2022年山東省濟(jì)寧市中考英語(yǔ)真題

1、參照秘密級(jí)管理啟用前試卷類型：A濟(jì)寧市二二二年初中學(xué)業(yè)水平考試英 語(yǔ) 試 題注意事項(xiàng)：1.本試卷分第I卷和第II卷兩部分，第I卷為選擇題：45分；第II卷為非選擇題：55分；共100分。考試時(shí)間為120分鐘（含聽(tīng)力20分鐘），共10頁(yè)。2.答題前，考生務(wù)必先核對(duì)條形碼上的姓名，準(zhǔn)考證號(hào)和座號(hào)，然后0.5毫米黑色墨水簽字筆將本人的姓名，準(zhǔn)考證號(hào)和座號(hào)填寫在答題卡相應(yīng)位置。3.答第I卷時(shí)，必須用2B鉛筆填涂答題卡上相應(yīng)題目的答題標(biāo)號(hào)，如需改動(dòng)，必須先用相比擦干凈，再改涂其它答案。4.答第II卷時(shí)，必須使用0.5毫米黑色墨水簽字筆在答題卡上書(shū)寫，務(wù)必在題號(hào)所指示的答題區(qū)域內(nèi)作答。5.考試結(jié)束后，將本

2、試卷和答題卡一并交回。第I卷（選擇題 共45分）一、聽(tīng)力選擇(共15小題，滿分15分) (一)請(qǐng)聽(tīng)錄音中八組短對(duì)話。每組對(duì)話后有一個(gè)小題，從題中所給的A、B、C三個(gè)選項(xiàng)中，選出與對(duì)話內(nèi)容相符的圖片或能回答所給問(wèn)題的最佳答案。（每組對(duì)話讀兩遍）1. Which animal are the speakers talking about? A. B. C. 2. What does the girl want to be? A. B. C. 3. What is Tom looking for? A. B. C. 4. How long has the man waited for the bus

3、? A. 10 minutes.B. 20 minutes.C. 30 minutes. 5. Where will Mary go after school? A. To the cinema.B. To the club.C. To the library. 6. How was the weather in the mountains yesterday? A. Hot.B. Cool.C. Cloudy. 7. Whats the relationship between the two speakers? A. Teacher and student.B. Doctor and pa

4、tient.C. Guide and tourist. 8. Why does the man say sorry? A. He speaks too fast.B. He cant help the woman.C. He doesnt know the answer. (二)請(qǐng)聽(tīng)錄音中兩段較長(zhǎng)的對(duì)話。每段對(duì)話后有幾個(gè)小題，從題中所給的A、B、C三個(gè)選項(xiàng)中，選出能回答所給問(wèn)題的最佳答案。(每段對(duì)話讀兩遍)聽(tīng)第一段較長(zhǎng)的對(duì)話，完成第9至第11三個(gè)小題。9. What are the speakers mainly talking about? A. Their weekends.B. The

5、Science Museum.C. After-school classes. 10. How was Toms weekend? A. Awful.B. Great.C. Boring. 11. What is Laura going to do this weekend? A. To pay a visit to his friend.B. To take after-school classes. C. To go to the Science Museum. 聽(tīng)第二段較長(zhǎng)的對(duì)話，完成第12至第15四個(gè)小題。12. How are the speakers communicating?

6、A. By phone.B. By e-mail.C. By video. 13. Whats the problem between Paul and his mom? A. They dont care for each other.B. They often argue with each other. C. They never communicate with each other. 14. What does Jenny advise Paul to do? A. To buy a present for his mom.B. To help his mom do housewor

7、k. C. To have a good talk with his mom. 15. What can we know about Pauls mom from the conversation? A. She knows her son well.B. She often listens to her son. C. She always controls her son. 二、閱讀選擇(共15小題，滿分30分) 閱讀下列短文，從每小題A、B、C、D四個(gè)選項(xiàng)中，選出能回答問(wèn)題的最佳答案。AA Picture of My Own CityHow will your dream city lo

