%
%	gbb60166@gmail.com	https://unilab.gbb60166.jp/prekou/prekou.htm
%
% aspectratio= は 1610, 169, 149, 54, 32 の中から選べる（省略時は 43）
% C:\texlive\2024\texmf-dist\tex\latex\beamer\beamer.cls
%\documentclass[20pt,dvipdfmx,usepdftitle=false,hyperref={pdfpagemode=FullScreen},aspectratio=169]{beamer}
%\documentclass[20pt,dvipdfmx,usepdftitle=false,hyperref={pdfstartview={XYZ null null 8.00}},aspectratio=169]{beamer}
\documentclass[20pt,dvipdfmx,usepdftitle=false,aspectratio=169]{beamer}
% pdfの栞の字化けを防ぐ
%\AtBeginDvi{\special{pdf:tounicode EUC-UCS2}}
% テーマ
\usetheme{Copenhagen}
% navi. symbolsは目立たないが，dvipdfmxを使うと機能しないので非表示に
\setbeamertemplate{navigation symbols}{} 
\usepackage{bxdpx-beamer,pxjahyper,minijs}
%\usepackage{graphicx}
%\usepackage{tkokugo,furikana,tsayusen,shiika,sfkanbun,jdkintou,plext}
\usepackage{type1cm}
\usepackage[deluxe]{otf}
%\usepackage{tikzsymbols}
%\usepackage[dvipdfmx]{graphicx}%
\def\pgfsysdriver{pgfsys-dvipdfmx.def}%（graphicxパッケージを使用しない場合はこの行を有効に）
%\def\pgfsysdriver{pgfsys-dvips.def}%デフォルト
%\usepackage[e]{esvect}
\usepackage{tikz}%（これで、pgfとpgfforが読み込まれます。）
%\usepackage{tikz-3dplot}
\usetikzlibrary{intersections}
%\usetikzlibrary{calc,arrows.meta,patterns,angles,backgrounds}
%\usepackage{animate}
%\usepackage{pgfplots}
%\pgfplotsset{compat=newest}
%\pgfplotsset{compat=newest, every axis/.append style={line width=1pt}}
%\PassOptionsToPackage{dvipdfmx}{graphicx}
\nofiles

\hypersetup{% Jul 18 2023
	pdftitle={プレ高数学科（LaTeX Beamer で汎用PDFプレゼンを作る）},
	pdfauthor={gbb60166@gmail.com},
	pdfsubject={https://unilab.gbb60166.jp/prekou/prekou.htm}
	}

% フォントはお好みで
%\usepackage{txfonts}

\mathversion{bold}
\renewcommand{\familydefault}{\sfdefault}
\renewcommand{\seriesdefault}{bx}
\renewcommand{\kanjifamilydefault}{\gtdefault}
\renewcommand{\kanjiseriesdefault}{bx}
\setbeamerfont{title}{size=\normalsize,series=\bfseries}
\setbeamerfont{frametitle}{size=\normalsize,series=\bfseries}
\setbeamertemplate{frametitle}[default][center]
\usefonttheme{professionalfonts}

% 参考にしたURL
% http://windom.phys.hirosaki-u.ac.jp/fswiki/wiki.cgi?page=LaTeX+Beamer%A4%C7%A5%D7%A5%EC%A5%BC%A5%F3%A5%C6%A1%BC%A5%B7%A5%E7%A5%F3

\newcommand{\Slash}[1]{\ooalign{\hfil\kern-3pt／\hfil\crcr$#1$}}
\everymath{\displaystyle}

\newcommand{\maruwaku}[1]{\begin{tikzpicture}[scale=0.7, baseline={([yshift=-22pt] current bounding box.north)}]
\filldraw[color=CUDBlue, line width=1pt, rounded corners=2pt] (-0.1,0)--(2.1,0)--(2.1,1.1)--(-0.1,1.1)--cycle;
\draw(1,0.5) node[white]{#1};
\end{tikzpicture}
}

