黄金分割专项练习
1．定义：如图1，点C在线段AB上，若满足AC2=BC?AB，则称点C为线段AB的黄金分割点．如图2，△ABC中，AB=AC=1，∠A=36°，BD平分∠ABC交AC于点D．
（1）求证：点D是线段AC的黄金分割点；
（2）求出线段AD的长．
2．如图，用长为40cm的细铁丝围成一个矩形ABCD（AB＞AD）．
（1）若这个矩形的面积等于99cm2，求AB的长度；
（2）这个矩形的面积可能等于101cm2吗若能，求出AB的长度，若不能，说明理由；
（3）若这个矩形为黄金矩形（AD与AB之比等于黄金比），求该矩形的面积．（结果保留根号）
9．在数学上称长与宽之比为黄金分割比的矩形为黄金矩形，如在矩形ABCD中，当时，称矩形ABCD
为黄金矩形ABCD．请你证明黄金矩形是由一个正方形和一个更小的黄金矩形构成．
10．如图，设AB是已知线段，在AB上作正方形ABCD；取AD的中点E，连接EB；延长DA至F，使EF=EB；以线段AF为边作正方形AFGH．则点H是AB的黄金分割点．
为什么说上述的方法作出的点H是这条线段的黄金分割点，你能说出其中的道理吗请试一试，说一说．
12．已知AB=2，点C是AB的黄金分割线，点D在AB上，且AD2=BD?AB，求的值．
14．五角星是我们常见的图形，如图所示，其中，点C，D分别是线段AB的黄金分割点，AB=20cm，求EC+CD的长．
15．人的肚脐是人的身高的黄金分割点，一般来讲，当肚脐到脚底的长度与身高的比为时，是比较好看的黄金身段．一个身高的人，他的肚脐到脚底的长度为多少时才是黄金身段（保留两位小数）
17．如图，点P是线段AB的黄金分割点，且AP＞BP，设以AP为边长的正方形面积为S1，以PB为宽和以AB为长的矩形面积为S2，试比较S1与S2的大小．
18．如图，在平行四边形ABCD中，E为边AD延长线上的一点，且D为AE的黄金分割点，即，BE交DC于点F，已知，求CF的长．
20．（如图1），点P将线段AB分成一条较小线段AP和一条较大线段BP，如果，那么称点P为线段AB的黄金分割点，设=k，则k就是黄金比，并且k≈．
（1）以图1中的AP为底，BP为腰得到等腰△APB（如图2），等腰△APB即为黄金三角形，黄金三角形的定义为：满足≈的等腰三角形是黄金三角形；类似地，请你给出黄金矩形的定义：；
（2）如图1，设AB=1，请你说明为什么k约为；
（3）由线段的黄金分割点联想到图形的“黄金分割线”，类似地给出“黄金分割线”的定义：直线l将一个面积为S的图形分成面积为S1和面积为S2的两部分（设S1＜S2），如果，那么称直线l为该图形的黄金分割线．（如
21．在人体躯干（脚底到肚脐的长度）与身高的比例上，肚脐是理想的黄金分割点，即比例越接近，越给人以美感．张女士原来脚底到肚脐的长度与身高的比为，她的身高为，她应该选择多高的高跟鞋穿上看起来更美（精确到十分位）
23．如图，用纸折出黄金分割点：裁一张正方的纸片ABCD，先折出BC的中点E，再折出线段AE，然后通过折叠使EB落到线段EA上，折出点B的新位置B′，因而EB′=EB．类似地，在AB上折出点B″使AB″=AB′．这时B″就是AB的黄金分割点．请你证明这个结论．
25．如图，在△ABC中，点D在边AB上，且DB=DC=AC，已知∠ACE=108°，BC=2．
（1）求∠B的度数；
（2）我们把有一个内角等于36°的等腰三角形称为黄金三角形．它的腰长与底边长的比（或者底边长与腰长的比）等于黄金比．
①写出图中所有的黄金三角形，选一个说明理由；
②求AD的长；
③在直线AB或BC上是否存在点P（点A、B除外），使△PDC是黄金三角形若存在，在备用图中画出点P，简要说明画出点P的方法（不要求证明）；若不存在，说明理由．
28．折纸与证明﹣﹣﹣用纸折出黄金分割点：
第一步：如图（1），先将一张正方形纸片ABCD对折，得到折痕EF；再折出矩形BCFE的对角线BF．
第二步：如图（2），将AB边折到BF上，得到折痕BG，试说明点G为线段AD的黄金分割点（AG＞GD）
29．三角形中，顶角等于36°的等腰三角形称为黄金三角形，如图1，在△ABC中，已知：AB=AC，且∠A=36°．（1）在图1中，用尺规作AB的垂直平分线交AC于D，并连接BD（保留作图痕迹，不写作法）；
（2）△BCD是不是黄金三角形如果是，请给出证明；如果不是，请说明理由；
（3）设，试求k的值；
（4）如图2，在△A1B1C1中，已知A1B1=A1C1，∠A1=108°，且A1B1=AB，请直接写出的值．
30．如图1，点C将线段AB分成两部分，如果，那么称点C为线段AB的黄金分割点．某研究小组在进行课题学习时，由黄金分割点联想到“黄金分割线”，类似地给出“黄金分割线”的定义：直线l将一个面积为S的图形分成两部分，这两部分的面积分别为S1，S2，如果，那么称直线l为该图形的黄金分割线．
（1）研究小组猜想：在△ABC中，若点D为AB边上的黄金分割点（如图2），则直线CD是△ABC的黄金分割线．你认为对吗为什么
（2）请你说明：三角形的中线是否也是该三角形的黄金分割线
（3）研究小组在进一步探究中发现：过点C任作一条直线交AB于点E，再过点D作直线DF∥CE，交AC于点F，连接EF（如图3），则直线EF也是△ABC的黄金分割线．请你说明理由．
（4）如图4，点E是平行四边形ABCD的边AB的黄金分割点，过点E作EF∥AD，交DC于点F，显然直线EF是平行四边形ABCD的黄金分割线．请你画一条平行四边形ABCD的黄金分割线，使它不经过平行四边形ABCD各边黄金分割点．
黄金分割专项练习30题参考答案:
