SoR Meet 4
When and Where
Meet 4 is scheduled for Monday, 25 January 2021. It will take place online via the Math League online application at scoringmnmathleague.org. The start time is 4:30 pm. The meet is expected to last about an hour and a half.
Topics
BIG HINT
Here is a direct message from Mr. Tom Kilkelly, head of the problem-writing team, from the Math League Coaches newsletter
Good luck to students on Meet 4. A prepared student will have studied:
- secants of a circle (Event B)
- binomial expansion (Event C)
- conic sections (Event D) [okay, as this is the general topic, this isn't much of a hint]
4A Event A (Algebra 1) General Topic: Algebraic Manipulation
Here are the event subtopics:
4B Event B (Geometry) General Topic: Circular Figures and Solids
Here are the event subtopics:
4C Event C (Precalculus & Trigonometry) General Topic: Miscellaneous Topics
Here are the event subtopics:
4D Event D (Algebra 2) General Topic: Analytic Geometry of the Conic Sections
Here are the event subtopics:
Notes
Mr Mac's Notes
Math Notes for Meet 4 Event A (Algebra 1)
Original: 12/18/2020 Update: 12/26/2020 More notes. Update: 1/5/2021 More problems. |
Math Notes for Meet 4 Event B (Geometry)
Original: 12/25/2020 Update: 1/18/2021 More problems. |
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Math Notes for Meet 4 Event C (Precalculus & Trigonometry)
Original: 12/26/2020 Update: 1/7/2021 Correct-meet problems. |
Math Notes for Meet 4 Event D (Algebra 2 and Analysis)
Original: 12/26/2020 Update: 1/7/2021 More notes. More problems. |
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Art of Problem Solving
If you would like a more comprehensive treatment of a particular subtopic, but you no longer have the textbook from which you learned it, you are in luck. Here are four tables, one for each event in the upcoming meet. Each table has three columns:
- Column 1 lists the subtopics for the event.
- Column 2 lists 0 or more sections (e.g., 7.2 for chapter 7 section 2) within the Art of Problem Solving Volume 1: The Basics textbook, with a link to that chapter (you will need to track down the section yourself).
- Column 3 lists 0 or more chapters and sections within the Art of Problem Solving Volume 2: and Beyond textbook, with a link to that chapter.
4A Event A (Algebra 1) General Topic: Algebraic Manipulation
Meet 4 Event A (Algebra 1) Subtopic |
AoPS Vol 1 Section(s) |
AoPS Vol 2 Section(s) |
4A1 Factoring |
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4A2 Sums, products, quotients of rational expressions |
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4A3 Solving equations (including radical equations) involving rational expressions by factoring or the quadratic formula (no complex roots) |
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4A4 Rational exponents |
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4A5 Simplifying radical expressions |
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4A6 Functional notation and variational dependencies |
4B Event B (Geometry) General Topic: Circular Figures and Solids
Meet 4 Event B (Geometry) Subtopics |
AoPS Vol 1 Section(s) |
AoPS Vol 2 Section(s) |
4B1 Central, inscribed, tangential, and exterior angles |
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4B2 Power of a point (chords, secants, and tangents) |
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4B3 Interior and exterior tangents of two circles |
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4B4 Intercepted arcs |
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4B5 Areas of circles, sectors, circular segments |
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4B6 Cylinders, cones, and spheres (including volume and surface area) |
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4C Event C (Precalculus & Trigonometry) General Topic: Miscellaneous Topics
Meet 4 Event C (Precalculus) Subtopics |
AoPS Vol 1 Section(s) |
AoPS Vol 2 Section(s) |
4C1 Sequences: patterns and recursion formulas, arithmetic and geometric sequences |
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4C2 Series: partial sums, formulas for 1+2+...+n, 1^2+2^2+...+n^2, and 1^3+2^3+...+n^3 |
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4C3 Function notation |
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4C4 Factorial notation and the Binomial Theorem |
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4D Event D (Algebra 2) General Topic: Analytic Geometry of the Conic Sections
Meet 4 Event A (Algebra 2) Subtopics |
AoPS Vol 1 Section(s) |
AoPS Vol 2 Section(s) |
4D1 Use of the standard forms of equations of the conic sections |
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4D2 Graphs, including the location of foci, directrices, and asymptotes |
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4D3 Use of properties of conics to solve applied problems, including max-min problems using parabolas |
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Director's Presentation: A Primer on Conic Sections
Mr. Tom Young, the Executive Director of the Minnesota State High School Mathematics League, has compiled the following series of PowerPoint presentations on conic sections for the express purpose of preparing mathletes for Meet 4 Event D.
Part 1: Introduction and Overview
conics.pptx |
Part 2: Circles
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Part 3: Ellipses
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Part 3: Ellipses
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Part 4: Hyperbolas
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Noah's Sheets
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
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.
Practice Problems and Solutions
Past problems and solutions:
Sessions
Tu 12/15/2020 Forum AB: Meet 3 Review or AMC 10/12 Algebra 1 & Geometry
- Introduction to our new AMC 10 page.
- Review some 2020 AMC 10A problems.
2020 AMC 10A Problems
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2020 AMC 10A Selected Solutions
(For full solutions, see AMC 10 Problems & Solutions link above) |
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Th 12/17/2020 Forum CD: Meet 3 Review & AMC 10/12 Precalculus & Trig and Algebra 2 & Analysis
Cancelled; no attendees.
Tu 1/5/2021 Forum AB: Problems #1, #2
MSHSML Meet 4 Events AB Problems 1-2 (2019-20 and 2018-19) (blank)
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MSHSML Meet 4 Events AB Problems 1-2 (2019-20 and 2018-19) (filled-in)
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Th 1/7/2021 Forum CD: Problems #1, #2
MSHSML Meet 4 Events CD Problems 1-2 (2019-20 and 2018-19) (blank)
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MSHSML Meet 4 Events AB Problems 1-2 (2019-20 and 2018-19) (filled-in)
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MSHSML Meet 4 Events CD Problems 1-2 (2017-18 and 2016-17) (blank)
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MSHSML Meet 4 Events CD Problems 1-2 (2017-18 and 2016-17) (filled-in) [We didn't get to it during the session]
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Tu 1/12/2021 Forum AB: AMC 10/12 Algebra 1 & Geometry
We examined some AMC 10 and 12 problems from 2020. See the AMC 10 and AMC 12 pages for more information on the AMC 10/12 exams.
Forum AB notes on rational functions and factoring
era_sor_math_team_forum_ab_notes_on_rational_functions_and_factoring_-_maclennan_-_2021-01-11.pdf |
Th 1/14/2021 Forum CD: AMC 10/12 Precalculus & Trig and Algebra 2 & Analysis
Cancelled due to lack of mathlete interest.
Tu 1/19/2021 Forum AB: Problems #3
Cancelled due to coach unavailability.
Th 1/21/2021 Forum CD: Problems #3
By mathlete request we did circle problems in preparation for Event B Geometry. See the problems from Tu 1/5/2021 above. Here are some additional notes, concerning keeping the formulae for the circumference and area of a circle straight, and also why opposite angles of a *cyclic* quadrilateral are supplementary.
era_sor_math_team_forum_cd_notes__on_circles__-_maclennan_-_2021-01-21.pdf |