\setbeamersize{text margin left=5mm,text margin right=5mm}
\fboxrule=0.8pt

\makeatletter
\newcommand{\hooklen}[2]{\settowidth{\@tempdima}{\(#1\)}
%\advance\@tempdima by.3ex
% ↑ 数式モードで式の前後に入るスペースを制御したかったが、
%    難しいのでやめた。段々難解なコードになっているのでやめた方がよい？
\hbox to\@tempdima{\hfil \(#2\)\hfil}}
%■等号付き不等号 by 美文書作成入門
\newcommand{\myleqq}{\mathrel{\mathpalette\gl@align<}}
\newcommand{\mygeqq}{\mathrel{\mathpalette\gl@align>}}
\newcommand{\gl@align}[2]{\lower.6ex\vbox{\baselineskip\z@skip\lineskip\z@
	\ialign{$\m@th#1\hfil##\hfil$\crcr#2\crcr=\crcr}}}
\makeatother

% カラーユニバーサルデザインを調べたつもりだがあまり自信がありません
% http://www.fukushihoken.metro.tokyo.jp/kiban/machizukuri/kanren/color.files/colorudguideline.pdf
% http://jfly.iam.u-tokyo.ac.jp/colorset/

% ■ アクセントカラー小面積を目立たせる高彩度色
\definecolor{CUDRed}{RGB}{255,75,0}
\definecolor{CUDGreen}{RGB}{3,175,122}
\definecolor{CUDBlue}{RGB}{0,90,255}
\definecolor{CUDCyan}{RGB}{77,196,255}
\definecolor{CUDMagenta}{RGB}{153,0,153}
\definecolor{CUDYellow}{RGB}{255,241,0}
\definecolor{CUDBrown}{RGB}{128,64,0}

\definecolor{CUDOrange}{RGB}{246,170,0}

% ■ ベースカラー広い面積の塗り分けに用いる低・中彩度色
\definecolor{CUDPink}{RGB}{255,202,191}
\definecolor{CUDBrightGreen}{RGB}{119,217,168}
\definecolor{CUDLime}{RGB}{216,242,85}
\definecolor{CUDCream}{RGB}{255,255,128}
\definecolor{CUDBrightCyan}{RGB}{191,228,255}
%\definecolor{CUD}{RGB}{}%

\setbeamercolor{CUDBrightGreen}{fg=black,bg=CUDBrightGreen!50}
\setbeamercolor{CUDBrightCyan}{fg=black,bg=CUDBrightCyan}
\setbeamercolor{CUDCream}{fg=black,bg=CUDCream!75}

%\setbeamercolor{frametitle}{use=structure,fg=white,bg=structure.fg}
%\setbeamercolor{palette primary}{use=structure,fg=white,bg=structure.fg}
%\setbeamercolor{frametitle}{bg=CUDOrange}
%\setbeamercolor{palette primary}{bg=CUDOrange}
%\setbeamercolor{frametitle}{bg=CUDCyan!25,fg=black}
%\setbeamercolor{palette primary}{bg=CUDCyan!25,fg=black}
%\setbeamercolor{frametitle}{bg=CUDCream!75,fg=black!80}
%\setbeamercolor{palette primary}{bg=CUDCream!75,fg=black!80}

\newcommand{\myfrac}[2]{\mathchoice%■ 修正 Oct 8,2023
	{%\fontsize{20}{20}\selectfont%	\displaystyle
		\frac{\raisebox{-.6ex}{\(#1\)}}{\raisebox{.4ex}{\(#2\)}}}%
	{\textstyle{\frac{#1}{#2}}}%	\textstyle
	{%\fontsize{13}{13}\selectfont%	\scriptstyle
		\frac{\raisebox{0ex}{\(#1\)}}{\raisebox{-.4ex}{\(#2\)}}}%
	{%\fontsize{11}{11}\selectfont%	\scriptscriptstyle
		\frac{\raisebox{0ex}{\(#1\)}}{\raisebox{-.4ex}{\(#2\)}}}%
	}


