Example sentences
míng明tiān天kǎo考shì试le了。
The exam is tomorrow.
tā他kǎo考dé得bù不cuò错。
He did well on the exam.
About this word
考 is "to examine" and 试 is "to try, to test", so 考试 is an exam, and it works as both noun and verb: 明天有考试, "there is an exam tomorrow", and 我明天考试, "I have an exam tomorrow". The verb use takes no object. You cannot 考试数学. The subject being tested attaches to 考 alone, as in 考数学 or 考汉语, and that is a very common slip. 高考 is the national university entrance exam, the one that shapes a whole family's summer.
The story behind the character
考
考 is 老 (old) cut down on top, with 丂 below giving the sound. Xu Shen was direct: 考，老也. It meant aged, the same territory as 老. The exam sense arrived later, by way of "examining into" a thing. So 考试 is built on a character that once meant nothing more than old.
试
试 is 讠 (speech) with 式 on the right giving the sound. Xu Shen wrote 試，用也: to use, to put something to work. Use a thing and you find out what it can do, so "try out" slid into "test." 考试 pairs it with 考, which got to the exam hall by its own crooked road.