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AMC数学竞赛真题2016年12B 5-6

2018-09-05 重点归纳

AMC12是针对高中学生的数学测验，该竞赛开始于2000年，分A赛和B赛，于每年的2月初和2月中举行，学生可任选参加一项即可。其主要目的在于激发学生对数学的兴趣，参予AMC12的学生应该不难发现测验的问题都很具挑战性，但测验的题型都不会超过学生的学习范围。这项测验希望每个考生能从竞赛中享受数学。那么接下来跟随小编来看一下AMC12的官方真题以及官方解答吧：

Problem 5

The War of $1812$ started with a declaration of war on Thursday, June $18$ , $1812$ . The peace treaty to end the war was signed $919$ days later, on December $24$ , $1814$ . On what day of the week was the treaty signed?

$美国数学竞赛amc12真题$

Solution

By: dragonfly

To find what day of the week it is in $919$ days, we have to divide $919$ by $7$ to see the remainder, and then add the remainder to the current day. We get that $\frac{919}{7}$ has a remainder of 2, so we increase the current day by $2$ to get $\boxed{\textbf{(B)} \text{Saturday}}$

Question: Why don't we have to account for leap years?

Answer: Although 1812 is a leap year, June 18 is after February 29. Plus, it gives you the number of days...so...

Problem 6

All three vertices of $\bigtriangleup ABC$ lie on the parabola defined by $y=x^2$ , with $A$ at the origin and $\overline{BC}$ parallel to the $x$ -axis. The area of the triangle is $64$ . What is the length of $BC$ ?

$amc12真题$

Solution

By: Albert471

Plotting points $B$ and $C$ on the graph shows that they are at $\left( -x,x^2\right)$ and $\left( x,x^2\right)$ , which is isosceles. By setting up the triangle area formula you get: $64=\frac{1}{2}*2x*x^2 = 64=x^3$ Making x=4, and the length of $BC$ is $2x$ , so the answer is $amc官方考题$ .