8、ok in 100 years time? What kind of city do you hope our children, grandchildren or great grandchildren will be living in? Now paint your very own idea about our city & youll have a chance to win 5,000 dollars! What: = 1 * GB3 The ides of your painting must be your won. = 2 * GB3 Write down the idea

9、behind your painting in 100 words. Where: Send your painting to A Picture of My Own City 9F, No. 168, Swan Road, Swan City. When: Send your painting before June 30, 2022. Prize: 1st Prize: $5,000 (3winners) 2nd Prize: $2,500 (5 winners) 3rd Prize: $1,000 (10 winners) 4th Prize: $ 500 (20 winners)To

10、learn more, please visit: / 16. What does the ad ask people to do? A. To paint a future city.B. To live with their children. C. To offer 5,000 dollars.D. To write a 100-word story. 17. How much do you get if you win the third prize? A. $ 5,000. B. $2,500.C. $ 1,000.D. $ 500. 18. Which of the followi

11、ng is most probably a picture for the competition? A. B. C. D. BWhen I got up this morning, I was so surprised to find a new watch on my desk. I couldnt help crying. I lost my old watch last Monday. It was a present from my father for my thirteenth birthday. I still dont know where or how I lost it.

12、 I felt really sad when I couldnt find the watch. I stayed at school to look for it until very late. When I came home, no one was there. At nine oclock, Mom called back and told me that Dad was hit by a car on his way to look for me. He was sent to the hospital. I went to the hospital that night and

13、 told Dad I was sorry. I also told him I lost my watch, but he did not get angry. Dads left leg was badly hurt, and he stayed in the hospital for several days. He just came back home yesterday, and this morning I found the new watch. Thank you, Dad, for loving me so much. 19. Why did the writer star

14、t crying this morning? A. Because she got up too late.B. Because she had lost her watch. C. Because her dad was in hospital.D. Because she was moved by her dad. 20. Where did the writer lose her watch? A. Nobody knows.B. In the hospital.C. On the playground.D. On her way to school. 21. What happened

15、 to Dad while he was looking for her? A. He suddenly fell ill.B. He lost his way. C. He was hit by a car.D. He hit someone. 22. Who most probably bought the new watch? A. Her mom.B. Her dad.C. Her friend.D. Her teacher.C As we all know, too much trash is a big problem for our environment. A woman in

16、 Indonesias Java island has come up with a great idea lending books to children in exchange for trash. Raden Roro Hendarti, nearly 50 years old, is a librarian in Muntang village. She started a “trash library”, hoping to make children read more as well as make them realize the importance of environm

17、ent protection. Each weekday, Raden puts all kinds of books on the back of her three-wheeler (三輪車) and rides to Muntang village. There, children line up to exchange plastic cups, bags and other trash for books from Radens mobile library. After finishing the exchange, Raden carries back all the trash

18、. In the library where Raden works, there are thousands of books. Every time she shows up, children run to her “trash library”. They all carry trash bags, and Radens three-wheeler quickly fills with trash as the books fly out. Raden collects about 100kg of trash each week. It is then sorted out (分類)

19、 and sent for recycling or sale. She is happy that children spend less time on online games because of the books. Raden plans to take the mobile library service to neighboring areas as well. She says, “We all should take care of our trash in order to fight climate (氣候) change and save the earth.”23.

20、 What does the underlined word “trash” mean? A. plasticB. rubbishC. paperD. information24. Which of the following shows how Radens idea works? = 1 * GB3 She rides to Muntang village. = 2 * GB3 She carries back all the trash. = 3 * GB3 Children line up to get books for their trash. = 4 * GB3 She puts

21、 books on her three-wheeler. 25. How much trash can Raden collect each weekday? A. About 100 kg.B. About 50 kg.C. About 25 kg.D. About 20 kg. 26. Whats Raden going to do next? A. To ask her neighbors for help.B. To give the mobile library to her neighbors. C. To exchange books for trash in more vill