\begin{document}

\title{プレ高数学科}\author{gbb60166}

%■ 本文と数式モードの間に挿入される空白スペース
%\mathsurround=-1pt
%■ \( \log\log \)でlogとlogの間に挿入される細スペース（省略形は \,）
%\thinmuskip=3mu
%■ \( a+b \)で+の前後に挿入される中スペース（省略形は \>）
%\medmuskip=2mu plus 1mu minus 1mu
\medmuskip=2mu minus 1mu
%■ \( x=5 \)で=の前後に挿入される太スペース（省略形は \;）
\thickmuskip=3mu plus 2mu
% mu は math units の省略で長さの単位

%■ 新しいプラスマイナス記号を自作（TikZを利用）
\newcommand{\newpm}{\,\tikz[baseline=-0.1ex]
	\draw[line width=0.1ex,line cap=round](0,0)--++(0.6em,0)
					(0,0.8ex)--++(0.6em,0)
					(0.3em,0.25ex)--++(0,1.1ex);
	\,}


%■■■■■■■■■■■■■　テスト領域　■■■■■■■■■■■■■■



%\end{document}
%■■■■■■■■■■■■■　完成品　■■■■■■■■■■■■■■


\begin{frame}[t]
\frametitle{判別式$D$\qquad discriminant}
%https://lsd-project.jp/cgi-bin/lsdproj/ejlookup04.pl?opt=o&dicmode=voice&query=15754%2Emp3&eng=discriminant
\( ax^2+bx+c=0 \)が、どんな解を持つかは\\
\colorbox{CUDCream}{判別式\(D=b^2-4ac\)}を調べるとわかる。

\vskip3ex
$D$は、解の公式\( \myfrac{-b\newpm\sqrt{
{\fboxsep=0pt\colorbox{CUDCream}{\(b^2-4ac\)}}}}{2a} \)の√の中身である。
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{判別式\ \(b^2-4ac\)}
\begin{minipage}[t]{0.36\textwidth}
\vspace*{-3ex}
\begin{tikzpicture}[thick,scale=1.2, >=stealth,
	baseline=(current bounding box.north)]
\draw[->,name path=axisX](-1,0) -- (3,0);
\draw[->](0,-1) -- (0,4);
\footnotesize
\draw(-0.3,-0.3) node {\textrm{O}};
\draw(3,-0.3) node {$x$};
\draw(-0.3,4) node {$y$};
\draw[ultra thick,name path=para](-0.2,2.5)
	parabola bend (1.4,-0.5) (3,2.5);

\fill[CUDRed,name intersections={of=axisX and para, name=i, total=\t}]
\foreach \s in {1,...,\t}{(i-\s) circle (3pt)};

\draw(2,2.8) node {\tiny\(y=ax^2+bx+c\)};
\end{tikzpicture}
\end{minipage}
\hfill
\begin{minipage}[t]{0.6\textwidth}
\textcolor{CUDRed}{\( b^2-4ac>0 \)}のときは

\vskip3ex
\centerline{\textcolor{CUDRed}{異なる$2$つの実数解}をもつ}

\bigskip
\centerline{（$x$軸と異なる$2$点で交わる）}
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{判別式\ \(b^2-4ac\)}
\begin{minipage}[t]{0.36\textwidth}
\vspace*{-3ex}
\begin{tikzpicture}[thick,scale=1.2, >=stealth,
	baseline=(current bounding box.north)]
\draw[->,name path=axisX](-1,0) -- (3,0);
\draw[->](0,-1) -- (0,4);
\footnotesize
\draw(-0.3,-0.3) node {\textrm{O}};
\draw(3,-0.3) node {$x$};
\draw(-0.3,4) node {$y$};
\draw[ultra thick,name path=para](-0.2,3)
			parabola bend (1.4,0) (3,3);

