/ 让教学更有效 高效备考 | 英语学科
Unit 2 Amazing numbers
Section 4 Focusing culture,Cross-curricular connection,Project
（分层练习）
基础达标 01 能力提升 02 拓展培优 03
一、单项选择
1.The lion is often used as a ____ of courage.
A. signal B. sign C. symbol D. mark
2.—Can you ____ the books on the shelf
—Sure. Let me see. There are 20 books.
A. read B. write C. count D. see
3.The human body has a complex ____ that helps it fight against diseases.
A. system B. structure C. pattern D. framework
4.The cheongsam（旗袍）is often worn by Chinese women to ____ Chinese culture around the world.
A. discover B. represent C. create D. divide
5.The man ______described what he saw so that the police could understand clearly.
A. exactly B. simply C. gradually D. probably
6.This kind of flower is very ____ in spring. You can find it in almost every garden.
A. common B. unique C. particular D. extraordinary
7.The olive branch（橄榄枝） always ____ peace all over the world.
A. stands out B. stands for C. stands up D. stands by
8.When you listen to the teacher in class, you should ____ important points so that you can review them later.
A. put down B. look down C. turn down D. write down
9.Before you travel abroad, you'd better ____ the opening hours of the embassy in case you need to get some help.
A. check B. choose C. collect D. correct
10. About ________ of the teachers in our school ________ born in ________.
A. two-thirds; was; 1970 B. two-thirds; were; the 1970s
C. two-third; was; 1970s D. two third; were; the 1970
二、根据首字母或汉语提示完成单词
1.The central computer s________ can control (控制)all lights in this building.
2. Sichuan opera was first performed in the Tang dynasty in Sichuan and later d___________ into a popular art form in China.
3. If you go to Xi’an, a(n) a_______ capital of thirteen dynasties, you can’t miss its places of historical interest.
4.News about the school sports meeting s_____ quickly among the students.
5. As usual, it's time to go to the sea to feed t________ of seabirds there.
6. She asked the children to c____ the number of stars drawn on the blackboard.
7. It’s c_______ for people to feel nervous before a job interview.
8. The flag’s colors r________ the history and culture of the nation.
9. She knew e_______ what to say to comfort her friend in trouble.
10. We can c_____ beautiful cards with colored paper and crayons in art class.
三、用词的适当形式填空
1. The ____ student in line is ______ years old, and he loves drawing cats. (nine)
2. My aunt became a teacher when she was in her _______. (twenty)
3. The _____ grade has eighteen classes, and my friend is in Class _____. (eight)
4. It's easy _______apples because they are _________objects. (count)
5. She drank water instead of _______(eat)eating snacks during the break.
6. The ______ price of the book is 25 yuan, and I _______ have 25 yuan in my wallet. (exact)
7. My pen pal from _____ can speak both English and _____ languages. (India)
8. Rice is _______________(common) food in many Asian countries.
9. My grandpa used ________ (tell) me stories every night before bed.
10. The _____ hopes ________more wonderful cartoons for children, and each ________ makes kids happy. (create)
四、完成句子
1.在课上，没有必要把屏 幕上所有的东西都记下来。
In class there is no need to______ ______ all the things on the screen.
2.面对这么多困难，我们 决定继续奋斗，而不是放弃。
Facing so many difficulties, we decide to fight on ______ ____giving up.
3.把一个梦想变成现实 的最好方式就是立刻行动。
The best way to____ _____ _____ _____reality is by acting right away.
4.袁隆平，世界上最伟大的科学家之一，作为 “杂交水稻之父”而出名。
Yuan Longping, one of the greatest scientists in the world,____ ____ ____ “the Father of Hybrid Rice”.
5.罗马数字不如阿拉伯数字常见，也许是因为它们太难使用了！
Roman numerals are not ____ ____ ____Arabic numerals, maybe because they are _____ difficult ____ use!
6.不同的文化有不同的象征，一颗心往往代表爱。
Different cultures have _____ ________, and a heart often ____ _____love.
7.计数棒很容易理解，但写下大数字可能需要很长时间。
Tally sticks are easy ___ ________, but it can take a long time to _____ _____ large numbers.
8.多亏了老师的帮助，我过去数学很差，但现在我擅长了
____ ___my teacher's help, I ___ ____be weak in math, but now I'm good at it
五、短文填空
A 短文填词
Chinese people are used to thinking the numbers 6, 8 and 9 are lucky ones, but how about 142857 This number seems (1) c____________, not special. but it is the most amazing number in the world. Why Let’s look at a few facts about this number.
First, get the number multiplied (乘) by 1 to 6 and all the results are amazing because they are made up of the same numbers but in different (2) o_________. For example, 142857 multiplied by 2 is 285714 while 142857 multiplied by 6 is 857142. Second, if it is multiplied by 7 and we get a more amazing number 999999. Third, the number is multiplied by itself and we can get a super large number 20408122449. However, when we (3) a______ the front five numbers to the back six numbers, we can (4)e________ get the same number 142857 again. Is it amazing
In fact, people found this mysterious（神秘的）number inside the pyramids（金字塔）of Egypt. People also (5)d_________ the number is linked to seven days of a week. So you see, how amazing the number (6) s_________ is! And we can learn a lot from it.
B 语法填空
Have you heard of the saying “Fall down seven times, stand up eight” It means that no matter what 1 (challenge) you meet, keep on going over a long time. This is called perseverance (毅力). And it can help you achieve lots of things.
It is true that you can achieve 2 goal if you stick to it. You practice a skill on your bike over and over again and you make it. Or you continue to play basketball in face of difficulties. After a long time, you can play basketball 3 (perfect). Florence, 11, says, “I go running with my mom three times a week, even when I don’t feel like it, I try hard 4 (push) myself. I’m the fastest in my class now.”
