<p>2019å¹´(å¹³æ31å¹´)度ã«å¼ççã§è¡ãããå ¬ç«é«æ ¡å ¥è©¦æ°å¦ã®åé¡ã¨è§£èª¬ã§ãã<br />
å ¨é¨ã§å¤§åã4ã¤ãããå°åãå²ã¨ããã¾ãã®ã§é·ããªããååãã¨ã«åãã¦èª¬æãã¦ããã¾ãã<br />
ä¸é¨å¦æ ¡é¸æåé¡ã¨åãåé¡ãããã¾ãããæ°ã«ããç¨é£ãããã®ã§ã¯ããã¾ããã<br />
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<p>â»ï¼ä¾é ¼äººã§ããï¼<br />
2019å¹´(å¹³æ31å¹´)度å¼ççå ¬ç«é«æ ¡å ¥è©¦çµããã¾ãããã<br />
åé¨çã®ã¿ãªããããç¶ãããæ¯ãããç²ããã¾ã§ããã</p>
<p>æ©éãåé¨åå¥æå°ã®ããã¨ãã¦å ¨å½ã§æ´»èºããã¦ãããã®ææåçã«ãå¿ããæç°å çã«ç¡çãè¨ã£ã¦ãé¡ãã2019å¹´(å¹³æ31å¹´)度ã®å¼ççå ¬ç«é«æ ¡å ¥è©¦ã®æ°å¦ã®è§£èª¬ããã¦ããã ãã¾ããã<br />
ä»åã®è§£èª¬ãååï¼2018å¹´ å¹³æ30年度ï¼åæ§ãæ°¸ä¹ ä¿åçã«ãã¦ãè¯ãããã価å¤ãããã¾ããã<br />
ã§ã¯ãè¶ å¼·åãªè§£èª¬ãã覧ä¸ããã</p>
<p>åé¡ã¯å¼ççã®å ¬å¼ãã¼ã¸ã§ãå ¬éãã¦ããã¦ãã¾ãã</p>
<p>⇒ã<a href="https://arakannotie.com/wp-content/uploads/2019/03/2019saitama.pdf" rel="noopener" target="_blank">2019å¼ççå ¬ç«å ¥è©¦æ°å¦åé¡</a></p>
<h3>å¼ã®è¨ç®ãæ¹ç¨å¼ãé¢æ°ãå³å½¢ã®åºæ¬å°åéå</h3>
<p>ã\(\large{1}\)ã</p>
<p>å°åéåã並ãã§ãã¾ããããã¹ããæ°ãã¤ããã°èãããããªåé¡ã¯ããã¾ããã</p>
<h4>å¼ã®è¨ç®ã¨æåå¼ã®è¨ç®</h4>
<p>(1)<br />
ã\(\hspace{10pt}-2a+5a\\<br />
=\underline{ã3aã}\)</p>
<p><span class="red b">åé¡é ãã¾ã¨ãã</span>ã ãã§ãã</p>
<p>(2)<br />
ã\(\hspace{10pt}(-8)\div (-4)-1\\<br />
=2-1\\<br />
=\underline{ã1ã}\)</p>
<p>足ãç®å¼ãç®ããã<span class="red b">ããç®å²ãç®ãå </span>ã§ããã</p>
<p><span class="blue b">å²ãç®ãéæ°ã®ããç®</span>ã«ããã¨ããåºæ¬ã身ã«ã¤ãã¦ãã人ã¯ã</p>
<p>ã\(\hspace{10pt}(-8)\color{blue}{\div (-4)}-1\\<br />
\displaystyle =(-8)\color{blue}{\times \frac{1}{(-4)}}-1\\<br />
\displaystyle =\frac{8}{4}-1\\<br />
=2-1\\<br />
=\underline{ã1ã}\)</p>
<p>ã¨ãã¦è¯ãã§ãã符å·ã«ã ãã¯æ°ãã¤ãã¦ããã¾ãããã</p>
<p>ãã®å¾ã注æç¹ã¯æ¨å¹´åº¦ã®è§£èª¬ã§ã¦ãããã«ãã¦ããã®ã§ããã§ã¯æå°éã«ãã¦ããã¾ãã</p>
<p>⇒ã<a href="https://arakannotie.com/12656.html" rel="noopener" target="_blank">å¼ççå ¬ç«é«æ ¡å ¥è©¦(å¹³æ30年度)ã®æ°å¦éå»åé¡ã®è§£èª¬ã¨å¯¾ç</a></p>
<p>(3)ããããããªãããã§ããå²ãç®ã®ç´å¾ã¯åæ¯ã¸ãã¨ããè¨ç®ã«ããã°åãªãç´ååé¡ã§ãã</p>
<p>ã\(\hspace{10pt}3x^2\color{red}{\div(-y^3)}\times 2xy^3\\<br />
