一年级上数学竞赛试题

2024-08-10

一年级上数学竞赛试题（8篇）

1.一年级上数学竞赛试题篇一

一年级数学上学期的期末测试题

小学数学的学习至关重要，大家一定要掌握科学的学习方法，提高数学的学习效率。

一、我会算。

3+6= 9-7= 4+9= 6+7= 12-10= 7+5= 3+8= 16-6= 9-4= 10-8=

二、我会填。

1、( )，4，，( )，( )，12，14，( )

2、1，2，3，()，5，( )，( )

3、4个一和1个十合起来是( )。

4、19添上( )是20，是( )个十。

5、13和18这两个数，( )接近20，( )接近10。

6、个位上数是2，十位上的数比它少1，这个两位数是( )?与它相邻的两个数是( )和( )。

7、在6、12、3、7、16、9、10中，最大的数是( )，比9大的数有( )个?在其中任选三个数写出四道算式。

8、10+( )15， 4+( )12。

9、选择合适的符号填空，“”?“”或“﹦”。

19()20 12()3 8+5()8-5 10-7()4+3

10、估一估，每组两个算式中，在得数小的算式后面画“√”。

6+5□ 10-7□ 5+8□ 10-8□

三、巧手画一画。

1、接着画○，和△同样多。

△△△△△

2、画△和☆加起来一共12个。

☆☆☆☆☆☆☆

○○

3、按规律接着画

▲○▲▲○▲▲▲○

四、走进生活。

1、☆☆ ☆☆☆☆☆

☆☆☆ ☆☆☆☆☆

2、小明拍了6下球，小方拍的和他同样多，两人一共拍了多少下?

3、树上先飞走了8只小鸟，又飞走了5只?两次一共飞走了多少只小鸟?

2.一年级上数学竞赛试题篇二

课外作业是教师设计的,由学生在家里完成的一种学习任务,它是课堂教学的补充和延续,对于巩固课堂教学、提高学生的学业成绩起着重要的作用。每一次作业都是学生成长的生长点,及学生成长的履历,激发着学生成长的积极情感、态度与价值观。低年级的课外作业就是口头作业,作为一线老师,我和大部分低年级数学老师一样,对于如何布置出有效的口头作业一直在探索。

一、低年级数学口头作业应该是玩味的、竞赛的、充分“说”的作业

低年级的孩子注意力持续时间不会很长,绝大部分的孩子没有自制力、没有自我管理能力,他们天性好玩。而低年级的孩子对于孩子之间的比赛相当感兴趣,老师或家长一句夸奖的话都能让他们高兴半天。结合低年级孩子的特征,我们可以从以下三个方面设计作业。

1. 玩味型作业

儿童天性好玩,为了让学生体会数学与生活的密切联系,体会学习的乐趣,教师可以把一些数学家庭作业设计成玩味题,让学生在玩中学,在学中玩,感觉学和玩是可以同时存在的。如,在布置“比高矮”的作业时,老师可让学生回家和家长排排队,看看谁最高谁最矮;布置“前后、左右”的作业时,可设计:请家长坐好,说说家长及自己前后、左右有些什么;布置“10以内的加法”作业时,可让学生回家和爸爸妈妈玩凑数游戏。

2. 竞赛型作业

在教学中,适当的竞赛可以激发学生的学习积极性,增强学生学习的信心。因此,我们在教学中要尽可能多地设计一些竞赛型作业。如,在教学“表内除法”时,可设计让同桌之间、学生与家长之间进行比赛,看谁能把乘法口诀变换形式背下来,并且背得又准又快。在比赛中,两者之间互相监督、互相评价,最后进行自我评价,明确自己以后努力的方向。这样既满足了学生争强好胜的心理,又使学生在比赛活动中获得了成功的体验,树立了他们学好数学的信心。

3.“说”型作业

“说”相对于计算来说,学生更乐意接受。如,在教学“数一数”时,教师可布置学生数一数教室里的物体有几个,数一数生活中他们喜欢的物体有几个。学生对于这种作业的形式会很喜欢,而且兴趣会很浓,收到的教学效果也会非常好。另外,教师可以鼓励学生把有关数学的趣事讲给朋友听,还可以让学生把自己在生活中发现的“数学”说给好朋友听。学生在交流中不仅巩固了数学知识,培养了使用数学语言的能力,还让学生体验到了学数学的乐趣。

二、低年级数学口头作业应该发挥学校、社会、家庭的合力作用

1. 发挥学校的作用,即通过不同的活动形式让学生参与到学习数学的热情中

去年十月,我校2~6年级举办了“数学小报”设计比赛,全校学生都精心准备和积极参与。学生的小报在题目上设计新颖,很有童趣,如:“数学天地”“趣味数学”“数学直通车”……在内容上,丰富多样,如:“数学故事”“你知道吗?”“数学万花筒”“考考你”“数学家的故事”……另外,学生的小报结构形式合理,排版新颖,色彩搭配十分协调,并且还大胆创新,把每张小报都装饰得非常漂亮!学生可以将平时搜集的信息、资料编成一张手抄报。这样学生在编数学小报的过程,通过大量自觉的阅读、收集、思考、分析等系列活动,扩大了学生的知识面,锻炼了学生的能力。

2. 发挥社会的作用,即让孩子将数学融入生活中

孩子们学习数学的最终目的是能够运用到生活中,体会数学的作用,而在这方面老师可以通过引导学生关心身边的数学,善于用数学的眼光去审视客观世界中丰富多彩的现象,同时也让学生感受数学生活及社会各个领域中的广泛应用。例如,在教学完“简单的统计”后,我布置了这样一个作业:统计傍晚时,凤凰西街与汉北路十字路口10分钟过往车辆的数量,写一个调查报告。其中有些学生写信给镇长,建议政府拓宽两旁的街道;有人建议在这里装上红绿灯,这样会更加安全;还有人建议在这里建造一座立交桥,既美观又安全……把数学与生活紧紧连在一起,学生的创造性思维也得到了发展。

3. 发挥家庭的作用,即充分调到家长的作用

在上面两位老师的数学作业设计过程中,如果能调动家长的作业,一定能够事半功倍。低年级的孩子需要在老师与家长的监督下养成良好的习惯。如布置口算练习册的作业可以要求家长在身边督促孩子一定要读3遍,鉴于确定是否读过,可以让家长在作业上签字,等孩子习惯养成之后,家长可以放手让自己去完成作业。而每天的作业老师与家长一定要交流配合好,这样才能使作业发挥它应有的作用。

总之,低年级数学口头作业不仅仅要关注形式上的变化,更重要的是能调动孩子完成作业的热情,让孩子愿意且爱上作业,而这些不单单靠一方面力量就可以办到的,需要整合各方面的力量,调动各方面的资源。口头作业不仅仅是一种形式上的摆设,它应该是一种孩子课堂学习的延伸。当然,口头作业布置的方法还有很多,需要我们在教学过程中不断地摸索和创新。

参考文献

3.一年级上数学竞赛试题篇三

(A) 根据句意、首字母及汉语提示，完成单词。

1. ——Where is my backpack?