Studies show that feeling hopeful and working towards a goal that you really want to reach can cut down stress and make you feel 5 (happy). Achieving something you’ve worked hard for, and overcoming difficulties along the way, can also develop ___6____ (you )courage and make you feel braver to try new things. Angela Duckworth, who is an expert (专家) in thoughts and feelings, studies perseverance. Duckworth believes that it doesn’t matter how talented, clever or rich you are, perseverance really 7 (help) you succeed.
Duckworth believes perseverance is something anyone can learn, and the best way to do this is to have a growth mind. This means 8 (believe) that your brain can grow, and that you can achieve anything if you work hard at it. 9 instead of thinking, “I can’t do this”, try thinking “I can’t do this… yet.” As the book The Big Life Journal says, “People 10 a growth idea know they can get better by working hard. They keep trying even when things are difficult.”
六、阅读配对
下面的材料A-F是六个AI工具网站的介绍。请根据Eric、Tom、Jack、Sally、Lily五位同学的需求为他们推荐合适的网站。
1 Eric has difficulty in speaking English, so he wants to practice his pronunciation and hear how it sounds. 2 Tom is in charge of a drama. Now she is looking for music that matches the different scenes. 3 Jack needs to put his thoughts together and make a brief summary for a group project. He wants to see them clearly. 4 Sally is working on her speech draft and she needs some writing suggestions on “Environmental Protection”. 5 Lily wants to make special posters for a school event but right now she only has some ideas. A. https: //yige. You can create amazing pictures for your school projects with this AI. It will turn your ideas into pictures. It is also great for art class or decorating your room. B. https: //tianyin. If you want to make your own music for school plays or just for fun, try this tool. It will let you choose different music styles to fit your feelings. C. https: //www. chatmind. tech Stuck on a project This AI may help you organize your ideas and show them as a mind map. It’s like having a helper for planning your school work. D. https: //translate. This is a translation tool that can help you read and enjoy foreign books easily. It can also help you explore books in different languages and learn about new cultures. E. https: //aimwriting. mtutor. Do you want to get better at writing articles This AI will give suggestions for your English writings and exam preparations. F. https: // This is a useful tool which can turn text into sound. It helps make your school speeches more interesting or listen to your written work read aloud.
七、语法选择
Now, we live in the 21st century, many changes have taken place in people’s life in the past 40 years. English is becoming one of 1 subjects, but some students often have trouble learning English. They say the subject takes up 2 of their time. They have to read many passages, 3 new words in the dictionary and do lots of exercises. Even though they work hard, they still cannot get good grades on tests. “Why ” they ask. “How can I enjoy success ” The story of Chinese astronaut Deng Qingming might help answer their questions.
Deng was chosen as 4 astronaut trainee (实习生) in 1998. That was long ago—you readers hadn’t even been born yet. From then on, he has spent almost all of his time training hard to become an astronaut. Over the years, Deng has seen his fellow trainees go into space one after 5 . He, however, was always a backup (后备人员). Sometimes he even cried. Deng still tries his 6 for the dream. Although he is now in his 7 , he keeps training hard. “I must be ready whenever the chance comes to me.” he once said. Finally, 8 the night of November 21, 2022, he and two other astronauts boarded the Shenzhou 15 aircraft and flew into space. Deng had waited 24 years for that very moment.
So, if you want to give up learning English or 9 , think about Deng’s story. Your efforts might not succeed at once. But be patient, try to improve your methods and keep 10 . You probably won’t have to wait many years for that moment like Deng. One day, success will knock at your door.
1. A. important B. more important C. most important D. the most important
2. A. too many B. too much C. much too D. too little
3. A. look up B. looked up C. looking up D. to look up
4. A. a B. an C. the D. /
5. A. other B. others C. another D. the other
6. A. good B. well C. best D. better
7. A. fifty B. fifties C. fiftieth D. the fiftieth
8. A. on B. in C. at D. before
9. A. something else B. else something C. anything else D. else anything
10. A. go B. to go C. going D. gone
八、完形填空
There was once a bad king in a small country. He didn’t 1 his people, all the people in the county disliked him very much.
One day when he was swimming alone in a river, his leg suddenly hurt. He went up and down in the water. He was so 2 that he cried, “Help! Help!”At that time, two 3 were working nearby. They ran over 4 , jumped into the water and got him out. They didn’t know he was the king 5 he was pulled out of the water.
The king was happy, he said to the farmers, “You 6 my life. Now you may 7 anything, and I’ll give it to you.”
One of the farmers said, “We are very poor and my son can’t get any 8 . Please send him to a good school.” The king 9 . Then he asked the other one. “And what about you, old man ” But the old man didn’t say a word. The king was surprised and asked him again. “I don’t want 10 . Please don’t tell others that we saved you.” The old man answered.
1 . A. worry about B. hear about C. care about D. talk about
2 . A. glad B. excited C. pleased D. afraid
3 . A. drivers B. servants C. writers D. farmers
4 . A. slowly B. fast C. heavily D. angrily
5. A. because B. but C. until D. during
6. A. saved B. accepted C. shared D. touched
7. A. send for B. ask for C. look for D. prepare for
8. A. job B. money C. girlfriend D. education
9. A. refuse B. agreed C. cried D. left
10. A. everything B. something C. anything D. nothing
十、阅读理解
A
You may feel that math is hard and boring. Is it possible that you’ve been looking at math in the wrong way With International Day of Math coming on March 14, Teens interviewed Li Xing, a math professor (教授) at Ning Xia University. We asked if math can be beautiful and fun. Here’s what he said.