\fill[CUDGreen, name intersections={of=axisX and para, name=i, total=\t}]
\foreach \s in {1,...,\t}{(i-\s) circle (3pt)};
\draw(2,3.3) node {\tiny\(y=ax^2+bx+c\)};
\end{tikzpicture}
\end{minipage}
\hfill
\begin{minipage}[t]{0.6\textwidth}
\textcolor{CUDGreen}{\( b^2-4ac=0 \)}のときは

\vskip3ex
\centerline{\textcolor{CUDGreen}{重解}をもつ}

\bigskip
\centerline{（$x$軸と$1$点で交わる）}

\medskip
\centerline{（$x$軸と接する）}
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{判別式\ \(b^2-4ac\)}
\begin{minipage}[t]{0.36\textwidth}
\vspace*{-3ex}
\begin{tikzpicture}[thick,scale=1.2, >=stealth,
	baseline=(current bounding box.north)]
\draw[->,name path=axisX](-1,0) -- (3,0);
\draw[->](0,-1) -- (0,4);
\footnotesize
\draw(-0.3,-0.3) node {\textrm{O}};
\draw(3,-0.3) node {$x$};
\draw(-0.3,4) node {$y$};
\draw[ultra thick,name path=para](-0.2,3.5)
		parabola bend (1.4,0.5) (3,3.5);

%\fill[CUDRed, name intersections={of=axisX and para, name=i, total=\t}]
%\foreach \s in {1,...,\t}{(i-\s) circle (3pt)};
\draw(2,3.8) node {\tiny\(y=ax^2+bx+c\)};
\end{tikzpicture}
\end{minipage}
\hfill
\begin{minipage}[t]{0.6\textwidth}
\textcolor{CUDBlue}{\( b^2-4ac<0 \)}のときは

\vskip3ex
\centerline{\textcolor{CUDBlue}{異なる$2$つの虚数解}をもつ}

\bigskip
\centerline{（実数解をもたない）}

\bigskip
\centerline{（$x$軸と交わらない）}
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( 3x^2-5x+2=0 \)の解を判別しなさい\hfill
	{\footnotesize\#$9$\ajKaku{1}\,類題}}
\pause
\vskip-1ex
\textcolor{CUDRed}{\( D>0 \)}\quad
\textcolor{CUDGreen}{\( D=0 \)}\quad
\textcolor{CUDBlue}{\( D<0 \)}どれか調べる。
\pause

\vskip-4ex
\begin{eqnarray*}
\alt<6->{\textcolor{CUDRed}{D}}{D}
	&=& \hooklen{(-5)^2}{b^2}-4\ a\ c \\\pause
&=& (-5)^2-4\times3\times2 \\\pause
&=& \hooklen{(-5)^2}{25}-\hooklen{4\times3\times2}{24} \\
&=& \hskip0.15\textwidth \alt<6->{\textcolor{CUDRed}{1}}{1}
\end{eqnarray*}
\pause
\textcolor{CUDRed}{\( D>0 \)}なので
\hfill\□答 異なる$2$つの実数解をもつ
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( 2x^2+4x+7=0 \)の解を判別しなさい}
\pause
\vskip-1ex
\textcolor{CUDRed}{\( D>0 \)}\quad
\textcolor{CUDGreen}{\( D=0 \)}\quad
\textcolor{CUDBlue}{\( D<0 \)}どれか調べる。
\pause

\vskip-4ex
\begin{eqnarray*}
\alt<6->{\textcolor{CUDBlue}{D}}{D}
	&=& \hooklen{16}{b^2}-4\ a\ c \\\pause
&=& \hooklen{16}{4^2}-4\times2\times7 \\\pause
&=& 16-\hooklen{4\times2\times7}{56} \\
&=& \ \alt<6->{\textcolor{CUDBlue}{-40}}{-40}
\end{eqnarray*}
\pause
\textcolor{CUDBlue}{\( D<0 \)}なので
\hfill\□答 異なる$2$つの虚数解をもつ
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




\end{document}

\textcolor{CUDRed}{

