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A(2026·镇江外国语中学期中)
The exam is always on its way. Still worried about your math? You may feel it is difficult and boring. Is it because the way you look at math is not right? Teens talked with Li Xing, a math teacher at Ningxia University. We interviewed him if math can be beautiful and fun. Here's what Li said.
Many people today want to have beautiful looks. But there is math in beautiful human bodies. The length from your head to your belly button and the length from your belly button to your feet have a ratio(比率) that is always around 0. 618. This is the golden ratio, and we can see it everywhere, like in nature, music, and drawings. In Chinese poems, we can also see the beauty of numbers.
Besides numbers, beauty can also be found in curves(曲线). Just like sine curves(正弦曲线), they go to the two opposite directions(相反方向) and never stop. When you look at them, you may feel like standing by the sea and watching the water moving slowly. While the tangent curve is like a waterfall. That really "going down three thousand feet from on high". If you do a math problem and get that curve, you'll feel excited and fun.
What's more, formulas(公式) can also be beautiful. Take a look at Euler's Formula:$e^{\wedge}(iθ)=\cosθ+\mathrm{i}·\sinθ$. 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!
1. 新考法 推断文章开篇方式 The writer starts the passage by
A. expressing his opinion
B. raising questions
C. giving advice
D. telling stories
2. What can be inferred ( 推 断 ) from the passage?
A. The number "e" isn't an irrational number.
B. Li Xing thinks math is difficult and boring.
C. We can often see the golden ratio in the drawings.
D. The tangent curve is always three thousand feet high.
3. 新考法 主旨归纳 What is the passage mainly about?
A. Why math is beautiful and fun.
B. Why math is difficult and boring.
C. How we can learn math in a right way.
D. How math helps us live a better life.
The exam is always on its way. Still worried about your math? You may feel it is difficult and boring. Is it because the way you look at math is not right? Teens talked with Li Xing, a math teacher at Ningxia University. We interviewed him if math can be beautiful and fun. Here's what Li said.
Many people today want to have beautiful looks. But there is math in beautiful human bodies. The length from your head to your belly button and the length from your belly button to your feet have a ratio(比率) that is always around 0. 618. This is the golden ratio, and we can see it everywhere, like in nature, music, and drawings. In Chinese poems, we can also see the beauty of numbers.
Besides numbers, beauty can also be found in curves(曲线). Just like sine curves(正弦曲线), they go to the two opposite directions(相反方向) and never stop. When you look at them, you may feel like standing by the sea and watching the water moving slowly. While the tangent curve is like a waterfall. That really "going down three thousand feet from on high". If you do a math problem and get that curve, you'll feel excited and fun.
What's more, formulas(公式) can also be beautiful. Take a look at Euler's Formula:$e^{\wedge}(iθ)=\cosθ+\mathrm{i}·\sinθ$. 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!
1. 新考法 推断文章开篇方式 The writer starts the passage by
B
.A. expressing his opinion
B. raising questions
C. giving advice
D. telling stories
2. What can be inferred ( 推 断 ) from the passage?
A. The number "e" isn't an irrational number.
B. Li Xing thinks math is difficult and boring.
C. We can often see the golden ratio in the drawings.
D. The tangent curve is always three thousand feet high.
3. 新考法 主旨归纳 What is the passage mainly about?