Numbers are beautiful
Many people today want to have beautiful looks. But there is math hidden in beautiful human bodies. Measure (测量) the length from your head to your belly button (肚脐) and from your belly button to your feet. The ratio (比例) of these two numbers is always around 0.618. This is the golden ratio, which can be seen everywhere, like in nature, music and paintings.
In Chinese poems, we can also see the beauty of numbers, which reminds us of a line, “ ▲ ”—the numbers show how fast Li Bai traveled and how happy he felt. Numbers give us freedom to imagine.
Curves are beautiful
Sine curves (正弦切线) are beautiful. They go towards the two opposite directions on and on without ever ending. When you look at them, you may feel like standing by the sea and watching the waves slowly moving. The tangent curve (正切曲线) is like a waterfall. That’s really “dashing down three thousand feet from on high (飞流直下三千尺)”. If you do a math problem and get that curve, you’ll feel wonderful.
Formulas (公式) are beautiful
What’s more, you may not know Euler’s Formulas: e^(iπ) +1=0. It’s beautiful, too. The number “e” is an irrational number (无理数), whose digits (位数) go on and on and never stop. “π” is also such an irrational number. However, when these two numbers come together, things become different. How amazing! Just as the Chinese-American mathematician Chern Shiing-shen said, “Math is fun!”
1. If the ratio of a thing is around 0.618, ________.
A. it has a golden color B. it will look like a human body
C. it is as long as a person’s leg D. it can bring us a sense of beauty
2. Which line can best fill in ________
A. 碧玉妆成一树高 B. 千里家书动隔秋 C. 轻舟已过万重山 D. 百万雄师过大江
3. What does a sine curve look like
A. B. C. D.
4. We can infer from the passage that ________.
A. Li Xing thinks math is difficult and boring
B. we can often see the golden ratio in the drawings
C. then tangent curve is always three thousand feet high
D. e^(iπ) isn’t an irrational number
5. What is the passage mainly about
A. Math is hard and important. B. The life of a math professor.
C. Math is beautiful and interesting. D. The International Day of Math.
B
Take a pen and write the number 6174 on a piece of paper. It looks just like any other number, doesn’t it But what if I told you that it was a magic number
Do you think this is a joke Well, let’s see the magic with a quick experiment (实验).
Start with a four-digit (四位) number — make sure that at least two of the digits are different, and if three digits are the same, the other digit can’t be different by 1, for example,1112 and 6566 are not the suitable numbers. You may use, for example, 1113.
Now take 7173 as the example. Put the digits in the new order to make the smallest possible number: 1377. Then, the largest number: 7731.
Let’s subtract the smaller number from the larger number: 7731-1377 = 6354.
Go back to the second step and repeat the process:
6543-3456 = 3087 8730-0378 = 8352 8532-2358 = 6174
Ta-da! There you have it: 6174!
You can repeat this experiment with another number. What do you end up with Is it 6174
This number is known as Kaprekar’s constant. It is named after the Indian mathematician Dattatreya Ramchandra Kaprekar. He discovered the magic behind this number in 1949 after performing the above process.
Kaprekar had always enjoyed playing with numbers. But when he showed the magic of 6174 at an international mathematics meeting, other mathematicians didn’t roll out the red carpet. They thought it was a useless discovery and made fun of him. Yet to this day, no scientist can fully explain why this magic works.
Would you like to dive deeper Try different numbers and see how many steps you need to get to 6174. Which number requires the most steps How about the least
1. Which of the following is suitable for the experiment
A. 1111. B. 1112. C. 1113. D. 6566.
2. If the number for the experiment is 2025, which of the following is the next step
A. 5220-0225 B. 5220-2520 C. 2025-0252 D. 2025-0225
3. What does the underlined part “roll out the red carpet” probably mean
A. Show their opinions. B. Talk loudly.
C. Express their welcome. D. Understand clearly.
4. What does the writer think of this experiment
A. It’s useless. B. It’s worth studying. C. It’s explainable. D. It’s hard to carry out.
5. What’s the best title of the text
A. A Magic Number B. A Math Competition
C. A Great Scientist D. An International Discovery/ 让教学更有效 高效备考 | 英语学科
Unit 2 Amazing numbers
Section 4 Focusing culture,Cross-curricular connection,Project
（分层练习）
基础达标 01 能力提升 02 拓展培优 03
一、单项选择
1.The lion is often used as a ____ of courage.
A. signal B. sign C. symbol D. mark
【答案】C
【解析】句意：狮子常被用作勇气的一种象征。
signal：信号、暗号。sign：含义广泛，有符号、迹象、招牌等意思。symbol：象征意义上代表某种概念或品质的符号。mark：做辨认用的标记、记号，也可表示分数。狮子常被看作勇气的象征，这里表示象征意义，所以用 symbol，C 选项符合语境。
2.—Can you ____ the books on the shelf
—Sure. Let me see. There are 20 books.
A. read B. write C. count D. see
【答案】C
【解析】句意：— 你能数一下书架上的书吗？— 当然。让我看看。有 20 本书。read意为 阅读；write意为 写；count意为 数，计数；see意为 看见。根据答语 There are 20 books.可知是要对书的数量进行统计，所以应该用 count。
3.The human body has a complex ____ that helps it fight against diseases.
A. system B. structure C. pattern D. framework
【答案】A
【解析】句意：人体有一个复杂的系统，能帮助它抵抗疾病。
system 意为:系统，the human body system 即:人体系统，人体的免疫系统等能帮助身体抵抗疾病，符合语境。structure 主要指 结构；构造，强调事物的组成架构， pattern 表示 模式；图案， framework 意为 框架；构架
4.The cheongsam（旗袍）is often worn by Chinese women to ____ Chinese culture around the world.
