%
%	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=0pt
%■ \( \log\log \)でlogとlogの間に挿入される細スペース（省略形は \,）
%\thinmuskip=3mu%■default
%■ \( a+b \)で+の前後に挿入される中スペース（省略形は \>）
%\medmuskip=4mu plus 2mu minus 4mu%■default
\medmuskip=2mu plus 1mu minus 1mu
%■ \( x=5 \)で=の前後に挿入される太スペース（省略形は \;）
%\thickmuskip=5mu plus 5mu%■default
\thickmuskip=3mu plus 2mu minus 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{animateinline}[autoplay,loop]{2}
\multiframe{12}{i=0+1}{
\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+\i/10})
	parabola bend (1.4,{-0.5+\i/10}) (3,{2.5+\i/10});

\ifnum\i<6
	\ifnum\i=5
		\fill[CUDGreen, name intersections
			={of=axisX and para, name=i, total=\t}]
		\foreach \s in {1,...,\t}{(i-\s) circle (3pt)};
	\else
		\fill[CUDRed, name intersections
			={of=axisX and para, name=i, total=\t}]
		\foreach \s in {1,...,\t}{(i-\s) circle (3pt)};
	\fi
\fi

\draw(2,{2.8+\i/10}) node {\tiny\(y=ax^2+bx+c\)};
\end{tikzpicture}
}
\end{animateinline}
\end{minipage}
\hfill
\begin{minipage}[t]{0.6\textwidth}
グラフを動かして、交点の個数を調べよう。
\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](-0.2,2.5)
	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{（$x$軸と交わらない）}
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\#$9$ \ajKaku{2}\hfill
	\( \alt<4->{\textcolor{CUDGreen}{1}}{\phantom{1}}x^2
	\alt<4->{\textcolor{CUDBlue}{{}-2}}{-2}x
	\alt<4->{\textcolor{CUDOrange}{{}+k}}{+k}=0\)が
	\alt<2->{\textcolor{CUDRed}{重解}}{重解}をもつときの$k$？
	\hfill }
\vspace*{-1ex}
\pause
\( \textcolor{CUDRed}{b^2-4ac=0} \)となればよい。\pause

\vspace*{-3ex}
\begin{eqnarray*}
%\textcolor{CUDRed}{D}=
	\hooklen{(-2)^2}{\alt<5->{\textcolor{CUDBlue}{b}}{b}^2}
	-4 \phantom{{}\times{}} \alt<5->{\textcolor{CUDGreen}{a}}{a} 
	\phantom{{}\times{}} \alt<5->{\textcolor{CUDOrange}{c}}{c} 
	&\textcolor{CUDRed}{=}& \textcolor{CUDRed}{0}\\\pause\pause
  (\textcolor{CUDBlue}{-2})^2
	-4\times\alt<5->{\textcolor{CUDGreen}{1}}{1}\times
	\alt<5->{\textcolor{CUDOrange}{k}}{k} & = & 0\\\pause
  \hooklen{(-2)^2}{4}-\hooklen{4\times1\times k}{4k} &=& 0 \\\pause
  -4k &=& -4 \\\pause
  k &=& 1  \quad\text{\□答}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\begin{frame}[t]
%\frametitle{\small\#$9$ \ajKaku{1}\hfill\(x^2\!-\!2x\!+\!k=0\)が
%\alt<2->{\textcolor{CUDRed}{重解}}{重解}をもつときの$k$？
%\hfill}
%\vspace*{-1ex}
%\pause
%\( \textcolor{CUDRed}{D=0} \)となればよい。\pause
%
%\vspace*{-3ex}
%\begin{eqnarray*}
%\textcolor{CUDRed}{D}=\hooklen{(-2)^2}{b^2}-4 \phantom{{}\times{}} a 
%	\phantom{{}\times{}} c 
%	&\textcolor{CUDRed}{=}& \textcolor{CUDRed}{0}\\\pause
%  (-2)^2-4\times1\times k & = & 0\\\pause
%  \hooklen{(-2)^2}{4}-\hooklen{4\times1\times k}{4k} &=& 0 \\\pause
%  -4k &=& -4 \\\pause
%  k &=& 1  \quad\text{\□答}
%\end{eqnarray*}
%\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\(k\)の式だとピンと来ないという人は}
\vspace*{-1ex}
$x$に置き換えるとよいだろう

