otago problem solving questions and answers 2023

Previous questions

Welcome to the Junior Mathematics Competition!

This year the competition will be held in two parts - the first being a multiple-choice and short answer exam sat entirely online , while the second part will be a paper exam limited to the top 15 percent of participants in the first part.

The first part of the competition will be sat from Monday April 8 to Friday April 12 , while the second part will be held on Wednesday May 15 .

2024 is the 39th year of this highly successful Competition.

This mathematics competition is for students in years 9 to 11 (forms 3 to 5), although younger students may also take part. Every student throughout New Zealand sits the competition on exactly the same days, usually two Wednesdays in April in May (one for each part).

The competition lasts for 50 minutes per part (so one hour, 40 minutes in total). The emphasis is on problem solving, so expect surprises!

Mathematical skills are important, but so is careful reading. Students who read the questions carefully and work out exactly what is being asked generally do better than those who jump in and write down the first thing that springs to mind.

Although many of the same questions are asked for each year level, students only compete against students at the same level as themselves. (However students in years 7 or 8 are regarded as being in year 9 for the purposes of the competition.)

Full details of the competition may be found here , with a note on who can enter here .

Note: This competition should not be confused with Problem Challenge , which is run by a separate unit within the Department of Mathematics and Statistics at the University of Otago. For Problem Challenge enquires please contact the Problem Challenge organisers directly.

© Department of Mathematics & Statistics

University of Otago Problem Challenge

• October 26, 2023

Southland Girls’ High School 328 Tweed Street, Georgetown, Invercargill 9812, New Zealand

+64 3 211 6030

[email protected]

• How to Enrol
• Student Achievements
• Student Wellbeing
• Extra-Curricular
• Enwood Boarding House
• Whanau Hononga Booklet
• Online Shop
• Accommodation
• Curriculum Overview
• Key Dates / Terms
• Apply Online
• Permission Forms
• Latest News
• SGHS Friday Flyer
• Performing Arts Noticeboard
• Sport Noticeboard
• Parent Portal

© Southland Girls High School 2024   |    Privacy Policy    |   School Website Design by AllTeams

Book a Tour of Enwood House

Come and see all that Southland Girls’ High School offers boarders with a tour of Enwood House that allows you to see our facilities in action, while meeting the staff and the students.

To book in for a tour of the boarding house, please email Jenni Dennis, [email protected] or telephone 03 211 6030 .

RISKS Disclosure

Weekly sports contains risks, including common injuries like strains, sprains, bruises and dislocations. These events are managed by the appropriate sporting body in conjunction with school staff who will manage risk and hazards according to the school’s safety management plan. This includes careful consideration of the risks, all risks will be outlined to the students. While risks can be maintained to acceptable levels they cannot be totally eliminated. Some risk is retained for its learning and experiential value. If you wish to come in to school to see our safety management systems or have any questions, feel free to contact Ashleigh Rabel 03 211 6030 or [email protected] .

It is important for safety reasons that students follow instructions given to them by all staff and follow all appropriate school rules. Behaviour by students that is deemed dangerous and puts themselves and/or others at undue risk will result in your child facing disciplinary actions on their return or sent home at the cost of the Whanau/parents or caregivers.

This event contains risks, including possible injuries. This event is managed by school staff or other organisations who will manage risk and hazards according to the school’s/organisation’s safety management plan. This includes careful consideration of all procedures while carrrying out the activites. While risks can be maintained to acceptable levels they cannot be totally eliminated. Some risk is retained for its learning and experiential value.

If you wish to come in to school to see our safety management systems or have any questions please phone 03 211 6030 .

STUDENT CODE OF CONDUCT

I understand that playing sport is an opportunity for me to learn, practice skills, and gain attitudes and values in an environment outside of the school.  I realise that this requires me to take on genuine responsibility for my own enjoyment and safety and that of others.

I agree to do the following to make this happen:

• Show courtesy and consideration to others.
• Follow the rules and instructions of staff and other supervisors at the events.
• Look after myself and my personal belongings.
• Declare medical conditions that could affect participation in the events.
• Accept the rules set by the school for the events.

I understand that my parents / caregivers will be contacted and I may be sent home at their expense if:

• My actions are considered unacceptable by staff / supervisors of these events.
• I breach the behaviour / discipline standards of the school.
• My actions put me or others in any danger.

Book a School Tour

Come and see all that Southland Girls’ High School offers students with a school tour that allows you to see our facilities in action, while meeting the staff and the students.

Student tour guides will answer questions and offer a student’s perspective, before meeting with a senior member of staff to discuss your child’s enrolment.

To book in for a tour of the school, please email Nicola Macpherson on  [email protected] or telephone 03 211 6030 .

