寒假即将结束，AMC12数学竞赛备考也进入了黄金备考阶段！AMC12竞赛考察了高中阶段所有数学内容，所以考生们需要对基础知识点熟练掌握，并依据AMC12竞赛历年真题进行拔高备考。
根据2023年的AMC12获奖分数线分析：AMC12晋级AIME最低在85.5分、全球5%（Honor Roll ）奖项分数最低在112.5分、全球1%奖项分数最低（Honor Roll of Distinction）在136.5分。
结合AMC考试的得分规则（答对1题得6分，未答得1.5分，答错不扣分）可知参加AMC考试，参赛者在AMC竞赛考试中如果能答对14道题（84分），剩余11道题（16.5分）全部空白不写，就可以得100.5分，如果大家再多做一道题，后面10道题即使一道不做，总分也就是105分，按照2023年的晋级数据，是可以入围晋级赛AIME。
备考AIME竞赛的一些建议：
复习基础知识：回顾并加强你在代数、几何、数论、概率等高中数学领域的基础知识。确保你对基本概念和解题方法有清晰的理解。可以通过复习教科书、笔记和做相关练习来巩固基础知识。
做过往真题：AIME的题目风格和难度与AMC系列有所不同。尝试做一些过去的AIME真题，了解考试的题型和难度，熟悉解题思路。这有助于你在考试中更加游刃有余。可以从简单的题目开始，逐渐挑战更难的题目。
理解解题方法：不仅仅要会做题，还要理解题目背后的解题思路。学习一些典型问题的解法，提高问题解决能力。可以阅读相关的解题技巧和策略，学习其他同学或专业教师的解题思路。尝试多种解题方法，培养灵活性和创造力。
刷题和反复练习：刷题是提高解题能力的关键。除了做过往的AIME真题，还可以尝试其他数学竞赛的题目，如美国数学奥林匹克（USAMO）等。通过反复练习，你可以熟悉各种题型，掌握解题技巧，并提高解题速度和准确性。
竞赛真题
AIME冲刺高分请扫码&免费获取AIME资料包
kilometer walk, and then finishes at the coffee shop. One day, she walks at 
kilometers per hour, and the walk takes 
hours, including 
minutes at the coffee shop. Another morning, she walks at 
kilometers per hour, and the walk takes 
hours and 
minutes, including 
kilometers per hour, how many minutes will the walk take, including the 
and 
with 
satisfy 
What is the value of 
?
tokens lies before them. The players take turns with Alice going first. On each turn, the player removes 
token or 
such that there is a strategy that guarantees that Bob wins, regardless of Alice’s moves.
She wins a prize if at least two of her numbers were 
where 
and 
.
and 
are drawn such that 
are collinear. Also, 
all lie on a circle. If 
and 
what is the length of 
?![[asy] import graph; unitsize(0.1cm); pair A = (0,0);pair B = (70,0);pair C = (70,16);pair D = (0,16);pair E = (3,16);pair F = (90,16);pair G = (90,33);pair H = (3,33); dot(A^^B^^C^^D^^E^^F^^G^^H); label("$A$", A, S);label("$B$", B, S);label("$C$", C, N);label("$D$", D, N);label("$E$", E, S);label("$F$", F, S);label("$G$", G, N);label("$H$", H, N); draw(E--D--A--B--C--E--H--G--F--C); [/asy]](https://latex.artofproblemsolving.com/1/2/f/12f0a4224f27ffa406ded2c01cfd349ecd0c04de.png)
that follow the lines from the lower left corner to the upper right corner on an 
grid. Find the number of such paths that change direction exactly four times, as in the examples shown below.![[asy] size(7.5cm); usepackage("tikz");label("\begin{tikzpicture}[scale=.4]\draw(0,0)grid(8,8);\draw[line width=2,red](0,0)--(2,0)--(2,3)--(5,3)--(5,8)--(8,8);\end{tikzpicture}",origin); label("\begin{tikzpicture}[scale=.4]\draw(0,0)grid(8,8);\draw[line width=2,red](0,0)--(0,3)--(3,3)--(3,5)--(8,5)--(8,8);\end{tikzpicture}",E); [/asy]](https://latex.artofproblemsolving.com/f/a/2/fa2be3ff5b03203d7779a7a359fa05e2bf9d0c55.png)
![\[222,222-22,222-2,222-222-22-2?\]](https://latex.artofproblemsolving.com/e/2/f/e2fbba6a2cccb3d60b70444a8b272999a204281e.png)
![\[\frac{44}{11} + \frac{110}{44} + \frac{44}{1100}\]](https://latex.artofproblemsolving.com/5/c/7/5c7e5b58fa8556742330357616baa41f8daabd7a.png)
, 
units are arranged in increasing size order so that their left edges and bottom edges align. The squares alternate in the color pattern white-gray-white-gray, respectively, as shown in the figure. What is the area of the visible gray region in square units?![[asy] size(150); filldraw((0,0)--(10,0)--(10,10)--(0,10)--cycle,gray(0.7),linewidth(1)); filldraw((0,0)--(9,0)--(9,9)--(0,9)--cycle,white,linewidth(1)); filldraw((0,0)--(7,0)--(7,7)--(0,7)--cycle,gray(0.7),linewidth(1)); filldraw((0,0)--(4,0)--(4,4)--(0,4)--cycle,white,linewidth(1)); draw((11,0)--(11,4),linewidth(1)); draw((11,6)--(11,10),linewidth(1)); label("$10$",(11,5),fontsize(14pt)); draw((10.75,0)--(11.25,0),linewidth(1)); draw((10.75,10)--(11.25,10),linewidth(1)); draw((0,11)--(4,11),linewidth(1)); draw((6,11)--(9,11),linewidth(1)); draw((0,11.25)--(0,10.75),linewidth(1)); draw((9,11.25)--(9,10.75),linewidth(1)); label("$9$",(5,11),fontsize(14pt)); draw((-1,0)--(-1,1),linewidth(1)); draw((-1,3)--(-1,7),linewidth(1)); draw((-1.25,0)--(-0.75,0),linewidth(1)); draw((-1.25,7)--(-0.75,7),linewidth(1)); label("$7$",(-1,2),fontsize(14pt)); draw((0,-1)--(1,-1),linewidth(1)); draw((3,-1)--(4,-1),linewidth(1)); draw((0,-1.25)--(0,-.75),linewidth(1)); draw((4,-1.25)--(4,-.75),linewidth(1)); label("$4$",(2,-1),fontsize(14pt)); [/asy]](https://latex.artofproblemsolving.com/5/e/6/5e6ea6522b82628aaadddaea887d0fa38d9bd19d.png)
. Which of the following integers cannot be the sum of the two numbers?
, 
, 
, and 
x
