Meet 3
When and Where
Meet 3 is scheduled for Monday, 14 December. It will take place online via the Math League online application. The start time is 4:30 pm. The meet is expected to last about an hour and a half.
Topics
3A Event A (Algebra 1) General Topic: Systems of Linear Equations in Two (or occasionally three) Variables
Here are the event subtopics:
3B Event B (Geometry) General Topic: Polygonal Figures and Solids
Here are the event subtopics:
3C Event C (Precalculus & Trigonometry) General Topic: Trigonometry
Here are the event subtopics:
3D Event D (Algebra 2 & Analysis) General Topic: Exponents and Logarithms
Here are the event subtopics:
Mr. Mac's Notes
The notes are intended as a compact review of some principles concerning the subtopics of each individual event. The notes are not comprehensive, so you are advised to supplement your preparation by studying past years' exams and reading textbooks.
Math Notes for Meet 3 Event A (Algebra 1)
Original: 11/28/2020 Update: 12/01/2020 More problems! Update: 12/02/2020 Minor notes modification. |
Math Notes for Meet 3 Event B (Geometry)
Original: 11/28/2020 Update: 12/01/2020 Many more notes! More problems! Update: 12/02/2020 Minor problem correction. |
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Math Notes for Meet 3 Event C (Precalculus & Trigonometry)
Original: 11/28/2020 Update: 12/02/2020 More notes more problems! |
Math Notes for Meet 3 Event D (Algebra 2 & Analysis)
Original: 11/28/2020 Update: 12/02/2020 More notes, more problems! |
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Other Notes
Formula Lists
Noah's Sheets are a collection of formulas valued by mathletes worldwide. They were not assembled with the Minnesota State High School Mathematics League in mind, so they include more than you need to know (but not more than you want to know).
The Elusive Formulas were assembled by the Mathematical Association of America (MAA), sponsors of the American Mathematics Competitions (AMCs), to support preparation for the AMC 10 and AMC 12. The edition here has been annotated to indicate what an ERA student who has completed Algebra 2 should know.
the_elusive_formulas__annotated_for_algebra_2_expectations__-_maclennan_-_2019-04-22.pdf |
The Art of Problem Solving
The two-volume Problem-Solving Series by the Art of Problem Solving (AoPS) is a helpful compact overview of mathematics that includes nearly all of the topics found in Minnesota State High School Mathematics League competitions.
The 7th-edition AoPS Problem-So;lving Series volume (1 or 2) and section(s) within that volume which addresses individual MSHSML subtopics for the current meet are listed below.
The 7th-edition AoPS Problem-So;lving Series volume (1 or 2) and section(s) within that volume which addresses individual MSHSML subtopics for the current meet are listed below.
Algebra 1
- 3A1 Numeric and literal systems of equations: AoPS vol. 1 sec. 3.3
- 3A2 Relation to graphical procedures: AoPS vol. 1 sec. 3.3
- 3A3: Word problems leading to systems of equations: AoPS vol. 1 sec 3.4
- 3A4: Systems of inequalities used to define a region in the plane: AoPS vol. 1 sec 22.2
- 3A5: Determinants: AoPS vol. 2 sec. 11.3-6
Geometry
- Special quadrilaterals and regular polygons (including area formulas): AoPS vol. 1, secs 12.1-6, 13.1-4
- Intersecting diagonals: AoPS vol. 1 sec. 12.1, 13.1
- Circumscribed polygons and Ptolemy's Theorem: AoPS vol. 2 sec. 4.3
- Polygonal prisms and pyramids (including volume and surface areas): AoPS vol. 18.4-5
Precalculus & Trigonometry
- Law of Sines, Law of Cosines: AoPS vol. 2 sec. 3.1
- Inverse functions and their graphs: AoPS vol. 2 sec. 2.2-3
- Solving trigonometric equations: AoPS vol. 2 sec. 2.5
- De Moivre's Theorem and the roots of unity: AoPS vol. 2 sec. 9.4-8
Algebra 2 & Analysis
- Use of fractional and negative exponents: AoPS vol. 1 sec. 1.1-2
- Simplifying expressions involving radicals: AoPS vol. 1 sec. 1.3-4
- Solving equations involving radicals: ....