A. discover B. represent C. create D. divide
【答案】B
【解析】句意：旗袍常被中国女性穿着，在全世界代表中国文化。
discover意思是 发现，通常指发现原本就存在但未被人知晓的事物。represent意为 代表；象征，旗袍作为中国传统服饰，被女性穿着向世界展示，能够代表中国文化，符合语境。create表示 创造。divide意思是 分开；划分。正确答案是 B
5.The man ______described what he saw so that the police could understand clearly.
A. exactly B. simply C. gradually D. probably
【答案】A
【解析】句意：这个男人准确地描述了他所看到的，以便警察能清楚地理解。
exactly 意为 精确地，准确地，修饰动词 described，强调描述得准确，符合警察需要准确信息来了解情况的语境。simply 意为 简单地；仅仅。gradually 意为 逐渐地。probably 意为 大概，或许。因为 exactly 能准确修饰动词 described，突出描述的精确性，以满足警察清楚理解的需求。
6.This kind of flower is very ____ in spring. You can find it in almost every garden.
A. common B. unique C. particular D. extraordinary
【答案】A
【解析】句意：这种花在春天非常常见。你几乎在每个花园都能找到它。
common意思是 常见的，普遍的，正符合花在春天很多，在各个花园都能找到的描述。
unique表示 独特的，独一无二的。particular意为 特别的，特定的。
extraordinary意思是 非凡的，特别的。因为只有 common能体现花在春天常见这一特点。
7.The olive branch（橄榄枝） always ____ peace all over the world.
A. stands out B. stands for C. stands up D. stands by
【答案】B
【解析】句意：在全世界，橄榄枝总是代表着和平。
stands for意为 代表；象征，橄榄枝在文化寓意中象征和平，该短语符合此处语境。
stands out表示 突出；显眼，强调在众多事物中显得与众不同。stands up有 站起来；起立的意思。
stands by可表示 支持。
8.When you listen to the teacher in class, you should ____ important points so that you can review them later.
A. put down B. look down C. turn down D. write down
【答案】D
【解析】句意：当你在课堂上听老师讲课时，你应该记下重要的知识点，以便之后复习。
write down意为 写下，记下，在课堂上把重要知识点记录下来，符合语境。
look down通常表示 向下看；轻视turn down拒绝；关小的意思。put down放下；镇压等含义。所以答案选 A。
9.Before you travel abroad, you'd better ____ the opening hours of the embassy in case you need to get some help.
A. check B. choose C. collect D. correct
【答案】A
【解析】句意：在你出国旅行之前，你最好核实一下大使馆的开放时间，以防你需要得到一些帮助。
check 检查；核实；查看的意思，核实大使馆开放时间符合语境需求。choose选择。collect收集。
correct 改正；纠正。因为 check能准确表达查看、核实开放时间的含义。
10. About ________ of the teachers in our school ________ born in ________.
A. two-thirds; was; 1970 B. two-thirds; were; the 1970s
C. two-third; was; 1970s D. two third; were; the 1970
【答案】B
【解析】句意：我们学校大约三分之二的教师出生在20世纪70年代。
考查分数的表达、主谓一致以及年代的表达。分数的表达方式为：分子为基数词，分母为序数词，分子大于一，分母加s。所以此处三分之二的表达方式为two-thirds，所以排除C和D；当分数作主语时，其后的谓语动词形式取决于后边的名词；teachers为复数，be born意为“出生于……”，且用于过去时，故此处用were，所以排除A；in the 1970s表示“20世纪70年代”。故选B。
二、根据首字母或汉语提示完成单词
1.The central computer s________ can control (控制)all lights in this building.
2. Sichuan opera was first performed in the Tang dynasty in Sichuan and later d___________ into a popular art form in China.
3. If you go to Xi’an, a(n) a_______ capital of thirteen dynasties, you can’t miss its places of historical interest.
4.News about the school sports meeting s_____ quickly among the students.
5. As usual, it's time to go to the sea to feed t________ of seabirds there.
6. She asked the children to c____ the number of stars drawn on the blackboard.
7. It’s c_______ for people to feel nervous before a job interview.
8. The flag’s colors r________ the history and culture of the nation.
9. She knew e_______ what to say to comfort her friend in trouble.
10. We can c_____ beautiful cards with colored paper and crayons in art class.
【答案】1.system 2.developed 3.ancient 4.spread 5.thousands 6.count 7.common
8.represent 9.exactly 10.create
三、用词的适当形式填空
1. The ____ student in line is ______ years old, and he loves drawing cats. (nine)
2. My aunt became a teacher when she was in her _______. (twenty)
3. The _____ grade has eighteen classes, and my friend is in Class _____. (eight)
4. It's easy _______apples because they are _________objects. (count)
5. She drank water instead of _______(eat)eating snacks during the break.
6. The ______ price of the book is 25 yuan, and I _______ have 25 yuan in my wallet. (exact)
7. My pen pal from _____ can speak both English and _____ languages. (India)
8. Rice is _______________(common) food in many Asian countries.
9. My grandpa used ________ (tell) me stories every night before bed.
10. The _____ hopes ________more wonderful cartoons for children, and each ________ makes kids happy. (create)
【答案】1.ninth nine 2.twenties 3.eighth Eight 4.to count countable 5.eating 6.exact exactly 7.India Indian 8.the most common 9.to tell 10.creator to create creation
四、完成句子
1.在课上，没有必要把屏 幕上所有的东西都记下来。
In class there is no need to______ ______ all the things on the screen.
2.面对这么多困难，我们 决定继续奋斗，而不是放弃。
Facing so many difficulties, we decide to fight on ______ ____giving up.
3.把一个梦想变成现实 的最好方式就是立刻行动。
The best way to____ _____ _____ _____reality is by acting right away.
