ADV

carefully, closely, in detail, minutely
Each case must be carefully examined. We shall now proceed to examine these two aspects of the problem in detail
exhaustively, fully, properly, thoroughly
briefly
further
critically
Critically examine your work as if you were looking at someone else's efforts
medically

VERB + EXAMINE

aim to, be designed to, seek to, set out to
This study sets out to examine the possible effects of climate change
proceed to
stop to
Anna stopped to examine a plant growing by the stream
be necessary to, need to
want to, wish to

PREP

for
The room was examined minutely for clues

PHRASES

let us examine …
Let us examine the implications of this theory

ADV

externally, internally
The course is externally examined (= by people from outside the college, university, etc.)

PREP

in
The students will be examined in all subjects at the end of term
on
You are only being examined on this semester's work