ENGR 121 (2020) - Home Page

Welcome to the home pages for ENGR 121: Engineering Mathematics Foundations.

Missing Page in lecture

Somebody alerted me to the fact that while I was talking about phase shift in sinusoids in the lecture on Weds 29 April, the video stops showing the paper I was writing on, This happens at time 30min 50sec. Something went wrong with the "sharing" of my phone camera, I think. Here is a snapshot of the missing page that I retrieved from my rubbish bin. Thank goodness for good old paper!

ka kite, Mark

PS I found the issue: I had inadvertently cut the last few minutes from that track of the video. I've been able to retrieve the missing frames so I think the video will be better now.

IMG 8823.JPG

Welcome Back!

Kia ora ENGR121 students,

I hope you are well and finding plenty to do! There is an opportunity to read ahead and do assignments ahead of time, in ENGR121, if you want to.

We resume teaching Tues 28 April, with the two Tutorials at 2:10 and 3:10pm, now on Zoom (links are under the "Zoom" folder in Blackboard). Assignment 2 is due midnight Weds 29 April. Then we have a zoom lecture Weds 10am. Times continue as before Easter, but as Zoom meetings. You can stay home!

We have revised the assessment and delivery of ENGR121, now that everything has to be online, especially Tests. The link


has detailed information about the new Assessment that is going into place for ENGR121. The final Exam is gone, replaced by beefed-up Tests 1 & 2, and by Assignments that are more valuable. Timings are also changed, and Labs are reduced to three. Test 1, Test 2, Labs, and Assignments are now worth 25% each. A poor result on a Test can be ignored with the extra value shifted to the Assignments, if it is to your advantage. Alternatively, a poor Assignment result can be ignored, and their value shifted to your best Test result, if that is to your advantage. We do both calculations and give you the best outcome.

You will also see in the new assessment details, that the best 4 out of 7 Assignments are used to calculate your Assignment result, and the best 2 out of the three lab reports are used to calculate your Labs result. We will offer you Sample Tests, that give you a good idea of the style to expect with the online multiple-choice Blackboard Test system.

Lecture times will be used for a brief delivery of material , followed by question and answer sessions, and may be shorter than 50 minutes. The delivery part of these zoom sessions will be recorded. Those recordings, plus an occasional offline video on key teaching points, will go into "Vstream Videos" on Blackboard. Tutorials will not be recorded, but I will put up some offline videos on the more challenging tutorial answers. There is a Reading Plan with the Lecture Notes already on the wiki.

Zoom links are posted in the "Zoom" folder on Blackboard. Here is a link to Zoom FAQs for new users: https://support.zoom.us/hc/en-us/articles/206175806-Frequently-Asked-Questions

If you have technical problems, help is available from email: info.vuw.ac.nz, or ph 0800 04 04 04.

Kia kaha


Closure of Vic Uni

Our Vice-Chancellor has announced that all teaching at Victoria University of Wellington will stop from the end of today Monday 23 March until the scheduled mid-trimester break ends. This will give staff an additional three-week period to prepare for a change in delivery methods. While most academic staff and tutors have been preparing for this possibility for some time now, this will allow us to have a consistent approach across the University.

Teaching will recommence online on Tuesday 28 April. Notwithstanding this, there was an ‘Online Student Engagement Day’ on Thursday 2 April. It was an opportunity to test our capacity to teach online and to engage with our students. About 130 students attended. As a result of one question from a student, I have posted a short video on Blackboard talking about changing a logical expression to be expressed purely using conjunction and negation.

We will make up the missing three weeks at the end of Trimester. Since the total time for Trimester One is now 12 rather than 15 weeks, we are required in consultation with the Student Union to reduce all workloads. This means a reduction in the content compared to that usually covered in ENGR121.

Kia kaha

Mark & Emma


Kia ora

You will have heard much about the ongoing measures to ensure that everyone is able to stay safe and healthy in the current environment.

As the university continually assesses measures to that effect, we are now preparing for the delivery of lectures and tutorials online, as well as how to adapt the assessments that take place within the course. We will be letting you know about any changes necessary, be assured that the university approach is guided by advice from the Ministry of Health.

As things develop over the coming weeks, if you need support please reach out to myself Prof Mark McGuinness, or to Dr Emma Greenbank, or to the administrator Dr Steven Archer. For help with labs please contact Dr Howard Lukefahr .

The school will be organising increased availability of tutorials online and we will be taking a proactive approach to the types of support that you will find available.

In the circumstances, if you should need to talk to someone about continuing with your studies, you should talk to your faculty office (most likely Science Faculty Science-Faculty@vuw.ac.nz ) as there may well be more flexibility with regard to fees refunds.