A. Why math is beautiful and fun.
B. Why math is difficult and boring.
C. How we can learn math in a right way.
D. How math helps us live a better life.
答案
A [文章大意]本文通过黄金比例、数学曲线和公式等例子,阐释了数学的美丽与趣味性,旨在改变读者对数学"枯燥困难"的刻板印象。
1. B [解析]细节理解题。根据"The exam is always on its way. Still worried about your math? You may feel it is difficult and boring. Is it because the way you look at math is not right?"可知,作者通过提出一系列问题开篇,引发读者思考。故选B。
2. C [解析]推理判断题。根据"This is the golden ratio, and we can see it everywhere, like in nature, music, and drawings"可知,黄金比例在绘画中很常见。故选C。
3. A [解析]主旨大意题。根据"We interviewed him if math can be beautiful and fun. Here's what Li said"及后文李老师从黄金比例、曲线、公式三个方面介绍数学的美和趣味性可知,文章核心是说明数学为何美丽又有趣。故选A。
语篇结构
解析
【分析】
拿到这篇阅读题后，我们可以按题型逐个梳理思路：第1题考查文章开篇方式，直接定位到文章开头段落，观察作者的行文开头特征，对照选项即可判断；第2题是推理判断题，需要把每个选项逐一和原文内容比对，排除和原文表述矛盾、不符合逻辑的错误选项，就能得到正确答案；第3题是主旨归纳题，结合给出的语篇思维导图，抓住全文核心主题“数学的美丽与趣味性”，梳理行文逻辑：开篇用问题引入，借李兴老师的观点，用黄金比例、数学曲线、欧拉公式三个例证支撑，最后得出数学兼具美感趣味的结论，就能判断出文章的核心讲述内容。
【解析】
1. 细节理解题：定位文章开篇部分，作者连续抛出"Still worried about your math? You may feel it is difficult and boring. Is it because the way you look at math is not right?"多个问题，通过提出问题的方式引入话题，对应选B，排除A（没有直接表达开篇观点）、C（没有给出相关建议）、D（没有讲述故事）。
2. 推理判断题：逐一比对选项：
选项A：原文明确提到"The number "e" is an irrational number"，和选项表述矛盾，错误；
选项B：李兴老师的核心观点是数学是美丽有趣的，并非认为数学难且无聊，错误；
选项C：原文说明黄金比例"we can see it everywhere, like in nature, music, and drawings"，可以推断出我们经常能在绘画中看到黄金比例，表述正确；
选项D：诗句"going down three thousand feet from on high"是用来形容正切曲线的形态，并非指正切曲线真的有三千英尺高，不符合文意，错误。
3. 主旨大意题：全文围绕“数学是否能美丽有趣”展开，借李兴老师的讲解，从黄金比例、数学曲线、欧拉公式三个维度举例说明数学的美感和趣味性，核心是解释为什么数学是美丽又有趣的，对应选A，排除B（文章是打破数学枯燥难的刻板印象，不是讲为什么数学难无聊）、C（没有介绍学习数学的正确方法）、D（没有讲述数学如何帮助我们更好生活）。
【答案】
1. B 2. C 3. A
【知识点】
阅读理解细节判断
阅读理解推理判断
阅读理解主旨归纳
【点评】
本题属于跨学科趣味阅读题，搭配语篇思维导图辅助梳理行文逻辑，覆盖了初中英语阅读的三类核心常考题型，既考查学生快速定位原文信息、比对甄别选项、归纳核心主旨的阅读能力，也能引导学生跳出对数学的刻板认知，体会不同学科交叉的趣味性。
【难度系数】
0.7
拿到这篇阅读题后，我们可以按题型逐个梳理思路：第1题考查文章开篇方式，直接定位到文章开头段落，观察作者的行文开头特征，对照选项即可判断；第2题是推理判断题，需要把每个选项逐一和原文内容比对，排除和原文表述矛盾、不符合逻辑的错误选项，就能得到正确答案；第3题是主旨归纳题，结合给出的语篇思维导图，抓住全文核心主题“数学的美丽与趣味性”，梳理行文逻辑：开篇用问题引入，借李兴老师的观点，用黄金比例、数学曲线、欧拉公式三个例证支撑，最后得出数学兼具美感趣味的结论，就能判断出文章的核心讲述内容。
【解析】
1. 细节理解题：定位文章开篇部分，作者连续抛出"Still worried about your math? You may feel it is difficult and boring. Is it because the way you look at math is not right?"多个问题，通过提出问题的方式引入话题，对应选B，排除A（没有直接表达开篇观点）、C（没有给出相关建议）、D（没有讲述故事）。
2. 推理判断题：逐一比对选项：
选项A：原文明确提到"The number "e" is an irrational number"，和选项表述矛盾，错误；
选项B：李兴老师的核心观点是数学是美丽有趣的，并非认为数学难且无聊，错误；
选项C：原文说明黄金比例"we can see it everywhere, like in nature, music, and drawings"，可以推断出我们经常能在绘画中看到黄金比例，表述正确；
选项D：诗句"going down three thousand feet from on high"是用来形容正切曲线的形态，并非指正切曲线真的有三千英尺高，不符合文意，错误。
3. 主旨大意题：全文围绕“数学是否能美丽有趣”展开，借李兴老师的讲解，从黄金比例、数学曲线、欧拉公式三个维度举例说明数学的美感和趣味性，核心是解释为什么数学是美丽又有趣的，对应选A，排除B（文章是打破数学枯燥难的刻板印象，不是讲为什么数学难无聊）、C（没有介绍学习数学的正确方法）、D（没有讲述数学如何帮助我们更好生活）。
【答案】
1. B 2. C 3. A
【知识点】
阅读理解细节判断
阅读理解推理判断
阅读理解主旨归纳
【点评】
本题属于跨学科趣味阅读题，搭配语篇思维导图辅助梳理行文逻辑，覆盖了初中英语阅读的三类核心常考题型，既考查学生快速定位原文信息、比对甄别选项、归纳核心主旨的阅读能力，也能引导学生跳出对数学的刻板认知，体会不同学科交叉的趣味性。
【难度系数】
0.7
B(2026·扬州树人教育集团期中)
①A library is a place for people to read and learn, but some libraries are special. In some areas, smart mobile libraries travel across deserts, mountains and seas to send books to those in need.
