（本题13分）已知函数

（1）已知一直线经过原点且与曲线相切，求的直线方程；

（2）若关于的方程有两个不等的实根，求实数的取值范围。

第二节  书面表达（满分25分）

假如你是张林，刚进入高三学习，需要购买一本有关英语书面表达的书，请根据下列提示，写信给你在外文书店工作的朋友Jack，请他帮你挑选。

要求：1．词数100个左右。

2．不可逐字翻译，但可适当增加内容，使行文连贯。

3．参考词汇：过渡词transitional words  版本edition

注：信的开头和结尾已为你写好，不计入总词数。

Dear Jack,

How are you getting along these days?

I’m in Senior Grade 3 now, and I’m writing to you ask for a favor.                             

Thank you very much, my dear friend. I wish I hadn’t put you to so much trouble.

                                                                   Yours,

                                                                   Zhang Lin

阅读下列应用文及相关信息，并按照要求匹配信息。请在答题卡上将对应题号的相应选项字母涂黑。

下面是一篇有关书籍介绍的应用文，请阅读下列应用文和相关信息，并按照要求匹配信息。

首先请阅读下列应用文：

A

I Am a Pencil

Sam Swope's job was teaching writing to third-graders in New York City. His students were from 21 countries, speaking 11 languages, with different backgrounds. But there were a few things they had in common. Family troubles, for one. Money struggles. And poetry. Every single student, with the help of this creative teacher, came forth with awesome writing. Swope leaves the reader with the inspiring conviction (坚信) that deep within each of us lives a poet.

B

Between a Rock and a Hard Place

Aron Ralston, 28, went hiking in a remote Utah canyon without telling anyone. An unexpected catastrophe struck. With enough supplies only for a day, Ralston knew his situation was full of danger. Sure enough, after five days he was in a fight against death. That was when he carried out a courageous plan - using a pocket knife to cut off his trapped arm. His amazing survival story rests at a place among the classics of the genre (体裁).

C

Our Brother's Keeper

Author Jedwin Smith spent 30 years trying to repress (克制) all memories of his brother, Jeff, who was killed in Vietnam. But in Our Brother's Keeper he tells what happens when the Internet brings him into contact with several of his brother's old Marine friends, including the guy who held Jeff in his arms as he died. First via e-mail, and then in person, Smith gets to know these men.

D

The All Americans

With his graduation from West Point, Henry Romanek sailed toward Omaha Beach on the eve of Dday. It was June 1944, and he was about to face the bloodiest battle of his life. Just yesterday, it seemed, he was a standout soldier on the Army team. Now, he was a leader of youngsters in battle, fighting, quite literally, for his country and the future of the free world. In this book, Lars Anderson retraces Romanek's life and that of three other soldiers.

E

Copies in Seconds

With the push of a button, anyone can make copies of almost anything - unlike the old days, when papers had to be rewritten long-hand, carbon-copied out of fussy mimeograph machines (蜡纸油印机). In Copies in Seconds, David Owen showed how a shy engineer named Chester Carlson perfected his xerography machine （静电复印机） and shopped it around until finally hooking up with the Haloid Corporation. That partnership led to the Xerox copier and changed the face of work forever.

F

State of Grace

Back in the late 1950s and early 1960s, the Lynvets was just a football team in a sandy New York City neighborhood. But to most of its members - the author, Robert Timberg, included - the team was their only experience of a happy family, their only chance to rise above terrible everyday circumstances, their only shot at being heroes. The friendships these men formed sustained (维持) them throughout their lives.

请阅读以下求书者的信息，然后匹配他们所要寻找的书籍：

1. Tom is looking for a book about the hiking stories to help him in his following outdoor activities.

2. Kate wants to find a book about the stories of the soldiers during World War II.   .

3. Mark wants to research into the history of technological development.

4. Jack is researching into education in a college. He is especially interested in the teaching methods. He wants to find a book which can tell him something about how to teach students from different backgrounds.

5. John wants to find some materials about the soldiers in Vietnam War to carry on his new research.

    求书者                           书籍

1. Tom                  A. I Am a Pencil

2. Kate                  B. Between a Rock and a Hard Place    

3. Mark                   C. Our Brother's Keeper

4.Jack                   D. The All Americans

5. John                   E. Copies in Seconds

                                   F. State of Grace

2．如图17所示，将质量M=1.20 kg的小沙箱，用轻质软绳（不可伸长）悬挂起来，开始处于静止状态，绳的长度l=0.80 m。用枪向沙箱发射质量m=0.05 kg的子弹，子弹以v₀=100 m/s 的速度向右水平击中小沙箱，并留在小砂箱中，小沙箱沿竖直面向上摆动。假设沙箱每次向左运动到最低点时就恰好有一颗同样速度的子弹射入沙箱，子弹射入沙箱的过程时间极短，可忽略不计，重力加速度g取10 m/s²，不计空气阻力。

   （1）求第一颗子弹射入沙箱的过程中子弹对砂箱的冲量大小；

   （2）求第一颗子弹射入沙箱并相对沙箱静止的瞬间，求砂箱对绳的拉力的大小；

   （3）求第一颗子弹射入沙箱后，砂箱摆动的最大高度；

   （4）要使沙箱摆动的最大角度小于60°，射入沙箱的子弹数目至少为多少