6/17/2025 2010 AMC 12A

The best math program for middle school students
from a 7th grader A.
2025 chapter test
June 29, 2025
2021 state sprint
20/30
Q14 Probability silly mistake I included one but I wasn't supposed to When it says inclusive only count the highest number from 1 to H.
Q18 Geometry silly mistake Instead of 6^2 I put 4^2 which messed up the answer First always label the given side lengths then find the unknown side lengths
Q19 Number theory had the right number but my thought process wasn't right For these type of problems first find the number by subtracting the remainder then find the number of divisors then subtract by the amount of the divisors that cannot have that remainder and that is your answer
Q22 Algebra didn't know how to this problem Learn how to do this problem a fast way and accurate way
Q24 Algebra didn't know how to this problem Learn how to do this problem a fast way and accurate way
Q25 Probability Had an idea got close but it didn't work Learn how to do this problem a fast way and accurate way
Q27 Number theory didn't know how to this problem Learn how to do this problem a fast way and accurate way
Q28 Counting Had an idea but it didn't work Learn how to do this problem a fast way and accurate way
Q29 geometry Had an idea got close but it didn't work Learn how to do this problem a fast way and accurate way
Q30 Algebra didn't know how to this problem Learn how to do this problem a fast way and accurate way
2015 Mathcounts National
sprint #22
If six
people randomly sit down at a table with six chairs, and they do not notice
that there are name tags marking assigned seats, what is the probability that
exactly three of them sit in the seat he or she was assigned? Express your
answer as a common fraction.
Try this yourself first (extremely), then scroll down for solutions.
Choose the three people who sit correctly:
\( \binom{6}{3}=20 \).
The remaining three must all sit incorrectly.
A quick check (or listing) shows only two ways: \((A\,B\,C)\) or \((A\,C\,B)\).
Total favourable seatings \(=20\times2=40\); total seatings \(=6!\).
Therefore \( P=\dfrac{40}{720}=\boxed{\tfrac{1}{18}} \).
Pick the three fixed seats: \( \binom{6}{3}=20 \).
Derange the other three: \( !3 = 2 \).
Again \( 20\times2 = 40 \) good seatings, so
\[
P \;=\; \frac{20\cdot!3}{6!} \;=\; \boxed{\tfrac{1}{18}} .
\]
Derange the remaining 3 people. The number of derangements of 3 items is \[ D_3 \;=\; 3!\left(1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!}\right) \;=\; 6\left(1 - 1 + \frac{1}{2} - \frac{1}{6}\right) \;=\; 2. \]
each week a space
SAT 14 #2 wrong , 15 #2
SAT 16, #5, 6, wrong , 17, 3 and 6
2 weeks later
18, #5 and 5
19 vocab. words 11 - 20
SAT practice test 8, later math don't know what to do
2 weeks later
20, #5, 21, #4
more than a month later
22, #4 and 5 , 23, #4, 6, 8, 12
30, #5, 31, #9
32, #4, 5, 33, 2, 9
local math competition : 21-22 meet 1, # 1, 2, 3 right
34, #4, 35, #6 and 8
21-22 math competition meet 2, #1 and 3 , #2 almost
36 #1,2,3 need to work on harder vocabulary words
37 # 6,9
Math 2021-22 meet 2 # 1 and 3
5/6/25 This week for reading I did Crack Sat tests 38 and 39 and I only gave myself 15 minutes for each test to time myself.
For test 38 the questions I got wrong were 1 and 11 and for test 39 the questions I got wrong were 2 and 5.
Although I felt rushed I was able to complete the test while still comprehending everything so that’s good.
For math this week I realized that I struggled a lot on the algebra 2 part of the (local math competition) tests so I decided that I should learn some of the curriculum.
To learn the course I went on Khan academy and did 2 units of the course and I plan on continuing learning the course to help with (local math competition) problems in the future. Thank you.
2010 Mathcounts
Nationals sprint :
22. Side AB of regular
hexagon ABCDEF is extended past B to point X such that AX = 3AB. Given that
each side of the hexagon is 2 units long, what is the length of segment FX?
Express your answer in simplest radical form.
Try this question first before you scroll down for the solution.
Q28 counting didn't know how to do it. learn how to do it
Q30 probability didn't know how to do it. learn how to do it
Target
Q4 geometry had an idea but it did not work learn how to do it
Q6 probability didn't know how to do it learn how to do it
Q7 2-D+3-D geometry had an idea but it did not work learn how to do it
Q8 probability had an idea but it did not work learn how to do it
Team
Q4 combinatorics didn't know how to do it learn how to do it
Q7 counting and geometry didn't know how to do it learn how to do it
Q8 geometry didn't know how to create a picture that suits this problem learn how to do use imagination to help create a picture that suits this problem
Q9 probability had an idea but it did not work learn how to do it
Q10 counting silly mistake didn't read the question right underline important phrases