22、ages. D. To tell children to spend less time on online games. DWhen you first meet Meggie, you may think shes strange. She often tells people which word “tastes” good and who has a “delicious” name. But shes not crazy. She has synesthesia (伴生感覺(jué)), something only one in 2,000 people has. People who ha

23、ve synesthesia experience the world differently. For some people, different words “taste” differently, for some, numbers or letters have colors, and for some, music “touches” parts of their bodies. Many of them experience more than one kind of synesthesia, while some have just one, like Meggie. Each

24、 of them has their own experience- two people with synesthesia may both “feel” music, but they almost never feel the music in the same way. For example, one may feel the music of the violin lightly brushing his face; the other may feel it on her ankle (腳踝). And ones experience of synesthesia is alwa

25、ys the same. If they see the number 5 in the color blue, then 5 is blue every time they see it. Theres one thing about synesthesia: it cant be “turned off”. If you have synesthesia, youll experience it all the time. Meggie once met a guy and his name made her think of the taste of bad eggs. He was a

26、 fun guy, but after thinking about his name all night, she felt too sick to be friends with him. Even so, she still likes this “gift” because thats what makes her different. 27. What do you learn about Meggie from the first paragraph? A. She has a strange name.B. She is a good person. C. She is a cr

27、azy person.D. She is special in a way. 28. What does Paragraph 2 mainly tell us? A. People with synesthesia experience the world differently. B. For some people with synesthesia, different words “taste” differently. C. For some people with synesthesia, numbers or letters have colors. D. Many people

28、with synesthesia experience more than one kind of it. 29. What did Meggie stop being friends with the guy? A. He often played jokes on her.B. He enjoys eating bad eggs. C. She couldnt stand his name.D. She did not like his gift. 30. Which of the following might be said by Meggie? A. “The sound of dr

29、ums touches my back.”B. “The number zero tastes like an apple.” C. “The name Shakespeare is in bright purple.” D. “The music of the violin lightly brushes my face.”第II卷（非選擇題 共55分）三、聽(tīng)力填詞(共5小題，滿分5分) 請(qǐng)聽(tīng)下面一則通知。根據(jù)所聽(tīng)到的內(nèi)容，寫出可以填入下表15空格處的適當(dāng)單詞，每空限填一詞。(通知讀兩遍)A Welcome PartyPurposeTo welcome the 1. _ members. T

30、imeAt 5:00 oclock on 2. _ afternoon. PlaceIn Room 4, on the 3. _ floor, Zhi Yuan Building. ActivitiesHave a welcome 4. _. Sing, dance and exchange 5. _. 四、單詞拼寫及運(yùn)用(共8小題；滿分8分) 1. A _ is the fourth month of the year. 2. The sun rises in the e_ and sets in the west. 3. Im h_. I want to buy something to

31、eat. 4. Alan is an honest boy. You can t_ him. 5. I usually _(借) some books from out school library. 6. Go to bed if you feel _(困倦的). 7. My sister Sally is always _(有禮貌的) to others. 8. China _(成功地) held the 24th winter Olympic Games. 1. April 2. east 3. hungry 4. trust 5. borrow 6. sleepy 7. polite

32、8. successfully 五、語(yǔ)法填空(共10小題，滿分10分) 閱讀下面短文，在空白處填入一個(gè)適當(dāng)?shù)膯卧~或括號(hào)內(nèi)單詞的正確形式， 必要時(shí)可加助動(dòng)詞或情態(tài)動(dòng)詞。A We cant imagine our life without inventions. TIME magazine has picked the 100 best inventions of 2021. Here is one of 1. _(they).Paper ShootPaper Shoot is a camera made mostly out of paper! Paper Shoot 2. _(work) ju

33、st like any other camera. But it is much 3. _(small) and lighter. You can take it around easily and get the fun moments of your life. It can hold 800 pictures. But be careful when you take 4. _(photo) on rainy days. Dont get it wet!B Mrs. Green is an old lady. She has a small car, and she always dri

34、ves to the shops 5. _ (buy) food. Sometimes her grandchildren say to her. “Please 6. _ (not, go) out in your car all by yourself, Granny. We can take you to the shops.” But she always says, “No, I like driving. I 7. _(drive) for thirty years, and Im not going to stop now.” Last Saturday she 8. _ (st