1．（1）证明：∵AB=AC=1，
∴∠ABC=∠C=（180°﹣∠A）=（180°﹣36°）=72°，∵BD平分∠ABC交AC于点D，
∴∠ABD=∠CBD=∠ABC=36°，
∴∠BDC=180°﹣36°﹣72°=72°，
∴DA=DB，BD=BC，
∴AD=BD=BC，
易得△BDC∽△ABC，
∴BC：AC=CD：BC，即BC2=CD?AC，
∴AD2=CD?AC，
∴点D是线段AC的黄金分割点；
（2）设AD=x，则CD=AC﹣AD=1﹣x，
∵AD2=CD?AC，
∴x2=1﹣x，解得x1=，x2=，
即AD的长为
2．解：（1）设AB=xcm，则AD=（20﹣x）cm，
根据题意得x（20﹣x）=99，
整理得x2﹣20x+99=0，解得x1=9，x2=11，
当x=9时，20﹣x=11；当x=11时，20﹣11=9，
而AB＞AD，
所以x=11，即AB的长为11cm；
（2）不能．理由如下：
设AB=xcm，则AD=（20﹣x）cm，
根据题意得x（20﹣x）=101，
整理得x2﹣20x+101=0，
因为△=202﹣4×101=﹣4＜0，
所以这个矩形的面积可能等于101cm2；
（3）设AB=xcm，则AD=（20﹣x）cm，
根据题意得20﹣x=x，
解得x=10（﹣1），
则20﹣x=10（3﹣），
所以矩形的面积=10（﹣1）?10（3﹣）=（400﹣800）cm2．3．解：（1）∵∠A=36°，AB=AC，
∴∠ABC=∠ACB=72°，
∵BD平分∠ABC，
∴∠CBD=∠ABD=36°，∠BDC=72°，
∴AD=BD，BC=BD，
∴△ABC∽△BDC，
∴=，即=，
∴AD2=AC?CD．
∴点D是线段AC的黄金分割点．
（2）∵点D是线段AC的黄金分割点，
∴AD=AC，
∵AC=2，
∴AD=﹣1
4．解：（1）腰与底之比为黄金比为黄金比如图，
（2）作法：①画线段AB作为三角形底边；
②取AB的一半作AB的垂线AC，连接BC，在BC上取CD=CA．
③分别以A点和B点为圆心、以BD为半径划弧，交点为E；
④分别连接EA、EB，则△ABE即是所求的三角形．
（3）证明：设AB=2，则AC=1，BC=，AE=BE=BD=BC﹣CD=﹣1，=．
5．解：（1）由于P为线段AB=2的黄金分割点，
则AP=2×=﹣1，
或AP=2﹣（﹣1）=3﹣；
（2）如图，点P是线段AB的一个黄金分割点．
6．解：（1）设AC=x，则BC=AB﹣AC=1﹣x，
∵AC2=BC?AB，
∴x2=1×（1﹣x），
整理得x2+x﹣1=0，
解得x1=，x2=（舍去），
所以线段AC的长度为；
（2）设线段AD的长度为x，AC=l，
∵AD2=CD?AC，
∴x2=l×（l﹣x），
∴x1=，x2=（舍去），
∴线段AD的长度AC；
（3）同理得到线段AE的长度AD；
上面各题的结果反映：若线段AB分成两条线段AC和BC（AC＞BC），且使AC是AB和BC的比例中项（即AB：AC=AC：BC），则C点为AB的黄金分割点
∵在△ABC中，AB=AC，∠A=36°，
∴∠ABC=∠ACB==72°．
∵∠1=∠2，
∴∠1=∠2=∠ABC=36°．
∴在△BDC中，∠BDC=180°﹣∠2﹣∠C=72°，∴∠C=∠BDC，
∴BC=BD．
∵∠A=∠1，
∴AD=BC．
∵△ABC和△BDC中，∠2=∠A，∠C=∠C，
∴△ABC∽△BDC，
∴，
又∵AB=AC，AD=BC=BD，
∴，
∴AD2=AC?CD，即D是AC的黄金分割点
8．证明：∵AB=AC，∠A=36°，
∴∠ABC=（180°﹣36°）=72°，
∵BD平分∠ABC，交于AC于D，
∴∠DBC=×∠ABC=×72°=36°，
∴∠A=∠DBC，
又∵∠C=∠C，
∴△BCD∽△ABC，
∴
∵AB=AC，
∴=，
∵AB=AC=2，BC=﹣1，
解得AD=，
AD：AC=（）：2．
∴点D是线段AC的黄金分割点．
9．证明：在AB上截取AE=BC，DF=BC，连接EF．
∵AE=BC，DF=BC，
∴AE=DF=BC=AD，
又∵∠ADF=90°，
∴四边形AEFD是正方形．
BE=，
∴，
∴矩形BCFE的宽与长的比是黄金分割比，矩形BCFE是黄金矩形．∴黄金矩形是由一个正方形和一个更小的黄金矩形构成．
10．解：设正方形ABCD的边长为2，
在Rt△AEB中，依题意，得AE=1，AB=2，
由勾股定理知EB===，
∴AH=AF=EF﹣AE=EB﹣AE=﹣1，
HB=AB﹣AH=3﹣；
∴AH2=（）2=6﹣2，
AB?HB=2×（3﹣）=6﹣2，
2
11．证明：（1）∵∠A=36°，∠C=72°，
∴∠ABC=180°﹣36°﹣72°=72°，
∵∠ADB=108°，
∴∠ABD=180°﹣36°﹣108°=36°，
∴△ADB是等腰三角形，
∵∠BDC=180°﹣∠ADC=180°﹣108°=72°，
∴△BDC是等腰三角形，
∴AD=B D=BC．
（2）∵∠DBC=∠A=36°，∠C=∠C，
∴△ABC∽△BDC，
∴BC：AC=CD：BC，
∴BC2=AC?DC，
∵BC=AD，
∴AD2=AC?DC，
∴点D是线段AC的黄金分割点．
12．解：∵D在AB上，且AD2=BD?AB，
∴点D是AB的黄金分割点
而点C是AB的黄金分割点，
∴AC=AB=﹣1，AD=AB﹣AB=AB=3﹣或AD=﹣1，AC=3﹣，∴CD=﹣1﹣（3﹣）=2﹣4，
∴==或==．
13．解：矩形ABFE是黄金矩形．
∵A D=BC，DE=AB，
∴==﹣1==．