4.袁隆平，世界上最伟大的科学家之一，作为 “杂交水稻之父”而出名。
Yuan Longping, one of the greatest scientists in the world,____ ____ ____ “the Father of Hybrid Rice”.
5.罗马数字不如阿拉伯数字常见，也许是因为它们太难使用了！
Roman numerals are not ____ ____ ____Arabic numerals, maybe because they are _____ difficult ____ use!
6.不同的文化有不同的象征，一颗心往往代表爱。
Different cultures have _____ ________, and a heart often ____ _____love.
7.计数棒很容易理解，但写下大数字可能需要很长时间。
Tally sticks are easy ___ ________, but it can take a long time to _____ _____ large numbers.
8.多亏了老师的帮助，我过去数学很差，但现在我擅长了
____ ___my teacher's help, I ___ ____be weak in math, but now I'm good at it
【答案】1.write down 2.instead of 3.turn your dream into 4.is known as 5.as common as too to
6.different symbols stands for 7.to understand to write down 8.Thanks to used to
五、短文填空
A 短文填词
Chinese people are used to thinking the numbers 6, 8 and 9 are lucky ones, but how about 142857 This number seems (1) c____________, not special. but it is the most amazing number in the world. Why Let’s look at a few facts about this number.
First, get the number multiplied (乘) by 1 to 6 and all the results are amazing because they are made up of the same numbers but in different (2) o_________. For example, 142857 multiplied by 2 is 285714 while 142857 multiplied by 6 is 857142. Second, if it is multiplied by 7 and we get a more amazing number 999999. Third, the number is multiplied by itself and we can get a super large number 20408122449. However, when we (3) a______ the front five numbers to the back six numbers, we can (4)e________ get the same number 142857 again. Is it amazing
In fact, people found this mysterious（神秘的）number inside the pyramids（金字塔）of Egypt. People also (5)d_________ the number is linked to seven days of a week. So you see, how amazing the number (6) s_________ is! And we can learn a lot from it.
【答案】1.common 2.orders 3.add 4.exactly 5. discovered 6.system
B 语法填空
Have you heard of the saying “Fall down seven times, stand up eight” It means that no matter what 1 (challenge) you meet, keep on going over a long time. This is called perseverance (毅力). And it can help you achieve lots of things.
It is true that you can achieve 2 goal if you stick to it. You practice a skill on your bike over and over again and you make it. Or you continue to play basketball in face of difficulties. After a long time, you can play basketball 3 (perfect). Florence, 11, says, “I go running with my mom three times a week, even when I don’t feel like it, I try hard 4 (push) myself. I’m the fastest in my class now.”
Studies show that feeling hopeful and working towards a goal that you really want to reach can cut down stress and make you feel 5 (happy). Achieving something you’ve worked hard for, and overcoming difficulties along the way, can also develop ___6____ (you )courage and make you feel braver to try new things. Angela Duckworth, who is an expert (专家) in thoughts and feelings, studies perseverance. Duckworth believes that it doesn’t matter how talented, clever or rich you are, perseverance really 7 (help) you succeed.
Duckworth believes perseverance is something anyone can learn, and the best way to do this is to have a growth mind. This means 8 (believe) that your brain can grow, and that you can achieve anything if you work hard at it. 9 instead of thinking, “I can’t do this”, try thinking “I can’t do this… yet.” As the book The Big Life Journal says, “People 10 a growth idea know they can get better by working hard. They keep trying even when things are difficult.”
【答案】1. challenges 2. a 3. perfectly 4. to push 5. happier 6. your 7. helps 8. believing 9. So 10. with
六、阅读配对
下面的材料A-F是六个AI工具网站的介绍。请根据Eric、Tom、Jack、Sally、Lily五位同学的需求为他们推荐合适的网站。
1 Eric has difficulty in speaking English, so he wants to practice his pronunciation and hear how it sounds. 2 Tom is in charge of a drama. Now she is looking for music that matches the different scenes. 3 Jack needs to put his thoughts together and make a brief summary for a group project. He wants to see them clearly. 4 Sally is working on her speech draft and she needs some writing suggestions on “Environmental Protection”. 5 Lily wants to make special posters for a school event but right now she only has some ideas. A. https: //yige. You can create amazing pictures for your school projects with this AI. It will turn your ideas into pictures. It is also great for art class or decorating your room. B. https: //tianyin. If you want to make your own music for school plays or just for fun, try this tool. It will let you choose different music styles to fit your feelings. C. https: //www. chatmind. tech Stuck on a project This AI may help you organize your ideas and show them as a mind map. It’s like having a helper for planning your school work. D. https: //translate. This is a translation tool that can help you read and enjoy foreign books easily. It can also help you explore books in different languages and learn about new cultures. E. https: //aimwriting. mtutor. Do you want to get better at writing articles This AI will give suggestions for your English writings and exam preparations. F. https: // This is a useful tool which can turn text into sound. It helps make your school speeches more interesting or listen to your written work read aloud.
