How to reduce the white space between top of the page and headrule ONLY on pages other than the first?

Question

See the figure below:

Here is the code:

\documentclass[a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[top=6mm,includehead,headheight=60pt, left=1.5cm,bottom=2cm,right=1.5cm,headsep=0.5cm]{geometry}
\usepackage{tikz}
\usepackage{float} 
\usepackage{multicol} 
\usepackage{xcolor}
\usepackage{fancyhdr} 
\pagestyle{fancy} 
\usepackage{pbox}
\usepackage{lipsum}

\renewcommand{\headrulewidth}{1.2pt}% linha no header 
\renewcommand{\footrulewidth}{1.2pt} % linha no footer

\setlength{\headsep}{\dimexpr\headsep+1.2\baselineskip+.4pt}

\makeatletter
\def\headrule{{
  \if@fancyplain\let\headrulewidth\plainheadrulewidth\fi
  \vskip10pt% change here
  \hrule\@height\headrulewidth\@width\headwidth   
  \vskip-\headrulewidth%
}}
\makeatother


 \lfoot{\tt \today}
 \rfoot{\tt 14 de dezembro de 2018}


\fancypagestyle{firststyle}
{
\lhead{
\def\sc{0.6}
\def\rc{\sc*0.1cm} % rc = 10% de sc
\begin{tikzpicture}[scale=\sc]
\definecolor{tempcolor}{RGB}{200,25,30}
\filldraw[tempcolor][rounded corners=\rc] (2cm,0cm) rectangle (1.2cm,-0.5cm);
\filldraw[tempcolor][rounded corners=\rc] (2cm,-0.6cm) rectangle (1.1cm,-1.1cm);
\filldraw[tempcolor][rounded corners=\rc] (2cm,-0.6cm) rectangle (1.5cm,-1.1cm);
\filldraw[tempcolor][rounded corners=\rc] (1.7cm,-1.2cm) rectangle (1.2cm,-1.7cm);
\filldraw[tempcolor][rounded corners=\rc] (0.6cm,-1.2cm) rectangle (1.1cm,-1.7cm);
\filldraw[tempcolor][rounded corners=\rc] (1.6cm,-1.2cm) rectangle (1.8cm,-1.7cm);
\filldraw[tempcolor][rounded corners=\rc] (1.7cm,-1.8cm) rectangle (1.2cm,-2.3cm);
\node[scale=\sc,fill=white] at (5.92,-0.85) {\resizebox{6.7cm}{0.5cm}{\sf \textbf{ESCOLA}}};
\node[scale=\sc,fill=white] at (4.52,-1.55) {\resizebox{5cm}{0.5cm}{\sf {Construindo o Futuro}}};
\end{tikzpicture}
}     
\rhead{\tikz \node at (0,0) { \textbf{Prova de Física}};\\ 
\tikz[baseline]{\node[anchor=base, draw=black, thick, minimum width=8.5cm, minimum height=7mm,rounded corners, yshift=-2mm,label={[fill=white,label distance=-2mm,inner xsep=2pt]90:{\tt Aluno(a)}:}] { \phantom{\tt 15,0} };}   
\tikz[baseline]{\node[anchor=base, draw=black, thick, minimum width=2cm, minimum height=7mm,rounded corners, yshift=-2mm,label={[fill=white,label distance=-2mm,inner xsep=2pt]90:{\tt Turma}:}] {\phantom{\tt 15,0}};}   
\tikz[baseline]{\node[anchor=base, draw=black, thick, minimum width=1.5cm, minimum height=7mm,rounded corners, yshift=-2mm,label={[fill=white,label distance=-2mm,inner xsep=2pt]90:{\tt Valor}:}] { \tt 15,0};} 
\tikz[baseline]{\node[anchor=base, draw=black, thick, minimum width=1.5cm, minimum height=7mm,rounded corners, yshift=-2mm,label={[fill=white,label distance=-2mm,inner xsep=2pt]90:{\tt Nota}:}] {\phantom{\tt 15,0}};}
}
 \lfoot{\tt Prof. Lucas}
 \rfoot{\tt \today}
}

\begin{document}

\thispagestyle{firststyle}

\begin{multicols}{2} 

\lipsum[3-20]

\end{multicols}

\end{document}

Could anyone help me with this?

