2011年南山中学实验学校自主招生各科考试模拟试题含答案(5)

（3）由题意知W??5?a?x?6?80?x??480??a?1?x??????9分 所以：① 当0?a?1时，x=48，W最大，即A型48套，B型32套；?????10分 ② 当a?1时，a?1?0三种制造方案获得利润相等；??????????11分 ③ 当a?1时，x=50，W最大，即A型50套，B型30套??????????12分 ． 23．解：（1）AO = BD，AO⊥BD； ??????4分 （2）证明：如图2，过点B作BE∥CA交DO于E， ∴∠ACO = ∠BEO． 又∵AO = OB，∠AOC = ∠BOE， ∴△AOC ≌ △BOE．∴AC = BE． 又∵∠1 = 45°， ∴∠ACO = ∠BEO = 135°． ∴∠DEB = 45°． ∵∠2 = 45°，∴BE = BD，∠EBD = 90°．∴AC = BD． 延长AC交DB的延长线于F， 如图4．∵BE∥AC，∴∠AFD = 90°．∴AC⊥BD．??????8分 （3）如图3，过点B作BE∥CA交DO于E，∴∠BEO = ∠ACO． 又∵∠BOE = ∠AOC ， D M O E A N 1 C 图2 D 2 B F M ∴△BOE ∽ △AOC． ∴BEBO． ?ACAOE A N 1 C 2 又∵OB = kAO， 由（2）的方法易得 BE = BD．∴O 图3 B BD?k． ??????12分 AC24．解：（1）y = 2t；??????3分 （2）当BP = 1时，有两种情形： ①如图4，若点P从点M向点B运动，有 MB = ∴PQ = 6．连接EM， ∵△EPQ是等边三角形， ?33． ∴EM⊥PQ．∴EMB P 数学试题第 21 页 （共 37 页） 21 M 图4 Q C A 1BC= 4，MP = MQ = 3， 2E D ∵AB = 33，∴点E在AD上． ∴△EPQ与梯形ABCD重叠部分就是△EPQ，其面积为93．???6分 ②若点P从点B向点M运动，由题意得 t?5． PQ = BM + MQ?BP = 8，PC = 7．设PE与AD交于点F，QE与AD或AD的 延长线交于点G，过点P作PH⊥AD于点H，则 HP = 33，AH = 1．在Rt△HPF中，∠HPF = 30°， ∴HF = 3，PF = 6．∴FG = FE = 2．又∵FD = 2， ∴点G与点D重合，如图5．此时△EPQ与梯形ABCD 27 的重叠部分就是梯形FPCG，其面积为23．??9分 B P M 图5 C Q A H F E G D （3）能．4≤t≤5．??????12分 25． 解：（1）由y?ax2?bx?c过点C(0,?)，b?3a 得y?ax?3ax?2323 2(x1?x2)2?4x1x2?12?(?3)2?4?(?2 3223?y?x2?3x???????4分 332?a?（2）由（1）得3)?12 2a2223333x?3x??0时，x1??，x2? 33222?A(?3333,0)，B(,0)，又C、D两点关于直线x??对称 2223?D点的坐标为(?3,?)， 2过B(3331,0)、D(?3,?)两点的直线解析式为y?x? 22322设?P与y轴另一交点为M(0,m)，圆心为P(0,n)，则OM?OC?OB ?OM?1 21?P点的坐标为(0,?) 2数学试题第 22 页 （共 37 页） 22 ?P点的坐标满足y?313x?2 ?直线BD经过圆心P??????8分 （3）设BD交?P于另一点E， y 过E作EF?y轴于F，如图6. 则?OPB??FPE A M O B ?PE?OP?12 P E F ?E点的坐标为(?32,?1)??????10分 D Q C 设过E点的?P的切线为l，交y轴于Q， 图6 则?PEQ?90?，EF?PQ ?EF2?PF?FQ ?34?12?FQ ?FQ?32 ?Q的坐标为(0,?52)??????12分 设l的解析式为y?k2x?b2 ?直线l过E、Q ?k?3，b52?2??2 ?经过E点的?P的切线的解析式是：y??3x?52??????14分 数学试题第 23 页 （共 37 页） 23 x 2011年绵阳南山中学实验学校自主招生考试模拟试题（一） 英语试题 本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分，第I卷1至9页第Ⅱ卷10至11页即答题卷。满分150分。考试时间120分钟。此卷无听力测试。 ★ 祝考试顺利★ 第I卷 （选择题，共100分） 注意事项： 1.答第I卷前，考生务必将自己的姓名、准考证号、考试科目准确涂写在答题卡上。考试结束后，请将试题卷和答题卡一并交回。 2.选择题的作答：每小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑。如需改动，用橡皮擦干净后，再选涂其他答案标号。不能答在试卷上。 第一部分：英语知识运用(共两节，满分50) 第一节：单项填空（共20小题，每小题1分，满分20分） 从A、B、C、D四个选项中，选出可以填入空白处的最佳选项，并在答题卡上将该项涂黑。 ( ) 1. Attention, please. _______ “h” in the word “honest” is silent. You can’t lose it. A. A B. An C. The D. / ( ) 2. At Chinese New Year, some people visit their relatives, _______ stay with their families. A. another B. others C. the other D. the others ( ) 3. The woman feels that she should let her son _______ his own decision this time. A. makes B. make C. to make D. making ( ) 4.—Would you like to drink coffee or milk? —_________. Please give me some tea. A. Neither B. Both C. Either D. None ( ) 5.—What do you think of the school? —Great! It can provide us _____ hot water, it can also provide food_____ us. A. for ; for B. with ; with C. with ; for ( ) 6. —I don’t know when she _____ back tomorrow. —Don’t worry. I’ll call you when she _____ back. A. will come; comes B. comes; comes C. comes; will come D. will come ; will come 数学试题第 24 页 （共 37 页） 24 D. for ; with ( ) 7. —Excuse me. Did you see a girl in red walking past just now? —No, sir. I a newspaper. A. read B. was reading C. have read D. am reading ( ) 8. — Could you tell me_____ to go to Mianyan by train? —Just a minute, please. I have to check my computer. A. how much does it cost C. how much it cost B. how much did it cost D. how much it costs ( ) 9. —Do you mind if I sit here? —_____. It’s for Mr. Lee. A. Not at all B. Never mind C. Better not D. Of course not ( ) 10. ______ Oscar night, the shining stars in beautiful clothes walk on red carpets and drink champagne to celebrate their success. A. At B. In C. On D. For ( ) 11. — Mary, you’re going to buy an apartment here, aren’t you? —Yes, but I can’t_______an expensive one. A. spend B. cost C. pay D. afford ( ) 12. They are your skirts. Please __________. A. put it away B. put out it C. put them away D. put them out ( ) 13. —How long have you _______ the car? — For about two weeks. A. had B. bought C. borrowed D. lent ( ) 14. Dashan has known a lot of Chinese since he_____ to China ten years ago. A. has come B. come C. came D. had come ( ) 15. — What a clean and bright school, isn’t it? — Yes, It’s always clean and bright because it ________every day. A. clean B. cleaned C. is cleaned D. was cleaned ( ) 16. At least 500 million people are using QQ ________ by Ma Huateng to chat on line. A. created B. create C. creating 25 D. to create 数学试题第 25 页 （共 37 页）