HIMCM數學建模競賽真題獲取，備戰2023-2024年HIMCM比賽

數學建模是一門將數學知識應用于實際問題解決的重要領域。對于參加即將舉行的HiMCM比賽的同學們來說，競爭激烈，想要在比賽中取得優異成績就需要在最后關頭進行強化訓練。而對于那些著眼未來的同學來說，更需要提前準備，通過學習歷年比賽的經典真題來增強自己的能力。

相信經過數模學術活動的“洗禮”，對于你挑戰高層次的學術科研也必然打下堅實基礎。

2021年HiMCM賽題

問題A：儲存太陽

你的團隊需要為一個偏遠地區的1600平方英尺的住宅提供太陽能電力，滿足家庭在晚上和陰天的能源需求。由于房子偏遠，連接到電網的成本非常昂貴，所以你決定投資于能源存儲。

對于儲能系統和相關電池規格標準，題目中都給出了詳細的介紹，學生需要為1600平方英尺的家庭做好能源需求規劃，并給出合適的模型。同時討論水泥電池的優缺點，并與太陽能電池進行比較，給出可行性建議。

問題B：應對干旱

米德湖是美國最大的水庫，但2021年的夏天米德湖達到了它自20世紀30年代初次蓄水以來的最低水平。由于氣候變化引發的干旱，同時隨著米德湖所服務的2500萬人對水的需求的增加，
水庫容量已經縮小到36%。

你的團隊決定用米德湖案例來調查和了解更多關于干旱對水庫的影響。學生需要討論不同因素對米德湖體積和水位的影響，根據提供的歷史數據簡單討論總體模型，對比不同時期的干旱，并開發兩個模型分別預測2025、2030年和2050年的米德湖水位。根據模型和預測，考慮廢水循環的可行性計劃。

HiMCM2022年真題參考

Problem A: The Need for Bees

(and not just for honey)

Honeybees, along with a few other key animals, are critical to human existence on our planet. Along with honey production, these insects provide the vital role of pollination of many trees and plants that provide food for our survival. In 2007, the term Colony Collapse Disorder (CCD) was created to describe the decline of honeybee populations around the world. Bee decline can be attributed to factors such as viruses, pesticides, predators, habitat destruction, and environmental conditions.

Some information to consider (but you may find other helpful information online):

· Honeybees can travel up to 20 km, but typically stay within 6 km of their hive.

· A typical honeybee hive contains between 20,000 and 80,000 honeybees.

· A single honeybee can visit approximately 2,000 flowers or more in a single day.

· Because of the high workload during summertime, most honeybees work themselves to death, resulting in a shorter lifespan.

· During autumn and wintertime, honeybees may live a bit longer (four to six months).

· A honeybee’s level of activity, pollen consumption, and protein abundance impacts its lifespan.

Requirements

1. Develop a model to determine the population of a honeybee colony over time.

2. Conduct sensitivity analysis on your model to determine which factors (e.g., lifespans, egg laying rates, fertilized/unfertilized egg ratios, or other factors) have the greatest impact on honeybee colony size.

3. Model and predict how many honeybee hives you will need to support pollination of a 20-acre

(81,000 square meters) parcel of land containing crops that benefit from pollination.

4. Create a non-technical, one-page blog or infographic for a website that provides the information you developed.

Your PDF solution of no more than 25 total pages should include:

· One-page Summary Sheet.

· Table of Contents.

· Your complete solution.

· One-page blog or infographic.

· References list.

Note: The HiMCM Contest has a 25-page limit to your PDF solution submission. All aspects of your submission count toward the 25-page limit (Summary Sheet, Table of Contents, Reference List, and any Appendices).

Problem B: CO2 and Global Warming

Prior to the Industrial Revolution, carbon dioxide (CO2) in the atmosphere was consistently around 280 parts per million (ppm). The concentration of CO2 in the atmosphere reached 377.7 ppm in March of 2004, resulting in the largest 10-year average increase up to that time. According to scientists from National Oceanographic and Atmospheric Administration (NOAA) and Scripps Institution of Oceanography (SIO) the monthly mean CO2 concentration level peaked at 421 ppm in May 2022. An Organisation for Economic Co-Operations and Development (OECD) report predicts a CO2 level of 685 ppm by 2050.

The editors of Scientific Today magazine have asked your team to address these claims of the current reported and future predictions of CO2 concentration levels. They provided two data sets (CO2 Data Set 1 & Temps Data Set 2) to assist in your research.

Requirements

1. Do you agree with CO2 level claims? Use CO2 Data Set 1 to analyze CO2 changes.

a. Do you agree that the March 2004 increase of CO2 resulted in a larger increase than observed over any previous 10-year period? Why or why not?

b. Fit various (more than one) mathematical models to the data to describe past, and predict future, concentration levels of CO2 in the atmosphere.

c. Use each of your models to predict the CO2 concentrations in the atmosphere in the year 2100. Do any of your models agree with claims and predictions that the CO2 concentration level will reach 685 ppm by 2050? If not by 2050, when do your models predict the concentration of CO2 reaching 685 ppm?

d. Which model do you consider most accurate? Why?

2. What’s the relationship between temperature and CO2? Many scientists think that there is a relationship between warming global temperatures and the concentration of CO2 in the atmosphere.

Use your work in part 1 and Temps Data Set 2 to assist in your comparison of land-ocean temperatures and CO2 concentration levels.

a. Build a model to predict future land-ocean temperatures changes. When does your model predict the average land-ocean temperature will change by 1.25°C, 1.50°C, and 2°C compared to the base period of 1951-1980?

b. Build a model to analyze the relationship (if any) between CO2 concentrations and landocean temperatures since 1959. Explain the relationship or justify that there is no relationship.

c. Extend your model from part 2.b. into the future. How far into the future is your model reliable? What concerns, if any, do you have with your model’s ability to predict future CO2 concentration levels and/or land-ocean temperatures?

3. Prepare a non-technical article

(1 page maximum) for Scientific Today to explain in your team’s findings and possible recommendations for the future.

Your PDF solution of no more than 25 total pages should include:

· One-page Summary Sheet.

· Table of Contents.

· Your complete solution.

· One-page blog or infographic.

· References list.

Note: The HiMCM Contest has a 25-page limit to your PDF solution submission. All aspects of your submission count toward the 25-page limit (Summary Sheet, Table of Contents, Reference List, and any Appendices).

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關于選擇比賽題目

HiMCM高中生團隊從2個建模問題中二選一。所有問題都涉及為開放式的解決并且不會只有一個解決方案。

團隊在提供解決方案時，可以使用：互聯網、圖書館資源、軟件、電腦，計算器等工具。在形成解決方案文書時，應注重清晰度、分析過程和解決方案的設計問題。

所有最終獲得“杰出方案”的正式論文都會被發表在Mathmodels.org中。