——Sorry, I don’t k____.

2. Is that your pen in the lost and f____?

3. Kate likes music and she wants to be a m____.

4. ——Can you tell me your e-mail a____, please?

——Kate@163.com.

5. I don’t like math at all. It’s d____.

6. He has a set of ____(钥匙) to the door of his house.

7. Music is ____(令人轻松的), so we all like it.

8. I like eating ____(健康的) food very much.

9. Can you sing this song ____(用) English?

10. Every evening, I watch TV for two ____(小时).

(B) 用所给单词的适当形式填空。

1. The girl in red clothes ____(be) my sister.

2. It’s very interesting ____(have) an English party.

3. Please take these ____(photo) to school.

4. September is the ____(nine) month of the year.

5. ——Who are the two ____(act)?

——Sorry, I don’t know.

Ⅱ.单项选择。

1. ——Hello, Li Ming! This is my new friend, Tom.

——____

——How do you do, Li Ming?

A. How are you, Tom?B. How do you do, Tom?

C. Nice to meet you, Tom. D. Good, Tom.

2. ——Excuse me. Who is that man?

——____.

A. Sorry, I don’t know B. He is at school

C. He is fine D. He is OK

3. I’m new here. I’m ____. I can’t find my way.

A. happy B. lost C. tiredD. strict

4. ——Can you speak Japanese?

——____.

A. Yes, I can B. Yes, I do C. Yes, I can’tD. No, I can

5. The man ____ red is my teacher.

A. wearB. with C. onD. in

6. He wants to talk ____ his teacher.

A. in B. at C. with D. before

7. What a funny thing! Can you let me ____ a try?

A. haveB. give C. to have D. to give

8. ——What’s this ____?

——It’s a hat.

A. in the English B. in English

C. for English D. at English

9. ——Let’s play tennis. Do you have a tennis racket, please?

——____.

A. Sorry, I doB. Yes, I don’tC. Sorry, I don’tD. Oh no, sorry

10. ——Is it ____ English dictionary?

——Yes, it is.

A. some B. the C. a D. an

11. We need lots of ____ food every day.

A. meatsB. vegetables C. healthy D. apples

12. They always sell their clothes ____ a very high price.

A. inB. for C. on D. at

13. ——____ kind of movies do you like?

——Action movies.

A. WhatB. Who C. How D. When

14. We often go ____ a movie on weekends.

A. seeB. watch C. to look D. to see

15. ——Here ____ some books for you, Jim.

——Thank you.

A. is B. are C. am D. isn’t

Ⅲ.句型转换。

1. His sister has a basketball. (改为一般疑问句)

____ his sister ____ a basketball?

2. My sister has chicken for lunch. (对划线部分提问)

____ ____ your sister ____ for lunch?

3. The shop sells the black shorts for $25. (改为同义句)

The black shorts are ____ ____ for $25 in the shop.

4. They have a basketball game on July 22nd. (对划线部分提问)

____ do they ____ a basketball game?

5. She goes to buy many vegetables with her mother. (改为否定句)

She ____ ____ to buy many vegetables with her mother.

Ⅳ.根据汉语意思完成句子。

1. 吉姆是你的朋友吗？

Is Jim ____ ____?

2. “你喜欢运动吗？”

“是的，非常喜欢。”

——Do you ____ ____?

——Yes, very ____.

3. 你喜欢什么颜色的裤子？

____ ____ pants ____ you ____?

4. 莎莉的生日聚会是什么时候？

____ is Sally’s ____ ____?

5. 请在明天早上5点前叫醒我。

_____________________

Ⅴ.补全对话。（每空一词）

A: Excuse me. Where __1__ you from?

B: I __2__ from France.

A: What do you know __3__ New York?

B: Well, a lot. New York is a big __4__. It is very beautiful.

A: Can you __5__ English?

B: Yes, but only a __6__. I think English is hard to learn.

A: I think I can __7__ you with English, and you can help me with

my __8__.

B: Thanks a __9__.

A: You’re __10__.

Ⅵ.完形填空。

Near my home there’s a big __1__. It’s called Hongpi Clothes Store. You can __2__ all kinds of __3__ in it. Do you like __4__? They have very beautiful sweaters for __5__ ￥95. Do you need __6__? They sell great bags __7__ ￥36. They __8__ have nice skirts for girls __9__ red, green, white and blue, and football socks for boys. And they __10__ many nice clothes. Do you want to go there with me? Let’s go together (一起) this Sunday!

1. A. schoolB. factory C. hospital D. store

2. A. sell B. buy C. takeD. come

3. A. vegetables B. clothes C. food D. fruit

4. A. socks B. trousersC. shortsD. sweaters

5. A. only B. also C. too D. but

6. A. bags B. pens C. booksD. hats

7. A. toB. on C. in D. for

8. A. tooB. alsoC. only D. often

9. A. inB. from C. on D. out

10. A. buy B. sellC. do D. like

Ⅶ.阅读理解。

(A)

My name is Jim and I live in Canada. My mother is from Korea and my father is from France, so we speak three languages at home. I think languages are very interesting and I want to study Portuguese and Chinese. But my favorite subject at school isn’t language. It’s math. I really like history, too.

I like sports, especially soccer and basketball, because they’re relaxing, but I don’t have much time to play. I go to music club after school on Mondays, have guitar lessons on Wednesdays, and go to the library on Fridays. But Saturdays and Sundays are great because I can play sports, sleep, and watch TV.