There is further information for students at: https://www.wgtn.ac.nz/covid-19/students

COVID-19 Contact Centre

The University has established a contact centre for student enquiries. You can reach us on the main information number 0800 04 04 04 or by emailing info@vuw.ac.nz.


Test 1 is now 20 May; it will be online using Blackboard.

Howard Lukefahr is running special tutorial sessions suitable for ENGR121 students who are having trouble with their mathematics, lecture material, tutorials, or assignments. These are offered every Monday and Wednesday, 6pm to 8pm. These will be Zoom sessions once Vic

Tutorials started on Thurs 12 March. You do not submit tutorial answers for marking, only assignment answers. We will set up Zoom sessions for tutorials now that students are unable to come to campus.

Labs started on Tues 17 March. They are now Zoom based..

The lectures continue to be recorded video. Go to Blackboard to view them. They are supported by short videos on key teaching points, and by reading lists based on lecture notes published online. Check out the Lecture Notes for more info. -Mark

Older announcements will go here.


The Course Coordinator is Prof Mark McGuinness. Mark is lecturing the first six weeks, and Dr Emma Greenbank is lecturing the last six weeks.

The Senior Tutor in charge of things administrative like assignments and tutorials and marking is Dr Steven Archer.

Dr Howard Lukefahr is in charge of the labs, their supervision, report marking, and the lab content for this course. Howard is also offering special tutorials and events aimed at giving you extra help in this course (Mondays and Wednesdays 6-8pm in AM106, to be confirmed). Howard is also available to students most times. There is a schedule on his door showing where he can be found pretty much all the time.

Class Representative

Well done, Calvin, Ella, Alex and Nathaniel for bravely standing up for the Class Rep vote. And well done, Eran De Silva, for winning the vote. You can contact your Class Rep, Eran, by email desilva dot eran123 at gmail dot com.

Facebook Page

Eran has set up this Facebook page for ENGR121 students, thanks Eran!


Here is the Discord channel for Engineering and Comp Sci. When you join you should go to the bot channel and type in

(exclamation mark)rank engr-121

and then you will have the maths role added, so you can access the 121 channel. You can also do this for your other courses.

Discord provides an alternative to Facebook for ENGR121 students to text or chat with other ENGR121 students. Thanks Steven for the updated link and information on this.

Rainbow Discord

The VUW UniQ discord server is to be found at https://discord.gg/PyxnDu6 . UniQ is our rainbow representative group on campus. They provide social and support space for students, a critical service during this potentially isolating time.

Extra Help

Howard Lukefahr has started special tutorial sessions suitable for ENGR121 students who are having trouble with their mathematics, lecture material, tutorials, or assignments. Every Monday and Wednesday, 6pm to 8pm, in AM101. These will soon change to Zoom sessions, online rather than on site.

Mathematics Help Desk is noon - 2pm in the Hub weekdays. This will likely change to Zoom sessions soon.

The office hours of math and statistics academics will be listed here.

Lecture Notes

Lecture notes will be put here

Assignments and Tutorials and Answers

Please click for Assignments and Tuts, and model answers.

Test One

Test One will be an online Blackboard Test on Wednesday 20 May (delayed from the original date of 1 April. Each student will be on their honour to ensure that the answers submitted are entirely their own work, done without collaboration with any other person. Tutorials from Thurs 14 to Tues 19 May will be a chance to revise, using the Sample Test 1, plus previous Tests.

Test Coverage: Test one will cover material lectured up to and including the end of Week 5, all of Mark's material. Material in Assignments 1-4 is included, and material in the corresponding tutorials (up to 13 May).

Two Tests will be given. Each Test is worth 25% towards your final grade.

Our policy in ENGR121 on showing working in assignments, Tests, and the Exam, is that it is always a good idea to show working. Some questions will explicitly ask you to show working, and in that case you will need to show your working to get full marks. If working is not asked for, you can get full marks for a correct answer even if there is no working shown. An incorrect answer with no working shown cannot attract any marks; this is the danger of not showing your working.

Exam Review Sessions
There will be multiple opportunities to review and get help before the Tests and the Exam. Keep an eye on the announcements.

This formula sheet will be provided with the Test and with the Exam.

Examples of Test One

The best indication of what to expect in Test 1 is the Sample Test 1 now available on Blackboard. Try it as many times as you like!

These are not as good as the Sample Test 1 on Blackboard, because they have more limited coverage:

Test Two

Test Two will be held online in Blackboard during during Weds 17 June, available from 10am-10pm.

These Tests from previous years cover less material than Test 2 will cover this Trimester, but provide some guideline as to what to expect. Another limitation of these previous Tests is that they were not online Blackboard Tests.

