otago problem solving 2021 answers

Previous Questions

You can download PDF files of the questions and solutions from previous competitions here:

Otago Problem Solving

Otago university maths  problem-solving challenge.

At Kenakena we have been focusing on delivering a school-wide maths programme where problem-solving is at the heart.

Problem Challenge is a mathematics problem solving competition aimed primarily at Intermediate School children. It is organised by members of the Department of Mathematics at the University of Otago ( https://www.maths.otago.ac.nz/pc/ ).

Children participating in the competition attempt to answer five questions in 30 minutes on each of five problem sheets, which are done about a month apart starting in April.

The Otago University programme is well suited to what we do and our participating students do really well. Children from Years 6 to 8 are nominated by their teachers based on a recognised ability to solve demanding mathematical problems. In 2015, 55% of our students who participated achieved an Excellence award!

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Examination scripts and results

Key dates and deadlines for 2024

The table below shows the key dates and deadlines (over a 12-week period) for the University's provisions for Recounts and return of examination scripts following the date of the release of confirmed results for the 2024 examination periods.

Final results

Final results for papers can be viewed in the Examinations and Results section of the student eVision portal as soon as they become available each teaching period. Initially "Unconfirmed" will be shown alongside them. Once "Unconfirmed" is no longer showing, results are official.

The University of Otago uses the following scale to convert numerical marks into grades:

Viewing your examination script

You may request to view your script from the start of week 1 to the end of week 12 from the date of the release of confirmed results.

There are no application forms or fees associated with viewing your examination script.

On-campus students

Contact the relevant teaching department to arrange a time to view your script in the Department.

Distance Learning students

Please email us for information regarding viewing your script:

Email [email protected]

Applications for a recount must be made within four weeks from the date of the release of confirmed results (see above for dates). A recount involves a careful re-check of the marks that count toward your final result in a paper. The purpose of a recount is to ensure that no answer, no portion of an answer, or any work undertaken during the teaching period which counts for the final result, has been overlooked. No personal information accompanying the application is passed onto the examiners.

Your work is not re-marked; at the University of Otago there is no provision for any work to be re-marked.

Application and payment information

To apply please complete the Recount of Results form .

The administration fee is $36 per paper, regardless of how many examinations a paper has. This is because a recount is a check of all marks that comprise the final grade in a particular paper. Please see below for information on paying administration fees . Where a recount results in a change of mark, the administration fee will be refunded.

The submitted form and payment must be received by the deadline. Late applications are not accepted.

The recount process

Once your application has been received and your payment processed, the relevant department(s) will be asked to re-check all components of your final mark, to ensure that nothing has been omitted or recorded incorrectly. Once this is done, the department advises Student Administration of the outcome, and we advise you via your student email address. The process can take several weeks, so if you haven't been notified of the outcome and would like to check the status of your application, please contact:

Student Administration Email [email protected]

Return of examination scripts

You may apply for the return of your examination script from the start of week 7 until the end of week 12 from the date of the release of confirmed results.

After twelve weeks from the date of the release of confirmed results, unclaimed scripts are disposed of by Departments.

Restrictions

Not all examination scripts can be returned. If your answers involved problem solving, were answered on multi-choice answer sheets for computer marking or a Department requires a particular examination paper to be embargoed from publication and not released into the public domain then you will not be able to have your script returned to you. However, you can still view it.

To find out if an examination script can be returned to you or not, go to the Library's past exam papers webpage and check the examination (embargoed examination papers are noted as such).

Past exam papers – University of Otago Library

Application information

Submit your application to AskOtago:

Return of examination scripts – AskOtago Service Portal

There is no administration fee associated with the return of examination scripts.

Final Examination Only

Students who have failed a paper but who have completed course work satisfactorily may apply for Final Examination Only enrolment. If approved, internal marks are carried over and the examination may be sat at the end of the next teaching period that the paper is offered.

• Approval for Final Examination Only enrolment is at the discretion of the relevant Head of Department.
• Some papers do not have the option of Final Examination Only; if this is the case, you will be advised.
• Final Examination Only enrolment may be granted only once for a particular paper.
• Final Examination Only enrolment is only available for the next teaching period in which the paper is offered after the paper is initially failed.
• Applications will not be approved if the content or assessment of the paper is going to be significantly altered when it is next offered, or if the paper is no longer offered.

Students approved for Final Examination Only enrolment are not entitled to:

• attend any lectures, laboratories, or tutorials
• receive assistance from academic staff
• have access to electronic holdings of course material
• receive printed course material.