1. Jim’s parents live in ____.

A. Argentina B. Japan C. Mexico D. Canada

2. Jim can speak ____ very well at home.

A. KoreanB. Chinese C. Portuguese D. Japanese

3. His favorite subject is ____.

A. a language B. math C. history D. Chinese

4. He can’t play soccer on ____.

A. Mondays and Fridays B. Tuesdays and Sundays

C. Saturdays and Thursdays D. Saturdays and Sundays

5. Jim thinks sports are ____.

A. interesting B. funnyC. relaxing D. happy

(B)

The children next door often play football in the garden and sometimes break my windows. Today I stay at home and read a book. After an hour, I close my eyes and go to sleep. A sound at the door makes me get up. In a moment a little boy comes in. “Break one of my windows again?”

“Oh, no,” the boy answers. “Your window is open this time and our ball is in your bedroom. May we get it, please?”

根据文章内容判断正（T）误（F）。

1. Sometimes I watch the children play football in the garden.

2. I open the window to get their football.

3. I’m sleeping when the boy comes.

4. The children often play football in the garden.

5. I think they break my window but they want to get the ball.

Ⅷ.书面表达。

4.五年级数学上第一单元测试题篇四

一、神机妙算我能行!(共35分)

1、口算(5分)

0.2×0.4=8.2+1.8=100-35.22=2.5×0.4=0.8×50=

2.4×5=0.9-0.52=3.99×1=0×3.52=12.5×8=

2、列竖式计算(12分)

42×5.45.6×1.80.25×0.046

(保留两位小数)

验

算

3500×0.961.08×250.12×0.44

(保留到十分位)

3、怎么简便就怎么算.(18分)

0.125×320.78×1013.26×5.7-3.26×0.7

56.5×99+56.51.25×213×0.819.625-(4.716+9.625)

二、填空。(共28分)

1、根据321×23=7383，很快写出下面各题的积。

3.21×23=3.21×2.3=32.1×2.3=

32.1×0.23=3.21×0.23=321×0.023=

2、在下面的圆圈里填上“>”、“<”或“=”。

23.2×0.9○0.915.6×3.2○3.2×15.6

1×0.36○13.6×5.2○52×0.36

3、5个1.6相加，用加法表示是，用乘法表示是()，

结果是()。

4、0.35×2.73的积有()位小数，a×2.3的积是三位小数，那么a至少是()

位小数。

5、0.27扩大到它的100倍是()。325缩小到它的是()。

6、填空。

31.69618.94530.463

保留整数

保留一位小数

精确到百分位

7、一块玻璃长是1.2米，宽是0.85米，这块玻璃的面积是()平方米，如果每

平方米的售价是18.5元，这块玻璃是()元。

三、判断题(共5分)

1、0.36时=36分。 ( )

2、一个数的1.65倍一定大于这个数。()

3、两个小数相乘的`积一定大于1。()

4、“1.6×0.35×5=0.35×(1.6×5)”应用了乘法的交换律和乘法的结合律。

()

5、一个因数扩大10倍，另一个因数缩小到它的，积不变。 ( )

四、文字题。(共6分)

1、1.25乘4.2减5，差是多少?

2、比4.7的1.5倍多3.05的数是多少?

3、3.5与4.9的积是多少?(精确到个位)

4、25.26的3.6倍是多少?(保留两位小数)

五、我能解答生活问题。(共26分)(第4题6分)

1、五(3)班的黑板长3.2米，宽1.5米，同学们在黑板的一周围上花边，花边长多少米?

2、湘江花园的一幢大楼有16层，每层高2.96米，这幢大校高约多少米?(得数保留整数)

门票成人：每张4.5元

儿童：每张2.5元

3、小玲和爷爷、奶奶、爸爸、妈妈一起去公园游玩，只见入门处写着：

请你帮她算一算，买门票一共要几元?

4、小兰家每天平均用电2.3度，八月份她家共用电多少度?如果每度电0.79元，她家八月份一共应缴纳电费多少元?(得数保留一位小数)

5.七年级数学上竞赛试题篇五

1、已知代数式的值是4，则代数式的值是（）

A、10 B、9 C、8 D、不能确定

2、用四舍五入得到的近似数中，含有三个有效数字的是（）

A、0.5180 B、0.02380 C、800万 D、4.001

23．某项科学研究，以45分钟为1个时间单位，并记每天上午10时为0，10时以前记为负，10时以后记为正，例如9∶15记为－1，10∶45记为1等等，依此类推，上午7∶45应记为（）

A、3 B、－3 C、－2.15 D、－7.454、一台电视机成本价为a元，销售价比成本价增加25％，因库存积压，所以就按销售价的70％出售。那么每台实际售价为（）．

A、（1+25％）（1＋70％）a元B、70％（1+25％）a元

C、（1+25％）（1－70％）a元D、（1+25％＋70%）a元

5、现定义两种运算“”，“”。对于任意两个整数，，则（68）（35）的结果是（）

A、60 B、69 C、112D、906、在一次“人与自然”知识竞赛中，竞赛试题共有25道题．每道题都给出4个答案，其中只有一个答案正确．要求学生把正确答案选出来．每道题选对得4分，不选或选错倒扣2分．如果一个学生在本次竞赛中的得分不低于60分；那么，他至少选对了多少道题？（）

A、15B、16C、19D、20

二、填空题：

7、已知，则____

8、关于x的一元一次方程（2m－6）x│m│－2=m2的解为.9、某商品价格为元,降低10%后,又降低10%,销售量猛增,于是商店决定再提价20%,此时这种商品的价格为______元.10、写出一个大于3而小于5的无理数:

11、把1000个黑球与白球按如下图规律摆放，则黑球有______个，白球有______个。

●○●○○●○○○●○○○○●○○○○○●○○○○○○●……

三、解答题：

12、计算（每小题5分，共15分）

13、（本题6分）先化简再求值

14、（本题8分）乐乐每天早晨在7∶30前赶到离家1千米的学校上学．一天，乐乐以80米／分的速度从家出发去学校，５分钟后，乐乐的爸爸发现他忘记带语文书了，于是，爸爸立即以180米/分的速度去追，并在途中追上了乐乐．问：

（1）爸爸追上乐乐用了多长时间？(请用列方程的方法解)

（2）追上乐乐时，距离学校还有多远？

15、（本题6分）某旅行社组织36名游客拟乘汽车赴杭州西湖旅游，可租用车子有两种：一种每辆乘8人；另一种每辆乘4人。要求租用的车子不留空座，但也不能超载。

问：①请给出至少三种不同的租车方案？（3分）

②若每辆8个座位的车子租金300元/天，每辆4个座位的车子的租金200元/天，请你设计费用最少的租车方案，并说明理由。（3分）

16、（本题11分）某租赁公司拥有100辆汽车，当每辆车的月租金为3000元时，可全部租出，当每辆车的月租金每增加50元时，未租出的车将会增加一辆，租出的车每辆每月公司需要维护费150元，未租出的车每辆每月公司需要维护费50元．

（1）已知2月份每辆车的月租金为3600元时，能租出多少辆车?