∴矩形ABFE是黄金矩形．
∴AD=AB=10﹣10，
∵EC+CD=AC+CD=AD，
∴EC+CD=（10﹣10）cm．
15．解：设他的肚脐到脚底的长度为xm时才是黄金身段，
根据题意得x：=，
即x=×≈（m）．
答：他的肚脐到脚底的长度为时才是黄金身段．
16．解：（1）在Rt△APD中，AP=1，AD=2，由勾股定理知PD===，∴AM=AF=PF﹣AP=PD﹣AP=﹣1，
DM=AD﹣AM=3﹣．
故AM的长为﹣1，DM的长为3﹣；
（2）点M是AD的黄金分割点．
由于=，
∴点M是AD的黄金分割点．
17．解：∵点P是线段AB的黄金分割点，且AP＞BP，
∴AP2=BP×AB，
又∵S1=AP2，S2=PB×AB，
∴S1=S2．
18．解：∵四边形ABCD为平行四边形，
∴∠CBF=∠AEB，∠BCF=∠BAE，
∴△BCF∽△EAB，
∴，即，
把AD=，AB=+1代入得，=，
解得：CF=2．
故答案为：2．
19．解：矩形EFDC是黄金矩形，
证明：∵四边形ABEF是正方形，
又∵，
∴，
即点F是线段AD的黄金分割点．
∴，
∴，
∴矩形CDFE是黄金矩形．
20．解：
（1）满足≈的矩形是黄金矩形；
（2）由=k得，BP=1×k=k，从而AP=1﹣k，
由得，BP2=AP×AB，
即k2=（1﹣k）×1，
解得k=，
∵k＞0，
∴k=≈；
（3）因为点P是线段AB的黄金分割点，所以，
设△ABC的AB上的高为h，则
，
∴
∴直线CP是△ABC的黄金分割线．
（4）由（2）知，在BC边上也存在这样的黄金分割点Q，则AQ也是黄金分割线，设AQ与CP交于点W，则过点W 的直线均是△ABC的黄金分割线，故黄金分割线有无数条．
设选择的高跟鞋的高度是xcm，则根据黄金分割的定义得：=，
解得：x≈．
故她应该选择左右的高跟鞋穿上看起来更美．
22．解：设正方形ABCD的边长为2a，
在Rt△AEB中，依题意，得AE=a，AB=2a，
由勾股定理知EB==a，
∴AH=AF=EF﹣AE=EB﹣AE=（﹣1）a，
HB=AB﹣AH=（3﹣）a；
∴AH2=（6﹣2）a2，
AB?HB=2a×（3﹣）a=（6﹣2）a2，
∴AH2=AB?HB，
所以点H是线段AB的黄金分割点．
23．证明：设正方形ABCD的边长为2，
E为BC的中点，
∴BE=1
∴AE==，
又∵B′E=BE=1，
∴AB′=AE﹣B′E=﹣1，
∴AB″
∴点B″是线段AB的黄金分割点．
24．证明：∵正方形ABCD的边长为2，E为BC的中点，
∴BE=1
∵EF=BE=1，
∴AF=AE﹣EF=﹣1，
∴A M=AF=﹣1，
∴AM：AB=（﹣1）：2，
∴点M是线段AB的黄金分割点．
25．解：（1）∵BD=DC=AC．
则∠B=∠DCB，∠CDA=∠A．
设∠B=x，则∠DCB=x，∠CDA=∠A=2x．
又∠BOC=108°，
∴∠B+∠A=108°．
∴x+2x=108，x=36°．
∴∠B=36°；
（2）①有三个：△BDC，△ADC，△BAC．
∵DB=DC，∠B=36°，
∴△DBC是黄金三角形，
（或∵CD=CA，∠ACD=180°﹣∠CDA﹣∠A=36°．∴△CDA是黄金三角形．
或∵∠ACE=108°，
∴∠ACB=72°．又∠A=2x=72°，
∴∠A=∠ACB．
∴BA=BC．
∴△BAC是黄金三角形．
②△BAC是黄金三角形，
∴，
∵BC=2，∴AC=﹣1．
∵BA=BC=2，BD=AC=﹣1，
∴AD=BA﹣BD=2﹣（﹣1）=3﹣，
ⅰ）以CD为底边的黄金三角形：作CD的垂直平分线分别交直线AB、BC得到点P1、P2．ⅱ）以CD为腰的黄金三角形：以点C为圆心，CD为半径作弧与BC的交点为点 P3．
26．证明：在正方形ABCD中，取AB=2a，
∵N为BC的中点，
∴NC=BC=a．
在Rt△DNC中，．
又∵NE=ND，
∴CE=NE﹣NC=（﹣1）a．
∴．
故矩形DCEF为黄金矩形．
27．解：（1）
（2）CM=AB（4分）
28．证明：如图，连接GF，设正方形ABCD的边长为1，则DF=．
在Rt△BCF中，BF==，
则A′F=BF﹣BA′=﹣1．
设AG=A′G=x，则GD=1﹣x，
在Rt△A′GF和Rt△DGF中，有A'F2+A'G2=DF2+DG2，
解得x=，
即点G是AD的黄金分割点（AG＞GD）．
29．解：（1）如图所示；
（2）△BCD是黄金三角形．
证明如下：∵点D在AB的垂直平分线上，∴AD=BD，
∴∠ABD=∠A．
∵∠A=36°，AB=AC，
∴∠ABC=∠C=72°，
∴∠ABD=∠DBC=36°．
又∵∠BDC=∠A+∠ABD=72°，
∴∠BDC=∠C，
∴BD=BC，
∴△BCD是黄金三角形．
（3）设BC=x，AC=y，
由（2）知，AD=BD=BC=x．
∵∠DBC=∠A，∠C=∠C，
∴△BDC∽△ABC，
整理，得x2+xy﹣y2=0，
解得．
因为x、y均为正数，所以．
（4）．
理由：延长BC到E，使CE=AC，连接AE．
∵∠A=36°，AB=AC，
∴∠ACB=∠B=72°，
∴∠ACE=180°﹣72°=108°，
∴∠ACE=∠B1A1C1．
∵A1B1=AB，
∴AC=CE=A1B1=A1C1，
∴△ACE≌△B1A1C1，
∴AE=B1C1．
由（3）知，
∴，，
∴．30．解：（1）直线CD是△ABC的黄金分割线．理由如下：设△ABC的边AB上的高为h．
则，，，∴，．
又∵点D为边AB的黄金分割点，
∴，
∴．
故直线CD是△ABC的黄金分割线．
