【正文】 …7分②當時，在上有最小值；………………………8分③當時，在上單調(diào)遞減，在上單調(diào)遞增，在上有最小值．…………………………………………………………9分所以當時，函數(shù)在上有最小值．……………………………………………10分方法2：因為…………………………………………………………6分因為，所以．所以函數(shù)是單調(diào)遞減的．………………………………………………7分要使在上有最小值，必須使在上單調(diào)遞增或為常數(shù)．……8分即，即．……………………………………………………………………………………9分所以當時，函數(shù)在上有最小值． ……………………………………………10分若是真命題，則是真命題且是真命題，即是假命題且是真命題．……………11分所以 …………………………………………………………………………12分解得或． ………………………………………………………………………13分故實數(shù)的取值范圍為．…………………………………………………………14分20．（本小題主要考查動點的軌跡和直線與圓錐曲線的位置關(guān)系、導(dǎo)數(shù)的幾何意義等基礎(chǔ)知識，考查運算求解能力和推理論證能力等，本小題滿分14分）解：（1）方法1：設(shè)動圓圓心為，依題意得，．…………………………1分整理，得．所以軌跡的方程為．…………………………………………………2分方法2：設(shè)動圓圓心為，依題意得點到定點的距離和點到定直線的距離相等，根據(jù)拋物線的定義可知，動點的軌跡是拋物線．……………………………………………………1分且其中定點為焦點，定直線為準線．所以動圓圓心的軌跡的方程為．………………………………………………………2分（2）由（1）得，即，則．設(shè)點，由導(dǎo)數(shù)的幾何意義知，直線的斜率為．…………………………3分ABCDOxylE由題意知點．設(shè)點，則，即．……4分因為，．……………………………5分由于，即．………………………6分所以．…………………………………………………………………………………7分（3）方法1：由點到的距離等于，可知．………………………………8分不妨設(shè)點在上方（如圖），即，直線的方程為：．由解得點的坐標為．……………………………………………………………10分所以．由（2）知，同理可得．………………………………11分所以△的面積，解得．……………………………………………………………………………………………12分當時，點的坐標為，直線的方程為，即．…………………………………………13分當時，點的坐標為，直線的方程為，即． ……………………………………14分方法2：由點到的距離等于，可知．…………………………………8分由（2）知，所以，即．由（2）知，．所以．即． ①由（2）知． ②不妨設(shè)點在上方（如圖），即，由①、②解得…………………………10分因為，同理． ………………………………………………………………………………11分以下同方法1．21．（本小題主要考查函數(shù)的零點、函數(shù)的導(dǎo)數(shù)和不等式的證明等基礎(chǔ)知識，考查運算求解能力和推理論證能力等，本小題滿分14分）證明：（1）因為，且在上的圖像是一條連續(xù)曲線，所以函數(shù)在內(nèi)有零點．………………………………………………………………………1分因為，所以函數(shù)在上單調(diào)遞增．………………………………………………………………………2分所以函數(shù)在上只有一個零點，且零點在區(qū)間內(nèi)．而是函數(shù)的零點，所以．……………………………………………………………………………………………3分（2）先證明左邊的不等式：因為，由（1）知，所以．……………………………………………………………………………………………4分即．所以．…………………………………………………………………………………………5分所以．…………………………………………………6分以下證明． ①方法1（放縮法）：因為，…………………………………………7分所以．………………………………………………………………9分方法2（數(shù)學(xué)歸納法）：1）當時，不等式①成立．2）假設(shè)當（）時不等式①成立，即．那么．以下證明． ②即證．即證．由于上式顯然成立，所以不等式②成立．即當時不等式①也成立．根據(jù)1）和2），可知不等式①對任何都成立．所以．…………………………………………………………………………9分再證明右邊的不等式：當時，．由于，所以．…………………………………………………………………………………………10分由（1）知，且，所以． ……………………………11分因為當時，…………………………………………………………12分所以當時， ．所以當時，都有．綜上所述，．……………………………………………………………14分試卷類型：B20 1 3年廣州市普通高中畢業(yè)班綜合測試(二)英 語 20 1 3．4 本試卷共1 2頁，三大題，滿分1 35分。 注意事項：1．答卷前，考生務(wù)必用2B鉛筆在“考生號處填涂考生號。用2 B鉛筆將試卷類型(B)填涂在答題卡相應(yīng)位置上。 3．非選擇題必須用黑色字跡鋼筆或簽字筆作答，答案必須寫在答卷紙各題目指定區(qū)域內(nèi)相應(yīng)位置上；如需改動，先劃掉原來的答案，然后再寫上新的答案；不準使用鉛筆和涂改液。4．考生必須保持答題卡的整潔。 I 語言知識及應(yīng)用(共兩節(jié)，滿分45分) 第一節(jié) 完形填空(共1 5小題；每小題2分，滿分30分) 閱讀下面短文，掌握其大意，然后從1～1 5各題所給的A、B、C和D項中，選出最佳選項，并在答題卡上將該項涂黑。s author, says most teachers would find this method 6 because it needs only a small change in the way they teach. They already read storybooks in class. The only 7 in the new method would be increased attention to the print. Ms. Piasta says if adults can 8 children in the stories and get them to pay attention to letters and words, it makes sense that they will do better at 9 recognition. But few parents and teachers do this in a 10 way starting first with letters, then 11 moving to words, sentences and paragraphs. Teachers and parents can point to a letter and outline its 12 with a finger. They can point out a word and 13 , This is ‘dog’ . They can discuss the 14 of the print to find how the words bine to tell the story. And they can talk about the 15 of the print for example, how words are written from left to fight. 1. A. clearer B. better C. higher D. happier2. A. pared B. paired C. related D. involved3. A. avoiding B. solving C. developing D. forcing4. A. found B. locked C. interviewed D. observed5. A. studied B. discussed C. saw D. ignored6. A. reliable B. illogical C. unbelievable D. manageable7. A. difference B. concern C. problem D. challenge8. A. annoy B. leave C. interest D. puzzle9. A. word B. voice C. story D. number10. A. easy B. systematic C. different D. typical11. A. silently B. suddenly C. gradually D. mostly12. A. route B. shape C. move D. sound13. A. guess B. think C. explain D. answer14. A. size B. style C. form D. meaning15. A. organization B. development C. information D. improvement第二節(jié)語法填空(共1 O小題；每小題1．5分，滿分1 5分) 閱讀下面短文，按照句子結(jié)構(gòu)的語法性和上下文連貫的要求，在空格處填人一個適當?shù)脑~或使用括號中詞語的正確形式填空，并將答案填寫在答題卡標號為16～25的相應(yīng)位置上。s people were very weling of tourists, and never tried 19 (cheat) them. As I read I felt deeply touched by these warm words. Suddenly, a monkey came down from a nearby tree, snatched the book from my hand and took 20 away, along with my bag which contained all my belongings. I couldn39。A Are you petitive enough to make it in America? There is an undeniable excitement about ing to study in the ., but it39。 it is the land of freedom。s the place where different cultures clash ... and live together in peace. However, you guys might agree with me. it39。s all true. I remember how my heart was racing the first time I visited Times Square in New York. I can39。s List if you have all A39。t just e from your test performances. The requirements of classes in the . are much more varied and this is the biggest adjustment that overseas students have to manage. Some have papers that you have to write every week, others have group projects you must do with your classmates, presentations you make in the class, or research you do by yourself to prove your own idea. There es a night when you have a couple of projects for different classes, a paper, and an exam to study for. And that night you ask yourself, What did I get myself into?