\displaystyle =\frac{3x^2\times 2xy^3}{\color{red}{-y^3}}\\<br />
=\underline{ã-6x^3yã}\)</p>
<p>å²ãç®ã¯éæ°ã®ããç®ãªã®ã§</p>
<p>ã\(\hspace{10pt}3x^2\color{blue}{\div(-y^3)}\times 2xy^3\\<br />
\displaystyle =3x^2\color{blue}{\times \frac{1}{-y^3}}\times 2xy^3\\<br />
=\underline{ã-6x^3yã}\)</p>
<p>ã§ãè¯ãã§ããåæ¯ã¨ååãã¯ã£ããåãã¦è¨ç®ããæ¹ãç´åééãã¯æ¸ãã¾ãã<br />
符å·ã¯å¥æ°åããã£ã¦ããã®ã§å ¨ä½ã¯ãã¤ãã¹ã§ãã<br />
<span class="red b">符å·ãå¿ããªãããã«</span>æ°ãã¤ãã¦ããã¾ãããã</p>
<h4>ç¡çæ°ã®è¨ç®ã¨å æ°å解</h4>
<p>(4)ç¡çæ°ã®åæ¯ã®æçåã¨å¼ãç®ã§ãã</p>
<p>ã\(\hspace{10pt}\displaystyle \frac{10}{\sqrt{5}}-\color{blue}{\sqrt{45}}\\<br />
\displaystyle =\frac{10\color{red}{\times \sqrt{5}}}{\sqrt{5}\color{red}{\times \sqrt{5}}}-\color{blue}{3\sqrt{5}}\\<br />
\displaystyle =\frac{10\sqrt{5}}{5}-3\sqrt{5}\\<br />
\displaystyle =2\sqrt{5}-3\sqrt{5}\\<br />
=\underline{ã-\sqrt{5}ã}\)</p>
<p>ç´ å æ°å解ã¯åé¡ç¨ç´ã®çé ã«ã§ãæ¸ãã¦ç¢ºå®ã«ãã£ã¦ãããæ¹ãè¯ãã§ããã</p>
<p>ã\(\color{magenta}{3}\,\underline{)\,45}\\<br />
\color{magenta}{3}\,\underline{)\,15}\\<br />
\hspace{16pt}5\)</p>
<p>1ã¤ã®è¨ç®ãã¹ã§\(\,4\,\)ç¹ã§ãã</p>
<p>(5)å æ°å解ã§ãã</p>
<p>ã\(x^2+6x-27\)</p>
<p>å®æ°é \(\,-27\,\)ã«çç®ãã¾ãã</p>
<p>ããã¦\(\,27\,\)ã«ãªãã®ã¯<br />
ã\(\color{black}{\fbox{ã1ã×ã27ã}}\)ã\(\color{red}{\fbox{ã3ã×ã9ã}}\)<br />
ã ãã§ãã</p>
<p>ãããã¦å®æ°é ã®\(\,\color{red}{-27}\,\)<br />
ã足ãã¦\(\,x\,\)ã®\(\,1\,\)次ã®é ã®ä¿æ°\(\,\color{blue}{6}\,\)ã«ãªãã®ã¯</p>
<p>ã\(\color{red}{(-3)\times 9=-27}\)<br />
ã\(\color{blue}{(-3)+9=6}\)<br />
ãªã®ã§</p>
<p>ã\(\hspace{10pt}x^2+6x-27\\<br />
=\underline{ã(x-3)(x+9)ã}\)</p>
<h4>é£ç«æ¹ç¨å¼ã¨2次æ¹ç¨å¼</h4>
<p>(6)é£ç«æ¹ç¨å¼ã解ãã ãã§ãããä»£å ¥æ³ã§ãå æ¸æ³ã§ãã©ã¡ãã§ããã¾ãã¾ããã<br />
ä»£å ¥æ³ã®æ¹ã楽ãªåé¡ã§ãã</p>
<p>ã\( \begin{cases}<br />
\hspace{7pt} \color{red}{y}=\color{blue}{5-3x}ã･･･â \\ \\<br />
\hspace{7pt} x-2\color{red}{y}=4ã･･･â¡<br />
\end{cases}\)</p>
<p>â ã®\(\,y\,\)ãâ¡ã®\(\,y\,\)ã«ä»£å ¥ãã¾ãã</p>
<p>ã\(\begin{eqnarray}<br />
x-2(\color{red}{\color{blue}{5-3x}})&#038;=&#038;4\\<br />