∴，即，
故三角形的中线不可能是该三角形的黄金分割线．
（3）∵DF∥CE，
∴△DFC和△DFE的公共边DF上的高也相等，
∴S△DFC=S△DFE，
∴S△ADC=S△ADF+S△DFC=S△ADF+S△DFE=S△AEF，S△BDC=S四边形BEFC．
又∵，
∴．
因此，直线EF也是△ABC的黄金分割线．（7分）
（4）画法不惟一，现提供两种画法；
画法一：如答图1，取EF的中点G，再过点G作一条直线分别交AB，DC于M，N点，则直线MN就是平行四边形ABCD 的黄金分割线．
画法二：如答图2，在DF上取一点N，连接EN，再过点F作FM∥NE交AB于点M，连接MN，则直线MN就是平行四边形ABCD的黄金分割线．
（9分
中考复习改错专项训练 1． Old Sarah was a strange rich woman. He did not 80. ________ hope to see any of her relative. She felt what they 81. ________ were interested in was her money. She was all right 82. ________ After she died, the relatives got together to hear Sarah's 83. ________ lawyer(律师) to read her will (遗嘱). They were sure that 84. ________ Sarah had left many money and they quarreled strongly 85. ________ with each other when they waited the lawyer to arrive. 86. ________ After the lawyer came in the living room, he asked them 87. ________ to sit down. He began to read the will in a seriously 88. ________ voice. Sarah has left all her money to her cats. 89. ________ 2． Mr Green come from England . 81. _________ He teaches English in middle school . 82. _________ He can speak some Chinese. He 83. ________ goes at Chinese classes very week . 84. __________ He likes working in Chinese very much . 85. _________ 3． Have you ever wanted to write a song? Two Sister. 59._________ Mildred and Patty Hill, once write a little song. 60._________ It was a happily song that they loved to sing. It 61._________ was calling "Good Morning to You. "However, most 62._________ other people didn't know the song very well. A day, 63._________ Mildred and Patty had a idea. It turned out (证明) to be 64._________ a very bad idea. They changed the words of the song. They 65.__________ called the new song "Happy Birthday to You." Theirs short 66._________ birthday song is now very famous. Almost every body know 67.__________ the words, Did anyone sing it at your test birthday party? 68.__________ 4. Hundred of years ago, news was carded by 6. _____________ people on foot or by a horse. It took a long 7. _____________ time people to receive news. Now it is possible 8. _____________ to send words and pictures in seconds. Billions of 9. _____________ people learn about news either by watching TV and by reading. 10. ____________ 5. Yesterday I went for shopping for shoes. The largest pair 1. I could find was an size 9 and I wear an 11! Everyone 2.
