句中的 taking 不可改为 taking part in。

以下内容摘自某英语用法词典，网友可以参考其中的第4条的第(1)点：

1. 表示“检查”，注意以下与动词和介词的常用搭配：

He made an examination of the room. 他检查了房间。

We carried out a medical examination. 我们进行了体格检查。

2. 表示具体的一次一次的“检查”或“考试”，它通常是可数名词，但有时表示抽象意义的检查或考试，则为不可数名词。如：

On examination I found the goods of poor quality. 我一检查就发现了这些货物质量不行。

Admission to this school is by examination. 进入该校须经过考试。

3. 用于under examination，其意为“在检查中”“在审查中”。如：

The prisoner is still under examination. 囚犯仍在受审。

His conduct is under examination. 正在对他的行为进行审查。

4. 表示“考试”，还需注意以下几点：

(1) 表示参加考试，通常用动词 take, sit (for), enter (sb) for 等；表示通过考试或考试及格，通常用动词pass；表示考试没通过或没及格，通常用动词 fail (in)。如：

About 500 students took [sat, sat for] the examination. 大约有500学生参加了考试。

Of those who took the exam, only thirty percent passed. 参加考试的人中间，只有30%的人通过了。

Both of them failed (in) the examination. 他们俩人考试都没有及格。

注意，“参加考试”可用动词 take, 但不用 take part in。不过，口语中有时也用动词do。

(2) 表示某一方面的考试，可直接用名词用定语，也可在其后接介词 in。如：a maths examination（数学考试），an examination in chemistry（化学考试）。

(3) 我们平时说的“高考”，其实就是指“大学入学考试”，说成英语通常是college entrance examinations，也可说成examinations for college entrance或examinations for admission to college。

“参加考试”通常用take或sit, 但在正式文体，可以用take part in. 不过请注意，在本句中应改为过去进行时,但不如was taking the entrance exam for... 更多见。这个题可能是中国人编的，第一句为现在进行is　taking, 第二句又接上一句过去时句子fainted，时态混用错误。

但就take part in 这个搭配本身而言，是可以的。The free dictionary 在解释这一用法时的例句本身就使用了take part in. When someone takes part in an exam, you say that they take it or sit it. https://www.thefreedictionary.com/Exams

请看外媒例句：

1. Teachers at one of the schools asked if the arrests could be postponed to allow them to take part in exams. (Guardian)

2. It will also have a profound effect on students, who will take part in a series of new exams designed to help administrators grade teachers in specialized subjects. (NYT)

3. The family agreed to pay the school fees, but funds were so insecure that Monica sometimes wasn't sure she could take part in her exams. (UNICEF)

4. In order to take part in the exam, the candidates must be over 27 years old and have three years of pertinent legal experience. （语料库）

5. Some of them worked for a period of time and then gave up the work to begin to take part in the entrance exam of master's degree. （语料库）

6. At the age of seventeen, I had the opportunity to take part in the entrance exam for college. （语料库）