（2）已知1月份的维护费开支为12900元，问该月租出了多少辆车?

（3）请你比较1、2两月的月收益，哪个月的月收益多?多多少?

17、（本题11分）某移动通讯公司开设了两种通讯业务．一是“全球通”，使用者先交50元月租费，然后每通话一分钟，再付话费0.4元；二是“神州行”，不交月租费，每通话1分钟，付话费0.6元．若一个月内通话x分钟，两种方式的费用分别为y1和y2元．

（1）直接用含的代数式表示出y1、y2。

（2）请你替郑老师选择一种较合算的通讯业务。

18、（本题12分）某初中为全体学生办理了“学生团体住院医疗保险”．保险公司按下表级距分段计算给付“住院医疗保险金”．

级数被保人住院医疗费用级距保险公司给付比例

在保险期间，被保险人按上述标准累计自付金额超过6000元的部分，保险公司按100％的标准给付.（1）小林同学在一次打篮球时不慎意外受伤，并住院治疗，总共化去医疗费用3500元，问小林同学可以收到保险公司的保险金有多少元？（4分）

（2）小蔡同学也生病住院，住院治疗期间，老师同学都去探望。出院后，保险公司根据他所化去的住院治疗费用给他送来了3120元保险金，你能知道小蔡共化去多少元住院治疗费吗？（4分）

6.二年级上数学竞赛试题篇六

1.直接写出得数。

6×1= 9÷3= 54÷6= 30+5=

27÷3= 4×8= 36÷9= 6×7=

3×5= 9×2= 48-8= 5÷5=

84-8= 3×6÷9= 40÷5÷8 3×3×5=

3+5×4= 9-4×2= 15-7×2= 8+20÷4=

2.用竖式计算。（8分）

65-8+25= 74+16-28=

95-27-39= 45+46-23=

二、我是思维小能手。

1. □×△=30 △-□=1

□=（） △=（）

2.小红有20颗糖，小亮有12颗糖，小红给小亮（）颗糖，两人的糖一样多，都是（）颗。

3.小刚身高132（），他从家到学校的路程长约800（）。

4.一根长绳原来长20米，第一次减去5米，第二次减去10米，现在这根绳子比原来短了（）米。

5.猴妈妈摘了一些桃子，比20个多，比40个少，把他们平均分给一些小猴，每只猴分得的个数和猴的只数同样多，猴妈妈摘了（）个桃子，有（）只猴。

7.一年级上数学竞赛试题篇七

本大题共12小题, 每小题5分, 共60分.在每小题给出的四个选项中, 只有一项是符合题目要求的.

1.设集合A={1, 2, 3}, B={1, 3, 5}, x∈A, 且 x∉B, 则 x= ( )

(A) 1 (B) 2 (C) 3 (D) 5

2.已知复数 z1=m+2i, z2=3-4i, 若 $\frac{z_{1}}{z_{2}}$ 为实数, 则实数 m 等于 ( )

$(A) \frac{8}{3} (B) - \frac{3}{2} (C) - \frac{8}{3} (D) \frac{3}{2}$

3.已知0<a<1, loga (1-x) <logax, 则 ( )

$\begin{array}{l} (A) 0 ＜ x ＜ 1 (B) x ＜ \frac{1}{2} \\ (C) 0 ＜ x ＜ \frac{1}{2} (D) \frac{1}{2} ＜ x ＜ 1 \end{array}$

4.m、n 是互不垂直的直线, 平面α、β分别过 m、n, 则下列关系不可能的是 ( )

(A) m//β (B) α//β

5.曲线 $y = \frac{1}{3} x^{3} - 2 x$ 在 x=1处的切线的倾斜角是 ( )

$(A) \frac{π}{6} (B) \frac{3 π}{4} (C) \frac{π}{4} (D) \frac{π}{3}$

6.已知正四棱锥S—ABCD的侧面与底面所成的二面角的大小为 $\arccos \frac{2}{3}$ , 则这个正四棱锥的侧面面积与底面面积之比为

(A) 3∶2 (B) 2∶3

7.“lgx>lgy”是“10x>10y”的 ( )

(A) 充分不必要条件

(B) 必要不充分条件

(D) 不充分不必要条件

8.若函数 y=f (x+1) , x∈R的图象与函数 y=lg (x+1) 的图象关于直线 x-y=0对称, 则 f (x) 等于 ( )

(A) 10x (B) 10x-1

9.下列四个函数中, 最小正周期为π, 且其图象关于直线 $x = \frac{π}{6}$ 对称的函数是 ( )

$\begin{array}{l} (A) y = \sin (2 x - \frac{π}{6}) \\ (B) y = \sin (x - \frac{π}{6}) \\ (C) y = \sin (2 x + \frac{π}{6}) \\ (D) y = \sin (x + \frac{π}{6}) \end{array}$

10.若数列{an}中, $a_{n} = \frac{10^{n}}{n ！}$ , 则下列答案正确的是 ( )

(A) 数列{an}为递增数列

(B) 数列{an}为递减数列

(D) 从某项起递增

11.在△AOB (O为坐标原点) 中, $\vec{Ο A} = (\cos α ‚ \sin α) ‚ \vec{Ο B} = (2 \cos β ‚ 2 \sin β)$ , 若 $\vec{Ο A} \cdot \vec{Ο B} = - 1$ , 则△ABC的面积为 ( )

$(A) \sqrt{3} (B) \frac{\sqrt{3}}{2} (C) 2 \sqrt{3} (D) 1$

12.如图1, A1, A2是椭圆 $\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1$ 的长轴上的两个顶点, P是椭圆上异于A1、A2的一点, A1P、A2P分别交左准线于M、N, 则以线段MN为直径的圆恒过定点 ( )

$\begin{array}{l} (A) (- 3 ‚ 0) (B) (- 5 ‚ 0) \\ (C) (0 ‚ 0) (D) (\frac{25}{3} ‚ 0) \end{array}$

二、填空题:本大题共4小题, 每小题4分, 共16分.把答案填在题中的横线上.

