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考題練習
題型與計分都照真實考試。多選題採學測的部分給分：答錯 k 個選項得 (n − 2k)/n，算出負值以零分計——所以亂猜的期望值是負的。
綜合測驗：The Quiet Hour
At 8 a.m. on Tuesdays, a supermarket in Manchester turns off its music, dims half its lights, and asks staff not to stack shelves. The scanners are set to their lowest volume. For sixty minutes the store is, by ordinary retail standards, almost 1.
The practice began as an accommodation for autistic shoppers, for whom a normal supermarket — fluorescent glare, overlapping announcements, the constant clatter of trolleys — can be genuinely painful. A parent who had given up shopping with her son wrote to the manager describing what a weekly trip cost the family. The manager, 2 of any policy from head office, simply tried it.
What surprised everyone was who else showed up. People recovering from concussion came. So did shift workers, migraine sufferers, and older customers who had quietly stopped going out. Within a year, the quiet hour had the highest customer-satisfaction score of any hour in the week, and other branches began to 3 it.
The lesson is one that designers call the curb-cut effect. Ramps cut into sidewalks were fought for by wheelchair users, but they are now used by anyone pushing a stroller or pulling a suitcase. A change made for a group at the margin turns out to serve a much 4 population than anyone predicted.
None of this makes the quiet hour easy to sell. It reduces impulse purchases, and music in stores exists precisely because it raises them. Managers who keep the practice tend to justify it in terms of loyalty rather than 5 takings — a harder argument to make to a spreadsheet, and one that only works if head office is willing to wait.
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閱讀測驗：Every Map Lies
Take an orange, peel it, and try to flatten the peel on a table. It tears. No amount of care will make a curved surface lie flat, and this small kitchen failure is the entire problem of cartography. Every map of the world is a compromise, and every compromise loses something.
The projection most of us grew up with was published by Gerardus Mercator in 1569. It was designed for sailors: on a Mercator map, a straight line is a line of constant compass bearing, so a captain could rule a course and follow it. That single property made it indispensable for four hundred years. The price is size. Because the projection stretches the map east–west near the poles, it must stretch north–south by the same amount to keep angles true. Greenland ends up looking as large as Africa. Africa is fourteen times larger.
In 1973 the historian Arno Peters presented an alternative and argued, loudly, that Mercator's distortions had shaped how Europeans saw the rest of the world. His projection preserves relative area: Africa appears as vast as it is. Geographers were unimpressed, partly because the projection was not new — it had been described by James Gall a century earlier — and partly because preserving area badly distorts shape. On a Gall–Peters map, continents look stretched, as though seen in a warped mirror.
The dispute is often reported as a fight about politics, but cartographers see something narrower. A projection cannot preserve area, shape, distance, and direction at once; this is not a technical limitation but a mathematical certainty, proved by Gauss in 1827. The only question is which property you need. A pilot, an ecologist counting habitat, and a teacher explaining colonial history need different maps, and no single one of them is the honest map.
What has changed is that we no longer have to choose once and for all. A digital globe can be rotated, and a phone can switch projections in the time it takes to zoom. The generation now in school may be the first for whom the world does not have a single default shape.
第 1 題
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What is the purpose of the orange peel example in the first paragraph?
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Why did the Mercator projection remain in use for so long?
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Why were geographers unimpressed by the Peters projection?
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What does the author suggest by saying "no single one of them is the honest map"?
閱讀測驗：The Return of the Night Train
For most of the 2000s, the night train looked like a museum piece. Budget airlines could move a passenger from Vienna to Brussels for less than the price of a bunk, and European operators closed sleeper routes one after another. Between 2001 and 2015 the number of overnight services in Western Europe fell by roughly two-thirds. The carriages were sold, scrapped, or left to rust in sidings.
Then, quietly, the direction reversed. Austria's national operator bought a batch of second-hand sleeper cars that Germany was discarding and rebuilt the network around them. Ten years later it runs the largest night-train fleet in Europe and, unusually for the sector, does not lose money on it.
The reasons for the revival are not what most reports assume. Climate concern is real, and a night train from Zurich to Amsterdam emits a small fraction of what the equivalent flight does. But surveys of passengers put something else first: the trip does not cost a working day. Boarding at ten at night and arriving at seven in the morning converts travel time into sleeping time, which is time nobody was going to use anyway. The train competes not with the two-hour flight but with the hotel night plus the airport morning.