②In some places of Kenya, most children want to go to school. But there are no roads, only deserts. Cars are of no use and only camels can travel across the deserts. So children usually learn from the books that camels carry on their backs. Usually in a camel team, one camel carries about 180 kilos of books, and the other carries a tent. At each place, a worker sets up the tent and puts the books inside for people to read. Two weeks later, the camels come back to the tent with new books.
③Some people in Thailand live in the mountains and the forests. Their libraries are on the backs of elephants. These big animals can work well along the way. They carry heavy books in metal(金属) boxes. The boxes protect the books from the heavy rain.
④ In Indonesia, there are over 17,000 islands around the country. Most people travel by boat, and their library books are delivered(递送) in the same way. $\underline\blacktriangle$. People on the islands keep these books for a few weeks before new books arrive.
⑤ Now, some areas have also introduced greener ways like newly-powered cars or drones(无人机) to transport books. But for people who live far away and can't get to the library, a mobile library brings more than books. It also brings a new world.
1. Why do some people use camels to carry library books in Kenya?
A. Because there are no cars.
B. Because they can travel across the deserts.
C. Because there are few workers.
D. Because they can carry more books.
2. How do the people in Thailand protect books from the heavy rain?
A. They put books in metal boxes.
B. They cover books with thick plastic.
C. They build new libraries in the mountains.
D. They set up a tent and put books inside.
3. 新考法 句子还原 Which of the following can be put in "$\underline\blacktriangle$" in Paragraph 4?
A. There are many books in their libraries
B. A wooden boat can carry about 500 library books
C. The libraries help the local people make a living
D. It's difficult to build such a library on these islands
4. 新考法 推断篇章结构 Which of the following shows the structure(结构) of the passage?
①A library is a place for people to read and learn, but some libraries are special. In some areas, smart mobile libraries travel across deserts, mountains and seas to send books to those in need.
②In some places of Kenya, most children want to go to school. But there are no roads, only deserts. Cars are of no use and only camels can travel across the deserts. So children usually learn from the books that camels carry on their backs. Usually in a camel team, one camel carries about 180 kilos of books, and the other carries a tent. At each place, a worker sets up the tent and puts the books inside for people to read. Two weeks later, the camels come back to the tent with new books.
③Some people in Thailand live in the mountains and the forests. Their libraries are on the backs of elephants. These big animals can work well along the way. They carry heavy books in metal(金属) boxes. The boxes protect the books from the heavy rain.
④ In Indonesia, there are over 17,000 islands around the country. Most people travel by boat, and their library books are delivered(递送) in the same way. $\underline\blacktriangle$. People on the islands keep these books for a few weeks before new books arrive.
⑤ Now, some areas have also introduced greener ways like newly-powered cars or drones(无人机) to transport books. But for people who live far away and can't get to the library, a mobile library brings more than books. It also brings a new world.
1. Why do some people use camels to carry library books in Kenya?
A. Because there are no cars.
B. Because they can travel across the deserts.
C. Because there are few workers.
D. Because they can carry more books.
2. How do the people in Thailand protect books from the heavy rain?
A. They put books in metal boxes.
B. They cover books with thick plastic.
C. They build new libraries in the mountains.
D. They set up a tent and put books inside.
3. 新考法 句子还原 Which of the following can be put in "$\underline\blacktriangle$" in Paragraph 4?
A. There are many books in their libraries
B. A wooden boat can carry about 500 library books
C. The libraries help the local people make a living
D. It's difficult to build such a library on these islands
4. 新考法 推断篇章结构 Which of the following shows the structure(结构) of the passage?