13.以正五棱柱10个顶点为顶点的四面体共有__个 (用数字作答) .

14.设 an 为 (2-x) n 展开式中 x2 的系数 (n≥2) , 则 $\lim_{n \to \infty} (\frac{2^{2}}{a_{2}} + \frac{2^{3}}{a_{3}} + \dots + \frac{2^{n}}{a_{n}}) =$ __.

15.已知离散型随机变量ξ的一个分布列为

且 $E ξ = \frac{11}{6}$ , 则 a+3b=__.

16.圆 x2+y2-2ay=0的圆心与抛物线 $y = \frac{1}{4} a x^{2}$ 的焦点重合, 则 a=__.

三、解答题:

本大题共6小题, 共74分.解答应写出文字说明、证明过程或演算步骤.

17. (本小题满分12分)

在斜三角形ABC中, 内角A、B、C满足 $\frac{\sin^{2} B - \sin^{2} A - \sin^{2} C}{s i n C} = \frac{\cos (A + C)}{c o s A}$ , 求角A的大小.

18. (本小题满分12分)

如图2, 在棱长为 a 的正方体ABCD—A1B1C1D1中, M为DD1的中点, 设 l 为平面MAC的垂线.

(1) 求 l 与B1C所成角的大小;

(2) 求B1到平面MAC的距离.

19. (本小题满分12分)

在某电视台举办的青年歌手大奖赛上有一个环节, 就是每个选手必须参加文化素质考核, 考查方式是完成一道连线题, 考试内容涉及天文、地理、历史、政治等知识, 有位选手恰好抽到了一道地理知识方面的题:有A, B, C, D四个城市, 它们都有一个著名的旅游点, 依次记为 a, b, c, d, 把A, B, C, D和 a, b, c, d 分别写成左、右两列, 用4条线把左右全部连接起来, 构成“一一对应”.由于该选手对地理知识不熟悉, 只好随机用4条线把左右全部连接起来, 若已知连接正确一对得3分, 连错的得0分.

(1) 写出该选手得分的分布列;

(2) 求该选手所得分的数学期望.

20. (本小题满分12分)

已知数列{an}中, a1=1, 其前 n 项和为Sn, 且 n, an, Sn 成等差数列 (n∈N*) .

(1) 求数列{an}的通项公式;

(2) 当Sn>57时, 求 n 的取值范围.

21. (本小题满分12分)

已知函数 $f (x) = \ln x - \frac{1}{2} a x^{2} - 2 x .$

(1) 若函数 f (x) 存在单调递减区间, 求实数 a 的取值范围;

(2) 令 g (x) =xexf ′ (x) (其中 f ′ (x) 为 f (x) 的导函数) , 当 a<0时, 求 g (x) 取得最小值时的 x 的值.

22. (本小题满分14分)

已知椭圆C的中心为坐标原点, F1、F2分别为它的左、右焦点, 直线 x=4为它的一条准线, 又已知椭圆C上存在点M使以下两个等式同时成立: $| \vec{Μ F_{1}} | = | \vec{Μ F_{2}} | ‚ 2 \vec{Μ F_{1}} \cdot \vec{Μ F_{2}} = | \vec{Μ F_{1}} | | \vec{Μ F_{2}} | .$

(1) 求椭圆C的方程;

(2) 若PQ为过椭圆右焦点F2的弦, 且 $\vec{Ρ F_{2}} = λ \vec{F_{2} Q} ‚$ 求△PF1Q内切圆面积最大时的λ值.

参考答案

一、BBCDB AADCC BA

二、13.180;14.8;15.4;16.±1

15.根据离散型随机变量分布列性质和期望公式得:

${\begin{cases} b + \frac{1}{2} + \frac{1}{6} = 1 ‚ \\ b + 1 + \frac{a}{6} = \frac{11}{6} ‚ \end{cases}$

解得

所以 a+3b=4.

16.因为圆心和焦点坐标分别为 (0, a) 、 $(0 ‚ \frac{1}{a})$ , 所以 $a = \frac{1}{a}$ , 即 a=±1.

三、17.因为A+B+C=π,

所以 cos (A+C) =-cosB.

$\begin{array}{l} 所以 \frac{\sin^{2} B - \sin^{2} A - \sin^{2} C}{s i n C} = \frac{\cos (A + C)}{c o s A} \\ \Rightarrow \frac{\sin^{2} B + \sin^{2} C - \sin^{2} B}{2 s i n A s i n C} = \frac{c o s B}{2 s i n A c o s A} . \end{array}$

由正弦定理和正弦的二倍角公式, 则上式可化为

$\frac{a^{2} + c^{2} - b^{2}}{2 a c} = \frac{c o s B}{\sin 2 A}$ ,

又由余弦定理得

$\cos B = \frac{c o s B}{\sin 2 A} .$

由题设知 $B \neq \frac{π}{2} \Rightarrow \cos B \neq 0$ ,

所以 sin2A=1.

因为A∈ (0, π) ⇒2A∈ (0, 2π) ,

所以 $2 A = \frac{π}{2}$ , 即 $A = \frac{π}{4} .$

18.解法1: (1) 取对角面D1DBB1, 可知

B1N2+MN2=B1M2,

所以 MN⊥B1N.

又由AB1=CB1, N是AC中点, 故B1N⊥AC, 于是B1N⊥平面MAC, 因此B1N与B1C所成的角即为直线 l 与B1C所成的角.