Applications for Final Examination Only must be received by:

• Summer School papers – 10 January
• Semester 1 and full year papers – 1 March
• Semester 2 papers – 31 July

Further information about Final Examination Only is available here:

Paying administration fees

Recounts and Health Sciences Professional Programme Special Examinations incur an administration fee. If you have applied for one of these options and are due to pay a fee, you can do so in the following ways:

In person – recounts

• AskOtago Central Hub, Information Services Building by Eftpos

In person – Health Sciences Professional Programmes Special Examinations

Internet banking and telegraphic transfer.

The University of Otago also accepts payment by internet Banking or Telegraphic Transfer with the account details listed below:

Account number:   01-1839-0944124-00 Account name: University of Otago Swift Code: ANZBNZ22 (for payments outside New Zealand)* *Please note that for payments paid by telegraphic transfer, there is a bank fee of NZD $20 charged for each transaction so you will need to add this amount onto the amount payable.

References for online banking

If your payment does not have the appropriate references, we will not be able to identify your payment and this will delay your application. Please see the table below for more information.

Credit card payment to University of Otago

For students outside Dunedin who would like to pay administration fees by credit card, please contact us for further details:

• Services A-Z
• Knowledge Base
• KA-10000393

Past examination papers

Copies of past examination papers are available online through the Library website.

Not all examination papers are available online as departments sometimes embargo the publication of particular examinations.

Past exam papers

Paper co-ordinators may request an embargo on the publication of an exam paper:

Email [email protected] AND [email protected]

Lists of embargoed papers can be found in AskOtago Teams, in the relevant folder for year and semester: Examinations and Exam Support

See also Return of exam scripts for more information.

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Programming and Problem Solving for Year 12

A workbook for year 12 programming.

In 2012, many teachers without a formal background in programming will be asked to teach program design and the coding of a solution in a programming language. This is a significant step up and we are doing what we can to help.

In 2011, we developed a workbook which is compatible with the new Digital Technology Achievement Standards 2.45 and 2.46 for NCEA level 2. The student version of the workbook has now been revised and is ready to be used in the classroom. Any teacher who wishes to look at it with a view to using it should request a copy from [email protected] .

The workbook covers the material required for assessment standards 2.45 and 2.46 and a little bit more, but is not "teaching to the standard". The workbook tries to stay focused on the process of problem solving rather than the syntax of any particular language. The problems should be able to be coded in any language from a common algorithm.

After some debate and many trials, we decided to provide a choice of two real-world programming languages in our examples. We use Python and Java. This will make the flow on to year 13 easy, as both of these languages allow Object Oriented design, although we will do not use this aspect of them in the year 12 workbook. There is plenty of on-line assistance for these languages, there are well-tested and reliable (and free) platforms and development environments for both Windows and Mac.

If you have a favourite language, you could take the concepts and ideas and adapt them to the syntax it uses. Any language that can easily produce textual output to the display/screen and has indexed data structures could be used.

What, no graphics? We have unashamedly chosen not to use graphical output because the amount of material to be learned covering the core programming concepts as well as graphics and animation would not fit in the 60 hour target. We believe that problem solving is an enjoyable exercise in its own right.

The material is written with as little jargon as possible and uses plenty of examples. The problems range from easy to challenging. It is impossible to write a "one size fits all" lesson, so each student will be able to choose whether they wish to have a go at the more challenging exercises, or be satisfied with completing the elementary problems.

Each school which uses this material will be charged $100, a share of the cost of its development.

Workbook Contents

• Chapter 0 - Java and Python, setting up (teacher's version only)
• Chapter 1 - The process of programming
• Chapter 2 - Variables and Expressions
• Chapter 3 - Modular programming
• Chapter 4 - Getting input, formatting output
• Chapter 5 - Boolean and Selection
• Chapter 6 - Repetition
• Chapter 7 - Arrays (Java) / Lists (Python)
• Chapter 8 - Strings
• Appendix - contains model answers and notes for the teacher (teacher's version only)
• A Bridge to the Standards - an adaptation of the paper presented to the December 2011 CS4HS workshop in Christchurch (teacher's version only)

We have also produced Python and Java workbooks for Year 13 / Digital Technology Achievement Standard 3.46 / NCEA level 3. The books follow on from the Year 12 versions in the same language, and cover Object Oriented Programming and Graphical User Interfaces. We ask for $200 from each school using these books as a share in the cost of their development.

Professional Practice Fellow Sandy Garner and Professor Anthony Robins

We are the people who design and teach the first year of the computer science degree program at the University of Otago. We have many years of experience teaching programming at this level. We know where high school students should be aiming if they are intending to study programming at a higher level. We are also parents with children at various stages of the NZ secondary school system, and have taught programming at primary, intermediate and secondary schools through our involvement with robotics and RobocupJuniorNZ.

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Previous questions

Previous Questions

Note that the Questions and Solutions available here are as they were presented to schools. Any errors in the questions have not been corrected, although with any luck such errors will be noted in the relevant solutions.

© Department of Mathematics & Statistics