1.化学老师做的实验激发了同学们的好奇心。（curiosity)

  The experiment conducted/done/performed by the chemistry teacher stimulated the students’ curiosity.

2. 具有中国特色的月饼正日益受到西方人的青睐。（special）

   The moon cake which is special to China is increasingly gaining popularity among westerners.

   The moon cake which is special to China is becoming more and more popular among westerners.

3. 在位育中学举办的古尔邦节上你可以享用到多种多样的民族食品。（Corban Festival）

   You can/could enjoy various ethnic foods in the Corban Festival held in Weiyu High School.

   Various ethnic foods are / were available to you in the Corban Festival held in Weiyu High School.

4. 尽管有精心组织的防守，我们的篮球队还是在第一轮比赛中被淘汰了。(eliminate )

   Despite/ In spite of the well-organized defense our basketball team was eliminated in the first round.

5. 直到那时他才意识到，一个人如果遇到困难就任凭命运的摆布，永远也无法实现自己的预期目标。( Not until…. )

Not until then did he realize that a person couldn’t accomplish/achieve his expected goal/ambition for good if he was at the mercy of fate when coming across difficulties.

1.化学老师做的实验激发了同学们的好奇心。（curiosity)

  The experiment conducted/done/performed by the chemistry teacher stimulated the students’ curiosity.

2. 具有中国特色的月饼正日益受到西方人的青睐。（special）

   The moon cake which is special to China is increasingly gaining popularity among westerners.

   The moon cake which is special to China is becoming more and more popular among westerners.

3. 在位育中学举办的古尔邦节上你可以享用到多种多样的民族食品。（Corban Festival）

   You can/could enjoy various ethnic foods in the Corban Festival held in Weiyu High School.

   Various ethnic foods are / were available to you in the Corban Festival held in Weiyu High School.

4. 尽管有精心组织的防守，我们的篮球队还是在第一轮比赛中被淘汰了。(eliminate )

   Despite/ In spite of the well-organized defense our basketball team was eliminated in the first round.

5. 直到那时他才意识到，一个人如果遇到困难就任凭命运的摆布，永远也无法实现自己的预期目标。( Not until…. )

Not until then did he realize that a person couldn’t accomplish/achieve his expected goal/ambition for good if he was at the mercy of fate when coming across difficulties.