$B_{1} Ν = \frac{\sqrt{6} a}{2} ‚ B_{1} C = \sqrt{2} a ‚ C Ν = \frac{\sqrt{2} a}{2}$ ,

所以在Rt△B1NC中,

$\cos Ν B_{1} C = \frac{B_{1} Ν}{B_{1} C} = \frac{\frac{\sqrt{6}}{2} a}{\sqrt{2} a} = \frac{\sqrt{3}}{2}$ ,

于是 $∠ Ν B_{1} C = \frac{π}{6}$ ,

即 l 与B1C所成角的大小为 $\frac{π}{6} .$

(2) B1到平面MAC的距离即为线段B1N的长, $B_{1} Ν = \frac{\sqrt{6} a}{2}$ , 所以B1到平面MAC的距离为 $\frac{\sqrt{6} a}{2} .$

解法2: (1) 分别以DA、DC、DD1为 x、y、z 轴, 建立空间直角坐标系.

则 $Μ (0 ‚ 0 ‚ \frac{a}{2}) ‚ A (a ‚ 0 ‚ 0) ‚ C (0 ‚ a ‚ 0) ‚ B_{1} (a ‚ a ‚ a) .$

设直线 l 的方向向量为 l= (x, y, z) , 于是

$\vec{Μ A} = (a ‚ 0 ‚ - \frac{a}{2}) ‚ \vec{Μ C} = (0 ‚ a ‚ - \frac{a}{2})$ ,

由有

得

取 z=2, 得 l= (1, 1, 2) .

而

所以l与B1C所成角为

, 设B1到平面MAC的距离为 d, 则

$d = | \frac{l \cdot \vec{B_{1} Μ}}{| l |} | = \frac{\sqrt{6}}{2} a .$

19. (1) 设答对题的个数为X, 得分的随机变量为ξ, 则有X=0, 1, 2, 4, 所以得分为ξ=0, 3, 6, 12.

一个都没有连对的概率:

$Ρ (ξ = 0) = \frac{9}{A_{4}^{4}} = \frac{9}{24} = \frac{3}{8}$ ,

有一个连对的概率:

$Ρ (ξ = 3) = \frac{C_{4}^{1} \times 2}{A_{4}^{4}} = \frac{8}{24} = \frac{1}{3}$ ,

有两个连对的概率:

$Ρ (ξ = 6) = \frac{C_{4}^{2} \times 1}{A_{4}^{4}} = \frac{6}{24} = \frac{1}{4}$ ,

有四个连对的概率:

$Ρ (ξ = 12) = \frac{1}{A_{4}^{4}} = \frac{1}{24} .$

则ξ的分布列为:

(2) 该选手所得分的数学期望

$\begin{array}{l} E ξ = 0 \times \frac{3}{8} + 3 \times \frac{1}{3} + 6 \times \frac{1}{4} + 12 \times \frac{1}{24} \\ = 3 . \end{array}$

答:该选手所得分的数学期望为3分.

20. (1) 因为 n, an, Sn 成等差数列,

所以 2an=n+Sn,

即 Sn=2an-n,

所以 Sn-1=2an-1- (n-1) (n≥2) .

由 an=Sn-Sn-1 (n≥2) 得,

an=2an-1+1 (n≥2) ,

所以 an+1=2 (an-1+1) (n≥2) .

又因为 a1=1⇒a1+1=2≠0,

知 an-1+1≠0 (n≥2) ,

所以 $\frac{a_{n} + 1}{a_{n - 1} + 1} = 2 (n \geq 2) .$

可知数列{an+1}是首项为2, 公比为2的等比数列, 所以

an+1=2·2n-1.

即数列{an}的通项公式为

an=2n-1.

(2) 由 (1) 知 Sn=2n+1-n-2.

所以 Sn+1-Sn

=[2n+2- (n+1) -2]- (2n+1-n-2)

=2n+1-1>0,

即 Sn+1>Sn.

所以数列{Sn}为递增数列.

因为Sn>57,

所以2n+1-n-2>57,

即 2n+1-n>59.

又当 n=5时, 26-5=59,

所以 n>5.

所以当Sn>57时, n 的取值范围是 n≥6.

21. (1) 求得f′ (x)

由题设知, 不等式1-2x-ax2<0有正数解, 即 ax2+2x-1>0有正数解.

①当 a≥0时, 适合题意.

②当 a<0时, 应满足

${\begin{cases} a ＜ 0 ‚ \\ Δ = 4 + 4 a ＞ 0 ‚ \\ x_{1} + x_{2} = - \frac{2}{a} ＞ 0 ‚ \\ x_{1} x_{2} = - \frac{1}{a} ＞ 0 \end{cases}$

(其中 x1, x2 是方程 ax2+2x-1=0的两根) ,

解得 -1<a<0.

综上所述, a 的取值范围是

a∈ (-1, +∞) .

(2) 由题设及 (1) 知,

g (x) =ex (1-2x-ax2) (x>0) .

所以 g′ (x) =-ex[ax2+2 (1+a) x+1]

(x>0) .

令 g′ (x) =0, 得

ax2+2 (1+a) x+1=0. (*)

因为Δ=4 (a2+a+1) >0,

所以方程 (*) 有两个不等实根.

设实根为 x1, x2, 而 a<0,

$\begin{array}{l} 所以 x_{1} = \frac{a + 1 + \sqrt{a^{2} + a + 1}}{- a} \\ ＞ \frac{a + 1 + \sqrt{a^{2} + 2 a + 1}}{- a} \\ = \frac{a + 1 + | a + 1 |}{- a} \\ \geq 0 ‚ \end{array}$

即 x1>0.

又 $x_{1} x_{2} = \frac{1}{a} ＜ 0$ ,

所以 x2<0.

又因为 x>0,

所以当 x∈ (0, x1) 时, g′ (x) <0;

当 x∈ (x1, +∞) 时, g′ (x) >0.

所以 g (x) 在 (0, x1) 上单调递减, 在 (x1, +∞) 上单调递增.

所以 $x = - \frac{a + 1 + \sqrt{a^{2} + a + 1}}{a}$ 时, g (x) 取得最小值.