【答案】1. F 2. B 3. C 4. E 5. A
【解析】 本文是5位同学的制作需求以及六个AI工具网站的介绍。
1. 根据“he wants to practice his pronunciation and hear how it sounds.”可知，埃里克想练习他的英语演讲并听听它的发音。选项F“https:// 这是一个有用的工具，可以将文本转换为声音。它有助于让你的学校演讲变得更有趣，或者让你的书面作业大声朗读。”与之匹配。故选F。
2. 根据“Tom is in charge of a drama. Now she is looking for music that matches the different scenes.”可知，汤姆正在寻找与他学校戏剧的不同场景相匹配的音乐。选项B“https://tianyin. 如果您想为学校戏剧或只是为了好玩而制作自己的音乐，请尝试这个工具。它会让你选择不同的音乐风格来适合你的感受。”与之匹配。故选B。
3. 根据“Jack needs to put his thoughts together and make a brief summary for a group project. He wants to see them clearly.”可知，杰克需要为一个小组项目整理他的想法，并希望清楚地看到它们。选项C“https://www.chatmind.Tech 陷入项目困境？这个人工智能可以帮助你组织你的想法并将它们显示为思维导图。这就像有一个帮手来规划你的学校作业一样。”与之匹配。故选C。
4. 根据“Sally is working on her speech draft and she needs some writing suggestions on “Environmental Protection”.”可知，莎莉需要一些关于“环境保护”的英文文章的写作建议。选项E“htrps://aimwriting.mtutor. 您想提高文章写作能力吗？该人工智能将为您的英语写作和考试准备提供建议。”与之匹配。故选E。
5. 根据“Lily wants to make special posters for a school event but right now she only has some ideas.”可知，莉莉想为学校活动制作特别海报，但现在她只有一些想法。选项A“https://yige. 你可以使用此 AI 为你的学校项目创建令人惊叹的图片或制作你自己的炫酷海报。它将把你的想法变成图片。它也非常适合艺术课或装饰你的房间。”与之匹配。故选A。
七、语法选择
Now, we live in the 21st century, many changes have taken place in people’s life in the past 40 years. English is becoming one of 1 subjects, but some students often have trouble learning English. They say the subject takes up 2 of their time. They have to read many passages, 3 new words in the dictionary and do lots of exercises. Even though they work hard, they still cannot get good grades on tests. “Why ” they ask. “How can I enjoy success ” The story of Chinese astronaut Deng Qingming might help answer their questions.
Deng was chosen as 4 astronaut trainee (实习生) in 1998. That was long ago—you readers hadn’t even been born yet. From then on, he has spent almost all of his time training hard to become an astronaut. Over the years, Deng has seen his fellow trainees go into space one after 5 . He, however, was always a backup (后备人员). Sometimes he even cried. Deng still tries his 6 for the dream. Although he is now in his 7 , he keeps training hard. “I must be ready whenever the chance comes to me.” he once said. Finally, 8 the night of November 21, 2022, he and two other astronauts boarded the Shenzhou 15 aircraft and flew into space. Deng had waited 24 years for that very moment.
So, if you want to give up learning English or 9 , think about Deng’s story. Your efforts might not succeed at once. But be patient, try to improve your methods and keep 10 . You probably won’t have to wait many years for that moment like Deng. One day, success will knock at your door.
1. A. important B. more important C. most important D. the most important
2. A. too many B. too much C. much too D. too little
3. A. look up B. looked up C. looking up D. to look up
4. A. a B. an C. the D. /
5. A. other B. others C. another D. the other
6. A. good B. well C. best D. better
7. A. fifty B. fifties C. fiftieth D. the fiftieth
8. A. on B. in C. at D. before
9. A. something else B. else something C. anything else D. else anything
10. A. go B. to go C. going D. gone
【答案】1. D 2. B 3. A 4. B 5. C 6. C 7. B 8. A 9. A 10. C
【导语】本文由学生学习英语的不如意引出宇航员邓清明的故事，从而告诉我们：当你的努力还没有结果时，要改进方法并坚持下去，成功必将到来。
1. 句意：英语正成为最重要的科目之一，但一些学生在学习英语时经常遇到困难。
important重要的，形容词原级；more important比较级；most important最高级；the most important定冠词加最高级。此处是结构one of the+最高级+名词复数“最……的……之一”。故选D。
2. 句意：他们说这门课占用了他们太多的时间。
too many太多（修饰可数名词复数）；too much太多（修饰不可数名词）；much too太；too little太少。根据“They have to read many passages,…new words in the dictionary and do lots of exercises.”可知，一些学生说英语这门课占用了他们太多的时间。time“时间”为不可数名词，too much符合题意。故选B。
3. 句意：他们要读很多文章，在字典中查单词，做很多练习。
look up查找，动词原形；looked up动词过去式/过去分词；looking up现在分词/动名词；to look up动词不定式。and连接的动词形式一致，此处用动词原形。故选A。
4. 句意：1998年，邓被选为宇航员实习生。
a不定冠词，修饰以辅音音素开头的单词；an不定冠词，修饰以元音音素开头的单词；the定冠词，表特指；/零冠词。此处表示泛指，astronaut以元音音素开头，用不定冠词an。故选B。
5. 句意：多年来，邓看着他的学员们一个接一个地进入太空。
other其他的；others其他人/物；another另一个；the other两者中的另一个。one after another“接连地；一个接一个地”，固定短语。故选C。
6. 句意：邓仍然在为这个梦想而努力。
good好的；well好地；best最好的；better更好的。try one’s best“尽某人最大努力”。故选C。
7. 句意：虽然他现在已经五十多岁了，但他仍然努力训练。
fifty五十；fifties五十多岁；fiftieth第五十；the fiftieth第五十。in one’s+整十数的复数形式表示“某人的岁数是多少”，in his fifties“他五十多岁”。故选B。
8. 句意：最后，2022年11月21日晚，他和另外两名宇航员登上神舟十五号飞船，飞向太空。
on后接具体的某一天；in后接年/月/季节；at后接时刻；before在……之前。空后是具体某一天的晚上，用介词on。故选A。
9. 句意：所以，如果你想放弃学习英语或其他东西，想想邓的故事。
something else一些其他的事；else something错误形式；anything else一些其他的事；else anything错误形式。根据“if you want to give up learning English or”可知句子是肯定句，用something。故选A。
10. 句意：但是要有耐心，试着改进你的方法并坚持下去。
go去，动词原形；to go动词不定式；going现在分词/动名词；gone过去分词。keep doing sth.“一直做某事”，动名词作宾语。故选C。
八、完形填空
There was once a bad king in a small country. He didn’t 1 his people, all the people in the county disliked him very much.