x-10+6x&#038;=&#038;4\\<br />
x+6x&#038;=&#038;4+10\\<br />
7x&#038;=&#038;14\\<br />
x&#038;=&#038;2<br />
\end{eqnarray}\)</p>
<p>ãã®\(\,x=2\,\)ãâ ãâ¡ã«æ»ãã°è¯ãã®ã§ããããã¡ããâ ã«æ»ãã¾ãããã</p>
<p>ã\(\begin{eqnarray}<br />
y&#038;=&#038;5-3\times (2)\\<br />
&#038;=&#038;5-6\\<br />
&#038;=&#038;-1<br />
\end{eqnarray}\)</p>
<p>çãã\(\,\underline{ãx=2\,,\,y=-1ã}\,\)</p>
<p>å æ¸æ³ã使ã£ã¦è§£ãã¨</p>
<p>ã\( \begin{cases}<br />
\hspace{7pt} y=5\color{red}{-3x}ã･･･â \\ \\<br />
\hspace{7pt} x-2y=4ã･･･â¡<br />
\end{cases}\)</p>
<p>â ã®\(\,\color{red}{-3x}\,\)ã移é ãã¦</p>
<p>ã\(3x+y=5ã･･･â &#8217;\)</p>
<p>ããã¨â¡ãé£ç«ãã¦</p>
<p>ã\( \begin{cases}<br />
\hspace{7pt} 3x+y=5ã･･･â &#8217;\\ \\<br />
\hspace{7pt} x-2y=4ã･･･â¡<br />
\end{cases}\)</p>
<p>é£ç«æ¹ç¨å¼ã解ãã¨ãã®æ¹éã¯ä¸æåæ¶å»ã§ãã<br />
ã©ã¡ãã®æåãæ¶å»ãã¦ãè¯ãã§ãããããã§ã¯\(\,y\,\)ãæ¶å»ãã¾ãããã<br />
\(\,â ’\,\)ã両辺\(\,2\,\)åãã¦ä¸¡è¾ºã足ãã¾ãã</p>
<p>ã\(\hspace{14pt}6x+2y=10\\<br />
\underline{+)\hspace{7pt}x-2y=\hspace{4pt}4}\\<br />
\hspace{14pt}7x\hspace{20pt}=14\\<br />
\hspace{39pt}x=\hspace{4pt}2\)</p>
<p>ããã\(\,â â¡â ’\,\)ã®ã©ãã§ãè¯ãã®ã§ããâ ã«æ»ãã¨\(\,y\,\)ã®å¤ãç´æ¥åºã¾ãã</p>
<p>(7)ã2次æ¹ç¨å¼ã解ãããã¨ã¨ãã2次æ¹ç¨å¼ã®è§£ãæ±ããããã¨ã¯åããã¨ã§ãã</p>
<p>2次æ¹ç¨å¼ã解ãã¨ãã¯å æ°å解ãã試ãã®ãè¯ãã§ãã\(\,x^2\,\)ã®ä¿æ°ã\(\,1\,\)ã§ã¯ãªããå ±éå æ°ããªãã®ã§è§£ã®å ¬å¼ã§ãã</p>
<p>ä»ããå¿ è¦ç¡ãã¨ã¯æãã¾ããã\(\,2\,\)次æ¹ç¨å¼ã®è§£ã®å ¬å¼ã§ãã</p>
<p>2次æ¹ç¨å¼<br />
ã\(ax^2+bx+c=0\)<br />
ã®è§£ã¯<br />
ã\(\displaystyle \color{red}{x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}\)</p>
<p>\(\,2\,\)次æ¹ç¨å¼ã¯<br />
ã\(2x^2-3x-1=0\)<br />
ãã£ã¦è§£ã¯</p>
<p>ã\(\begin{eqnarray}\displaystyle<br />
x&#038;=&#038;\frac{-(-3)\pm\sqrt{(-3)^2-4\times (2)\times (-1)}}{2\times 2}\\<br />
&#038;=&#038;\frac{3\pm\sqrt{9+8}}{4}\\<br />
&#038;=&#038;\underline{ã\frac{3\pm\sqrt{17}}{4}ã}<br />
\end{eqnarray}\)</p>
<p>ä»£å ¥ããã¨ãã¯è¨ç®ãã¹ãæ¸ããããï¼ãã£ãï¼ãã¤ãã¦ä»£å ¥ããã®ãåºæ¬ã§ãã</p>
<h4>1次é¢æ°ã®æ±ãæ¹</h4>
<p>(8)\(\,2\,\)ç¹ãéãç´ç·ã®æ¹ç¨å¼ã\(\,1\,\)次é¢æ°ãæ±ããåé¡ã§ãã</p>
