一、 請說明動態規劃（Dynamic Programming）與分治法（Divide and Conquer）兩 種程式撰寫方法之異同。

二、 AI 技術可以根據其學習方式進行分類，例如監督式學習、非監督式學習、強化學 習等。東華附小在課程中希望讓學生學習到監督式學習、非監督式學習的差異， 並且能讓學生以流程圖表現兩者的差異，請您說明如何設計達成上述目標且符合 大多數小學六年級學生學習能力的課程與評量。

三、 教室中現有 Microbit 開發板、超音波感測器，且學生已經學會 Scratch 的模組， 請問您如何結合自然課程，並且以 PBL 的方式達成以下學習目標?◎學習目標：學生可以設計和建造一個運用超音波感測器的測距儀，並測試其準 確性和可靠性。

IV. Chinese-English Translation (15%) Please translate the following Chinese passage into English. Please note that there is NO need to copy the Chinese passage on your answer sheet. 近年來，社交媒體已成為人們揭露不當行為和伸張正義的有力工具。在我 看來，社交媒體讓弱勢群體發聲，使他們能夠公佈原來可能無法被看見的不公 不義，影響事件並改變現實世界。但是，任何人都可以在網路上扮演法官和陪 審團是一種詛咒。即使是罪犯也有權為自己辯護。因此，我們在網路上羞辱他 人之前應該要三思而後行。

V. Essay Question (20%) Please read the following questions carefully and write an essay to express your opinions. The word limit is 300 English words.        Cross-disciplinary courses, one representative feature of the new curriculum, demand considerable effort in preparation and instruction. Teachers of which domains do you want to collaborate with? What difficulties and challenges might occur during the discussion and how would you overcome them? How does such dedication reflect the values of cross-disciplinary lessons?

VI. Lesson Plan Design (25%) Please use the following article to make a lesson plan of one period (50 minutes). Your target students are 11th graders. Please note that your lesson plan should include at least the following components: (1) course objectives, (2) in-class activities you’ll introduce to the students (time allotment should be specified), (3) teaching aids and tools, and (4) assignments. No, the image of an explosion at the Pentagon is not real        An image of black smoke billowing next to a bureaucratic-looking building spread across social media Monday morning, with the claim that it showed an explosion near the Pentagon.        The posts sent a brief shiver through the stock market and were quickly picked up by news outlets outside the U.S., before officials jumped in to clarify that no blast actually took place and the photo was a fake. Experts say the viral image had telltale signs of an AI-generated forgery, and its popularity underscores the everyday chaos these now increasingly sophisticatedand easy-to-access programs can inflict.               Here’s a closer look at the facts.        CLAIM: An image shows an explosion near the Pentagon.        THE FACTS: Police and fire officials in Arlington, Virginia, say the image is not real and there was no incident at the U.S. Department of Defense headquarters across the Potomac from the nation’s capital.        Despite this, the image and claim was spread by outlets including RT, a Russian government-backed media company formerly known as Russia Today. It was also widely shared in investment circles, including an account bearing Twitter’s signature blue verification check mark that falsely suggested it was associated with Bloomberg News.        The timing of the fake image, which appeared to spread widely just after the U.S. stock market opened for trading at 9:30 a.m., was enough to send a ripple through the investment world.        The S&P 500 briefly dropped a modest 0.3% as social media accounts and investment websites popular with day traders repeated the false claims.        Other investments also moved in ways that typically occur when fear enters the market. Prices for U.S. Treasury bonds and gold, for example, briefly began to climb, suggesting investors were looking for someplace safer to park their money.        The image’s rapid spread prompted the Arlington County Fire Department to take to social media to knock down the rumors.

1. 阿特午機是能直接證明牛頓第二定律的儀器，也可以用來測定重力加速度 g 值。兩個質量為 M 的 相同物塊懸掛於滑輪兩側，滑輪與繩子重量與阻力不計，其中一個物塊上方放置一質量為 m 的方 形小游碼。物塊釋放後，向下加速一段距離 H，游碼會卡在一個圓環上，但物塊可照常通過，接著量測物塊再落下一段距離 D 所需的時間 t。根據以上資訊求出重力加速度 g 值為何？(以 M、m、 H、D、t 作答)

2. 一個半徑為 R 的實心均質球，質量為 M，球心定在 x 軸的原點處。今在右側挖去一個以 x= R/2 為圓心，半徑為 R/2 的球。請問剩下的質量在 x=5R/2 處建立的重力場量值為何？(萬有引力常數為 G)

3. 假設一質量為 m 的物體受到空氣阻力與速度的關係式為 ，請問此物體自靜止開始落下，此 物體的速度量值隨時間的關係式 v(t)為何？(重力加速度量值為 g)

4. 六個同相點光源等距離 d 排列，在與光源距離 L 處的光屏上進行六狹縫干涉，使用波長 λ 的單 色光且 L＞＞d，問光屏上干涉的中央亮紋寬度應為 ?

5. 在光滑水平絕緣平面上，放置一長為的彈簧，兩端各連接相同小球，兩球原為靜止，如附圖所示。 今使二小球突然帶相同電量，因斥力作用可使彈簧彈開。設第一次兩小球之帶電量均為＋q1，最大伸長量為 ；第二次兩球的帶電量皆為＋q2，可使彈簧最大伸長量為 ，則彈簧達到最大伸長量時，兩次電力之比為？

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