广东·高一英语·上学期·高考模拟试卷

阅读下面短文，从每题所给的 A、B、C、D 四个选项中选出最佳选项。 The world of mathematics is full of patterns and beauty. One of the most famous sequences is the Fibonacci sequence, where each number is the sum of the two preceding ones, starting from 0 and 1. This sequence appears unexpectedly often in nature, such as in the arrangement of leaves on a stem, the spirals of a pinecone, or the branching of trees. It's a wonderful example of how abstract mathematical concepts can ___21___ the real world. For centuries, mathematicians have been fascinated by the properties of numbers. The ancient Greeks, for instance, studied "perfect numbers" – numbers that are equal to the sum of their proper divisors. The smallest perfect number is 6, because 1 + 2 + 3 = 6. Finding these numbers was considered a ___22___ pursuit, linking mathematics to philosophy and even mysticism. Today, mathematics is the ___23___ of modern technology. From the algorithms that power search engines to the complex calculations needed for space exploration, math is essential. It provides the language and tools to describe everything from the motion of planets to the behavior of financial markets. Without a solid understanding of mathematics, many of the technological ___24___ we take for granted would be impossible. The beauty of math lies not just in its applications, but in its logical ___25___. A mathematical proof, once established, is a thing of elegance and certainty. It is this pursuit of absolute truth and clarity that continues to ___26___ mathematicians and students alike, driving them to solve problems that have puzzled humanity for generations. 21. A. transform B. mirror C. replace D. ignore 22. A. practical B. noble C. casual D. temporary 23. A. foundation B. obstacle C. alternative D. decoration 24. A. failures B. advances C. debates D. expenses 25. A. structure B. emotion C. fiction D. mystery 26. A. confuse B. discourage C. inspire D. interrupt

阅读下面短文，从每题所给的 A、B、C、D 四个选项中选出最佳选项。 The development of calculus in the 17th century by Isaac Newton and Gottfried Wilhelm Leibniz was a monumental achievement. It provided a powerful tool for understanding change and motion. One of its core ideas is the derivative, which measures the instantaneous rate of change of a function. For instance, if we have a function describing the position of a moving car, its derivative tells us the car's speed at any given moment. However, the concept was not without controversy. Newton and Leibniz famously disputed over who deserved credit for its invention. More importantly, the mathematical foundations of calculus were initially shaky. The idea of infinitesimals—quantities infinitely close to zero but not zero—seemed paradoxical and lacked rigorous definition. It wasn't until the 19th century that mathematicians like Augustin-Louis Cauchy and Karl Weierstrass provided a solid logical framework through the theory of limits, putting calculus on firm footing. Calculus is now indispensable in fields like physics, engineering, and economics. It allows us to model complex systems, from the flow of electricity to the growth of populations. The story of its development reminds us that even the most powerful ideas often require time and collective effort to be fully understood and accepted. 34. What is the main purpose of the first paragraph? A. To praise Newton and Leibniz. B. To introduce the concept of the derivative. C. To explain the history of cars. D. To argue for the importance of physics. 35. What problem did early calculus have? A. It was too difficult for students to learn. B. It was only useful for describing motion. C. Its logical basis was not yet solid. D. It was invented by two people at once. 36. How was the problem with calculus solved? A. By abandoning the idea of infinitesimals. B. By developing the theory of limits. C. By letting Newton and Leibniz share credit. D. By applying it to economics and engineering. 37. What can we learn from the passage about mathematical ideas? A. They are always perfect from the start. B. They often become useful before being fully understood. C. They are usually invented by a single genius. D. They have no application outside of pure mathematics.

阅读下面短文，从每题所给的 A、B、C、D 四个选项中选出最佳选项。 Music and mathematics might seem like separate worlds, but they are deeply connected. Musical scales are based on mathematical ratios. The pleasing sound of an octave, for example, corresponds to a frequency ratio of 2:1. The structure of chords and harmonies follows patterns that can be described using set theory and algebra. Rhythm, the pattern of beats in time, is essentially a division of time into fractions. A whole note can be divided into half notes, quarter notes, and so on, creating a hierarchy similar to mathematical fractions. Composers like Johann Sebastian Bach were known for using mathematical structures, such as symmetry and recursion, in their compositions. In modern times, computer algorithms use mathematical models to generate music. These algorithms can analyze existing pieces to learn rules of melody and harmony, then create new, original compositions. This field, known as algorithmic composition, shows how math can be a creative tool. It challenges the notion that art and science are opposites, revealing instead how they can inform and enrich each other. 38. According to the passage, what is the relationship between music and mathematics? A. Mathematics is used to analyze music after it is created. B. Music is a practical application of mathematical principles. C. They are completely unrelated fields of study. D. Mathematics makes music less artistic. 39. What example is given to show the mathematical basis of music? A. The life story of a famous composer. B. The frequency ratio of an octave. C. The popularity of different music genres. D. The cost of musical instruments. 40. What is the main idea of the last paragraph? A. Computer-generated music is always better than human-composed music. B. Algorithms can only copy existing music, not create new pieces. C. The use of algorithms in music shows the union of art and science. D. Modern composers no longer need to understand mathematics.

阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。 The concept of zero is one of the most important ___27___ (contribute) to mathematics. It might seem simple, but the idea of representing "nothing" with a symbol was a revolutionary step. Before its widespread use, calculations were much more ___28___ (difficulty). The zero acts as a placeholder, allowing us to distinguish between numbers like 10 and 100 easily. Zero also plays a crucial role in algebra and calculus. It is the ___29___ (origin) point of the number line, the point from which we measure all other numbers. In equations, finding the "zero" or "root" means finding the value that makes the equation true. For example, the zeros of the function f(x) = x² - 4 are the values of x ___30___ make f(x) equal to zero, which are x = 2 and x = -2. The history of zero is a story of cultural exchange. It was first developed in ancient Babylon and India, and later ___31___ (carry) to Europe by Arab scholars. Its adoption was slow, as some viewed the idea of "nothing" with suspicion. However, its ___32___ (use) in commerce and astronomy eventually made it indispensable. Today, it is a fundamental symbol ___33___ underpins all of modern mathematics and science.