35、op) her car at some traffic lights because they were red, and then the car didnt start again. The lights were green, then yellow, then red, and then green again, 9. _ her car did not start again. “What 10. _ I 10. _ (do) now?”Then a policeman came and said to her kindly, “Good morning, madam! Dont y

36、ou like any of our colors today?”六、完形填空。(共7小題，滿分7分)閱讀下面短文，從方框中選擇適當(dāng)?shù)脑~語(yǔ)填空。方框中有兩個(gè)詞語(yǔ)是多余的。 badly, because, family, friends, health, leave, perfectly, poor, stay withMatt Owens of New Zealand was on his way home one day when he saw an injured (受傷的) bird on the side of the road. The 1. _ bird looked very l

37、onely, so Matt decided to take him home and bring him back to 2. _. And he gave the bird a name: Swoop. After spending plenty of time caring for his new friend, Matt helped him walk and even fly. Finally, it was time to set Swoop free back into the wild, but the bird chose to 3. _ Matt and his cat M

38、owgli instead! At the beginning, Matt didnt want to introduce Swoop to Mowgli 4. _ he was afraid Mowgli might not like him. But since Swoop was part of their 5. _, Matt sat down with Mowgli and helped the cat accept his new brother. It worked out 6. _! Today, Swoop gets on well with Mowgli. “They ha

39、ve become very good 7. _, and they play with each other all the time,” Matt said. Swoop has mad Matts life better in more ways than one!七、閱讀表達(dá)(共5小題，滿分10分) 閱讀短文，根據(jù)要求完成15題。 On the evening of September 26, 2019, the streets of Geneva in Switzerland went dark. This usually happens when there is a proble

40、m with the electricity, but this time the lights were turned off to allow people to go outside and look at the starts. This is often impossible in a city because of light population. Light pollution is when light from streetlights or buildings makes the night less dark. There are many reasons why th

41、is is a problem. Animals sleep less because they think it is still daytime. Birds that fly to warmer countries in the autumn need to see the moon and stars to find their way, but light pollution makes this difficult. Insects and birds in cities often fly towards lights at night, knock into buildings

42、 and die. Light pollution is also bad for us. It can stop us sleeping and give up headaches. Also, we dont see the same sky that people in the past did. This means we almost never see one of the greatest scenes in the world: the millions of stars. Hundreds of thousands of people have never seen it i

43、n their lives. However, it is not difficult to do a few things to reduce (減輕) light pollution: we can all turn lights off when we dont need them and we can cover our windows. If there is less light pollution, we will once again be able to enjoy the beauty of the night sky. 1. Why were the streetligh

44、ts turned off in Geneva? (no more than 11 words) _2. What helps birds find their way? (no more than 4 words) _3. Please list one way we can reduce light pollution. (no more than 3 words) _4. 請(qǐng)將文中畫(huà)線的句子翻譯成漢語(yǔ)。 _5. 請(qǐng)給短文擬一個(gè)適當(dāng)?shù)赜⑽臉?biāo)題。 _八、寫作(共1小題，滿分15分) 假設(shè)你是李華，正和英國(guó)筆友Jack尋找假期共讀的書(shū)。你發(fā)現(xiàn)下圖中的書(shū)特別適合你們共讀。請(qǐng)你根據(jù)下面的提示信息，

45、給他寫一封e-mail，介紹此書(shū)并征求他的意見(jiàn)。 tell how things change from start to finish win many world awards (獎(jiǎng)) six topics of interest (nature, food, animas)written in both English and Chinese. hundreds of color photos 注意：1.須包括以上所有提示信息，可適當(dāng)發(fā)揮；2.文中不得出現(xiàn)任何透露考生真實(shí)身份的信息；3. 100詞左右(開(kāi)頭和結(jié)尾已給出，不計(jì)入總詞數(shù))。Dear Jack, Ive just found

