v9 εγενετο (γινομαι) it came to pass. en + dat. "at [that time]" ηλθεν (ερχομαι) aor. "he came" απο "from" τηϖ Γαλιλαιας (α) gen. "in Galilee"
εβαπτισθη (βαπτιζω) aor. pas. "He was baptized" υπο + gen. "by [John]"
v10 αναβαινων (αναβαινω) pres. part. " coming up” participle is adverbial, probably temporal, so " as soon as Jesus came up out of the water".
τους ουρανους (ος) gen. pl. "the heavens"
σχιζομενους (σχιζω) pres. pas. part. "torn open" split, divided- an image reflected in both the crucifixion (the veil of the temple is “σχιζω”) and perhaps a referent back to the creation account (the heavens and the earth are “σχιζω” i.e. divided!)
katabainon (katabainw) pres. part. “descending" εις "on him" "came down and entered into him", BAGD, is possible.
ως "like [a dove]" – a comparative; either descending as a dove would descend, or descending looking like a περιστεραν (α) "a dove" – actually a pigeon. An allusive image, either the divine is being represented as a bird-like creature coming to rest on Jesus, or the dove (a common symbol of Israel at the time, serves to identify Jesus as the new Spirit-filled corporate Israel. The second option seems best.
v11 ο ουιος (ος) "[my] Son" Probably messianic rather than filial.
ο αγαπητος "whom I love" - the adjective functions as a substantive; pushing toward the idea of "unique/only son", given that the Hebrew "only" is often translated by the same Greek word in the LXX, obviously in messianic rather than filial terms.
ευδοκησα (ευδοκεω) aor. "I am well-pleased" – is a timeless aorist, best represented by a present tense. So "I think this good", or "I have chosen you", or more gently "on you my favor rests."
v12 εκβαλλει (εκβαλλω) pres. "sent [him] out" - thrust him out- the present tense of a very forceful word.
την ερημον (ος ον) "the desolate place” a place of testing and confrontation with the divine but also a haunt for evil powers.
v13 τεσσερακοντα "forty [days]" - alluding to the forty years of Israel's wanderings in the wilderness prior to entering the promised land. Unlike the old Israel, Jesus, the new Israel, does not fail the test.
πειραζομενος (πειραζω) pres. pas. part. "being tested” Satan puts Jesus to the test as Israel was tested in the wilderness, therefore "was put to the test by Satan", NJB.
διηκονουν (κιακονεω) imperf. "served" - "ministered/attended" is better.
1:14 μετα .. το παραδοθηναι (παραδιδωμι) aor. inf. "after [John] was put in prison" - Mark clearly has Jesus' public ministry following John's.
κηρυσσων (κηρυσσω) pres. part. "proclaiming" - an attendant circumstance participle identifying action accompanying the main verb "went", so “Jesus went .... and preached", The ministry of Jesus, as with the ministry of John, is defined as one of communicating a message.
το ευαγγελιον (on) "the good (important) news" such as news reported from a battlefront. The message may be good or bad news, either way it is important.
της βασιλειας (a) "of the kingdom" - "the important message concerning the kingdom is widely attested, but is discounted by most scholars. None-the-less, it does remind us of the content of the message, namely, the coming kingdom of God - the dawning of God's promised righteous reign.
του θεου "of God" – an ablative, expressing source/origin.
v15 ο καιρος (ος) "the appointed time.
πεπληρωται (πληροω) perf. "has been fulfilled, the sense "completed" is best, in that the prophecies concerning the coming of the messiah and the inauguration of his kingdom, have come to fruition in the person and work of Christ, therefore, the kingdom is upon us, is "now". The perfect tense underlines the idea of completion.
η βασιλεια (α) "the kingdom" - referring to the righteous rule του θεου "of God"
ηγγικεν (εγγιζω) perf. "is near" - expresses motion toward, so the perfect tense is expressing the idea that the motion in time toward the realization of the kingdom has virtually reached its completion, therefore "at hand", or "is rubbing up next to." Of course, this word leads to the great debate over the "now/not yet" of the kingdom.
μετανοιετε (μετανοεω) imp. "change direction; turn around", the imperative is "turn from your opposition to, God", of course, the word "repent" means something quite different in modern language, so we are best not to use it!
πιστευετε (πιστευω) pres. imp. "believe" - the sense of the word is "to put one's weight on", rather than "give intellectual ascent to" so perhaps “trust” is a better translation.