Get ready for the AMC 10/12: What you need to know now

August 23, 2022 mathproblemsolvingskillsLeave a comment

Date November 10 and 16. (The AMC 8 is pushed back to January.) The MAA is offering paper and online formats.
Location Check with your school. If you are homeschooled or your school doesn’t host the AMC, check the MAA zip code search for a site near you. You’ll need to register with the local contact, not with the MAA.
Prep Don’t overthink this. Take old exams and study the problems you couldn’t solve.
Your goal Always to get to the next level. If you are new to the AMC, then your ultimate goal is to qualify for AIME. If you’re already AIME-qualified, then look to USAMO. Don’t bother with trying to get a perfect score. Move forward to more difficult problems. Each tier means greater achievement and greater prestige.
Strategy This isn’t the exam where with 5 minutes left you bubble in all the remaining answers. You’ll lose points you could have earned for each blank answer. Write a clean exam: all answers are correct or left blank.

My Interview with AoPS

August 10, 2022 mathproblemsolvingskillsLeave a comment

AoPS recently interviewed me about my thoughts on math education and math contests. I shared a number of unconventional ideas around math education, including:

Math isn’t always fun. Learning often feels awkward and uncomfortable. If our mantra is “Learning is Fun!” what message do we send, when it clearly isn’t?
Using math creatively means students need to know why their algorithms work. Otherwise, it’s like telling a student how use red paint or blue paint, but never showing them how they combine to make purple.
Studying a math curriculum without participating in a contest is like going to soccer practice every day without ever playing a game.
Math contest rules are not the boss of you.
Normalize frustration. Did I mention that learning isn’t fun?

Click here for the full interview.

2021 AIME I #9

August 1, 2022 mathproblemsolvingskillsLeave a comment

Let $ABCD$ be an isosceles trapezoid with $AD = BC$ and $AB<CD$ . Suppose that the distances from $A$ to lines $BC, CD$ , and $BD$ are $15, 18,$ and $10$ , respectively. Let $K$ be the area of $ABCD$ . Find $\sqrt{2} \cdot K$ .

2021 AIME I #8

July 17, 2022 mathproblemsolvingskillsLeave a comment

(Note: I have the wrong problem number written in the video whiteboard.)

Find the number of integers $c$ such that the equation $||20|x|-x^2|-c|=21$ has $12$ distinct solutions.

2021 AIME I #7

July 5, 2022 mathproblemsolvingskillsLeave a comment

Find the number of pairs $(m,n)$ of positive integers with $1 \le m < n \le 30$ such that there exists a real number $x$ satisfying $\sin(mx)+\sin(nx)=2$ .

2021 AIME #5

June 18, 2022 mathproblemsolvingskillsLeave a comment

Call a three-term strictly increasing arithmetic sequence of integers special if the sum of the squares of the three terms equals the product of the middle term and the square of the common difference. Find the sum of the third terms of all special sequences.

2021 AIME I #4

June 11, 2022 mathproblemsolvingskillsLeave a comment

Find the number of ways $66$ identical coins can be separated into three nonempty piles so that there are fewer coins in the first pile than in the second pile and fewer coins in the second pile than the third pile.

2016 AIME I #15

June 3, 2022 mathproblemsolvingskillsLeave a comment

Circles $\omega_1$ and $\omega_2$ intersect at points $X$ and $Y$ . Line $l$ is tangent to $\omega_1$ and $\omega_2$ at $A$ and $B$ , respectively, with line $AB$ closer to point $X$ than to $Y$ . Circle $\omega$ passes through $A$ and $B$ intersecting $\omega_1$ again at $D \neq A$ and intersecting $\omega_2$ again at $C \neq B$ . The three points $C, Y,$ and $D$ are collinear, $XC = 67, XY = 47,$ and $XD = 37$ . Find $AB^2$ .

2016 AIME I #14

May 26, 2022 mathproblemsolvingskillsLeave a comment

Centered at each lattice point in the coordinate plane are a circle with radius 1/10 and a square with sides of length 1/5 whose sides are parallel to the coordinate axes. The line segment from (0,0) and (1001, 429) intersects m of the squares and n of the circles. Find m+n.