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AMC数学竞赛8真题2014年 5-7

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 5

Margie's car can go $32$ miles on a gallon of gas, and gas currently costs $ $4$ per gallon. How many miles can Margie drive on $\textdollar 20$ worth of gas?

$amc数学竞赛$

Solution

Margie can afford $20/4=5$ gallons of gas. She can go $amc美国数学竞赛真题$ miles on this amount of gas.

Problem 6

Six rectangles each with a common base width of $2$ have lengths of $1, 4, 9, 16, 25$ , and $36$ . What is the sum of the areas of the six rectangles?

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Solution

The sum of the areas is equal to $2\cdot1+2\cdot4+2\cdot9+2\cdot16+2\cdot25+2\cdot36$ . This is simply equal to $2(1+4+9+16+25+36)$ , which is equal to $2\cdot91$ , which is equal to our final answer of $\boxed{\textbf{(D)}~182}$ .

Problem 7

There are four more girls than boys in Ms. Raub's class of $28$ students. What is the ratio of number of girls to the number of boys in her class?

$amc数学竞赛真题$

Solution

We can set up an equation with $x$ being the number of girls in the class. The number of boys in the class is equal to $x-4$ . Since the total number of students is equal to $28$ , we get $x+x-4=28$ . Solving this equation, we get $x=16$ . There are $16-4=12$ boys in our class, and our answer is $16:12=\boxed{\textbf{(B)}~4:3}$ .