高三英语短文改错专项训练(每日一篇） (1) Last Sunday I saw the worst storm in years. It came sudden and went on for over three hours. After lunch, I went into my room to have a rest. The air was hotter, and all is quiet. Then a strong wind started to blow into my room. Pieces of paper on my desk flew high into the air and some flew out the open window. As I ran out to catch them, big drop of rain began to fall. When I came back into house, it was raining harder and harder. I tried very hard to close the window. Then I heard a loudly crashing(碰撞的)sound from the back of the house. When I ran out to find that a big tree had fallen down and broke the top of the back room. (2) I have been planning to join in our college basketball team next year, so now I am spending as more time as I can with other people who likes to play. They are teaching me the most important rules and technologies of the game, and I am getting the better all the time. We have a neighborhood team that play against other teams in the area. One of my neighbors is helping rest of us improved our skills. Tonight we are playing against one of the best teams in the city, and I think we can beat them if we won't make any mistakes. (3) Fang Tong is 34 years old, an actor, director and teacher of Beijing Opera Theater. Most of his students are from other part of China and have come to Beijing at a very young age of sixteen or seventeen. He hopes create an environment for his students that it is much more relaxing than the one he used to study in. He thought that an actor should relax himself when performing. Yet his students deep respect him and he never needs to raise his voice in order to be hearing. For his opinion, actors should go on even when they feel they have made a mistake in their performances because the moment is already gone but people can never be back to it. . . So art is always changing and
专题二新题精选30题 一、选择题 1．观察下列汽车图标，其中既是轴对称图形又是中心对称图形的有（）个． A．5个B．4个C．3个D．2个 【答案】D． 考点：轴对称图形；中心对称图形． 2．某市户籍人口1694000人，则该市户籍人口数据用科学记数法可表示为（） A．1.694×104人B．1.694×105人C．1.694×106人D．1.694×107人 【答案】C． 【解析】 试题分析：将1694000用科学记数法表示为：1.694×106．故选C． 考点：科学记数法—表示较大的数． ，则 A C=（）3．在△ABC中，∠C=90°，∠B=∠22．5°，DE垂直平分AB交BC于E，BC=222 A．1 B．2 C．3 D．4 【答案】B． 【解析】 试题分析：∵DE垂直平分AB，∴∠B=∠DAE，BE=AE，∵∠B=22．5°，∠C=90°，∴∠AEC=∠CAE=45°，
∴AC =CE ，∴2AC 2=AE 2 ，∴AE =2AC ， ∴BC =BE +CE =AE +AC =2AC +AC ，∵BC =222+，∴2AC +AC =222+，∴AC =2，故选B ． 考点：线段垂直平分线的性质． 4．已知两点A （5，6）、B （7，2），先将线段AB 向左平移一个单位，再以原点O 为位似中心，在第一象限内将其缩小为原来的 1 2 得到线段CD ，则点A 的对应点C 的坐标为（ ） A ．（2，3） B ．（3，1） C ．（2，1） D ．（3，3） 【答案】A ． 考点：位似变换；坐标与图形变化-平移；几何变换． 5．若代数式 1 1 x x +-有意义，则实数x 的取值范围是（ ） A ．1x ≠ B ．0x ≥ C ．0x ≠ D ．0x ≥且1x ≠ 【答案】D ． 【解析】 试题分析：∵代数式 1 1x x +-有意义，∴100 x x -≠?? ≥?，解得0x ≥且1x ≠．故选D ． 考点：二次根式有意义的条件；分式有意义的条件． 6．关于x 的不等式组314(1) x x x m ->-??
