I would rewrite your minimal file as follows:

% \documentclass[english]{article} % <-- load language options with babel
\documentclass[a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{showframe}          % http://www.ctan.org/pkg/showframe
\usepackage{geometry}
\geometry{verbose,
tmargin=1cm,bmargin=1cm,lmargin=1cm,rmargin=1cm,
headheight=0cm,headsep=0cm,footskip=0cm,
nomarginpar % <-- comment out this option to see the difference
}
\pagestyle{empty}
\setlength{\parskip}{0bp}
\setlength{\parindent}{0pt}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{setspace}
\usepackage[english]{babel}
\begin{document}
Text
\end{document}

If you comment out nomarginpar, you'll see the difference (thanks to the package showframe).

I would rewrite your minimal file as follows:

% \documentclass[english]{article} % <-- load language options with babel
\documentclass[a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{showframe}          % http://www.ctan.org/pkg/showframe
\usepackage{geometry}
\geometry{verbose,
tmargin=1cm,bmargin=1cm,lmargin=1cm,rmargin=1cm,
headheight=0cm,headsep=0cm,footskip=0cm,
nomarginpar % <-- comment out this option to see the difference
}
\pagestyle{empty}
\setlength{\parskip}{0bp}
\setlength{\parindent}{0pt}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{setspace}
\usepackage[english]{babel}
\begin{document}
Text
\end{document}

If you comment out nomarginpar, you'll see the difference (thanks to the package showframe). Note also that depending on your settings, you may not need to specify that you want to use A4 paper. The default is either A4 or 'letterpaper' (i.e., the 8.5'x11' paper common only to North America). If your setup defaults to the wrong kind of paper, you can change this, but it depends on your system and setup.