agil
agile
Physically nimble, flexible, and quick.
Trotz seines hohen Alters ist der Turner noch sehr agil.
Despite his advanced age, the gymnast is still very agile.

agile
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agile
Physically nimble, flexible, and quick.
Trotz seines hohen Alters ist der Turner noch sehr agil.
Despite his advanced age, the gymnast is still very agile.

You can recognize the meaning of 'agil' (agile) from the context. If people are talking about the body or sports, it refers to physical mobility. In the context of work and projects, it is about flexible methods. If people are talking about thinking and learning, it refers to mental agility.
Ein agiler Projektmanager kann schnell auf neue Anforderungen reagieren.
An agile project manager can respond quickly to new requirements.
In connection with physical nimbleness, 'agil' (agile) is often used to describe movements, people, or animals. Typical combinations are 'agile Bewegungen' (agile movements), 'ein agiler Sportler' (an agile athlete), or 'körperlich agil sein' (to be physically agile).
Der Tänzer beeindruckte das Publikum mit seinen agilen Bewegungen.
The dancer impressed the audience with his agile movements.
In this meaning, 'agil' (agile) is a technical term from the modern workplace, especially from project management and software development. Outside this context, the word is rarely used this way.
Viele Start-ups organisieren ihre Entwicklung in agilen Teams.
Many start-ups organize their development in agile teams.
In a professional context, you will find 'agil' (agile) in fixed terms such as 'agiles Projektmanagement' (agile project management), 'agile Methoden' (agile methods), 'agiles Arbeiten' (agile working), or 'agile Softwareentwicklung' (agile software development).
Agiles Arbeiten erfordert viel Kommunikation im Team.
Agile working requires a lot of communication within the team.
When it comes to mental abilities, 'agil' (agile) is often combined with the adverb 'geistig' (mentally) or describes the 'Geist' (mind). Common phrases are 'geistig agil bleiben' (to stay mentally agile) or 'einen agilen Geist haben' (to have an agile mind).
Regelmäßiges Lesen hilft dabei, geistig agil zu bleiben.
Regular reading helps you stay mentally agile.
awake / alert
'wach' and 'agil' can both describe a mentally active person. 'wach' mainly emphasizes attention and receptiveness: someone listens, thinks along, and is not mentally tired. 'agil' goes a bit further and means that someone thinks quickly, stays flexible, and adapts well to new situations. 'wach' fits very well in everyday life, in class, or in conversations. 'agil' sounds somewhat stronger and is often used when talking about flexibility in thinking or acting.

In dem neuen Projekt bleibt die Gruppe agil und ändert den Plan schnell.
In the new project, the group remains agile and quickly changes the plan.
Am Nachmittag ist Frau Weber noch wach und folgt der langen Besprechung.
In the afternoon, Ms. Weber is still alert and follows the long meeting.