高考复习必看短文改错专项训练15篇（附答案） 1 Dear Jack， Next Saturday will my birthday.I’m going to hold a birthday party at home on the evening.It will start at 7：30.Some classmates as good as some foreign friends have been invited.The activities include singing，dancing and sharing interesting experiences.Surely，we’ll have a good time.I would feel honoring if you could come.I live at 656 Minzu Street.You can take Bus No.11 or No.15 and got off at the stop of Guang Ming High School.Justly on the opposite side is my house，what is red with a white door.I’m sure of you can’t miss it.I do hope they will come. Best wish. Yours， Li Hua 2 (2017·昆明市高三复习教学质量检测) I’m one of the students in our class who has ever been to https://www.doczj.com/doc/e82363532.html,st summer I was lucky enough to be sent there to study.As soon as I arrived on England by plane.I was picked up by the Smiths，which I would live with for the next two weeks.We felt like a fish out of water when I got there.The Smiths did what they could make me feel at home.I study at an international school，where I met friend from all over the world.I seized the opportunity to practise my speak English.Soon I made such a rapid progress that I received highly praise from all the people around. 答案 I’m one of the students in our class who has have ever been to https://www.doczj.com/doc/e82363532.html,st summer I was lucky enough to be sent there to study.As soon as I arrived on in England by plane.I was picked up by the Smiths，which whom I would live with for the next two
短文改错 John went shopping in a store, and he forgot to bring a bag. So he buys a shopping bag. After arriving home, it occurred him that he could make a bag by using his old trousers. Several hours earlier, he made himself a very nice bag. His mother was amazing at what he had done. Avoiding spending money unnecessarily is a way of saving. And making a good use of things is an approach to protect the environment. What's more, it is helpful for you to improve the ability to make things by hands. It not only brings us pleasure but reduce waste around us. 1.__________ 2.__________ 3.____________ 4.____________ 5.___________ 6.____________ 7.___________ 8.____________ 9.____________ 10._____________ 【答案】 第一处：and→but 句意为：约翰到一家商店购物，但是他忘了带购物袋。根据句意可知，此处前后为转折关系，并非顺承关系，故将and改为but。 第二处：buys→bought根据前一句中的went shopping可知，此处讲述发生在过去的事情，故应用一般过去时。故将buys改为bought。 第三处：在occurred后加to it occurred to sb.that为固定句式，意为“某人突然想到……”，故在occurred后加to。第四处：earlier→l ater根据上下文语境可知，此处指几小时后，他自己做了一个很好的袋子。故将earlier改为later。 第五处：amazing→amazed amazing用于形容物的性质，意为“令人惊异的",amazed用于描述人的感觉，意为“感到惊讶的”，本句的主语为His mother,指人，故此处应用表示人感觉的形容词作表语，故将amazing改为amazed。第六处：删除a .make good use of sth.为固定搭配，意为“充分利用某物”，a多余，故删除a。 第七处：protect→protect ing .approach后的to为介词，其后应用动名词，作介词to的宾语，故将protect改为protecting。 第八处：you→us根据下文中的“It not only brings us...around us"可知，此处应用第一人称，故将you改为us。第九处：hands→hand. by hand为固定搭配，意为“用手工做……”，故将hands改为hand。 第十处：reduce→reduces本句主语为It,谓语应用第三人称单数形式，设空处与brings为本句的两个并列谓语，故将reduce改为reduces。
高考短文改错专项练习 1 College students have a little ways to pay their college fees. Many students have their parents to pay the fees. Some students may apply to a bank loan and others will try to find part-time jobs in and out of the campus. Apart from this, many good student can win a scholarship. By this way they can pay at least part of the fees. As to me, I will let my parents pay half of their fees because they are rich enough. Beside my study, I will take up a part-time job by teach some high school students math, physics, chemistry and English, as I’m very good at these important subjects. Of course I will also work very hard at my lessons in order to I can easily win a scholarship. 2 I am angry about the act of dishonesty in the exams. I’m not saying that I’m a good student and that I’ve never cheated. I once write the answer on my hand for a history test but, unluckily, caught by my teacher. Because she was one of my most favorites, there were no words to describe how sorry I felt at once. I thought cheat would help me keep my straight A’s. Little I know that I was hurting not only herself but also my teachers. From this lesson I know teachers want students to succeed by learning with their own and do the best they can, not by cheating.
高考英语短文改错专项训练（含答案） 1.【2016·全国新课标I】短文改错（10 分） My uncle is the owner of a restaurant close to that 1 live .Though not very big ,but the restaurant is popular in our area .It is always crowded with customers at meal times .Some people even had to wait outside My uncle tells me that the key to his success is honest. Every day he makes sure that fresh vegetables or high quality oil are using for cooking. My uncle says that he never dreams becoming rich in the short period of time. Instead, he hopes that our business will grow steady. 2.【2016·全国新课标II】短文改错（共10小题，每小题1分，满分10分） The summer holiday is coming. My classmates and I are talking about how to do during the holiday. We can chose between staying at home and take a trip. If we stay at home, it is comfortable but there is no need to spend money. But in that case, we will learn little about world. If we go on a trip abroad, we can broaden you view and gain knowledges we cannot get from books. Some classmates suggest we can go to places of interest nearby. I thought that it is a good idea. It does not cost many, yet we can still learn a lot. 3.【2016·全国新课标III】短文改错（共10小题；每小题1分，满分10分） The teenage year from 13 to 19 were the most difficult time for me . They were also the best and worse years in my life . At the first, I thought I knew everything and could make decisions by yourself. However, my parents didn’t seem to think such. They always tell me what to do and how to do it. At one time , I even felt my parents couldn’t understand me so I hoped I could be freely from them. I showed them I was independent by wear strange clothes. Now I am leaving home to college. At last, I will be on my own, but I still want to have my parents to turn to whenever need help. 4.【2016·四川】短文改错（共10小题；每小题1分，满分10分） It is Mother’s Day today. Though it’s a western festival, it’s popular in China now. Mom has a full-time job, so she has to do most of the houseworks. She is a great mother. Both Dad or I planned to do something on Mother’s Day. We get up early in the morning. Dad cleaned the house, and then went on shopping. When he came back, I found a bunch of flowers in her hand. I asked Mom to stay in the sitting room and I cooked in kitchen. The dishes what I cooked were Mom’s favoritiest. At dinner, we said to her, “Happy Mother’s Day！”Mom was grateful and moving.
