第一节 阅读下列短文，从 A、B、C、D 四个选项中选出最佳选项。（每小题1.5分，共15分）
A 跨学科 数学
The Pythagorean theorem(勾股定理)，$a^2 + b^2 = c^2$，is a big maths idea. It tells us that in a right triangle, the square of the longest side is the sum of the squares of the other two sides.
In school, the Pythagorean theorem allows students to work out the length of the third side of a right triangle when the other two are known. In real life, it helps planes find the shortest way to fly. People who design buildings use this maths idea too.
When this idea first appeared, many people tried to show it was true in different ways, and there were about 370 different ways to do this. In 1927, a mathematician(数学家) named Elisha Loomis said that proving this with trigonometry(三角学) was impossible. His reason was that you can’t prove an idea is true by using the idea itself. However, a mathematician named Jason Zimba first proved it successfully in 2009. And the second proof was published six years later by mathematician Nuno Luzia. In 2022, two high school students, Ne’Kiya Jackson and Calcea Johnson, also found a way to prove the Pythagorean theorem based on trigonometry.
In March 2023, the two showed their work at a maths meeting. Publishing their findings was challenging, and they had to learn new skills. Encouraged by Zimba’s proof, they developed more proofs. One of them includes filling a large triangle with smaller triangles and using maths to find side lengths. This amazed other mathematicians. Jackson and Johnson also left five proofs for others to explore, which give a starting point for more research. Their journey shows that exploring maths is timeless and exciting, and that the new way of thinking encourages more young mathematicians to be creative and challenges the usual rules.
（
A. Showing how to find the longest side of a triangle.
B. Describing how the Pythagorean theorem is used in study and life.
C. Explaining why the Pythagorean theorem is difficult to prove.
D. Explaining why buildings are designed with the Pythagorean theorem.
（
A. Because trigonometry is only for dealing with angles.
B. Because trigonometry was not well developed at that time.
C. Because mathematicians didn’t know much about triangles.
D. Because he believed that the same idea shouldn’t be used to prove itself.
（
A. Jason Zimba. B. Calcea Johnson. C. Nuno Luzia. D. Ne’Kiya Jackson.
（
A. Sharing their ideas at a maths meeting.
B. Publishing their findings successfully.
C. The new way they used to prove the theorem.
D. Dividing a larger triangle into smaller ones.
（
A. New ways of thinking can lead to further development in maths.
B. The theorem has already been proved in the best way.
C. Exploring maths is less interesting than other school subjects.
D. Young people prefer learning skills to exploring new ideas.
A 跨学科 数学
The Pythagorean theorem(勾股定理)，$a^2 + b^2 = c^2$，is a big maths idea. It tells us that in a right triangle, the square of the longest side is the sum of the squares of the other two sides.
In school, the Pythagorean theorem allows students to work out the length of the third side of a right triangle when the other two are known. In real life, it helps planes find the shortest way to fly. People who design buildings use this maths idea too.
When this idea first appeared, many people tried to show it was true in different ways, and there were about 370 different ways to do this. In 1927, a mathematician(数学家) named Elisha Loomis said that proving this with trigonometry(三角学) was impossible. His reason was that you can’t prove an idea is true by using the idea itself. However, a mathematician named Jason Zimba first proved it successfully in 2009. And the second proof was published six years later by mathematician Nuno Luzia. In 2022, two high school students, Ne’Kiya Jackson and Calcea Johnson, also found a way to prove the Pythagorean theorem based on trigonometry.
In March 2023, the two showed their work at a maths meeting. Publishing their findings was challenging, and they had to learn new skills. Encouraged by Zimba’s proof, they developed more proofs. One of them includes filling a large triangle with smaller triangles and using maths to find side lengths. This amazed other mathematicians. Jackson and Johnson also left five proofs for others to explore, which give a starting point for more research. Their journey shows that exploring maths is timeless and exciting, and that the new way of thinking encourages more young mathematicians to be creative and challenges the usual rules.
（
B
）1. What is the main idea of Paragraph 2?A. Showing how to find the longest side of a triangle.
B. Describing how the Pythagorean theorem is used in study and life.
C. Explaining why the Pythagorean theorem is difficult to prove.
D. Explaining why buildings are designed with the Pythagorean theorem.
（
D
）2. Why did Elisha Loomis think it was impossible to prove the theorem with trigonometry?A. Because trigonometry is only for dealing with angles.