22. (1) 由题设知, 所求椭圆方程可设为

$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 (a ＞ b ＞ 0)$ ,

则 $a^{2} = b^{2} + c^{2} ‚ \frac{a^{2}}{c} = 4 .$

因为 $2 \vec{Μ F_{1}} \cdot \vec{Μ F_{2}} = | \vec{Μ F_{1}} | | \vec{Μ F_{2}} |$ ,

则 $\cos ∠ F_{1} Μ F_{2} = \frac{1}{2} \Rightarrow ∠ F_{1} Μ F_{2} = \frac{π}{3} .$

又 $| \vec{Μ F_{1}} | = | \vec{Μ F_{2}} |$ ,

所以△F1MF2是等边三角形.

又根据椭圆的定义知 a=2c.

由以上三个关于 a, b, c 的方程解得

$a = 2 ‚ b = \sqrt{3} ‚ c = 1 .$

所以椭圆C的方程是 $\frac{x^{2}}{4} + \frac{y^{2}}{3} = 1 .$

(2) 设PQ:my=x-1,

即 x=my+1,

代入 $\frac{x^{2}}{4} + \frac{y^{2}}{3} = 1$ , 整理得

(3m2+4) y2+6my-9=0.

知Δ=36m2+36 (3m2+4)

=144m2+144>0.

$\begin{array}{l} 则 | Ρ Q | = \sqrt{1 + m^{2}} \cdot \frac{\sqrt{Δ}}{3 m^{2} + 4} \\ = \frac{12 (m^{2} + 1)}{3 m^{2} + 4} . \end{array}$

又F1 (-1, 0) 到PQ:x-my-1=0的距离 $d = \frac{2}{\sqrt{m^{2} + 1}}$ ,

则△PF1Q的面积

$S = \frac{1}{2} | Ρ Q | \cdot d = \frac{12 \sqrt{m^{2} + 1}}{3 m^{2} + 4} .$

由椭圆定义知△PF1Q的周长为8.设内切圆半径为 r, 则

$S = \frac{r}{2} \times 8 = 4 r .$

可知当S最大时, 内切圆面积也最大.

而 $S = \frac{12}{3 \sqrt{m^{2} + 1} + \frac{1}{\sqrt{m^{2} + 1}}} .$

记 $u = \sqrt{m^{2} + 1} (u \geq 1)$ , 则

$3 \sqrt{m^{2} + 1} + \frac{1}{\sqrt{m^{2} + 1}} = 3 u + \frac{1}{u}$ 在[1, +∞) 上是增函数.

所以当 u=1, 即 m=0时, $3 \sqrt{m^{2} + 1} + \frac{1}{\sqrt{m^{2} + 1}}$ 取最小值4, 从而Smax=3.

而 m=0时, F2为PQ中点, 则λ=1.

8.（新目标）八年级上期中测试题篇八

A）根据句意及汉语提示，填写句中所缺的单词

1. Some friends have opposite views and ____ (兴趣).

2. Beijing is in the ____ (北部的) part of China.

3. I can’t find the last page of the ____ (日历).

4. Mr and Mrs Wang go shopping by ____ (地铁) every day.

5. They stay here the ____(整个的) afternoon.

B）用括号内所给动词的适当形式填空

1. My uncle often ____ (walk) to the library.

2. It’s six o’clock. The students ____ (play) football on the playground.

3. ____ your mother ____ (cook) Chinese food last Friday?

4. ____ (not read) the books now.

5. Can you ____ (help) me with my Chinese?

6. ——What day ____ (be) it yesterday?

——It ____ (be) Friday.

7. Look at the clouds. It ____ (rain).

8. Thanks for ____ (ask) me to your party.

9. Lily has to ____ (eat) lunch at home.

10. Tom ____ (visit) his friends yesterday evening.

Ⅱ.单项选择

1. ——____

——By taxi.

A. Why does he go to work?B. How does he go to work?

C. When does he go to work?D. Where does he work?

2. Kelly has ____ breakfast. Then she leaves home.

A. quickB. a quickC. one quickD. an quick

3. ——Is your home ____ the post office?

——No, it’s ____ the post office.

A. far to; near fromB. far from; near from

C. far from; nearD. far to; near to

4. ——____ is it from your school to the bank?

——It’s about six miles.

A. How muchB. How manyC. How longD. How far

5. I like to ____ my bike ____ the weekend.

A. take; inB. catch; atC. live; onD. ride; on

6. ——Can you come to my party?

——____.

A. Sure, I’d love toB. I’m sorry to hear that

C. You’re rightD. That’s all right

7. ——Let’s ask Jack to play ____ piano for the party.

——That’s a good idea.

A. /B. aC. anD. the

8. ——They have ____ homework to do on Sundays.

——That’s too bad.

A. too muchB. too manyC. much tooD. many too

9. ——Happy birthday to you.

——____.

A. The same to youB. Thank you

C. Happy birthday to you, tooD. That’s great

10. ____ he was tired, ____ he went on working.

A. Though; butB. Because; soC. Though; /D. Because; /

11. You don’t look well. What’s the matter ____ you?

A. withB. onC. inD. about

12. We enjoy ____ TV at home.

A. watchB. watchingC. to watchD. seeing

13. ____, we’re quite different from each other.

A. On a handB. In one hand

C. On the other handD. On other hand

14. I think you ____ lie in bed and have a good rest.

A. mustB. canC. needD. should

15. It is not good ____ your health.

A. forB. atC. withD. to

16. She is telling them ____ and they are all laughing.

A. interesting somethingB. something interesting

C. anything interestedD. interested anything

17. What are you doing ____ vacation?

A. inB. withC. forD. at

18. All of them like to go ____.

A. campB. to campC. campsD. camping

19. ____ is it like in Nanjing?

A. WhatB. HowC. SoD. When

20. ____ is the weather in Haikou?

A. WhatB. HowC. WhenD. Where

21. We are staying there ____ about two weeks.

A. forB. inC. beforeD. after

22. I’m sorry ____ late.

A. toB. to beC. forD. because of

23. Make a new conversation ____ all the information below.

A. useB. to useC. usingD. used

24. WTO stands ____ World Trade Organization.

A. atB. asC. forD. like

25. It must be ____ fun than watching TV at home.

A. lotB. a lotC. lot moreD. a lot more

26. They go to school ____ the school bus.

A. withB. byC. inD. on

27. She is different from her sister ____ some ways.

A. inB. onC. aboutD. from

28. Her home is quite far ____ the school.

A. toB. fromC. awayD. off

29. The light turns red. They stop ____.

A. walkB. to walkC. walkedD. walking

30. They have a son ___ Nicolas.

A. callB. callsC. calledD. calling

Ⅲ.句型转换按要求改写下列各句，每空一词

1. The bus ride usually takes about 25 minutes.(改为一般疑问句)

____ the bus ride usually ____ about 25 minutes?

2. Mary has to see the doctor.(对划线部分提问)

____ does Mary ____ to ____?

3. They can make cakes.(改为一般疑问句)

____ they ____ cakes?

4. Li Lei is ten years old. Lin Tao is twelve years old.(合并为一句)

Li Lei is ____ ____ Lin Tao.

