首页> 重点归纳 > AMC数学竞赛真题2017年10A 3-4

AMC数学竞赛真题2017年10A 3-4

2018-08-27 重点归纳

AMC10数学竞赛是美国高中数学竞赛中的一项，是针对高中一年级及初中三年级学生的数学测试，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。不管是对高校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AMC10数学竞赛真题以及官方解答吧：

Problem 3

Tamara has three rows of two $6$-feet by $2$-feet flower beds in her garden. The beds are separated and also surrounded by $1$-foot-wide walkways, as shown on the diagram. What is the total area of the walkways, in square feet?

[asy] draw((0,0)--(0,10)--(15,10)--(15,0)--cycle); fill((0,0)--(0,10)--(15,10)--(15,0)--cycle, lightgray); draw((1,1)--(1,3)--(7,3)--(7,1)--cycle); fill((1,1)--(1,3)--(7,3)--(7,1)--cycle, white); draw((1,4)--(1,6)--(7,6)--(7,4)--cycle); fill((1,4)--(1,6)--(7,6)--(7,4)--cycle, white); draw((1,7)--(1,9)--(7,9)--(7,7)--cycle); fill((1,7)--(1,9)--(7,9)--(7,7)--cycle, white); draw((8,1)--(8,3)--(14,3)--(14,1)--cycle); fill((8,1)--(8,3)--(14,3)--(14,1)--cycle, white); draw((8,4)--(8,6)--(14,6)--(14,4)--cycle); fill((8,4)--(8,6)--(14,6)--(14,4)--cycle, white); draw((8,7)--(8,9)--(14,9)--(14,7)--cycle); fill((8,7)--(8,9)--(14,9)--(14,7)--cycle, white); defaultpen(fontsize(8, lineskip=1)); label(

$\textbf{(A)}\ 72\qquad\textbf{(B)}\ 78\qquad\textbf{(C)}\ 90\qquad\textbf{(D)}\ 120\qquad\textbf{(E)}\ 150$

Solution

Finding the area of the shaded walkway can be achieved by computing the total area of Tamara's garden and then subtracting the combined area of her six flower beds.

Since the width of Tamara's garden contains three margins, the total width is $2\cdot 6+3\cdot 1 = 15$ feet.

Similarly, the height of Tamara's garden is $3\cdot 2+4\cdot 1 = 10$ feet.

Therefore, the total area of the garden is $15\cdot 10 =150$ square feet.

Finally, since the six flower beds each have an area of $2\cdot 6 = 12$ square feet, the area we seek is $150 - 6\cdot 12$, and our answer is $\boxed{\textbf{(B)}\ 78}$

Problem 4

Mia is helping her mom pick up $30$ toys that are strewn on the floor. Mia’s mom manages to put $3$ toys into the toy box every $30$seconds, but each time immediately after those $30$ seconds have elapsed, Mia takes $2$ toys out of the box. How much time, in minutes, will it take Mia and her mom to put all $30$ toys into the box for the first time?

$\textbf{(A)}\ 13.5\qquad\textbf{(B)}\ 14\qquad\textbf{(C)}\ 14.5\qquad\textbf{(D)}\ 15\qquad\textbf{(E)}\ 15.5$

Solution

Every $30$ seconds $3-2=1$ toys are put in the box, so after $27\cdot30$ seconds there will be $27$ toys in the box. Mia's mom will then put $3$toys into to the box and we have our total amount of time to be $27\cdot30+30=840$ seconds, which equals $14$ minutes. $\boxed{(\textbf{B})\ 14}$

Solution 2

Though Mia's mom places $3$ toys every $30$ seconds, Mia takes out $2$ toys right after. Therefore, after $30$ seconds, the two have collectively placed $1$ toy into the box. Therefore by $13.5$ minutes, the two would have placed $27$ toys into the box. Therefore, at $14$minutes, the two would have placed $30$ toys into the box. Though Mia may take $2$ toys out right after, the number of toys in the box first reaches $30$ by $14$ minutes. $\boxed{(\textbf{B})\ 14}$

以上就是小编对AMC10数学竞赛真题以及解析的介绍，希望对你有所帮助，更多学习资料请持续关注AMC数学竞赛网！


2017年AMC10A数学竞赛整套真题及解析，请点击下方查看：

AMC竞赛10A 01-02   AMC竞赛10A 03-04   AMC竞赛10A 05-06   AMC竞赛10A 07-08   AMC竞赛10A 09-10

AMC真题10A 11-12   AMC真题10A 13-14   AMC真题10A 15-16   AMC真题10A 17-18   AMC真题10A 19-20

AMC数学竞赛10A 21-22   AMC数学竞赛10A 23-24   AMC数学竞赛10A 25

上一篇： AMC数学竞赛真题2017年10A 5-6

下一篇： AMC考试都适合什么年龄段的学生参加？

你可能感兴趣

最新资讯

热门搜索

AMC考试

AMC备考

AMC 8

AMC年龄

AMC真题

含金量

咨询更多

1、在线咨询

课窝在线客服

咨询详情

2、微信咨询

扫描二维码，微信咨询