46、a book and cant wait to tell you about it. _Looking forward to your reply. Yours, Li Hua濟(jì)寧市二二二年初中學(xué)業(yè)水平考試英語(yǔ)試題參考答案一、聽(tīng)力選擇略二、閱讀選擇16-20ACDDA 21-25CBBAD 26-30CDACC 三、聽(tīng)力填詞略四、單詞拼寫及運(yùn)用1. April 2. east 3. hungry 4. trust 5. borrow 6. sleepy 7. polite 8. successfully五、語(yǔ)法填空1. them of 2. works 3. smaller much 4. p

47、hotos 5. to buy 6. dont go 7. have driven 8. stopped 9. but 10. should; do 六、完形填空1. poor 2. health 3. stay with 4. because 5. family 6. perfectly 7. friends 七、閱讀表達(dá)1. To allow people to go outside and look at the starts. 2. The moon and starts. 3. Turn off lights. / Cover our windows. 4.如果光污染少一點(diǎn)，我們將能

48、再次欣賞到夜空之美。5. Light pollution. 八、寫作略贈(zèng)送:初中數(shù)學(xué)必考定理公式匯編一、數(shù)與代數(shù)數(shù)與式實(shí)數(shù)實(shí)數(shù)的性質(zhì)：實(shí)數(shù)a的相反數(shù)是a，實(shí)數(shù)a的倒數(shù)是（a0）；實(shí)數(shù)a的絕對(duì)值：正數(shù)大于0，負(fù)數(shù)小于0，兩個(gè)負(fù)實(shí)數(shù)，絕對(duì)值大的反而小。二次根式：積與商的方根的運(yùn)算性質(zhì)：（a0，b0）；（a0，b0）；二次根式的性質(zhì)：（2）整式與分式同底數(shù)冪的乘法法則：同底數(shù)冪相乘，底數(shù)不變，指數(shù)相加，即（m、n為正整數(shù)）；同底數(shù)冪的除法法則：同底數(shù)冪相除，底數(shù)不變，指數(shù)相減，即（a0，m、n為正整數(shù)，mn）；冪的乘方法則：冪的乘方，底數(shù)不變，指數(shù)相乘，即（n為正整數(shù)）；零指數(shù)：（a0）；負(fù)整數(shù)指數(shù)

49、： HYPERLINK / （a0，n為正整數(shù)）；平方差公式：兩個(gè)數(shù)的和與這兩個(gè)數(shù)的差的積等于這兩個(gè)數(shù)的平方，即；完全平方公式：兩數(shù)和（或差）的平方，等于它們的平方和，加上（或減去）它們的積的2倍，即；分式分式的基本性質(zhì)：分式的分子和分母都乘以（或除以）同一個(gè)不等于零的整式，分式的值不變，即；，其中m是不等于零的代數(shù)式；分式的乘法法則：；分式的除法法則：；分式的乘方法則：（n為正整數(shù)）；同分母分式加減法則：；異分母分式加減法則：；方程與不等式一元二次方程(a0）的求根公式：一元二次方程根的判別式：叫做一元二次方程（a0）的根的判別式：方程有兩個(gè)不相等的實(shí)數(shù)根；方程有兩個(gè)相等的實(shí)數(shù)根；方程沒(méi)有實(shí)

50、數(shù)根；一元二次方程根與系數(shù)的關(guān)系：設(shè)、是方程 （a0）的兩個(gè)根，那么+=，=；不等式的基本性質(zhì)：不等式兩邊都加上（或減去）同一個(gè)數(shù)或同一個(gè)整式，不等號(hào)的方向不變；不等式兩邊都乘以（或除以）同一個(gè)正數(shù)，不等號(hào)的方向不變；不等式兩邊都乘以（或除以）同一個(gè)負(fù)數(shù)，不等號(hào)的方向改變；函數(shù)一次函數(shù)的圖象：函數(shù)y=kx+b(k、b是常數(shù)，k0)的圖象是過(guò)點(diǎn)（0，b）且與直線y=kx平行的一條直線；一次函數(shù)的性質(zhì)：設(shè)y=kx+b（k0），則當(dāng)k0時(shí)，y隨x的增大而增大；當(dāng)k0時(shí)，y隨x的增大而增大；當(dāng)k0，則當(dāng)x0時(shí)或x0時(shí)，y分別隨x的增大而減??；如果k0時(shí)或x0時(shí)，拋物線開(kāi)口向上，當(dāng)a0時(shí)，如果，則y隨x