Contact details

Phone: 03 211 6030

Email: [email protected]

Address: 328 Tweed Street, Invercargill 9812, New Zealand

International Student Emergencies: +64 21 767 089

Student Absences: Please contact Student Services on 03 211 6030 or email the School Attendance Officer at: [email protected]

Enwood Boarding House: 03 216 9148

Useful Links

• Enrol Online (Domestic Students)
• Enrol Online (International Students)

Welcome to the Junior Mathematics Competition!

This year the competition will be held in two parts – the first being a multiple-choice and short answer exam sat entirely online , while the second part will be a paper exam limited to the top 15 percent of participants in the first part.

The first part of the competition will be sat from Monday April 4 to Friday April 8 inclusive , while the second part will be held on Wednesday May 11 .

2022 is the 37th year of this highly successful Competition.

This mathematics competition is for students in years 9 to 11 (forms 3 to 5), although younger students may also take part. Every student throughout New Zealand sits the competition on exactly the same days, usually two Wednesdays in April in May (one for each part).

The competition lasts for 50 minutes per part (so one hour, 40 minutes in total). The emphasis is on problem solving, so expect surprises!

Mathematical skills are important, but so is careful reading. Students who read the questions carefully and work out exactly what is being asked generally do better than those who jump in and write down the first thing that springs to mind.

Although many of the same questions are asked for each year level, students only compete against students at the same level as themselves. (However students in years 7 or 8 are regarded as being in year 9 for the purposes of the competition.)

Hi there, this is another post.

This is a test post, without a title?

otago problem solving 2023 answers

Otago_problem_solving_Solutions_1_2023 - Free download as PDF File (.pdf), Text File (.txt) or read online for free.

Otago_problem_solving_Solutions_2_2023 (1) - Read online for free.

• business plan
• course work
• research paper

• News & Events

Otago Problem Solving

By Shona Mckenzie | Posted: Wednesday September 6, 2023

Five times a year, Year 7 & 8 students from around New Zealand compete in the Otago Problem Solving Competition.

60 students from Casebrook currently participate in Otago Problem Solving. This extra curricular competition requires students to independently solve a range of mathematics problems.

During each session, students are given five different problems that need to be solved within the 30 minute time frame. The questions vary, however, generally they include brain teasers. This year the competition began in April and will continue to take place each month.

The program has been running for 30 years with over one million students around New Zealand having already participated. It is organised by John Curran and John Shanks, retired members of the Department of Mathematics and Statistics at the University of Otago, with help from Leanne Kirk, also a member of the Mathematics Department.

The students with the highest scores at the end are invited to participate in the final challenge. We wish our mathematicians the best of luck. 

• Casebrook Intermediate School, 90 Veitches Road, Christchurch, New Zealand
• [email protected] | 03 359 7428 | Subscribe to Newsletter
• Copyright 2024 Casebrook Intermediate School - All rights reserved | Privacy Policy | Terms and Conditions
• Web Design by Firebrand | Powered by Hail
• Casebrook Intermediate School
• 90 Veitches Road, Christchurch, New Zealand
• [email protected]
• 03 359 7428
• Copyright 2024 Casebrook Intermediate School - All rights reserved
• Privacy Policy
• Terms and Conditions

Panekiretanga

Subscribe to our mailing list

Otago Problem Solving

The competition started around the early 1990’s in South Island schools, but after about two years, the competition became available to schools all over New Zealand with students in years 7 and 8. Some younger children can sometimes participate too. In most years about 650 schools enter problem challenges, involving over 35,000 children.

Each year students answer 5 questions in 30 minutes, over 5 sets of work, and at the end of each competition everyone receives a certificate. 10% get excellence, 30% get a merit, while the others receive a participation award.

We think that everyone who participated had a great time and enjoyed pushing themselves in that category. A quote from Harry, “I really loved the challenge and even though I didn’t do brilliantly I have thoroughly enjoyed it and improved on my maths.”

Here are some questions from the quiz

The school soccer team has played 15 games with a success rate of 80%. In order to raise their success rate to 90% in the shortest possible time, how many consecutive games must they win?

All of Toby’s marbles are either blue, red, green, or yellow. One third of his marbles are blue, one quarter of them are red, and seven of them are green.

What is the smallest number of yellow marbles that Toby could have?

Written by Aydin Khajehzadeh and Harry Baddington

Department of Mathematics and Statistics

Te tari pāngarau me te tatauranga, study mathematics and statistics at otago, understand the fundamentals of mathematics and statistics and solve real world problems.

Mathematics and statistics underpin virtually all aspects of modern life, with applications across the fields of sciences, technology and business. Mathematics and statistics teach analytical reasoning and logical thinking that make it possible to understand and solve all manner of quantitative problems across a wide range of career sectors.

Study Mathematics

Study statistics, explore what makes science at otago so special.

