Execute some code at the beginning of each page: how to do it in my case?

Question

I use an environment for my exercises that draw an horizontal rule before each exercise.

I would like to prevent the rule to be drawn if the exercise is at the beginning of a page.

I use a variable \isFirstExercise and I tried to play with \AtBeginShipout and \AtBeginningPage but it does not work.

Can you help me achieving this?

---

See the MWE:

\documentclass[a5paper]{article}
\usepackage{geometry}
\geometry{a5paper}
\usepackage{atbegshi}
\usepackage{bophook}
\setlength{\parindent}{0pt}
\def\varIsNewPageExercise{1}
\newenvironment{exercise}
{\begin{samepage}\if\varIsNewPageExercise1\else\medskip\hrule\medskip\fi\nopagebreak\textbf{Exercise}\par\nopagebreak}
{\end{samepage}\global\let\varIsNewPageExercise=0}
\AtBeginShipout{\global\let\varIsNewPageExercise=1}
\AtBeginPage{\global\let\varIsNewPageExercise=1}
\begin{document}
\begin{exercise}
$1+1 = 2$ \
$2+2 = 4$ 
\end{exercise}
\begin{exercise}
$1+1 = 2$ \
$2+2 = 4$ 
\end{exercise}
\begin{exercise}
$1+1 = 2$ \
$2+2 = 4$ 
\end{exercise}
\begin{exercise}
$1+1 = 2$ \
$2+2 = 4$ 
\end{exercise}
\begin{exercise}
$1+1 = 2$ \
$2+2 = 4$ 
\end{exercise}
\begin{exercise}
$1+1 = 2$ \
$2+2 = 4$ 
\end{exercise}
\begin{exercise}
$1+1 = 2$ \
$2+2 = 4$ 
\end{exercise}
\begin{exercise}
$1+1 = 2$ \
$2+2 = 4$ 
\end{exercise}
\begin{exercise}
$1+1 = 2$ \
$2+2 = 4$ 
\end{exercise}
\begin{exercise}
$1+1 = 2$ \
$2+2 = 4$ 
\end{exercise}
\begin{exercise}
$1+1 = 2$ \
$2+2 = 4$ 
\end{exercise}
\begin{exercise}
$1+1 = 2$ \
$2+2 = 4$ 
\end{exercise}
\end{document}