51、的增大而減小，如果，則y隨x的增大而增大；當(dāng)a0時(shí)，如果，則y隨x的增大而增大，如果，則y隨x的增大而減??；二、空間與圖形圖形的認(rèn)識(shí)(1)角角平分線的性質(zhì)：角平分線上的點(diǎn)到角的兩邊距離相等，角的內(nèi)部到兩邊距離相等的點(diǎn)在角平分線上。(2)相交線與平行線同角或等角的補(bǔ)角相等，同角或等角的余角相等；對(duì)頂角的性質(zhì)：對(duì)頂角相等垂線的性質(zhì)：過(guò)一點(diǎn)有且只有一條直線與已知直線垂直；直線外一點(diǎn)有與直線上各點(diǎn)連結(jié)的所有線段中，垂線段最短；線段垂直平分線定義：過(guò)線段的中點(diǎn)并且垂直于線段的直線叫做線段的垂直平分線；線段垂直平分線的性質(zhì)：線段垂直平分線上的點(diǎn)到線段兩端點(diǎn)的距離相等，到線段兩端點(diǎn)的距離相等的點(diǎn)在線段的垂直

52、平分線；平行線的定義：在同一平面內(nèi)不相交的兩條直線叫做平行線；平行線的判定：同位角相等，兩直線平行；內(nèi)錯(cuò)角相等，兩直線平行；同旁內(nèi)角互補(bǔ)，兩直線平行；平行線的特征：兩直線平行，同位角相等；兩直線平行，內(nèi)錯(cuò)角相等；兩直線平行，同旁內(nèi)角互補(bǔ)；平行公理：經(jīng)過(guò)直線外一點(diǎn)有且只有一條直線平行于已知直線。(3)三角形三角形的三邊關(guān)系定理及推論：三角形的兩邊之和大于第三邊，兩邊之差小于第三邊；三角形的內(nèi)角和定理：三角形的三個(gè)內(nèi)角的和等于；三角形的外角和定理：三角形的一個(gè)外角等于和它不相鄰的兩個(gè)的和；三角形的外角和定理推理：三角形的一個(gè)外角大于任何一個(gè)和它不相鄰的內(nèi)角；三角形的三條角平分線交于一點(diǎn)（內(nèi)心）；三

53、角形的三邊的垂直平分線交于一點(diǎn)（外心）；三角形中位線定理：三角形兩邊中點(diǎn)的連線平行于第三邊，并且等于第三邊的一半；全等三角形的判定：邊角邊公理（SAS）角邊角公理（ASA）角角邊定理（AAS）邊邊邊公理（SSS）斜邊、直角邊公理（HL）等腰三角形的性質(zhì)：等腰三角形的兩個(gè)底角相等；等腰三角形的頂角平分線、底邊上的中線、底邊上的高互相重合（三線合一）等腰三角形的判定：有兩個(gè)角相等的三角形是等腰三角形；直角三角形的性質(zhì)：直角三角形的兩個(gè)銳角互為余角；直角三角形斜邊上的中線等于斜邊的一半；直角三角形的兩直角邊的平方和等于斜邊的平方（勾股定理）；直角三角形中角所對(duì)的直角邊等于斜邊的一半；直角三角形的判定

