《2025年全品学练考高中英语必修第一册外研版》

高中生活
词数 320 难度 ★★★ 建议用时 7 分钟 正确率 _/4
Two years ago, two high - school classmates each worked out a trigonometric proof of the Pythagorean theorem (毕达哥拉斯定理的三角证明). Now, at age 19, they've reported finding 10 more proofs of it.
For 2,000 years, such proofs were considered impossible. But that didn't _deter_ Ne'Kiya Jackson and Calcea Johnson. The pair published their new ones on October 28 in _American Mathematical Monthly_.
“Some people have the impression that you have to be in the mathematical field for years and years before you can actually produce some new mathematics,” says Álvaro Lozano - Robledo, a mathematician who works at the University of Connecticut in Storrs. “But Jackson and Johnson show that you can make achievements even as a high - school student.”
The teens studied Pythagoras' theorem whose formula (公式) has been proven many times using _algebra_ and _geometry_ but people thought it could never be proven using the rules of trigonometry (三角学).
However, mathematician Jason Zimba _announced_ the first trig - based proof of Pythagoras' theorem in 2009. The second came six years later, from mathematician Nuno Luzia. These were the only two until 2022, when Jackson and Johnson _presented_ their first proofs. At the time, both were seniors at St Mary's Academy. It's a private school for young Black women in New Orleans.
Jackson and Johnson only published five proofs and decided to leave another five proofs “_for interested readers to discover_”, they wrote in the paper. Jackson hopes the proofs will encourage other students to “_see that difficulties are part of the process_. With this in your mind, you might find yourself achieving more than you thought possible”._
Publishing the proofs was a big achievement. But that doesn't mean the story is over. “Now, other people might take the paper and _generalize_ those proofs, or generalize their ideas,” mathematician Lozano - Robledo says. “It just opens up lots of mathematical conversations.”
(A)1. What does the underlined word “_deter_” in Paragraph 2 probably mean?
A. Stop.
B. Surprise.
C. Teach.
D. Trouble.
(B)2. Why are some mathematicians mentioned in the text?
A. To show their influence on the two girls.
B. To prove the two girls' achievements are great.
C. To explain their proof of Pythagoras' theorem.
D. To point out their different views of the theorem.
(A)3. What is Jackson's wish?
A. More students will take part.
B. Discovering another five proofs.
C. Becoming a great mathematician.
D. Their proofs will be used in teaching.
(D)4. What does Lozano - Robledo think of Jackson and Johnson's proofs?
A. They still need to be improved.
B. They are the first trig - based proofs.
C. They disagree with the Pythagorean theorem.
D. They could lead to further mathematical discoveries.
语篇分析

词海拾珠
1. _algebra n_. 代数
2. _geometry n_. 几何
3. _announce v_. 宣布→ _announcement n_. 宣布，声明
4. _present v_. 提出，展示
5. _process n_. 过程
6. _generalize v_. 推广，概括→ _general adj_. 一般的，普通的；综合的；大体的
举一反三
一词多义 _work out_
原句再现 _Two years ago, two high - school classmates each _worked out_ a trigonometric proof of the Pythagorean theorem (毕达哥拉斯定理的三角证明)._
两年前，两名高中生每人推导出了一个毕达哥拉斯定理的三角证明。
_work out_ 算出；想出；解决；锻炼；顺利进行
猜测词义
(1) _I couldn't _work out_ the maths problem and turned to him for help._ (算出,解出)
(2) _I _work out_ regularly to keep healthy every day._ (锻炼)
(3) _Things just didn't _work out_ as planned, which disappointed us._ (顺利进行)
句型透视
原句 _These were the only two until 2022, when Jackson and Johnson presented their first proofs._
分析 本句是一个复合句。句中 _until 2022_ 是时间状语，_when_ 引导非限制性定语从句_，when_ 在从句中作状语，_2022_ 是先行词_。_
翻译 直到 2022 年杰克逊和约翰逊提出了她们各自的第一个证明，这是仅有的两个证明。
仿写 曾有一段时间，这两名高中生对她们自己缺少自信。There was a time when
_ the two high - school students were not confident in themselves._

答案： 【文章大意】本文是一篇记叙文。文章主要讲述了两位高中生创造的数学奇迹——她们在两年前推导出了毕达哥拉斯定理的三角证明。现在,19岁的她们又找到了10个证明。
1. A 词义猜测题。根据第二段的“For 2,000 years, such proofs were considered impossible... published their new ones on October 28 in American Mathematical Monthly.”可知,2000年来,用三角理论证明毕达哥拉斯定理被认为是不可能的,但这并没有阻止Ne’Kiya Jackson和Calcea Johnson。deter意为“阻止”。故选A。
2. B 推理判断题。第三段提到数学家Alvaro Lozano-Robledo肯定了两位高中生的成就,第五段提到仅有两位数学家Jason Zimba和Nuno Luzia先后于2009年和2015年宣布了毕达哥拉斯定理基于三角理论的证明,而这两位高中生同样也根据三角理论推导出了毕达哥拉斯定理,由此推断作者提到几位数学家的目的是证明两位学生取得的成就是巨大的。故选B。
3. A 细节理解题。根据第六段中的“Jackson and Johnson only published five proofs and decided to leave another five proofs ‘for interested readers to discover’, they wrote in the paper. Jackson hopes the proofs will encourage other students to ‘see that difficulties are part of the process…’.”可知,她们只发表了五个证明,希望能够吸引感兴趣的学生去发现另外五个证明,也就是激励其他学生参与进来。故选A。
4. D 细节理解题。根据末段中的“But that doesn’t… ‘It just opens up lots of mathematical conversations.’”可知,其他人可能会基于她们的证明进行推广或发展新的想法,这表明这些证明有可能会引发更多数学发现。故选D。
【语篇分析】
1. achievements 2. introduction 3. hope 4. importance
【举一反三】
[猜测词义]
(1)算出,解出
(2)锻炼
(3)顺利进行
【句型透视】
[分析] 非限制性定语从句;先行词
[仿写] There was a time when