<p>ã\(\,(\hspace{8pt}4\,,\,3)\,\)<br />
ã\(\,(-2\,,\,0)\,\)</p>
<p>\(\,1\,\)次é¢æ°ã®<span class="red b">å¾ãã¨å¤åã®å²åã¯ä¸è´</span>ããã®ã§<br />
ã\(\displaystyle \color{red}{(å¤åã®å²å)=\frac{ã(\,y\,ã®å¢å é\,)ã}{ã(\,x\,ã®å¢å é\,)ã}}\)<br />
ãå©ç¨ãã¾ãããå¤åéãæ±ããã¨ãã«\(\,x,y\,\)ã¨ãã«åãæ¹åã«å¼ãã¾ãã<br />
å¼ãæ¹åãéãã¨å¤åã®å²åã®ç¬¦å·ãéã«ãªãã¾ãã</p>
<p>ããã§ã¯ã©ã¡ããä¸ããä¸ãå¼ãã¦ããã¾ãã</p>
<p>ã\(\,(\,x\,ã®å¢å é\,)=(-2)-(4)=-6\,\)<br />
ã\(\,(\,y\,ã®å¢å é\,)=0-(3)=-3\,\)</p>
<p>ãããã<br />
ã\(\displaystyle (å¾ã)=\frac{-3}{-6}=\frac{1}{2}\)</p>
<p>æ±ãã\(\,1\,\)次é¢æ°ã¯<br />
ã\(\displaystyle y=\frac{1}{2}x+b\)<br />
ã¨ããã¦ãä¸ãããã\(\,2\,\)ç¹ã®<span class="red b">ã©ã¡ããéã</span>ã®ã§ã©ã¡ãããä»£å ¥ãã¦\(\,b\,\)ï¼\(\,y\,\)åçï¼ãæ±ãã¾ãã</p>
<p>ã\(\,(-2\,,\,0)\,\)ãä»£å ¥ããã¨<br />
ã\(\begin{eqnarray}\displaystyle<br />
0&#038;=&#038;\frac{1}{2}\times (-2)+b\\<br />
-b&#038;=&#038;-1\\<br />
b&#038;=&#038;1<br />
\end{eqnarray}\)</p>
<p>ãã£ã¦æ±ãã\(\,1\,\)次é¢æ°ã¯</p>
<p>ã\(\displaystyle \underline{ãy=\frac{1}{2}x+1ã}\)</p>
<p>ãã¡ããããä¸ã¤ã®ç¹\(\,(\,\color{red}{4}\,,\,\color{blue}{3})\,\)ãéãã¾ãã</p>
<p>ã\(\displaystyle y=\frac{1}{2}\times (\color{red}{4})+1=\color{blue}{3}\,\)</p>
<p>ãããåããªããã°è¨ç®ãã¹ãã¦ãã¾ãã®ã§æ¤ç®ã«ä½¿ãã¨è¯ãã§ãã</p>
<h4>è§åº¦ãæ±ããæ¹æ³</h4>
<p>(9)ã\(\color{red}{\fbox{ãå¦æ ¡é¸æåé¡ã®1ã®(5)ã}}\)<br />
ä¸è§å®è¦ãéãªã£ã¦ããå³å½¢ã®è§åº¦ãæ±ãã¾ãã</p>
<p>è§åº¦ãæ±ããåé¡ã¯åããã¨ããã次ã ã«æ¸ãè¾¼ãã§è¡ãã°èªãã¨çããåºã¾ãã<br />
çããåºããªãã®ã¯å³ã«æ¸ãè¾¼ã¾ãªãããã§ããåãããªããã®ã§ã¯ãªãã解ãæ°ããªããã§ãã</p>
<p>ã©ãããã§ãè¯ãã®ã§åããè§åº¦ãæ¸ãè¾¼ãã§è¦ã¦ä¸ããã<br />
<img src="https://arakannotie.com/wp-content/uploads/2019/03/2019saitama001.jpg" alt="" width="496" height="134" class="aligncenter size-full wp-image-13169" />ä¸è§å®è¦ã®ããããã®è§åº¦ã§ãã<br />
ãã®ãã¨ããå³\(\,2\,\)ã®ããããã®è§åº¦ã¯ã<br />
ï¼éä¸ã¾ã§å ¥ãã¦ããã¾ããï¼<br />
<img src="https://arakannotie.com/wp-content/uploads/2019/03/2019saitama003.jpg" alt="" width="376" height="242" class="aligncenter size-full wp-image-13171" />ããããã®è§åº¦ã®æ±ãæ¹ã¯ã<br />