- Use of logarithms; identities involving logarithms: vol. 1 sec. 1.5
- Solving logarithmic equations: AoPS vol. 2 sec. 1
- Relationships between logarithms to different bases: AoPS vol. 2 sec. 1
Practice Problems and Solutions
Best practice for
- Emphasize more-recent exams. The further back in time you go, the more the meet event topics and subtopics may deviate from what they are today. For example, some years (such as 2013-14) featured special topics designed only for that year. Generally, though, exams from the current century are representative of today's exams.
- Actually take the exam. Set aside 12 minutes (for an individual exam). Gather scratch paper (blank, not graph paper), multiple pencils (sharpening or reloading lead during a timed exam is inefficient, unnecessary, and unintelligent), an eraser, and a calculator (if allowed). Ensure you will not be interrupted by shutting the door and/or telling family members you are not to be disturbed. Set a timer, press start, and work the full 12 minutes, even if and when you become stuck and, particularly if this is the first time you have taken the exam even if you finish early. Practicing when you are stuck and relying on yourself is one of the best things you can do to develop creativity in any mathematical setting, be it homework, school math tests, or math league exams. Practicing when you are "done" by checking your work in multiple ways is the mark of a professional.
- Self-grade your exam. Be honest and unmerciful - hold yourself to a high standard. If you got it wrong, mark it wrong. You can take it again, later, after a few days or weeks to allow for some short-term memory-loss magic.
- Review the detailed solution for each problem, even those you answered correctly. Can you follow the reasoning? Did you approach the problem in the same way as the solution or in a different way? If different, is your way valid? Does the solution suggest other methods? Can you improve upon the solution?
- If there is anything you do not understand about the problem or its given solution, resolve to follow up with a teammate, a classmate, a family member or friend, your math teacher, or your math coach.
- Take the team event. These are designed to be completed by a team of 8 mathletes in 20 minutes. Select a time (60 minutes? 40 minutes? 30 minutes?) and do the entire exam. Note that it is possible for a single person to complete the exam in 30 minutes. (One Minnesota mathlete who homeschools and competes as an individual received a perfect score on the 2020-21 Meet 1 Team Event.)
Past problems and solutions:
Sessions
Tuesday, 24 November 2020: Forum AB
Notes on determinants
forum_ab_notes_on_determinants_-_maclennan_-_2020-11-24.pdf |
Monday, 30 November 2020: Meet 2 Review
Reviewed 2020-21 Meet 2 individual events A, B, C, D and Team select problems and solutions.
2020-21_meet_2_problems_and_solutions_-_mshsml_-_2020-11-30.pdf |
Tuesday, 1 December 2020: Forum AB
Focus: Problems 1 and 2. Can you solve #1 in one minute? Can you solve #2 in two minutes?
Meet 3 Events AB Problems #1-2 2018-19 & 2019-20 (blank)
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Meet 3 Events AB Problems #1-2 2018-19 & 2019-20 (filled-in)
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Meet 3 Events AB Problems #1-2 2016-17 & 2017-18 (blank)
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Meet 3 Events AB Problems #1-2 2016-17 & 2017-18 (filled-in)
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Thursday, 3 December 2020: Forum CD
Focus: Problems 1 and 2. Can you solve #1 in one minute? Can you solve #2 in two minutes?
Meet 3 Events CD Problems #1-2 2018-19 & 2019-20 (blank)
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Meet 3 Events CD Problems #1-2 2016-17 & 2017-18 (filled-in)
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Meet 3 Events CD Problems #1-2 2016-17 & 2018-19 (blank)
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Meet 3 Events CD Problems #1-2 2016-17 & 2018-19 (blank)
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Tuesday, 8 December 2020: Forum AB
Focus: Problem 3. Can you solve #3 in three minutes? We won't examine Problem 4, but can you solve #4 in six minutes?
Meet 3 Events AB Problem #3 2018-19 & 2019-20 (blank)
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Meet 3 Events AB Problem #3 2018-19 & 2019-20 (filled-in
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Meet 3 Events AB Problem #3 2016-17 & 2017-18 (blank)
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Meet 3 Events AB Problem #3 2016-17 & 2017-18 (filled-in)
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Thursday, 10 December 2020: Forum CD
Focus: Problem 3. Can you solve #3 in three minutes? We won't examine Problem 4, but can you solve #4 in six minutes?
Meet 3 Events CD Problem #3 2018-19 & 2019-20 (blank)
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Meet 3 Events CD Problem #3 2018-19 & 2019-20 (filled-in)
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Meet 3 Events CD Problem #3 2016-17 & 2017-18 (blank)
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Meet 3 Events CD Problem #3 2016-17 & 2017-18 (filled-in)
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