5. Our bikes are not the same as theirs.(改为同义句)

Our bikes are ____ ____ theirs.

Ⅳ.根据汉语意思把下列各句译成英语

1．我们每天花三个小时看电视。

____ ____ us three hours ____ watch TV every day.

2．他妹妹擅长数学。

His sister is ____ ____ math.

3．王林今天没来上学，我想他一定在家。

Wang Lin doesn’t come to school today. I think he ____ ____ at

home.

4．晚饭后为什么不去散步呢？

____ ____ ____ for a walk after supper?

5．星期天我不得不为我的英语考试而学习。

I ____ ____ study ____ my English exam on Sunday.

Ⅴ.补全对话从下列方框中选择恰当的句子，完成下列对话

A: __1__

B: Yes, please. Could you tell me the way to the First People’s Hospital?

A: Let me see. Oh, it’s far from here.

B: __2__

A: About five miles. __3__

B: Which bus should I take?

A: No. 1 bus can take you there.

B: __4__

A: It’s about 30 minutes.

B: Thank you very much.

A: __5__

A. You’re welcome.

B. Can I help you?

C. You can take a bus to go there.

D. How long does it take to get there?

E. How far is it from here?

Ⅵ.完形填空

Mr White works in a middle school. He __1__ English. He is friendly to his __2__ and they also like him. He spends __3__ time on his work. He often does some reading and writing. When he’s __4__, he is also very busy, so he can’t help his wife to do any __5__. The woman is always angry with him.

It’s Saturday. Their daughter Kate is __6__ her homework in her bedroom. Mrs White finds her __7__ is out. She hopes her daughter will say she’s __8__ than her husband. She gives an apple to Kate and asks, “__9__ is cleverer, your father or I?”

Can you guess what the girl’s __10__ is?

“I’m the cleverest in our family!”Kate says without thinking.

1. A. teachesB. watchesC. studiesD. reads

2. A. friendsB. studentsC. worksD. drivers

3. A. manyB. littleC. muchD. any

4. A. at workB. in bed

C. in the classroomD. at home

5. A. houseworkB. homeworkC. schoolworkD. lessons

6. A. makingB. doingC. lookingD. finding

7. A. motherB. brotherC. husbandD. teacher

8. A. goodB. bestC. better D. bad

9. A. WhoseB. WhatC. WhyD. Who

10. A. answerB. playC. singD. think

Ⅶ.阅读理解

(A)

We cannot live a modern life without traveling. The fastest way of traveling is by air. With a plane one can travel in one day to places which it took a month or more to get to a hundred years ago.

Traveling by train is slower than by plane, but one can see the country he is traveling through. Modern trains have comfortable seats and dinning-cars. They make even the longest journey enjoyable.

Some people prefer to travel by sea when possible. There are large luxury liners(客轮) or river boats. They are not as fast as trains or planes, but traveling by sea is a very pleasant way to spend a holiday.

Many people like to travel by car. They can make their own timetable. They can travel hundreds of miles or only fifty miles a day, just as their wish. They can stop wherever they want to see something interesting or to enjoy a good meal at a good restaurant, or to spend the night at a hotel. That is why people choose traveling by car for pleasant trips, while they usually take trains or planes for business.

根据短文内容，选择最佳答案

1. People cannot live a modern life without ____.

A. travelingB. holidaysC. shoppingD. sports

2. According to the passage, the fastest way of traveling is ____.

A. by shipB. by planeC. by trainD. on foot

3. Modern trains have comfortable seats and ____.

A. parksB. gardensC. dinning-carsD. cars

4. If we travel by car, we can ____.

A. enjoy the longest journey

B. travel only fifty miles a day

C. make our own timetable

D. travel to a very far place in a few minutes

5. When people travel on business, they usually take ____.

A. a boat or a trainB. a car or a boat

C. a plane or a carD. a train or a plane

(B)

Basketball players are usually very tall because they need to put the ball into the basket. But other sports players are sometimes short. Some of the best football stars are not VERY TALL.

Short people often have better balance(平衡) than tall people, so they don’t fall over very often. In some sports the players must have good balance, for example, table tennis and running. You don’t need long legs to run fast! Some of the fast runners in the world are not very tall. Some people are tall and some are short. The tallest person in the world is 2.31 meters tall. She is an American. And the shortest person in the world is only 57 centimeters tall. Today young people in many countries grow taller than their parents. This is because they eat better food today. Good food can help children grow.

根据短文内容，回答下列问题

6. Are all sports players tall?

7. Is it better to be short than to be tall?

8. Do fast runners all have long legs?

9. How tall is the tallest person in the world?

10. Why do young people grow taller than their parents?

Ⅷ.综合填空

根据短文内容，在短文的空白处填写一个正确的单词（首字母已给出）

Most people can have t__1__ birthday every year. But Mr Smith c__2__. He is now thirty-three years old and he’s o__3__ had eight birthdays. Last year, he had his eighth birthday. His wife b__4__ him a big birthday cake and a beautiful watch. His five-year-old d__5__ picked a lot of flowers for him in their garden. Some other people came to his birthday party, t__6__. They lit (点着) the birthday candles and sang the birthday s__7__ for him. Then it was time for Mr Smith to say h__8__ wishes. Before he could s__9__, his little daughter said, “Poor Dad, he wishes for a birthday e__10__ year.”

Ⅸ.书面表达

每个人都有自己的爱好，有的人喜欢学习、有的人喜欢运动、有的人喜欢音乐。那么你喜欢什么呢？假如你叫张红，请你以“My Interests”为题写一篇短文。词数在80词左右。

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