æåã«åºã¦ããã®ã¯<br />
ã\(\begin{eqnarray}<br />
\mathrm{∠EAC}&#038;=&#038;\mathrm{∠BAC-∠BAE}\\<br />
&#038;=&#038;90^{\circ}-25^{\circ}\\<br />
&#038;=&#038;\color{blue}{65^{\circ}}<br />
\end{eqnarray}\)<br />
ãã<br />
ã\(\begin{eqnarray}<br />
\mathrm{∠FAC}&#038;=&#038;\mathrm{∠EAF-∠EAC}\\<br />
&#038;=&#038;90^{\circ}-65^{\circ}\\<br />
&#038;=&#038;\color{blue}{25^{\circ}}<br />
\end{eqnarray}\)<br />
ã ã¨æãã®ã§ããã\(\,\color{blue}{85°}\,\)ã®æ¹ã«é²ãã 人ãããããããã¾ããã<br />
ä»ã«ããããããªè§åº¦ãåããã¾ãã<br />
ï¼ãã¹ã¦ã®è§åº¦ã¯åºã¦ãã¾ããï¼</p>
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<p>ãããã<br />
ã<span class="red b">ä¸è§å½¢ã®å è§ã®åã¯å¸¸ã«\(\,180°\,\)ã§ä¸å®</span><br />
ã ã¨ãããã¨ãå©ç¨ããã°ã<br />
<img src="https://arakannotie.com/wp-content/uploads/2019/03/2019saitama005.jpg" alt="" width="381" height="274" class="aligncenter size-full wp-image-13173" /><span class="red b">対é è§ã¯çããã®ã§æ®ãã®äºè§ã®åãçãããªã</span>ãã¨ãã<br />
ã<br />
ã\(\mathrm{∠FAC+∠AFC=∠ACG+∠FGC}\)<br />
ãªã®ã§<br />
ã\(\begin{eqnarray}<br />
25^{\circ}+45^{\circ}&#038;=&#038;30^{\circ}+x\\<br />
70^{\circ}&#038;=&#038;30^{\circ}+x\\<br />
x&#038;=&#038;40^{\circ}<br />
\end{eqnarray}\)</p>
<p>ã¨æ±ããã®ãä¸çªã¯ããã§ãããã</p>
<p>ããã»ã©å¤ããã¾ããã®ã§ã©ã£ã¡ã§ãè¯ãã§ãã<br />
\(\,\color{blue}{85°}\,\)ã«éããã¨ããã°<br />
<img src="https://arakannotie.com/wp-content/uploads/2019/03/2018aomori17.jpg" alt="" width="246" height="141" class="aligncenter size-full wp-image-13174" />ãå©ç¨ããã¨æ¥½ã§ããã</p>
<h4>åç¹ãéãæ¾ç©ç·ï¼ï¼æ¬¡é¢æ°ï¼ã®æ§è³ª</h4>
<p>(10)ã\(\color{red}{\fbox{ãå¦æ ¡é¸æåé¡ã®1ã®(6)ã}}\)<br />
é¢æ°ã®åé¡ã§ãã</p>
<p>ãé¢æ°ã¯\(\,y=x^2\,\)</p>
<p>çãè¦ã¦ã°ã©ããæ¸ããã«èãããªãã¦ãã¨ã¯ããã¦ããã¾ãããã<br />
<img src="https://arakannotie.com/wp-content/uploads/2019/03/2019saitama006.jpg" alt="" width="225" height="243" class="aligncenter size-full wp-image-13175" />ä¸ã«å¸ãªæ¾ç©ç·ã§ããï¼ä¸ã«éããæ¾ç©ç·ã§ããï¼</p>
<p>ãã¢<br />
é¢æ°\(\,y=x^2\,\)ã§<br />
ã\(\,x=3\,\)ã®ã¨ã\(\,y=3^2=9\,\)<br />