That logic explains where night trains work and where they do not. The sweet spot is a journey of roughly nine to fourteen hours: shorter, and passengers arrive uncomfortably early; longer, and a second night is needed and the economics collapse. It also explains the awkward fact that sleeper travel is not especially cheap. A private compartment can cost more than a flight and a hotel combined, and the operators who have tried to compete on price have generally failed.
Whether the revival lasts will depend less on passengers than on track access charges, which are set by national governments and which currently treat a train carrying thirty sleeping passengers much like a freight train carrying containers. Change that, operators argue, and the map of European night travel would redraw itself within a decade.
第 1 題
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What happened to night trains in Western Europe between 2001 and 2015?
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According to passenger surveys, what matters most to night-train travelers?
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What does the author mean by "The train competes not with the two-hour flight but with the hotel night plus the airport morning"?
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What does the last paragraph suggest about the future of night trains?
克漏字：A Letter to My Future Self
On the first day of eighth grade, our homeroom teacher gave each of us a blank envelope. "Write a letter to yourself," she said. "I will give it back to you 1 you graduate."
Nobody knew what to write. Some students only wrote three lines. I wrote two pages, mostly about a math test I was worried 2.
Two years later, she kept her promise. On our last day of school she walked in carrying a box of envelopes, and the room went completely quiet.
Reading my own handwriting was strange. The math test I had been so afraid of turned out to be nothing — I could not even 3 what score I got. But I had also written that I hoped to make one real friend that year, and that part made me stop.
I looked across the classroom at Ya-ting, who was laughing at her own letter. We had met in September of that year and had been sitting together ever since. My past self had no idea she was 4 to happen.
I still keep the letter in my desk drawer. It is not well written, and half of it is about things that no longer matter. But it reminds me that the things I worry about now may look very small 5 two years.
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閱讀測驗：Bus 66 to Sunlight Beach
BUS 66 · Town Center ⇄ Sunlight Beach
Leaving Town Center
Weekdays 7:30 9:00 11:00 14:00 16:30
Weekends 7:30 8:30 9:30 10:30 11:30 13:00 15:00 16:30
Leaving Sunlight Beach
Weekdays 8:20 10:00 12:00 15:00 17:30
Weekends 8:20 9:30 10:30 11:30 12:30 14:00 16:00 17:30
The ride takes about 40 minutes each way.
Tickets
One way NT$60 Round trip NT$100
Students with a school card pay half price on weekdays only.
Notes
· The 7:30 bus does not run on national holidays.
· Bicycles are welcome, but only on the last bus of the day.
· Buy tickets on the bus. Drivers cannot give change for bills over NT$500.
第 1 題
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It is Saturday. Amy takes the 9:30 bus from Town Center. About what time will she arrive at Sunlight Beach?
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A student with a school card goes to the beach and comes back on a Tuesday. How much does the round trip cost?
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Wei-lun wants to bring his bicycle. Which bus from Town Center can he take on a weekday?
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Which of the following is true according to the schedule?
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Mr. Wang wants to pay with a NT$1,000 bill. What problem might he have?
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The consultant ___ that the deadline be moved to the following month.
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Residents ___ about the noise for eight months before the council finally acted.
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In an emergency, small teams tend to ___ on informal channels rather than official ones.
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___ of the two proposals addresses the funding gap, which is why the board rejected both.
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The alarm went off twice ___ the night, but nobody in the building got up.
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Most readers still ___ printed books to screens when they read for more than an hour.
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The witness could ___ what she had seen, but not why the two men had started arguing.
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The audience grew visibly ___ long before the second act came to an end.
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The evidence was not strong ___ to support a conviction, so the case was dropped.
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___ his complete lack of formal training, he became the leading authority in the field.
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It was ___ a convincing argument that even his longtime critics fell silent.
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The new evidence ___ the committee reconsider a decision it had announced only a week earlier.
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直角三角形的兩股長分別為 6 與 8，則斜邊長為何？
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若 3x − 7 = 2x + 5，則 x 的值為何？
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投擲一枚公正硬幣兩次，至少出現一次正面的機率為何？
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|−8| + |5| 的值為何？
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數線上 −4 與 3 兩點的距離為何？
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−6 的相反數與 |−6| 的和為何？
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(−12) ÷ 4 + (−5) 的值為何？
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(−2)³ + (−2)² 的值為何？
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下列哪一個算式的結果是正數？
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下列哪一個數不是有理數？
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2³ × 2⁴ 的值為何？
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(3²)³ 的值為何？
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0.00035 用科學記號表示為何？