It's not just our people – the experts in their fields and passionate students – but also the places we teach and learn: Otago Harbour, Fiordland, Stewart Island, Antarctica and the Pacific that mean our students leave here with highly sought-after skills and experiences.

Our community engagement

The Department also maintains important links with schools through two competitions: Problem Challenge and the Junior Mathematics Competition , run by Departmental staff, and by providing a comprehensive series of Statistics video presentations aimed at supporting the New Zealand Statistics curriculum.

Find out how your school can take part in our competitions and access our video series:

• Junior Mathematics Competition
• Problem Challenge
• Statistics video presentations

New Orleans teens solve 2,000-year-old math problem

W hen she started a math contest with a bonus question challenging students to create a new proof for the Pythagorean theorem using trigonometry, teacher Michelle Blouin Williams didn’t expect anyone to complete the task.

“I was just looking for some ingenuity,” she said, per CBS News .

Calcea Johnson and Ne’Kiya Jackson, however, blew Williams’ expectations out of the water by figuring it out in 2023. The teens were seniors at St. Mary’s Academy in New Orleans, a prestigious Catholic school for girls which has maintained a 100% acceptance rate to colleges and 100% graduation rate for 17 years, CBS News reported.

They appeared in an episode of CBS News’ “60 Minutes ” on Sunday to talk about their achievement.

How did the teens find the answer?

While they were motivated initially by the math competition’s $500 prize, an internal drive to finish what they started manifested when they reached the tricky bonus question. For two months, the high school seniors worked tirelessly to finish their proof.

CeCe Johnson, Calcea’s mother, told “60 Minutes,” “It was pages and pages and pages of, like, over 20 or 30 pages for this one problem.”

Her father, Cal Johnson, added, “Yeah, the garbage can was full of papers, which she would, you know, work out the problems and — if that didn’t work she would ball it up, throw it in the trash.”

When they finished, teachers at St. Mary’s recognized the importance of their work and submitted their proof to the American Mathematical Society for recognition at a conference in March 2023, where the students presented their work.

What is the Pythagorean theorem and what’s a proof?

In essence, the mathematical theorem states that knowing the lengths of two sides of a right triangle enables you to figure out the length of the third using this formula: a² + b² = c².

It’s associated with Greek mathematician Pythagoras, but evidence suggests it was known earlier, in Babylon and Iron Age India, per Britannica . Its practical uses include construction and architecture, two-dimensional navigation, and surveying.

A mathematical proof is exactly what it sounds like: reasoning that proves a mathematical theorem is true. American mathematician Daniel Kane explains proofs as being like essays, but using math.

Why is Calcea Johnson and Ne’Kiya Jackson’s work significant?

According to the “ 60 Minutes ” episode, “there had been more than 300 documented proofs of the Pythagorean Theorem using algebra and geometry, but for 2,000 years a proof using trigonometry was thought to be impossible.”

In 1927, mathematician Elisha Loomis said as much in his book, “ The Pythagorean Proposition .” Loomis argued that there could be no trigonometric proof of the theorem because it would be circular.

Stuart Anderson, a professor emeritus of mathematics at Texas A&M University–Commerce, told Scientific American , “A lot of the basic trig ‘identities’ are nothing more than Pythagoras’ theorem.”

So, because trigonometric functions are based upon the Pythagorean theorem, using them reflexively to prove the theorem would be akin to going in circles and a fundamental mathematical error, Loomis argued.

According to Scientific American , the teens refuted this in their presentation in 2023 and said that “a trigonometric identity called the law of sines didn’t depend on the Pythagorean theorem and that they could use it to prove the theorem.”

Calcea and Ne’Kiya have joined an extremely small group who’ve accomplished the same feat, including mathematician Jason Zimba, who successfully created a new proof in 2009. The two submitted their proof for final peer review this spring and continue to work on creating more proofs.

How did the world respond to their accomplishment?

The teens were given the keys to the city of New Orleans and a commendation from the governor of Louisiana, among other public recognitions.

While their achievement “blew up,” as Ne’Kiya described it, the two students remain humble, and laughed at being called geniuses.

When news of their accomplishment broke, some people seemed to be shocked and dismissed the news as fake, St. Mary’s president Pamela Rogers said in the interview .

“They were saying, ‘Oh, they could not have done it. African Americans don’t have the brains to do it.’ ... People — have a vision of who can be successful. And — to some people, it is not always an African American female. And to us, it’s always an African American female.”

When interviewer Bill Whitaker asked why they thought there’d been such a response, Ne’Kiya said, “Probably because we’re African American, one. And we’re also women. So I think — oh, and our age. Of course our ages probably played a big part.”

“I’d like to actually be celebrated for what it is. Like, it’s a great mathematical achievement,” she continued.