Answer 1

Set the page layout to match the bulk of your document. That is, for pages two onward. Then set the first page header with some added \vspace at the beginning, before your multicols:

\documentclass[a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[top=6mm,includehead,left=1.5cm,bottom=2cm,right=1.5cm,headsep=0.5cm]{geometry}
\usepackage{tikz}
\usepackage{multicol} 
\usepackage{xcolor}
\usepackage{fancyhdr} 
\usepackage{lipsum}

\renewcommand{\footrulewidth}{1.2pt} % linha no footer
\renewcommand{\headrulewidth}{1.2pt}% linha no header 

\lfoot{\ttfamily \today}
\rfoot{\ttfamily 14 de dezembro de 2018}

\pagestyle{fancy} 

\fancypagestyle{firststyle}{%
  \renewcommand{\headrulewidth}{0pt}% Remove header rule
  \lhead{%
    \def\scale{0.6}%
    \def\roundc{\scale*0.1cm}% rc = 10% de sc
    \raisebox{-2\baselineskip}[0pt][0pt]{\begin{tikzpicture}[scale=\scale]
      \definecolor{tempcolor}{RGB}{200,25,30}
      \filldraw[tempcolor][rounded corners=\roundc] (2cm,0cm) rectangle (1.2cm,-0.5cm);
      \filldraw[tempcolor][rounded corners=\roundc] (2cm,-0.6cm) rectangle (1.1cm,-1.1cm);
      \filldraw[tempcolor][rounded corners=\roundc] (2cm,-0.6cm) rectangle (1.5cm,-1.1cm);
      \filldraw[tempcolor][rounded corners=\roundc] (1.7cm,-1.2cm) rectangle (1.2cm,-1.7cm);
      \filldraw[tempcolor][rounded corners=\roundc] (0.6cm,-1.2cm) rectangle (1.1cm,-1.7cm);
      \filldraw[tempcolor][rounded corners=\roundc] (1.6cm,-1.2cm) rectangle (1.8cm,-1.7cm);
      \filldraw[tempcolor][rounded corners=\roundc] (1.7cm,-1.8cm) rectangle (1.2cm,-2.3cm);
      \node[scale=\scale,fill=white] at (5.92,-0.85) {\resizebox{6.7cm}{0.5cm}{\sffamily \textbf{ESCOLA}}};
      \node[scale=\scale,fill=white] at (4.52,-1.55) {\resizebox{5cm}{0.5cm}{\sffamily {Construindo o Futuro}}};
    \end{tikzpicture}}
  }
  \chead{\raisebox{-2\baselineskip}[0pt][0pt]{\rule[-2.5\baselineskip]{\linewidth}{1.2pt}}}
  \rhead{\raisebox{-2\baselineskip}[0pt][0pt]{\begin{tabular}{@{}r@{}}
    \tikz \node at (0,0) {\textbf{Prova de Física}};\\ 
    \tikz[baseline]{\node[anchor=base, draw=black, thick, minimum width=8.5cm, minimum height=7mm,rounded corners, yshift=-2mm,label={[fill=white,label distance=-2mm,inner xsep=2pt]90:{\ttfamily Aluno(a)}:}] {\phantom{\ttfamily 15,0}};}   
    \tikz[baseline]{\node[anchor=base, draw=black, thick, minimum width=2cm, minimum height=7mm,rounded corners, yshift=-2mm,label={[fill=white,label distance=-2mm,inner xsep=2pt]90:{\ttfamily Turma}:}] {\phantom{\ttfamily 15,0}};}   
    \tikz[baseline]{\node[anchor=base, draw=black, thick, minimum width=1.5cm, minimum height=7mm,rounded corners, yshift=-2mm,label={[fill=white,label distance=-2mm,inner xsep=2pt]90:{\ttfamily Valor}:}] {\ttfamily 15,0};} 
    \tikz[baseline]{\node[anchor=base, draw=black, thick, minimum width=1.5cm, minimum height=7mm,rounded corners, yshift=-2mm,label={[fill=white,label distance=-2mm,inner xsep=2pt]90:{\ttfamily Nota}:}] {\phantom{\ttfamily 15,0}};}
    \end{tabular}}
  }
  \lfoot{\ttfamily Prof. Lucas}
  \rfoot{\ttfamily \today}
}

\AtBeginDocument{
  \thispagestyle{firststyle}
  \vspace*{2\baselineskip}
}

\begin{document}

\begin{multicols}{2} 

\sloppy\lipsum[3-30]

\end{multicols}

\end{document}

To avoid issues with the header for the first page not matching that of the rest of the document, set the \smash the content (and/or move it into position with \raisebox{<len>}[0pt][0pt]).