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AMC数学竞赛8真题2014年 8-10

2018-09-14 重点归纳

AMC 8数学竞赛专为8年级及以下的初中学生设计，但近年来的数据显示，越来越多小学4-6年级的考生加入到AMC 8级别的考试行列中，而当这些学生能在成绩中取得“A”类标签，则是对孩子数学天赋的优势证明，不管是对美高申请还是今后在数学领域的发展都极其有利！那么接下来跟随小编来看一下AMC 8的官方真题以及官方解答吧：

Problem 8

Eleven members of the Middle School Math Club each paid the same amount for a guest speaker to talk about problem solving at their math club meeting. They paid their guest speaker $\textdollar\underline{1} \underline{A} \underline{2}$ . What is the missing digit $A$ of this $3$ -digit number?

$amc数学竞赛$

Solution

A number is divisible by $11$ if the difference between the sum of the digits in the odd-numbered slots (e.g. the ones slot, the hundreds slot, etc.) and the sum in the even-numbered slots (e.g. the tens slot, the thousands slot) is a multiple of $11$ . So $1 + 2 - A$ is equivalent to $0\pmod{11}$ . Clearly $1+2-A$ cannot be equal to $11$ or any multiple of $11$ greater than that. Also, if the expression $1+2-A$ is to be equal to a negative multiple of $A$ , $A$ must be 14 or greater, which violates the condition that A is a digit. So $美国数学竞赛申请$ .

Problem 9

In $\bigtriangleup ABC$ , $D$ is a point on side $\overline{AC}$ such that $BD=DC$ and $\angle BCD$ measures $70^\circ$ . What is the degree measure of $\angle ADB$ ?

amc8美国数学竞赛真题

$南京美国数学竞赛$

Solution

BD = DC, so angle DBC = angle DCB = 70. Then CDB = 40. Since angle ADB and BDC are supplementary, $美国数学竞赛AMC培训$ .

Problem 10

The first AMC $8$ was given in $1985$ and it has been given annually since that time. Samantha turned $12$ years old the year that she took the seventh AMC $8$ . In what year was Samantha born?

$amc真题$

Solution

The seventh AMC 8 would have been given in 1991. If Samantha was 12 then, that means she was born 12 years ago, so she was born in $\boxed{(\text{A})1979.}$