One day when he was swimming alone in a river, his leg suddenly hurt. He went up and down in the water. He was so 2 that he cried, “Help! Help!”At that time, two 3 were working nearby. They ran over 4 , jumped into the water and got him out. They didn’t know he was the king 5 he was pulled out of the water.
The king was happy, he said to the farmers, “You 6 my life. Now you may 7 anything, and I’ll give it to you.”
One of the farmers said, “We are very poor and my son can’t get any 8 . Please send him to a good school.” The king 9 . Then he asked the other one. “And what about you, old man ” But the old man didn’t say a word. The king was surprised and asked him again. “I don’t want 10 . Please don’t tell others that we saved you.” The old man answered.
1 . A. worry about B. hear about C. care about D. talk about
2 . A. glad B. excited C. pleased D. afraid
3 . A. drivers B. servants C. writers D. farmers
4 . A. slowly B. fast C. heavily D. angrily
5. A. because B. but C. until D. during
6. A. saved B. accepted C. shared D. touched
7. A. send for B. ask for C. look for D. prepare for
8. A. job B. money C. girlfriend D. education
9. A. refuse B. agreed C. cried D. left
10. A. everything B. something C. anything D. nothing
【答案】1 . C 2 . D 3 . D 4 . B 5. C 6. A 7. B 8. D 9. B 10. C
【解析】 本文讲述了一个国王掉入水中被两个农民救了起来，其中一个农民不求赏赐，只希望国王别把他们救他的事情告诉其他人的故事。
1 . 句意：他不关心他的子民，这个国家的所有的人都非常不喜欢他。
worry about担心；hear about听说；care about关心；talk about谈论。根据“a bad king”和“all the people in the county disliked him very much”可知，这个国王不关心他的子民。故选C。
2 . 句意：他非常害怕，叫道：“救命！救命！”
glad高兴的；excited激动的；pleased满意的；afraid害怕的。根据“he cried, ‘Help! Help!’ ”可推知，他很害怕。故选D。
3 . 句意：当时，两个农民正在附近干活。
drivers司机；servants仆人；writers作家；farmers农民。根据下文“The king was happy, he said to the farmers”可知，此处指两个农民。故选D。
4 . 句意：他们飞快地跑过去，跳进水里，把他救了出来。
slowly缓慢地；fast快速地；heavily沉重地；angrily生气地。根据“ They ran over ...”及常识可知，听到有人喊救命，应是快速地跑去救人。故选B。
5. 句意：直到把他从水里拉出来，他们才知道他是国王。
because因为；but但是；until直到；during在……期间。根据下文“please don’t tell others that we saved you”可推知，两个农民救人之前并不知道他是国王，until符合语境，not until“直到……才”。故选C。
6. 句意：你们救了我的命。
saved挽救；accepted接受；shared分享；touched触摸。根据“he was pulled out of the water”可知，两个农民把国王从水里救了出来。故选A。
7. 句意：现在你们无论求什么，我必赐给你。
send for派人去请；ask for请求得到；look for寻找；prepare for准备。根据“I’ll give it to you.”可知，此处指无论你们请求得到什么。故选B。
8. 句意：我们很穷，而且我的儿子不能接受任何教育。
job工作；money金钱；girlfriend女朋友；education教育。根据“Please send him to a good school.”可知，此处指不能接受任何教育。故选D。
9. 句意：国王同意了。
refuse拒绝；agreed同意；cried哭泣；left离开。根据“Then he asked the other one.”可知，国王同意了第一个农民的请求。故选B。
10. 句意：我什么都不想要。
everything一切；something某事物；anything任何事物；nothing没有什么。根据“I don’t want ...”是否定句可知，应用anything。故选C。
十、阅读理解
A
You may feel that math is hard and boring. Is it possible that you’ve been looking at math in the wrong way With International Day of Math coming on March 14, Teens interviewed Li Xing, a math professor (教授) at Ning Xia University. We asked if math can be beautiful and fun. Here’s what he said.
Numbers are beautiful
Many people today want to have beautiful looks. But there is math hidden in beautiful human bodies. Measure (测量) the length from your head to your belly button (肚脐) and from your belly button to your feet. The ratio (比例) of these two numbers is always around 0.618. This is the golden ratio, which can be seen everywhere, like in nature, music and paintings.
In Chinese poems, we can also see the beauty of numbers, which reminds us of a line, “ ▲ ”—the numbers show how fast Li Bai traveled and how happy he felt. Numbers give us freedom to imagine.
Curves are beautiful
Sine curves (正弦切线) are beautiful. They go towards the two opposite directions on and on without ever ending. When you look at them, you may feel like standing by the sea and watching the waves slowly moving. The tangent curve (正切曲线) is like a waterfall. That’s really “dashing down three thousand feet from on high (飞流直下三千尺)”. If you do a math problem and get that curve, you’ll feel wonderful.
Formulas (公式) are beautiful
What’s more, you may not know Euler’s Formulas: e^(iπ) +1=0. It’s beautiful, too. The number “e” is an irrational number (无理数), whose digits (位数) go on and on and never stop. “π” is also such an irrational number. However, when these two numbers come together, things become different. How amazing! Just as the Chinese-American mathematician Chern Shiing-shen said, “Math is fun!”
