?x?y?6?x?4,得?,所以A的坐标为(4,2)， 由??x?2y?y?2此时z的最大值为0.02?4?0.16?2?0.4（千万元），
所以公司投资养鱼场4千万元，远洋捕捞队2千万元时，两个项目的月平均利润之和最大．
19.（1）证明：∵四边形ABCD是菱形，∴AC?BD ∵BE?平面ABCD∴BE?AC ∴AC?平面BEFD ∴平面ACF⊥平面BEFD
（2）设AC与BD的交点为O，AB?a?a?0?， 由（1）得AC?平面BEFD， ∵BE?平面ABCD∴BE?BD， ∵DF//BE，∴DF?BD，
∴BD2?EF2??DF?BE??8，∴BD?22 ∴S四边形BEFD?1?BE?DF??BD?32， 2218∵cos?BAD?，∴BD2?AB2?AD2?2AB?AD?cos?BAD?a2?8 55∴a?5，∴OA2?AB2?OB2?3，∴OA?3 2∴VABCDEF?2VA?BEFD?S四边形BEFD?OA?26. 320.焦点坐标为(1,0) 可知
p?1 22所以p?2所以抛物线C的方程为y?4x
（Ⅱ）当直线l垂直于x轴时，?ABO与?MNO相似， 所以
OF21S?ABO?()? S?MNO24当直线l与x轴不垂直时，设直线AB方程为y?k(x?1) 设M(?2,yM)，N(?2,yN)，A(x1,y1)，B(x2,y2)， 解 ??y?k(x?1)?y?4x2整理得 k2x2?(4?2k2)x?k2?0，所以x1?x2?1
?
S?ABOS?MNO1?AO?BO?sin?AOBAOBOx1x21S1?2?????综上 ?ABO? 1S?MNO4?MO?NO?sin?MONMONO2242212x?1x?1x?121解：（Ⅰ）?(x)?f?x??，???x???． ?lnx??22x?1x?1x?x?1?x??x?1?∵x?0且x?1，∴???x??0∴函数?(x)的单调递增区间为?0,1?和?1，???． （Ⅱ）∵f?(x)?11，∴f?(x0)?，
x0x∴切线l的方程为y?lnx0?11(x?x0), 即y?x?lnx0?1, ① x0x0x设直线l与曲线y?g(x)相切于点(x1,e1)，
11?lnx0g(x)?e?，∴x1??lnx0,∴. 1x0x0lnx01111??x?lnx0?，即y?x??，② ∴直线l也为y?x0x0x0x0x0lnx01x?1?，∴lnx0?0． 由①②得lnx0?1?x0?1x0x0x∵g?(x)?ex，∴e1?下证：在区间（1,+?）上x0存在且唯一. 由（Ⅰ）可知，?(x)?lnx?x?1在区间上递增． （1,+?）x?1e?1?2e2?1e2?322又?(e)?lne???0，?(e)?lne?2??0，
e?1e2?1e?1e?1结合零点存在性定理，说明方程?(x)?0必在区间(e,e2)上有唯一的根，这个根就是所求的唯一x0，所以有且仅有一个x0．
?x2?x?2cos?22.解（1）∵?，∴?y2?1， 2??y?sin??x??cos?，由?得曲线C1的极坐标方程为y??sin???2=21?sin2?， 22x?y?2y?0，∴曲线C的极坐标方程为∵??2sin?； 2（2）由（1）得∴OA?OB?22OA??2?2222OB??2?4 sin2?1?sin?，， 2222?4sin???41?sin???4 ?1?sin2?1?sin2??20???6????1?sin2???9222，∴1?1?sin??2，∴1?sin?∵， ∴OA?OB22的取值范围为?2,5?. 1，∴2af?x?m??x?m?a?12a， 23.解：（1）∵f?x??x?a?∴f?x??f?x?m??x?a?x?m?a?m， ∴m?1，∴?1?m?1，∴实数m的最大值为1； a?12时， （2）当1??3x?a??1,x?a,?2a?11????x?a??1,a?x?,2a2??1113x?a??1,x?,g?x??f?x??2x?1?x?a?2x?1??2a2?2a g?x?min1?2a2?a?1?1?1?g????a???0222a2a??， ∴1??0?a?,?a?0,2???2a2?a?1?0??2a2?a?1?0∴?或? ?1?1??a?0??2,0??. ∴2，∴实数a的取值范围是?小升初英语检测试卷
姓名：_________ 得分：__________
听力部分（30分）
一、听录音，选出你所听到的内容。（10分）
( )1. A. play ( )2. A. waste ( )3. A. full ( )4. A. doctor ( )5. A. please ( )6. A. August 3rd ( )7. A. plastic bottles ( )8. A. father ( )9. A. sleepy ( )10. A. get out
B. pour B. wake B. cool B. dentist B. palace B. October 3rd B. paper bags B. fast B. sleeping B. come out
C. point C. water C. care C. pianist C. place
C. August 13th C. plastic bags C. fashion C. sweep C. look out
二、听录音，判断图片与录音内容是否相同，相同用T表示，不同用F表示。（5分）
1. 2. 3. 4. 5.