答案
B [文章大意]本文是一篇说明文,文章主要介绍了肯尼亚、泰国、印度尼西亚等不同地区的特殊移动图书馆,它们借助骆驼、大象、船只等方式为有需要的人递送书籍,展现了移动图书馆的独特运作与价值。
1. B [解析]细节理解题。根据第②段"But there are no roads, only deserts. Cars are of no use and only camels can travel across the deserts."可知,肯尼亚用骆驼运书是因为骆驼能穿越沙漠。故选B。
2. A [解析]细节理解题。根据第③段"They carry heavy books in metal boxes. The boxes protect the books from the heavy rain."可知,泰国人把书放在金属盒子里来防雨。故选A。
3. B [解析]句子还原题。第④段讲述印度尼西亚的图书馆书籍通过船只递送,结合"Most people travel by boat, and their library books are delivered in the same way"可知,选项B"A wooden boat can carry about 500 library books."能具体说明船只运书的情况,符合语境。故选B。
4. B [解析]篇章结构题。文章第①段总起介绍特殊移动图书馆;第②③④段分别介绍不同地区的移动图书馆;第⑤段总结其意义。属于"总—分—总"结构,对应选项B。故选B。
1. B [解析]细节理解题。根据第②段"But there are no roads, only deserts. Cars are of no use and only camels can travel across the deserts."可知,肯尼亚用骆驼运书是因为骆驼能穿越沙漠。故选B。
2. A [解析]细节理解题。根据第③段"They carry heavy books in metal boxes. The boxes protect the books from the heavy rain."可知,泰国人把书放在金属盒子里来防雨。故选A。
3. B [解析]句子还原题。第④段讲述印度尼西亚的图书馆书籍通过船只递送,结合"Most people travel by boat, and their library books are delivered in the same way"可知,选项B"A wooden boat can carry about 500 library books."能具体说明船只运书的情况,符合语境。故选B。
4. B [解析]篇章结构题。文章第①段总起介绍特殊移动图书馆;第②③④段分别介绍不同地区的移动图书馆;第⑤段总结其意义。属于"总—分—总"结构,对应选项B。故选B。
解析
【解析】
1. 细节理解题：根据文章第②段"But there are no roads, only deserts. Cars are of no use and only camels can travel across the deserts."可知，肯尼亚地区没有道路只有沙漠，汽车无法通行，骆驼可以穿越沙漠，因此人们用骆驼运送图书馆书籍，对应选项B。
2. 细节理解题：根据文章第③段"They carry heavy books in metal boxes. The boxes protect the books from the heavy rain."可知，泰国的人们将书籍放在金属盒子里，以此避免书籍被大雨打湿，对应选项A。
3. 句子还原题：第④段介绍印度尼西亚的移动图书馆通过船只递送书籍，前文提到当地多数人乘船出行，书籍也以同样的方式递送，B选项"A wooden boat can carry about 500 library books"具体补充说明船只运书的相关情况，和上下文语境衔接自然，其余选项均不符合该段围绕船运书籍展开的语境。
4. 篇章结构题：文章第①段总起引入特殊移动图书馆的话题；第②③④段分别介绍肯尼亚、泰国、印度尼西亚三个地区不同形式的移动图书馆，属于分述内容；第⑤段总结移动图书馆的意义，整体是"总—分—总"的结构，对应选项B。
【答案】
1. B
2. A
3. B
4. B
【知识点】
阅读理解细节查找
阅读理解句子还原
阅读理解篇章结构
【点评】
本题属于说明文类阅读理解，考点覆盖细节理解、句子还原、篇章结构三类典型题型，既考查学生定位文本信息的基础阅读能力，也通过新考法题型考查学生对文本逻辑衔接和整体行文框架的梳理能力，难度设置梯度合理。
【难度系数】
0.7
1. 细节理解题：根据文章第②段"But there are no roads, only deserts. Cars are of no use and only camels can travel across the deserts."可知，肯尼亚地区没有道路只有沙漠，汽车无法通行，骆驼可以穿越沙漠，因此人们用骆驼运送图书馆书籍，对应选项B。
2. 细节理解题：根据文章第③段"They carry heavy books in metal boxes. The boxes protect the books from the heavy rain."可知，泰国的人们将书籍放在金属盒子里，以此避免书籍被大雨打湿，对应选项A。
3. 句子还原题：第④段介绍印度尼西亚的移动图书馆通过船只递送书籍，前文提到当地多数人乘船出行，书籍也以同样的方式递送，B选项"A wooden boat can carry about 500 library books"具体补充说明船只运书的相关情况，和上下文语境衔接自然，其余选项均不符合该段围绕船运书籍展开的语境。
4. 篇章结构题：文章第①段总起引入特殊移动图书馆的话题；第②③④段分别介绍肯尼亚、泰国、印度尼西亚三个地区不同形式的移动图书馆，属于分述内容；第⑤段总结移动图书馆的意义，整体是"总—分—总"的结构，对应选项B。
【答案】
1. B
2. A
3. B
4. B
【知识点】
阅读理解细节查找
阅读理解句子还原
阅读理解篇章结构
【点评】
本题属于说明文类阅读理解，考点覆盖细节理解、句子还原、篇章结构三类典型题型，既考查学生定位文本信息的基础阅读能力，也通过新考法题型考查学生对文本逻辑衔接和整体行文框架的梳理能力，难度设置梯度合理。
【难度系数】
0.7
