﻿ 2011AMC12 & AIME(頁 1) - 高中的數學 - Math Pro 數學補給站

## Math Pro 數學補給站's Archiver

### 2011AMC12 & AIME

[url=http://i.imgur.com/tvMcF.jpg]http://i.imgur.com/tvMcF.jpg[/url]

100.3.15補充

100.3.19補充

101.2.5補充

101.5.28補充

### 回復 1# bugmens 的帖子

12的我可以問看看學生還有沒有留的

[quote]原帖由 [i]bugmens[/i] 於 2011-3-13 07:14 AM 發表 [url=https://math.pro/db/redirect.php?goto=findpost&pid=2855&ptid=1080][img]https://math.pro/db/images/common/back.gif[/img][/url]

[url=http://i.imgur.com/tvMcF.jpg]http://i.imgur.com/tvMcF.jpg[/url]

A power boat and a raft both left dock A on a river and headed downstream.
The raft drifted at the speed of the river current. The power boat maintained
a constant speed with respect to the river. The power boat reached dock B
downriver, then immediately turned and traveled back upriver. It eventually
met the raft on the river 9 hours after leaving dock A. How many hours did it
take the power raft to go from A to B?
(A) 3　(B) 3.5　(C) 4　(D) 4.5　(E) 5

[url=http://www.artofproblemsolving.com/Wiki/index.php/2011_AMC_12A]http://www.artofproblemsolving.com/Wiki/index.php/2011_AMC_12A[/url]
(台灣看起來是考AMC 12A)

[url]http://www.google.com.tw/search?client=opera&rls=zh-tw&q=%E7%BE%8E%E5%9C%8B+AMC12%E6%AD%B7%E5%B1%86%E8%A9%A6%E9%A1%8C1995~2010&sourceid=opera&ie=utf-8&oe=utf-8&channel=suggest[/url]

[url]https://math.pro/db/viewthread.php?tid=709&page=3#pid2866[/url]

### 回復 5# Ellipse 的帖子

[url]http://www.99cef.org.tw/news_02.php?id=86[/url]

### 一題函數的數學競賽題請教

(A)$$-226$$　(B)$$-144$$　(C)$$-20$$　(D)20　(E)144

### 回覆 1# aliher327 的帖子

$$f_{1}(x)=\sqrt{1-x}, D_{1}=(-\infty,1]$$

$$f_{2}(x)=f_{1}(\sqrt{4-x})$$

$$x\in D_{2}\Leftrightarrow\sqrt{4-x}\in D_{1}$$ 且 $$4-x\geq0 \Leftrightarrow0\le4-x\le1$$。

$$f_{3}(x)=f_{2}(\sqrt{9-x})$$

$$x\in D_{3}\Leftrightarrow\sqrt{9-x}\in D_{2}$$ 且 $$9-x\geq0 \Leftrightarrow9\le9-x\le16$$。

$$f_{4}(x)=f_{3}(\sqrt{16-x})$$

$$x\in D_{4}\Leftrightarrow\sqrt{16-x}\in D_{3}$$ 且 $$16-x\geq0 \Leftrightarrow16-x=0$$。

$$f_{5}(x)=f_{4}(\sqrt{25-x})$$

$$x\in D_{5}\Leftrightarrow\sqrt{25-x}\in D_{4}$$ 且 $$25-x\geq0 \Leftrightarrow x=5^{2}-16^{2}=-231$$。