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B 跨学科·数学
体裁：说明文 主题：科普知识 难度：★★★★★ 建议用时：8 min 正确率：/4
The Pythagorean theorem is a big math idea. It tells us that in a right triangle(直角三角形), the square of the longest side is equal(相等) to the sum of the squares of the other two sides. In school, it 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 math idea too.
When this idea first appeared, many mathematicians tried to show it was true in different ways, and there are about 370 different ways to do this. In 1927, a mathematician named Elisha Loomis said that proving(证明) 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. Two years ago, 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 math 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 math to find side lengths. This amazed other mathematicians. Jackson and Johnson also left five proofs for others to explore, which gives a starting point for more research. Their journey shows that exploring math is timeless and exciting, and the new way of thinking encourages more young mathematicians to be creative and challenge the norm.
1. 新趋势·学科融合 Which of the following calculations follows the Pythagorean theorem?
＞＞ 学科融合题解题策略见 P73 重点精讲
A. If a＝1, b＝1, then c＝2
B. If a＝2, b＝3, then c＝5
C. If a＝4, b＝6, then c＝20
D. If a＝5, b＝12, then c＝13
2. Why was it thought to be impossible to prove the Pythagorean theorem with trigonometry?
A. The theorem doesn’t work with trigonometry.
B. Trigonometry is only for working out triangles.
C. Mathematicians didn’t know much about triangles.
D. Someone thought you can’t use the same idea to prove itself.
3. What does the underlined word “This” in Paragraph 3 refer to?
A. Developing more proofs.
B. Publishing their findings.
C. Using math to find side lengths.
D. Filling a small triangle with larger triangles.
4. What’s the writer’s purpose(目的) of writing the passage?
A. To encourage students to explore math.
B. To tell a story about two students who like math.
C. To advise people to do more research on triangles.
D. To show the Pythagorean theorem is difficult to prove.
体裁：说明文 主题：科普知识 难度：★★★★★ 建议用时：8 min 正确率：/4
The Pythagorean theorem is a big math idea. It tells us that in a right triangle(直角三角形), the square of the longest side is equal(相等) to the sum of the squares of the other two sides. In school, it 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 math idea too.
When this idea first appeared, many mathematicians tried to show it was true in different ways, and there are about 370 different ways to do this. In 1927, a mathematician named Elisha Loomis said that proving(证明) 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. Two years ago, 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 math 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 math to find side lengths. This amazed other mathematicians. Jackson and Johnson also left five proofs for others to explore, which gives a starting point for more research. Their journey shows that exploring math is timeless and exciting, and the new way of thinking encourages more young mathematicians to be creative and challenge the norm.
1. 新趋势·学科融合 Which of the following calculations follows the Pythagorean theorem?