Final Exam

There is now no final exam in T1 2020.

This formula sheet was provided with the Test and with the Exam in previous years. Feel free to use it if you want to, when doing Test 1 and Test 2.

Previous Exams

Past exam papers are found on the library page: Go this page and EXAM PAPERS is an option at the top. Click and search for ENGR121. You'll find exam papers since 2014.


Or you can just go here for previous exams.

Here are some past exams and some model answers.


The textbook for ENGR 121 is: Engineering Mathematics: A Foundation for Electronic, Electrical, Communications and Sytems Engineers (4th Edition), by Anthony Croft, Robert Davison, Martin Hargreaves and James Flint, Pearson, 2012. We follow this book very closely, and it is also the text for ENGR 122 Engineering Mathematics with Calculus, so it will be very useful. It costs about $144 at Vic Books. It is recommended, not required, since the lecture notes are so detailed.

Also recommended, but not required, is Engineering Mathematics, by K.A. Stroud, with Dexter J. Booth, Palgrave MacMillan, London. About $133 at Vic Books.

Detailed lecture notes will also be posted on the course homepages from week to week.


To expand on the official assessment notes in the Course Outline, here is how your percentage mark is calculated, on which your final grade is based:

Assignments 10%, Labs 20%, Tests 10% each for a total of 20%, exam 50%.

If you do poorly on your assignments, we count 60% for the final exam and we don't count the assignment mark. If you do poorly on a Test, similarly we don't count it, adding 10% to the final exam maximum count (by rescaling it).

Labs always count for a total of up to 20%, no matter how low the mark. There will be four labs.

In fact, we add up a variety of possible marks, e.g. (10% ass, 10% T1, 10% T2, 50% exam), and (0% ass, 10% T1, 10% T2, 60% exam), and (0% ass, 0% T1, 10% T2, 70% exam), and (0% ass, 0% T2, 10% T1, 70% exam), and (0% ass, 0% T1, 0% T2, 80% exam), and we give you the maximum of the resulting set of marks, and then we add your total Lab mark, for an overall total %. Note that Lab marks always count.

As a consequence of this, you cannot lose by sitting a Test, you can only gain marks, since a poor mark winds up not being counted towards your final grade.

By the way, you can miss two assignments without penalty on the 10% that they attract towards the final grade. There will possibly be just 8 assignments on offer this year; if so then 6 satisfactory ones would get you the full 10% available.

To be satisfactory, an assignment gets a mark of 40% or more, and is on time.

If you miss more than two, the 10% is apportioned; eg doing three (out of six) satisfactory assignments would get 5% towards the final grade, half of the 10% available. Any assignments which are unsatisfactory due to having less than 40% will (if you need them) get a proportion of the full mark they would have got otherwise.

Videos Of Lectures

We record all lectures to video. To see videos of lectures, please go to Blackboard, select ENGR121, then select Vstream Videos on the top left-hand panel.


This schedule describes what we plan to cover during lectures in ENGR121.

Help Desk

The Mathematics Help Desk is a good place to come and ask questions if you are having trouble understanding tutorial and/or assignment questions, or material covered in lectures or in your extended reading. You are welcome here any time.

Dr Howard Lukefahr is running a Workshop every Monday and Wednesday evening, 5-8pm in AM106 for all ENGR students.

Extra Help from Student Support

There is more help available from Vic's Student Support. They will help you with ENGR121, and they can also help advise on study habits and how to pass courses. Take a look at their website:


Topic attachments
I Attachment Action Size Date Who Comment
ENGR121-Test 2-2018.pdfpdf ENGR121-Test 2-2018.pdf manage 180 K 20 May 2019 - 16:25 Main.smithpe  
Test2.pdfpdf Test2.pdf manage 84 K 20 May 2019 - 16:32 Main.smithpe  
Test2_2016.pdfpdf Test2_2016.pdf manage 223 K 17 May 2019 - 09:12 Main.smithpe  
Test2_2017.pdfpdf Test2_2017.pdf manage 117 K 17 May 2019 - 09:15 Main.smithpe  
Test2_2018.pdfpdf Test2_2018.pdf manage 224 K 17 May 2019 - 09:14 Main.smithpe  
Test2sol.pdfpdf Test2sol.pdf manage 142 K 04 Jun 2019 - 12:31 Main.smithpe  
Test_2017_sols.pdfpdf Test_2017_sols.pdf manage 89 K 03 Apr 2019 - 16:13 Main.smithpe  
test1sol.pdfpdf test1sol.pdf manage 139 K 08 May 2019 - 16:22 Main.smithpe  
test2revision.pdfpdf test2revision.pdf manage 53 K 17 May 2019 - 09:18 Main.smithpe