14. 已知隨機變數，當 k =＿＿＿時，機率 P (X=k ) 有最大值。

(1) 證明： ΔOAC ≅ ΔOBD 

(2) 求之值為__________。

15. 若 m n, 為正整數，方程式x4+5x3+mx2+nx+4=0的四根中，有兩相異實根和為−5 ，則此方程式的最小可能實根為＿＿＿。

(1) Provide specific examples of at least three different AI tools, and describe their functions and application methods in detail.

(2) Discuss the potential of AI tools in reducing teachers' workload, providing differentiated instruction, and promoting student-directed learning.

(1) Describe how you would design junior high English classroom activities to integrate gender equality education and guide students to reflect on gender issues.

(2) Discuss potential challenges in implementing this integration and propose concrete solutions.

3. The following text was written by a Chinese learner of English. Identify, describe the errors and indicate the sources of the errors. How will you deal with the errors? When I was a little boy, I must go to school to learn the knowledge. I must study hard day by day. I have took many test. I always fell that I have no time to do the things I like to do. They homework make my life free from happiness. My life is full of ancidite. I always study for the examination. If the government don’t take a method to solve this question, the youth will be lack in the power of creates their future.

 (1). 分析《青玉案·元夕》中所描繪元宵節景象及其藝術手法

(2). 探討「眾裡尋他千百度，驀然回首，那人卻在，燈火闌珊處」 所蘊含的哲理

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