＞＞ 学科融合题解题策略见 P73 重点精讲
A. If a＝1, b＝1, then c＝2
B. If a＝2, b＝3, then c＝5
C. If a＝4, b＝6, then c＝20
D. If a＝5, b＝12, then c＝13
2. Why was it thought to be impossible to prove the Pythagorean theorem with trigonometry?
A. The theorem doesn’t work with trigonometry.
B. Trigonometry is only for working out triangles.
C. Mathematicians didn’t know much about triangles.
D. Someone thought you can’t use the same idea to prove itself.
3. What does the underlined word “This” in Paragraph 3 refer to?
A. Developing more proofs.
B. Publishing their findings.
C. Using math to find side lengths.
D. Filling a small triangle with larger triangles.
4. What’s the writer’s purpose(目的) of writing the passage?
A. To encourage students to explore math.
B. To tell a story about two students who like math.
C. To advise people to do more research on triangles.
D. To show the Pythagorean theorem is difficult to prove.
答案
B
【语篇解读】本文是一篇说明文。文章主要介绍了毕达哥拉斯定理的应用和证明历程等。
1. D 推理判断题。根据第一段“It tells us that in a right triangle, the square of the longest side is equal to the sum of the squares of the other two sides.”可知毕达哥拉斯定理指直角三角形最长边的平方等于其他两边的平方和。故选 D。
2. D 细节理解题。根据第二段“His reason was that you can't prove an idea is true by using the idea itself.”可知路明思认为不能用理论本身来证明这个理论。故选 D。
3. A 代词指代题。根据上文“Encouraged by Zimba's proof, they developed more proofs. One of them includes filling a large triangle with smaller triangles and using math to find side lengths.”可知两名高中生更多的证明让其他数学家惊讶,此处 This 指代上文“they developed more proofs”。故选 A。
4. A 推理判断题。结合文章内容,尤其是最后一段“Their journey shows that exploring math is timeless and exciting, and the new way of thinking encourages more young mathematicians to be creative and challenge the norm.”可知,本文主要介绍了毕达哥拉斯定理的应用和证明历程等,探索毕达哥拉斯定理鼓励更多年轻数学家创新和挑战常规,由此可知本文的目的是鼓励学生探索数学。故选 A。
【语篇解读】本文是一篇说明文。文章主要介绍了毕达哥拉斯定理的应用和证明历程等。
1. D 推理判断题。根据第一段“It tells us that in a right triangle, the square of the longest side is equal to the sum of the squares of the other two sides.”可知毕达哥拉斯定理指直角三角形最长边的平方等于其他两边的平方和。故选 D。
2. D 细节理解题。根据第二段“His reason was that you can't prove an idea is true by using the idea itself.”可知路明思认为不能用理论本身来证明这个理论。故选 D。
3. A 代词指代题。根据上文“Encouraged by Zimba's proof, they developed more proofs. One of them includes filling a large triangle with smaller triangles and using math to find side lengths.”可知两名高中生更多的证明让其他数学家惊讶,此处 This 指代上文“they developed more proofs”。故选 A。
4. A 推理判断题。结合文章内容,尤其是最后一段“Their journey shows that exploring math is timeless and exciting, and the new way of thinking encourages more young mathematicians to be creative and challenge the norm.”可知,本文主要介绍了毕达哥拉斯定理的应用和证明历程等,探索毕达哥拉斯定理鼓励更多年轻数学家创新和挑战常规,由此可知本文的目的是鼓励学生探索数学。故选 A。
解析
【分析】
本题为跨学科英语阅读理解题，结合数学毕达哥拉斯定理考查说明文阅读能力。解题思路：1. 第1题需掌握毕达哥拉斯定理内容，计算各选项中两边平方和是否等于最长边平方；2. 第2题定位原文中路明思关于用三角学证明定理不可能的理由；3. 第3题根据代词指代的就近原则，定位前文提到的两名高中生的相关行为；4. 第4题结合最后一段主旨，判断作者写作目的。
【解析】
1. 根据第一段毕达哥拉斯定理内容：直角三角形最长边的平方等于其他两边平方和。计算选项：A选项1²+1²=2≠2²=4，错误；B选项2²+3²=13≠5²=25，错误；C选项4²+6²=52≠20²=400，错误；D选项5²+12²=169=13²，符合定理，故选D。
2. 第二段明确提到Elisha Loomis认为用三角学证明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，故选D。
3. 第三段划线词“This”指代前文“they developed more proofs”，即两名高中生开发更多证明的行为，对应选项A，故选A。
4. 最后一段提到“their journey shows that exploring math is timeless and exciting... encourages more young mathematicians to be creative and challenge the norm”，说明作者目的是鼓励学生探索数学，对应选项A，故选A。
【答案】
1.D 2.D 3.A 4.A
【知识点】
英语阅读理解、毕达哥拉斯定理、细节理解题
【点评】
本题为跨学科融合题，将英语说明文阅读与数学毕达哥拉斯定理结合，既考查学生的阅读信息提取、推理判断能力，又传递了鼓励探索数学、勇于创新的理念，符合学科融合的学习要求。
【难度系数】
0.2
本题为跨学科英语阅读理解题，结合数学毕达哥拉斯定理考查说明文阅读能力。解题思路：1. 第1题需掌握毕达哥拉斯定理内容，计算各选项中两边平方和是否等于最长边平方；2. 第2题定位原文中路明思关于用三角学证明定理不可能的理由；3. 第3题根据代词指代的就近原则，定位前文提到的两名高中生的相关行为；4. 第4题结合最后一段主旨，判断作者写作目的。
【解析】
1. 根据第一段毕达哥拉斯定理内容：直角三角形最长边的平方等于其他两边平方和。计算选项：A选项1²+1²=2≠2²=4，错误；B选项2²+3²=13≠5²=25，错误；C选项4²+6²=52≠20²=400，错误；D选项5²+12²=169=13²，符合定理，故选D。
2. 第二段明确提到Elisha Loomis认为用三角学证明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，故选D。
3. 第三段划线词“This”指代前文“they developed more proofs”，即两名高中生开发更多证明的行为，对应选项A，故选A。
4. 最后一段提到“their journey shows that exploring math is timeless and exciting... encourages more young mathematicians to be creative and challenge the norm”，说明作者目的是鼓励学生探索数学，对应选项A，故选A。
【答案】
1.D 2.D 3.A 4.A
【知识点】
英语阅读理解、毕达哥拉斯定理、细节理解题
【点评】
本题为跨学科融合题，将英语说明文阅读与数学毕达哥拉斯定理结合，既考查学生的阅读信息提取、推理判断能力，又传递了鼓励探索数学、勇于创新的理念，符合学科融合的学习要求。
【难度系数】
0.2
