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The test is a tool to meassure the knowledge level of your students and adjust the learning material accordingly. An exam or the examination is more formal and it tells you if a students passed or failed a class or course
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One difference between the two is that a test is used both as a noun and as a verb, whereas an examination is only used as a noun. Such as one can take a test (noun), or they can test (verb) somebody else, in both cases the term is used correctly.
An exam or examination is an official test that shows your knowledge or ability in a particular subject. The exam is the word most commonly used. The examination is more formal and is used mainly in written English.