
aufmerksam
attentive
To be fully concentrated and interested in something; to listen or watch carefully.
Die Kinder hörten der Geschichte aufmerksam zu.
The children listened attentively to the story.
attentive / considerate
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attentive
To be fully concentrated and interested in something; to listen or watch carefully.
Die Kinder hörten der Geschichte aufmerksam zu.
The children listened attentively to the story.

considerate
To be considerate and courteous toward other people; to notice their needs and wishes and respond to them.
Es war sehr aufmerksam von dir, mir zum Geburtstag zu gratulieren.
It was very considerate of you to congratulate me on my birthday.

to draw attention to
To deliberately direct another person's attention to a certain issue, problem, or detail.
Ich möchte Sie auf einen Fehler in der Abrechnung aufmerksam machen.
I would like to draw your attention to an error in the invoice.
The word is made up of the prefix 'auf', the stem of 'merken' (to notice/remember), and the ending '-sam'. Literally, it therefore means being inclined to notice something or remember something.
Ein aufmerksamer Schüler lernt schneller.
An attentive student learns faster.
The meaning depends strongly on context. If 'aufmerksam' refers to a task or perception, it means 'konzentriert' (concentrated). If it refers to behavior toward people, it means 'rücksichtsvoll' (considerate).
Der Detektiv beobachtete die Szene aufmerksam.
The detective observed the scene attentively.
In the meaning 'konzentriert' (concentrated), 'aufmerksam' is often used as an adverb with verbs of perception. Typical combinations are 'aufmerksam zuhören' (to listen attentively), 'aufmerksam zusehen' (to watch attentively), or 'aufmerksam lesen' (to read attentively).
Bitte lesen Sie den Vertrag aufmerksam durch.
Please read the contract carefully.
To describe a considerate action, the structure 'Es ist aufmerksam von [person in the dative]' is often used. This praises the person who carried out the action.
Es war sehr aufmerksam von Ihnen, an meinen Geburtstag zu denken.
It was very considerate of you to remember my birthday.
The expression 'jemanden auf etwas aufmerksam machen' (to draw someone's attention to something) has a fixed structure. The thing being pointed out is always in the accusative.
Ein Passant machte mich auf den platten Reifen aufmerksam.
A passerby drew my attention to the flat tire.
awake / alert
Aufmerksam and wach can both describe a mentally clear person. Aufmerksam directs the eyes or listening toward a specific thing, while wach describes the general mental state. Use aufmerksam with a specific object of attention and wach when mental clarity is meant in general.

Mara war im Unterricht aufmerksam und hörte der Erklärung genau zu.
Mara was attentive in class and listened closely to the explanation.
Nach dem kurzen Schlaf war Mara wieder wach und geistig aufnahmefähig.
After the short nap, Mara was awake again and mentally receptive.