( ) ( ) ( ) ( ) ( )
三、根据所听内容，选择正确的应答句。（5分）
( ) 1. A. Yes, I am. ( ) 2. A. At ten. ( ) 3.A. No, she won’t. ( ) 4. A. Take a taxi. ( ) 5. A. In the afternoon.
B. Yes, they do. C. No, we don’t. B. Ten. C. It’s ten. B. Yes, he will. C. Yes, he is. B. Wait for the green man. C. Great! B. Watched a film. C. The Heping Cinema.
四、根据所听对话和问题，选择正确的应答句。（5分）
( ) 1. A. No swimming. B. Don’t take photos. C. No eating or drinking.
( ) 2. A. He could jump. B. He could draw. C. He could walk. ( ) 3. A. It was sunny. B. It was rainy. C. It was windy. ( ) 4. A. Canada. B. The UK. C. The US.
( ) 5. A. He went to school by bike. B. He often goes to school by bus. C. He’ll go to school on foot.
五、根据所听内容，填入所缺单词。（5分）
Jack is my . He has many good . He his things in . He likes healthy food. This , he is
going to Taipei with his . Jack me about his travel plans on the last night .
笔试部分（70分）
一、书写。（5分）
A．按照字母表顺序默写Nn-Uu。（大小写）（3分）
B. 把下面的句子正确规范地写在四线三格内，注意大小写及标点符号（2分） excuse me how can I get to sunny road
二、判断下面每组单词划线部分读音是否相同，用S或D来表示。（3分）
( )1. clown window ( )3. reach easily ( )5. sport horse
( )2. sharp hard ( )4. mouse through ( )6. hear careful
三、英汉互译。（10分）
1.保持健康 2. on Chinese New Year’s Eve
3.对…感到兴奋 4. put his things in order 5.收集一些纸 6. put on an English play 7.很多好习惯 8. eight months ago 9.发电子邮件给我 10. wait on the pavement
四、按要求写词。（5分）
1.tooth(复数) 2.study(三单) 3.cook(名词) 4.they (宾格) 5.slowly(反义词) 6.wake(过去式) 7.happy(副词) 8.brought(动词原形) 9. right（同音词） 10. plan（现在分词）
五、选择填空。（12分）
( )1.There_______any tomatoes on the table. But there _______some tomato
juice in the fridge.
A. are; are B. aren’t; is C. aren’t; are ( )2.The lion and the mouse is from______________.
A. Chinese idiom books B. Aesop’s Fables C. Japanese cartoons ( )3.The boys were very _______about the _______game. A. exciting; excited B. excited; excited C. excited; exciting ( )4.Where_______you last night? I_______ in the supermarket. A. are; am B. were; was C. were; am ( )5. What would you like _______? I’d like _________ bread. A. to eat; a few B. eating; some C. to eat; a little ( )6. _______will she stay in the USA?---For three months.
2024全国卷Ⅲ高考压轴卷(文科数学)
