\documentclass[a4paper,12pt,oneside]{book}
\def\appendix{%
\chapter*{APP}
\addcontentsline{toc}{chapter}{APP}
\setcounter{section}{0}%
\renewcommand{\thesection}{APP.\arabic{section}}%
\setcounter{equation}{0}%
\renewcommand{\theequation}{\thesection.\arabic{equation}}%
\setcounter{figure}{0}%
\renewcommand{\thefigure}{\thesection.\arabic{figure}}%
\setcounter{table}{0}%
\renewcommand{\thetable}{\thesection.\arabic{table}}%
}
\begin{document}
\tableofcontents
\chapter{333}
\section{444}
\appendix
\section{test}
\begin{equation}
\label{eq:4.1}
\Delta_1^2=a^2-b^2
\end{equation}
\section{test2}
\begin{figure}
\caption{pic}
\end{figure}
\begin{table}\caption{tabl}\end{table}
\end{document}
\documentclass[a4paper,12pt,oneside]{book}
\usepackage[
title,
titletoc,
toc,
page,
header
]{appendix}
\begin{document}
\tableofcontents
\chapter{333}
\section{444}
\chapter{Test}
\section{Some test}
\begin{appendices}
\chapter{test 1}
\begin{equation}\label{eq:4.1}
\Delta_1^2=a^2-b^2
\end{equation}
\chapter{test 2}
\begin{figure}
\caption{pic}
\end{figure}
\begin{table}
\caption{tabl}
\end{table}
\end{appendices}
\end{document}
appendix
по вкусу.