54、：有兩個(gè)角互余的三角形是直角三角形；如果三角形的三邊長(zhǎng)a、b 、c有下面關(guān)系，那么這個(gè)三角形是直角三角形（勾股定理的逆定理）。(4)四邊形多邊形的內(nèi)角和定理：n邊形的內(nèi)角和等于（n3，n是正整數(shù)）；平行四邊形的性質(zhì)：平行四邊形的對(duì)邊相等；平行四邊形的對(duì)角相等；平行四邊形的對(duì)角線互相平分；平行四邊形的判定：兩組對(duì)角分別相等的四邊形是平行四邊形；兩組對(duì)邊分別相等的四邊形是平行四邊形；對(duì)角線互相平分的四邊形是平行四邊形；一組對(duì)邊平行且相等的四邊形是平行四邊形。矩形的性質(zhì)：（除具有平行四邊形所有性質(zhì)外）矩形的四個(gè)角都是直角；矩形的對(duì)角線相等；矩形的判定：有三個(gè)角是直角的四邊形是矩形；對(duì)角線相等的平行四

55、邊形是矩形；菱形的特征：（除具有平行四邊形所有性質(zhì)外菱形的四邊相等；菱形的對(duì)角線互相垂直平分，并且每一條對(duì)角線平分一組對(duì)角；菱形的判定：四邊相等的四邊形是菱形；正方形的特征：正方形的四邊相等；正方形的四個(gè)角都是直角；正方形的兩條對(duì)角線相等，且互相垂直平分，每一條對(duì)角線平分一組對(duì)角；正方形的判定：有一個(gè)角是直角的菱形是正方形；有一組鄰邊相等的矩形是正方形。等腰梯形的特征:等腰梯形同一底邊上的兩個(gè)內(nèi)角相等等腰梯形的兩條對(duì)角線相等。等腰梯形的判定：同一底邊上的兩個(gè)內(nèi)角相等的梯形是等腰梯形；兩條對(duì)角線相等的梯形是等腰梯形。平面圖形的鑲嵌：任意一個(gè)三角形、四邊形或正六邊形可以鑲嵌平面；(5)圓點(diǎn)與圓的位

56、置關(guān)系（設(shè)圓的半徑為r，點(diǎn)P到圓心O的距離為d）：點(diǎn)P在圓上，則d=r，反之也成立；點(diǎn)P在圓內(nèi)，則dr，反之也成立；圓心角、弦和弧三者之間的關(guān)系：在同圓或等圓中，圓心角、弦和弧三者之間只要有一組相等，可以得到另外兩組也相等；圓的確定：不在一直線上的三個(gè)點(diǎn)確定一個(gè)圓；垂徑定理（及垂徑定理的推論）：垂直于弦的直徑平分弦，并且平分弦所對(duì)的兩條??；平行弦?jiàn)A等?。簣A的兩條平行弦所夾的弧相等；圓心角定理：圓心角的度數(shù)等于它所對(duì)弧的度數(shù)；圓心角、弧、弦、弦心距之間的關(guān)系定理及推論：在同圓或等圓中，相等的圓心角所對(duì)的弧相等，所對(duì)的弦的弦心距相等；推論：在同圓或等圓中，如果兩個(gè)圓心角、兩條弧、兩條弦或兩條弦心距

57、中有一組量相等，那么它們所對(duì)應(yīng)的其余各組量分別相等；圓周角定理：圓周角的度數(shù)等于它所對(duì)的弧的度數(shù)的一半；圓周角定理的推論：直徑所對(duì)的圓周角是直角，反過(guò)來(lái)，的圓周角所對(duì)的弦是直徑；切線的判定定理：經(jīng)過(guò)半徑的外端并且垂直于這條半徑的直線是圓的切線；切線的性質(zhì)定理：圓的切線垂直于過(guò)切點(diǎn)的半徑；切線長(zhǎng)定理：從圓外一點(diǎn)引圓的兩條切線，這一點(diǎn)到兩切點(diǎn)的線段相等，它與圓心的連線平分兩切線的夾角；弧長(zhǎng)計(jì)算公式：（R為圓的半徑，n是弧所對(duì)的圓心角的度數(shù)，為弧長(zhǎng)）扇形面積：或（R為半徑，n是扇形所對(duì)的圓心角的度數(shù)，為扇形的弧長(zhǎng)）弓形面積(6)尺規(guī)作圖（基本作圖、利用基本圖形作三角形和圓）作一條線段等于已知線段，作