{\footnotesize （私は高校生の頃、ピンと来ませんでした。最初は…）}

\vspace*{-3ex}
\begin{eqnarray*}
  4-4\alt<2->{\textcolor{CUDRed}{k}}{k} &=& 0 \pause\qquad
	(\textcolor{CUDRed}{k} \Rightarrow
		\textcolor{CUDBlue}{x} \text{に置き換える})\\
  4-4\textcolor{CUDBlue}{x} &=& 0 \\\pause
  -4\textcolor{CUDBlue}{x} &=& -4 \\\pause
  \textcolor{CUDBlue}{x} &=& 1 \qquad
	( \textcolor{CUDBlue}{x}\Rightarrow
		\textcolor{CUDRed}{k}\ \text{に戻す})\\
  \textcolor{CUDRed}{k} &=& 1  \quad\text{\□答}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\footnotesize\#$9$ \ajKaku{8}
	\( \alt<4->{\textcolor{CUDGreen}{1}}{\phantom{1}}x^2
	\alt<4->{\textcolor{CUDBlue}{{}+2}}{+2}x
	\alt<4->{\textcolor{CUDOrange}{{}+(k+5)}}{+(k+5)}=0 \)
	\alt<2->{\textcolor{CUDRed}{異なる$2\!$つの実数解}}
		{異なる$2\!$つの実数解}、$k$の範囲？}
\vspace*{-1ex}
\pause
\( \textcolor{CUDRed}{b^2-4ac>0} \)となればよい。\pause

\vspace*{-3ex}
\begin{eqnarray*}
%\textcolor{CUDRed}{D}=
	\hooklen{2^2}{\alt<5->{\textcolor{CUDBlue}{b}}{b}^2}
	-4 \phantom{{}\times{}}
	\alt<5->{\textcolor{CUDGreen}{a}}{a} \phantom{{}\times{}}
	\hooklen{(k+5)}{\alt<5->{\textcolor{CUDOrange}{c}}{c}}
	&\textcolor{CUDRed}{>}& \textcolor{CUDRed}{0} \\\pause\pause
  \alt<5->{\textcolor{CUDBlue}{2}}{2}^2
	-4\times\alt<5->{\textcolor{CUDGreen}{1}}{1}\times
	\alt<5->{\textcolor{CUDOrange}{(k+5)}}{(k+5)} &>& 0\\\pause
  \hooklen{2^2}{4}-\hooklen{4\times1\times (k+5)}{4\ (k+5)} &>& 0 \\
  4-4k-20 &>& 0 \\
  -4k-16 &>& 0
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\footnotesize\#$9$ \ajKaku{6}\( \phantom{1}x^2+2x+(k+5)=0\)
異なる$2\!$つの実数解、$k$の範囲？}
\vspace*{-5ex}
\begin{eqnarray*}
  -4k-16 &>& 0 \\
  -4k &>& 16 \\[1ex]
  \myfrac{-4k }{\textcolor{CUDRed}{-4}} &\textcolor{CUDRed}{<}&
	\myfrac{\ 16\ }{\textcolor{CUDRed}{-4}} \\[1ex]
  k &<& -4 \quad\text{\□答}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\(k\)の式だとピンと来ないという人は}
\vspace*{-1ex}
$x$に置き換えるとよいだろう

{\footnotesize （私は高校生の頃、ピンと来ませんでした。最初は…）}

\vspace*{-3ex}
\begin{eqnarray*}
  -4\alt<2->{\textcolor{CUDRed}{k}}{k}-16 &>& 0 \pause\qquad
	(\textcolor{CUDRed}{k} \Rightarrow
		\textcolor{CUDBlue}{x} \text{に置き換える})\\
  -4\textcolor{CUDBlue}{x}-16 &>& 0 \\\pause
  \hooklen{-4x-16}{-4\textcolor{CUDBlue}{x}} &>& 16 \\[1ex]\pause
  \hooklen{-4x-16}{\myfrac{-4\textcolor{CUDBlue}{x}}{-4}}
	&\textcolor{CUDRed}{<}& \myfrac{\ 16\ }{-4}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\footnotesize\#$9$ \ajKaku{6}\( \phantom{1}x^2+2x+(k+5)=0\)
異なる$2\!$つの実数解、$k$の範囲？}
\vspace*{-3ex}
\begin{eqnarray*}
  \myfrac{-4\textcolor{CUDBlue}{x}}{ -4}
	&\textcolor{CUDRed}{<}& \myfrac{\ 16\ }{-4}\\[1ex]
  \textcolor{CUDBlue}{x} &<& -4 \qquad
	( \textcolor{CUDBlue}{x}\Rightarrow
		\textcolor{CUDRed}{k}\ \text{に戻す})\\[1ex]
  \textcolor{CUDRed}{k} &<& -4  \quad\text{\□答}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( x,\ y\)以外の式だとピンと来ない人は多いのでは？}
使う文字が$k$だろうが、$x$だろうが、本質的な違いはありません。

\bigskip
しかし学校では\( x,\ y\)の式を解く場合がほとんどなので、
$k$の式を見ても解き方がピンと来ない人が多いのでは
ないでしょうか？

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




\end{document}

\textcolor{CUDRed}{