高中英语短文改错专题练习（10篇） 答题要求：此题要求改正所给短文中的错误。对标有题号的每一行作出判断：如无错误，在该行右边横线上画一个勾(√)；如有错误(每行只有一个错误)，则按下列情况改正： 此行多一个词：把多余的词用斜线(＼)划掉，在该行右边横线上写出该词，并也用斜线划掉。 此行缺一个词：在缺词处加一个漏字符号(∧)，在该行右边横线上写出该加的词。 此行错一个词：在错的词下划一横线，在该行右边横线上写出改正后的词。 注意：原行没有错的不要改。 A While traveled to Paris on a bus, I became very sick. 1. _______________ A well-dressing man on the bus helped me greatly. He 2. _______________ took me off the bus, found out where the doctor’s office. 3. _______________ and took me to there himself. The next day, he came 4. _______________ to visit me. I didn’t speak French well, so I can’t talk with 5. _______________ him very much. However, even if we couldn’t talk, but 6. _______________ we could communicate. I communicated myself thanks 7. _______________ to his great kindness, and he communicated his concern 8. _______________ for my healthy. Through this experience I have learned 9. _______________ that communication can take place without much actual 10. ______________ language at all. B The Internet is playing a important part in81．＿＿＿＿＿ our daily life. On the net, we can learn about82．＿＿＿＿＿ news both home and abroad and some other83．＿＿＿＿＿informations as well．We can also make phone calls，84．＿＿＿＿＿ send messages by e-mails，go to net schools，and85．＿＿＿＿＿ learn foreign languages by ourselves．Beside，we86．＿＿＿＿＿ can enjoy music，watch sports matches，and play the87．＿＿＿＿＿ chess or cards．The net even help us do shopping，88．＿＿＿＿＿ make a chat with others and make friends with them．89．＿＿＿＿＿ In a word，the Internet has made our life more easier．90．＿＿＿＿＿ C A few months after returning the US from Germany, I took 81. part in a college course in French. Since I have learned to 82. speak German good in Germany, I thought that it might be 83. interested to begin studying another language. At the first 84. class, the teacher asked us to do a pronunciation exercise, 85. in which he would say one word or two in French, and each 86. student would do their best to copy. When he got to me, he 87. kept having me to say more words, and I finally asked him 88.
2019高考英语短文改错专题 (名师剖析解题思路与技巧+实战训练，建议下载练习) 一．改错题型特点： 高考短文改错是知识和能力的综合测试题型。主要考查考生在语篇中综合运用英语知识的准确性及词、句、篇和语法的综合水平。高考短文改错设置的考点灵活多变，知识层次多，覆盖面广，包括词法、句法、行文逻辑以及语篇结构等，是一种在较高层次上考查考生对英语知识的掌握和语言综合运用能力的测试题型。 二．短文改错常见考点设置： 考点1：名词 命题特点: 本来用复数,却用单数；本来用单数，却用复数。 记住常考的几个不可数名词：news, work(工作), advice, fun, progress, information, luck, weather, music, health, change(零钱),baggage(行李), luggage(行李),furniture, jewellery, equipment等 改正方法: (1)根据名词前的修饰限定成份(2)根据上下文的逻辑关系. 1. She said that she and my schoolmate all wished me success. 2. After class we become stranger at once. 3. They want me to devote all my time to my studies so that I’ll get marks in all my subject. 4. On the way up I was busy taking picture since the scenery was so beautiful. 5. There are advantage for students to work while studying at school. 6. Now we can get millions of informations from the Internet. 7. He had no ideas that the kitchen was not for guests. 8. She is one of the most intelligent girl in our class. 9. I looked at his other hands. 10. Most of them are peasant and some often go fishing in the sea. 11. We have made great progresses with Mr. Liu teaching us. 12. Head teacher Guy Holloway said the new rules should help students get higher grade. 13. He was tall, with broad shoulder and a beard that turned from black toward gray over the years. 14. He’s getting married next month and decides to buy some furnitures.