1. If the ratio of a thing is around 0.618, ________.
A. it has a golden color B. it will look like a human body
C. it is as long as a person’s leg D. it can bring us a sense of beauty
2. Which line can best fill in ________
A. 碧玉妆成一树高 B. 千里家书动隔秋 C. 轻舟已过万重山 D. 百万雄师过大江
3. What does a sine curve look like
A. B. C. D.
4. We can infer from the passage that ________.
A. Li Xing thinks math is difficult and boring
B. we can often see the golden ratio in the drawings
C. then tangent curve is always three thousand feet high
D. e^(iπ) isn’t an irrational number
5. What is the passage mainly about
A. Math is hard and important. B. The life of a math professor.
C. Math is beautiful and interesting. D. The International Day of Math.
【答案】1. D 2. C 3. A 4. D 5. C
【解析】 本文主要通过黄金比例、诗歌中的数字、曲线和公式等方面展示了数学的美。
1. 细节理解题。根据“Measure the length from your head to your belly button and from your belly button to your feet. The ratio of these two numbers is always around 0.618. This is the golden ratio, which can be seen everywhere, like in nature, music and paintings.”可知，物体的比例约为0.618，它可以给我们带来美感。故选D。
2. 细节理解题。根据“the numbers show how fast Li Bai traveled and how happy he felt.”可知，这些数字展示了李白旅行的速度和感受到的快乐。因此，李白的诗句“轻舟已过万重山”最能体现旅行的速度和快乐。故选C。
3. 推理判断题。根据“Sine curves are beautiful. They go towards the two opposite directions on and on without ever ending. When you look at them, you may feel like standing by the sea and watching the waves slowly moving.”可知，正弦曲线朝着两个相反的方向不断前进，永无止境。当你看着它们时，你可能会觉得自己站在海边，看着海浪慢慢移动。故选A。
4. 推理判断题。根据最后一段“ e^(iπ) +1=0.”可推知，e^(iπ)数值为-1，为具体的数值，而不是无理数。故选D。
5. 主旨大意题。根据“Numbers are beautiful”和“Just as the Chinese-American mathematician Chern Shiing-shen said, ‘Math is fun!’”以及全文可知，这篇文章主要讲数学是美丽而有趣的。故选C。
B
Take a pen and write the number 6174 on a piece of paper. It looks just like any other number, doesn’t it But what if I told you that it was a magic number
Do you think this is a joke Well, let’s see the magic with a quick experiment (实验).
Start with a four-digit (四位) number — make sure that at least two of the digits are different, and if three digits are the same, the other digit can’t be different by 1, for example,1112 and 6566 are not the suitable numbers. You may use, for example, 1113.
Now take 7173 as the example. Put the digits in the new order to make the smallest possible number: 1377. Then, the largest number: 7731.
Let’s subtract the smaller number from the larger number: 7731-1377 = 6354.
Go back to the second step and repeat the process:
6543-3456 = 3087 8730-0378 = 8352 8532-2358 = 6174
Ta-da! There you have it: 6174!
You can repeat this experiment with another number. What do you end up with Is it 6174
This number is known as Kaprekar’s constant. It is named after the Indian mathematician Dattatreya Ramchandra Kaprekar. He discovered the magic behind this number in 1949 after performing the above process.
Kaprekar had always enjoyed playing with numbers. But when he showed the magic of 6174 at an international mathematics meeting, other mathematicians didn’t roll out the red carpet. They thought it was a useless discovery and made fun of him. Yet to this day, no scientist can fully explain why this magic works.
Would you like to dive deeper Try different numbers and see how many steps you need to get to 6174. Which number requires the most steps How about the least
1. Which of the following is suitable for the experiment
A. 1111. B. 1112. C. 1113. D. 6566.
2. If the number for the experiment is 2025, which of the following is the next step
A. 5220-0225 B. 5220-2520 C. 2025-0252 D. 2025-0225
3. What does the underlined part “roll out the red carpet” probably mean
A. Show their opinions. B. Talk loudly.
C. Express their welcome. D. Understand clearly.
4. What does the writer think of this experiment
A. It’s useless. B. It’s worth studying. C. It’s explainable. D. It’s hard to carry out.
5. What’s the best title of the text
A. A Magic Number B. A Math Competition
C. A Great Scientist D. An International Discovery
【答案】1. C 2. A 3. C 4. B 5. A
【解析】 本文主要介绍了数字6174是一个神奇的数字，通过对任意一个符合条件的四位数进行特定的运算步骤，最终都会得到6174，这个数字被称为卡普雷卡尔常数，同时还讲述了其发现者卡普雷卡尔的相关故事。
11. 细节理解题。根据“ ... make sure that at least two of the digits are different, and if three digits are the same, the other digit can’t be different by 1, for example,1112 and 6566 are not the suitable numbers. You may use, for example, 1113.”可知，确保至少有两个数位上的数字不同，并且如果有三个数字相同，那么另一个数字与这三个相同数字的差值不能为1，因此1113符合条件。故选C。
2. 细节理解题。根据“Now take 7173 as the example. Put the digits in the new order to make the smallest possible number: 1377. Then, the largest number: 7731. Let’s subtract the smaller number from the larger number: 7731-1377 = 6354.”可知，对于数字2025，要得到下一步，需先组成最小的数0225，最大的数5220，然后用较大数减去较小数，即5220-0225。故选A。
3. 词句猜测题。根据“They thought it was a useless discovery and made fun of him.” 可知，其他数学家认为这是无用的发现并嘲笑他，并没有欢迎他的发现，由此可推测“roll out the red carpet”意思是表达欢迎。故选C。
4. 推理判断题。根据最后一段“Would you like to dive deeper Try different numbers and see how many steps you need to get to 6174. Which number requires the most steps How about the least ”可知，作者鼓励读者深入研究这个实验，说明作者认为这个实验值得研究。故选B。
26. 最佳标题题。通读全文可知，文章主要介绍了6174这个神奇的数字以及与之相关的实验和故事，选项A“一个神奇的数字”最能概括文章主旨，是最佳标题。故选A。

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