Finding [A] when looking for the velocity constant
For a first-order reaction, the half-life is constant and is given by the equation 

$$t_{1/2} = \frac{\ln 2}{k}$$

In $10~\mathrm{s}$, two half-lives have passed (the concentration of $\ce{A}$ drops to a quarter), so $t_{1/2} = 5~\mathrm{s}$. Accordingly,

$$\begin{align}
k &amp;= \frac{\ln 2}{5~\mathrm{s}} \\
&amp;= 0.1386~\mathrm{s^{-1}}
\end{align}$$