58、一個(gè)角等于已知角；作已知角的平分線；作線段的垂直平分線；過(guò)一點(diǎn)作已知直線的垂線；(7)視圖與投影畫(huà)基本幾何體（直棱柱、圓柱、圓錐、球）的三視圖（主視圖、左視圖、俯視圖）；基本幾何體的展開(kāi)圖（除球外）、根據(jù)展開(kāi)圖判斷和設(shè)別立體模型；2.圖形與變換圖形的軸對(duì)稱軸對(duì)稱的基本性質(zhì)：對(duì)應(yīng)點(diǎn)所連的線段被對(duì)稱軸平分；等腰三角形、矩形、菱形、等腰梯形、正多邊形、圓是軸對(duì)稱圖形；圖形的平移圖形平移的基本性質(zhì)：對(duì)應(yīng)點(diǎn)的連線平行且相等；圖形的旋轉(zhuǎn)圖形旋轉(zhuǎn)的基本性質(zhì)：對(duì)應(yīng)點(diǎn)到旋轉(zhuǎn)中心的距離相等，對(duì)應(yīng)點(diǎn)與旋轉(zhuǎn)中心的距離相等、對(duì)應(yīng)點(diǎn)與旋轉(zhuǎn)中心連線所成的角彼此相等；平行四邊形、矩形、菱形、正多邊形（邊數(shù)是偶數(shù)）、圓是中心對(duì)

59、稱圖形；圖形的相似比例的基本性質(zhì)：如果，則，如果，則相似三角形的設(shè)別方法：兩組角對(duì)應(yīng)相等；兩邊對(duì)應(yīng)成比例且?jiàn)A角對(duì)應(yīng)相等；三邊對(duì)應(yīng)成比例相似三角形的性質(zhì)：相似三角形的對(duì)應(yīng)角相等；相似三角形的對(duì)應(yīng)邊成比例；相似三角形的周長(zhǎng)之比等于相似比；相似三角形的面積比等于相似比的平方；相似多邊形的性質(zhì)：相似多邊形的對(duì)應(yīng)角相等；相似多邊形的對(duì)應(yīng)邊成比例；相似多邊形的面積之比等于相似比的平方；圖形的位似與圖形相似的關(guān)系：兩個(gè)圖形相似不一定是位似圖形，兩個(gè)位似圖形一定是相似圖形；RtABC中，C=，SinA=，cosA=, tanA=,CotA=特殊角的三角函數(shù)值：sincostan1cot1三、概率與統(tǒng)計(jì)1統(tǒng)計(jì)數(shù)

60、據(jù)收集方法、數(shù)據(jù)的表示方法（統(tǒng)計(jì)表和扇形統(tǒng)計(jì)圖、折線統(tǒng)計(jì)圖、條形統(tǒng)計(jì)圖）（1）總體與樣本所要考察對(duì)象的全體叫做總體，其中每一個(gè)考察對(duì)象叫做個(gè)體，從總體中所抽取的一部分個(gè)體叫做總體的一個(gè)樣本，樣本中個(gè)體數(shù)目叫做樣本的容量。數(shù)據(jù)的分析與決策（借助所學(xué)的統(tǒng)計(jì)知識(shí)，對(duì)所收集到的數(shù)據(jù)進(jìn)行整理、分析，在分析的結(jié)果上再作判斷和決策）（2）眾數(shù)與中位數(shù)眾數(shù)：一組數(shù)據(jù)中，出現(xiàn)次數(shù)最多的數(shù)據(jù)；中位數(shù)：將一組數(shù)據(jù)按從大到小依次排列，處在最中間位置的數(shù)據(jù)。（3）頻率分布直方圖頻率=，各小組的頻數(shù)之和等于總數(shù)，各小組的頻率之和等于1，頻率分布直方圖中各個(gè)小長(zhǎng)方形的面積為各組頻率。（4）平均數(shù)的兩個(gè)公式 n個(gè)數(shù)、, 的平