Hill
2018 chapter spring wrong 17 one off 20 arithmetic mean
2016 chapter target all 8 correct
AMC 2018 wrong 17 all others correct - 17 feet per step is not speed, can't time 5 to get other person's speed!
AMC 8 2016 8 (25 pair of 2's not 50!)15 (13^4-11^4 has 2 power)wrong; all other 23 right!
AMC 8 2014 wrong 10 22 24 25 others 21 correct
2122 mathcounts handbook 211-220 215 (3 power in 99!) 218 (circle of radius 5 lattice points; 0+5 3+4 and 4+3 total 12 not 8)wrong; other 8 right
1. 3D plane problem using mass point geometry.
1 A handy fact to know for MATHCOUNTS is that the volume of a regular tetrahedron with edge length 𝑠𝑠 is given by V = √2/12𝑠^3. In general, the volume of a tetrahedron with a triangular face of area𝐴 and perpendicular height with respect to that baseℎ is given by V = 1/3ℎ𝐴. Recall for a regular tetrahedron that each face is an equilateral triangle satisfying with area 𝐴=√3/4𝑠^2
1 odd 3 or 5 multiples - must separate odd 3 multiples vs odd 5 multiples first!
3 9 15 21... gaps of 6
5 15 25 35 45.. gaps of 10
then overlaping 15 multiples 15, 45, 75...
2. dot product vs cross product, differentiation
need to understand your own strength and weaknesses; fix past mistakes
1. 19s29
better solution of 19s29-
16C4-(5x11C4-10x6C4); the 5x11C4 includes twice of the two >=5H cases, so need to take away one;
https://artofproblemsolving.com/community/c3h1950938p13466408
https://artofproblemsolving.com/community/c3h1976740p13719538
https://artofproblemsolving.com/community/c3h1950938p13466408
We have tails, so 5 regions:
Now, we need to place heads in these regions, as such:
Now, we suppose there are in the first region, in the second, and so on. Then, we have , so this can be done in ways.
Now, we have to consider when we have one area with more than dots. There are ways to choose the area. WLOG, assume it is . Then, we have that , which can be done in ways. Thus, we need to subtract ways.
However, we overcomunted when we had numbers . Then, there are ways to choose them. WLOG, assume it is and . Then, , which can be done in ways. Thus, we need to add ways.
Thus our answer should be . Calculations give , , and . Thus our answer is ways.
1.
50 posts
#1 Jan 7, 2020, 5:04 pm
How many distinct circles of radius 2 units are in the coordinate place and pass through exactly two of the labeled points on this graph?
The points are (-1,1) (1,1) (3,1) (-1,-1) (1,-1) (3,-1)
my question -
https://artofproblemsolving.com/community/c3h1993131_past_mathcounts_problems_19901999
How many circles in the 2-D coordinate plane go through at least 3 lattice points (x, y) such that |x|, |y| ≤ 1?
(A) 39 (B) 63 (C) 72 (D) 78 (E) 84
past notes
#13 Jan 14, 2020, 8:35 pm
jlee28 wrote:
did anyone here get to nats countdown
too pr0
which state are you from? some states are much easier than others... speaking of free resources, you should do Alcumus (its organized by topic which is nice) and For The Win! (it helps to improve speed)
Use mathcounts trainer, do past mathcounts problems, and sleep a lot the day before. If you get a type of problem wrong often, like C&P, practice those problems and do the AoPS book.
I would recommend these applications:
a) Mathcounts Trainer
b) For the Win!
c) Alcumus
but before you try these out, please do some practice papers... it will tell you what you are good at and what you need to improve on....
Practice. Review missed problems, know ur weakness, practice in ur weaknesses, make them stronger, avoid making sillies by doing a lot of problems, and use your resources!
I was also first time MATHCOUNTS last year and I don’t know how many hours I spent on MATHCOUNTS trainer. It has a ton of old problems from other MATHCOUNTS competitions and lots of problems are similar to ones I did on the trainer. You can find it here: https://artofproblemsolving.com/mathcounts_trainer/play
When you get the question, don't pick up your pencil and start writing. Instead, read the whole question, and think about the steps you would take to solve it. Just get a rough plan in your head. In some cases, you may decide that the numbers given are good enough to do the question mentally. If so, then do it mentally. If you decide that you have a plan and the numbers are too big/messy for mental math, then use your pencil.
I used to just start writing without any idea of what I was doing. I was writing but had no aim. This got me faster. Think about it as if you're going somewhere. By thinking about it, you're giving yourself a map. If you had no map and you started writing, then it would be like you're driving without a map. If the distance was long, then which would be easier. Using the map, right?
Then, just start thinking through the question before touching your pencil. That should help.
I found a very simple solution using mass points. It is solvable in seconds now.
