10. 已知級數，其中p,q,r皆為整數，且p,q,r三述兩兩互質，則 p + q + r = _______ 。

III. Test Making: (30%) Task 1: Please summarize the following passage into an article of around 200 words. (20%) Task 2: Please number and underline four of the sentences in your summary to make a coherence test (篇章結構) for 12th graders, and briefly explain (50 words maximum) your choices. (10%) If you’re reading this, then congratulations, because you are studying English! You have made noteworthy progress to reach this level, too! However, you might think that English is not as important as your native language and might wonder why we study English. First of all, English is an immensely popular language worldwide. According to a piece of research on English users conducted in 2018, there are 378 million native speakers and 743 million non-native speakers in the world. Indeed, non-native English speakers are twice as numerous as native speakers! Second, English is important, considering it’s an official language of 59 different countries and serves as the most prominent language of business communication, technological society, and the Internet. In short, people who study English not only enhance their job prospects but also have a passport to the world of music, cinema, television, news, and much more. Perhaps a better question then is: Why NOT study English? Like other languages, English has an extensive and fascinating history. The English we speak and use today originated from West Germanic languages. Back in the 5th century A.D., three Germanic tribes, the Angles, Saxons, and Jutes, sailed across the North Sea from continental Europe looking for new lands to conquer. What these aggressive tribes did was invade Britain, and then they forced the inhabitants there to move west and north. Over time, their influence made their Germanic dialects become dominant, and what we recognize as Old English began to emerge. The evolution of English has thus far taken place over the course of more than 1,400 years, and it can be divided into four periods: Old English, Middle English, Modern English, and Late Modern English. Old English existed from around 450 to 1100. While it was vastly different from the language we use presently, some words like “drink,” “food,” and “strong” have managed to survive. Next, Middle English, which lasted from around 1100 to 1500, corresponded with the influence of the conquering Normans who invaded England from France in 1066. Whoever spoke French during this period was thought to be more civilized and have higher social status. Therefore, many French words related to art, law, and government were adapted for use, such as “painting,” “justice,” and “empire.” Modern English, which was used from about 1500 to 1800, borrowed in turn from Latin, giving us words like “concept,” “laboratory,” and “predict.” During this period, literacy increased and printing presses soon made books cheaper and more available. Since London had morepublishing houses than other locations, its dialect became the standard. Finally, Late Modern English has been in use since around 1800. It has been influenced in part by the Industrial Revolution, which required new words applicable to technological advancements. Furthermore, British colonization not only accelerated the spread of English around the globe but also led to the elaborate borrowing of many foreign words we use today like “koala” and “pajamas.” With so many speakers around the world, English continues to evolve. For instance, there are regional variations like New Zealand English, or Kiwinglish, named for the country’s national bird. Kiwinglish is influenced by the language of the Maori, New Zealand’s indigenous people. Words like kia ora, which means “hello,” and puku, which means “belly,” are borrowed from Maori. Singapore is even more diverse than New Zealand, and Singaporean English, or Singlish, mirrors the city-state’s multicultural population. Singlish borrows words from Malay, Chinese, and Hokkien. Thus, Singlish speakers often use lah and mah, both of which are particles attached to the end of the sentences, making it quite distinct from other types of English. As you can see, English has evolved over time into the language we use today. The different types of English spoken and utilized around the world reflect the distinct cultures in which they have developed. However, there’s also the unifying nature of English that has made it the universal language of business, the academic world, and popular culture. In conclusion, English is both unique and common. So, keep studying it, and with English, you can interact and communicate with the world all the time. (三民版第五冊第五課)

10. 已知級數，其中p,q,r皆為整數，且p,q,r三述兩兩互質，則 p + q + r = _______ 。

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