专题02 相互作用 1．(2013上海徐汇测试)如图所示，F 1、F 2为有一定夹角的两个力，L 为过O 点的一条直线，当L 取什么方向时，F 1、F 2在L 上分力之和 为最大（ ） （A ）F 1、F 2合力的方向， （B ）F 1、F 2中较大力的方向， （C ）F 1、F 2中较小力的方向， （D ）以上说法都不正确。 2. （2013河南三市联考）如图所示,倾角为0的固定斜面上有 一个固定竖直挡板，在挡板和斜面之间有一 个质量为m 的光滑 球，设挡板对球的支持力为F 1，斜面对球的支持力为F 2，将挡板绕挡板与斜面的接触点缓慢地转至水平位置。不计摩擦，在 此过程中 A. F 1始终增大，F 2始终减小 B. F 1始终增大，F 2先增大后减小 C. F 1先减小后增大，F 2先增大后减小 D. F 1先减小后增大，F 2始终减小 3．（2013四川资阳诊断）如图所示，两轻弹簧a 、b 悬挂一小铁球处于平衡状态，a 弹簧与竖直方向成30°角，b 弹簧水平，a 、b 的劲度系数分别 为k 1、k 2。则两弹簧的伸长量x 1与x 2之比为 A ． B ．21k k C ．212k k D ．21 2k k 4.（2013四川绵阳一诊） 风洞是进行空气动力学实验的. 种重要设备。一次检验 2
飞机性能的风洞实验示意图如图，代表飞机模型的截面，OZ是拉住飞机模型的绳。已知飞机模型重为G,当飞机模型静止在空中时，绳恰好水平，此时飞机模型截面与水平面的夹角为θ，则作用于飞机模型上的风力大小为 A．G/cosθ B．G cosθ. C．G/sinθ. D．G sinθ. 5．（2013四川资阳诊断）半圆柱体M放在粗糙的水平地面上，其右端有固定放置的竖直挡板PQ，M与PQ之间放有一个光滑均匀的小圆柱体N，整个系 统处于静止。如图所示是这个系统的纵截面图。若用 外力F使PQ保持竖直并且缓慢地向右移动，在N 落到地面以前，发现M始终保持静止。在此过程中， 下列说法正确的是 A．地面对M的摩擦力逐渐增大 B．MN间的弹力先减小后增大 C．PQ对N的弹力逐渐减小 D．PQ和M对N的弹力的合力逐渐增大 6．（2013山东莱州质检）如图所示，轻绳的一端系在质 量为m的物体上，另一端系在一个圆环上，圆环套在粗 糙水平横杆MN上，现用水平力F拉绳上一点，使物体 处在图中实线位置，然后改变F的大小使其缓慢下降到图 中虚线位置，圆环仍在原来位置不动，则在这一过程中，水平拉力F、环与横杆的摩擦力f和环对杆的压力N的大小变化情况是( ) A．F逐渐增大，f保持不变，N逐渐增大
预习案 近年高考，英语短文改错题，学生和老师都认为难度不大，然而，每年高考中部分同学还是对此深感头疼， 主要原因：一、英语基础知识不扎实 二、对短文改错题的考点不了解 三、最欠缺是行文逻辑能力，学生上下文联系呼应及翻译能力有待增强 目标：1、学生能加强对短文改错题型的了解， 2、通过针对性练习，学生能增强自信心和做题的准确度 重点：时态语态、逻辑一致 难点：逻辑一致 （每题一处错误） 1.My father and I stayed at the South Lake Hotel for a week when we visit Beijing last month. 2.The book you borrowed from the library should returned in five days. 3.Therefore, I told them interested stories and how I was enjoying Brazil. 4.In early January this year, the rate of UFO reports was steady, around three per weeks. 5.Unfortunate, the only problem was the journey home. 6.I knew that they would be worried about me because I was so farther away. 7.I’m sorry that I am abroad and can’t send your flowers. 8.There was one on particular I’d always wanted. 9.It is such great hotel that I would recommend it to any friend of mine. 10.In the end, we drove to a service station and waited there unless the road was clear. 11.He said it was best to stay until help arrived rather than go into the forest and getting lost. 预习案 近年高考，英语短文改错题，学生和老师都认为难度不大，然而，每年高考中部分同学还是对此深感头疼， 主要原因：一、英语基础知识不扎实 二、对短文改错题的考点不了解 三、最欠缺是行文逻辑能力，学生上下文联系呼应及翻译能力有待增强 目标：1、学生能加强对短文改错题型的了解， 2、通过针对性练习，学生能增强自信心和做题的准确度 重点：时态语态、逻辑一致 难点：逻辑一致 （每题一处错误） 1.My father and I stayed at the South Lake Hotel for a week when we visit Beijing last month. 2.The book you borrowed from the library should returned in five days. 3.Therefore, I told them interested stories and how I was enjoying Brazil. 4.In early January this year, the rate of UFO reports was steady, around three per weeks. 5.Unfortunate, the only problem was the journey home. 6.I knew that they would be worried about me because I was so farther away. 7.I’m sorry that I am abroad and can’t send your flowers. 8.There was one on particular I’d always wanted. 9.It is such great hotel that I would recommend it to any friend of mine. 10.In the end, we drove to a service station and waited there unless the road was clear. 11.He said it was best to stay until help arrived rather than go into the forest and getting lost. 探究案