBlackboard.

The MATHS FIRST YEAR LEARNING CENTRE at St Lucia offers applied class help. Appointments are not necessary; simply turn up with your questions. Please see Blackboard for details.

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

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.