B. Because trigonometry was not well developed at that time.
C. Because mathematicians didn’t know much about triangles.
D. Because he believed that the same idea shouldn’t be used to prove itself.
（
A
）3. Who first proved the Pythagorean theorem with trigonometry?A. Jason Zimba. B. Calcea Johnson. C. Nuno Luzia. D. Ne’Kiya Jackson.
（
C
）4. What does the underlined word “This” in Paragraph 4 refer to?A. Sharing their ideas at a maths meeting.
B. Publishing their findings successfully.
C. The new way they used to prove the theorem.
D. Dividing a larger triangle into smaller ones.
（
A
）5. What can we learn from Paragraph 4?A. New ways of thinking can lead to further development in maths.
B. The theorem has already been proved in the best way.
C. Exploring maths is less interesting than other school subjects.
D. Young people prefer learning skills to exploring new ideas.
答案：1. B 段落大意题。根据第二段内容可知，本段主要介绍了勾股定理在学校学习与现实生活中的多种应用。
2~3. DA
4. C 代词指代题。根据第四段可知，This 指代两位高中生提出的勾股定理新证明方法。
5. A 推理判断题。根据第四段最后一句可知，这种新的思维方式能鼓励更多年轻人创新，推动数学发展。
2~3. DA
4. C 代词指代题。根据第四段可知，This 指代两位高中生提出的勾股定理新证明方法。
5. A 推理判断题。根据第四段最后一句可知，这种新的思维方式能鼓励更多年轻人创新，推动数学发展。
解析：
【分析】
本题为英语阅读理解题，包含段落大意题、细节理解题、代词指代题、推理判断题。解题思路为：先通读题干明确考查方向，再定位原文对应段落，对比选项与原文内容，排除不符合原文的错误选项，最终选出最佳答案。
【解析】
1. 第1题：定位原文第二段，该段介绍了勾股定理在学校计算直角三角形边长、现实中帮助飞机找最短路径、建筑设计等方面的应用，对应选项B。
2. 第2题：定位原文第三段，Elisha Loomis认为用三角学证明勾股定理不可能的理由是“you can’t prove an idea is true by using the idea itself”，对应选项D。
3. 第3题：定位原文第三段，明确提到Jason Zimba是2009年第一个用三角学成功证明勾股定理的数学家，对应选项A。
4. 第4题：定位原文第四段，“This”指代前文提到的两位高中生提出的用小三角形填充大三角形找边长的新证明方法，对应选项C。
5. 第5题：定位原文第四段最后一句，可知新的思维方式能鼓励年轻人创新、推动数学发展，对应选项A。
【答案】
1.B 2.D 3.A 4.C 5.A
【知识点】
英语阅读理解、段落大意、细节理解
【点评】
本文是关于勾股定理证明的英语说明文，题目涵盖阅读常见题型，需学生具备快速定位原文、分析选项的能力，整体难度适中。
【难度系数】
0.6
本题为英语阅读理解题，包含段落大意题、细节理解题、代词指代题、推理判断题。解题思路为：先通读题干明确考查方向，再定位原文对应段落，对比选项与原文内容，排除不符合原文的错误选项，最终选出最佳答案。
【解析】
1. 第1题：定位原文第二段，该段介绍了勾股定理在学校计算直角三角形边长、现实中帮助飞机找最短路径、建筑设计等方面的应用，对应选项B。
2. 第2题：定位原文第三段，Elisha Loomis认为用三角学证明勾股定理不可能的理由是“you can’t prove an idea is true by using the idea itself”，对应选项D。
3. 第3题：定位原文第三段，明确提到Jason Zimba是2009年第一个用三角学成功证明勾股定理的数学家，对应选项A。
4. 第4题：定位原文第四段，“This”指代前文提到的两位高中生提出的用小三角形填充大三角形找边长的新证明方法，对应选项C。
5. 第5题：定位原文第四段最后一句，可知新的思维方式能鼓励年轻人创新、推动数学发展，对应选项A。
【答案】
1.B 2.D 3.A 4.C 5.A
【知识点】
英语阅读理解、段落大意、细节理解
【点评】
本文是关于勾股定理证明的英语说明文，题目涵盖阅读常见题型，需学生具备快速定位原文、分析选项的能力，整体难度适中。
【难度系数】
0.6