semblance - The way something appears on the surface, often without revealing the true nature or reality behind it.

In spite of their their kids' constant uncontrolled behavior, when they were outside they managed to keep up the semblance of calm, even though things were not so calm inside their house.
astute - Ability to understand things quickly and clearly, and to use the knowledge well
From a very early age, Gail instinctively knew everything about business, and and after college she proved to be an astute business woman, and became a millionaire before the age of 30.