Want to discuss the AMC 10/12B with AoPS instructors? Join us for the 2024 AMC 10B/12B Math Jam tonight, November 13, at at 7:30pm ET / 4:30pm PT, where we will discuss some of the most interesting problems from each test!
There is still time to train for the November 6th and November 12th AMC 10A/12A and AMC 10B/12B, respectively! Enroll in our weekend seminars to be held on November 2nd and 3rd (listed below) and you will learn problem strategies, test taking techniques, and be able to take a full practice test! Note that the “B” seminars will have different material from the “A” seminars which were held in October.
[list][*]Which problems did you get right?
[list][*]Was the topic a strength (e.g. number theory, geometry, counting/probability, algebra)?
[*]How did you prepare?
[*]What was your confidence level?[/list]
[*]Which problems did you get wrong?
[list][list][*]Did you make an arithmetic error?
[*]Did you misread the problem?
[*]Did you have the foundational knowledge for the problem?
[*]Which topics require more fluency through practice (e.g. number theory, geometry, counting/probability, algebra)?
[*]Did you run out of time?[/list][/list]
Once you have analyzed the results with the above questions, you will have a plan of attack for future contests! BEST OF LUCK to all competitors at this year’s AMC 10 and AMC 12!
Did you know that the day after both the AMC 10A/12A and AMC 10B/12B you can join a free math jam where our AoPS team will go over the most interesting problems? Find the schedule below under “Mark your calendars”.
Mark your calendars for these upcoming free math jams!
[list][*]November 20th: Amherst College Info Session, 7:30 pm ET: Matt McGann, Dean of Admission and Financial Aid at Amherst College, and Nathan Pflueger, math professor at Amherst College, will host an info session exploring both Amherst College specifically and liberal arts colleges generally. Topics include opportunities in math, the admission process, and financial aid for both US and international students.
[*]November 7th: 2024 AMC 10/12 A Discussion, Thursday, 7:30 pm ET:
[*]AoPS instructors will discuss problems from the AMC 10/12 A, administered November 6. We will discuss some of the most interesting problems from each test!
[*]November 13th: 2024 AMC 10/12 B Discussion, Wednesday, 7:30 pm ET:
[*]AoPS instructors will discuss problems from the AMC 10/12 B, administered November 12. We will discuss some of the most interesting problems from each test![/list] AoPS Spring classes are open for enrollment. Get a jump on the New Year and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!
Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile!
Whether you've taken our classes at AoPS Online or AoPS Academies or reached the top echelons of our competition training with our Worldwide Online Olympiad Training (WOOT) program, you can now add your AoPS experience to the education section on your LinkedIn profile.
Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.
Introductory: Grades 5-10
Prealgebra 1
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Introduction to Algebra A
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Introduction to Counting & Probability
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Introduction to Number Theory
Monday, Dec 2 - Mar 3
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Introduction to Algebra B
Wednesday, Dec 11 - Apr 9
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Introduction to Geometry
Monday, Nov 11 - May 12
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Intermediate Algebra
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Calculus
Tuesday, Dec 10 - Jun 10
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Contest Preparation: Grades 6-12
MATHCOUNTS/AMC 8 Basics
Mon, Wed & Fri, Dec 2 - Jan 10 (meets three times each week!)
Tuesday, Feb 4 - Apr 22
Sunday, Mar 23 - Jun 15
Wednesday, Apr 16 - Jul 2
MATHCOUNTS/AMC 8 Advanced
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Mon, Wed & Fri, Dec 2 - Jan 10 (meets three times each week!)
Tue, Thurs & Sun, Dec 10 - Jan 19 (meets three times each week!)
Sunday, Feb 16 - May 4
Friday, Apr 11 - Jun 27
Let , then . And , so if we have , and: , so , and it is seen that . And since and , has max at . So:
The maximum is , and this is reached when , i.e. being the roots of with the roots of . (They are real since the roots of are real iff , and in this case )
This post has been edited 2 times. Last edited by Mathias_DK, Jul 25, 2011, 9:09 PM
It follows from my solution.
Since and , we obtain , which is .
Hence, we can assume and .
From here we obtain and .
Thus, and we can use a calculus.
I think, your solution is better. forever!
After these solutions we see that
is true because .
If are real numbers and such that Prove that
Let prove that
Let such that .Prove:
Let Prove thath
Let be non-negative real numbers such that and .Prove that
Attachments:
This post has been edited 2 times. Last edited by sqing, Dec 2, 2020, 12:57 AM