ãªã®ã§<span class="red b">æ£ããããã¾ãã</span>ã</p>
<p>ãã¤<br />
ãæ¾ç©ç·ã¯ãã¹ã¦è»¸ã«å¯¾ç§°ã§ãã<br />
ãã®æ¾ç©ç·ã¯é ç¹ãåç¹ãªã®ã§\(\,y\,\)軸ã対称ã®è»¸ã§<span class="blue b">æ£ãã</span>ã</p>
<p>ãã¦<br />
å®ç¾©åï¼\(\,x\,\)ã®å¤åï¼ã\(\,-1\,≦\,x\,≦\,2\,\)ã®ã¨ãã®å¤åï¼\(\,y\,\)ã®å¤åï¼ã¯<br />
<img src="https://arakannotie.com/wp-content/uploads/2019/03/2019saitama007.jpg" alt="" width="241" height="207" class="aligncenter size-full wp-image-13176" />\(\,x=-1\,\)ã®ã¨ãã®å¤ã¯é¢ä¿ããã¾ããã<br />
<img src="https://arakannotie.com/wp-content/uploads/2019/03/2018tokyozenki33.jpg" alt="" width="273" height="190" class="aligncenter size-full wp-image-13177" /><br />
æå°å¤ã¯\(\,x=0\,\)ã®ã¨ãã®\(\,y=0\,\)ãªã®ã§<br />
ã\(\,y\,\)ã®å¤åã¯\(\,0\,≦\,y\,≦\,4\,\)</p>
<p><span class="red b">æ£ãããªã</span>ã</p>
<p>ãã¨<br />
å¤åã®å²åã¯<br />
ã\(\displaystyle (å¤åã®å²å)=\frac{ã\color{blue}{(\,y\,ã®å¢å é\,)}ã}{ã\color{red}{(\,x\,ã®å¢å é\,)}ã}\)<br />
ã§ããï¼8)ã«ãããã¾ãã</p>
<p>\(\,x\,\)ã\(\,2\,\)ãã\(\,4\,\)ã¾ã§å¢å ããã¨ãã®\(\,y\,\)ã®å¤åéãæ±ãã¾ãã</p>
<p>é¢æ°\(\,y=x^2\,\)ã®\(\,x=2,4\,\)ã®ããããã®åº§æ¨ãåºãã¦å¢å éãè¦ãã°è¯ãã§ãã</p>
<p>ã\((\,2\,,\,4\,)\)<br />
ã\((\,4\,,\,16\,)\)</p>
<p>ãªã®ã§<br />
ã<br />
ã\(\color{red}{(\,x\,ã®å¢å é\,)}=4-2=\color{red}{2}\)<br />
ã\(\color{blue}{(\,y\,ã®å¢å é\,)}=16-4=\color{blue}{12}\)</p>
<p>ãã£ã¦</p>
<p>ã\(\begin{eqnarray}\displaystyle<br />
ã (å¤åã®å²å)&#038;=&#038;\frac{ã\color{blue}{(\,y\,ã®å¢å é\,)}ã}{ã\color{red}{(\,x\,ã®å¢å é\,)}ã}\\<br />
&#038;=&#038;\frac{\color{blue}{12}}{\color{red}{2}}\\<br />
&#038;=&#038;6<br />
\end{eqnarray}\)<br />
<span class="blue b">æ£ãã</span>ã</p>
<p>ããª<br />
é¢æ°ã®å¢æ¸ã§ãã<br />
é¢æ°\(\,y=x^2\,\)ã®ã°ã©ããè¦ãã°æããã§ãã</p>
<p>\(\,x\,\)ãå¢å ããã¨ãããã¨ã¯ã°ã©ãã§å·¦ããå³ã«ç§»åããã¨ãããã¨ã§ãã<br />
<img src="https://arakannotie.com/wp-content/uploads/2019/03/2019saitama008.jpg" alt="" width="213" height="234" class="aligncenter size-full wp-image-13178" /><br />
ã\(\,\color{red}{x\,ï¼\,0}\,\)ã®ç¯å²ã§ã¯\(\,x\,\)ãå¢å ããã°\(\,y\,\)ã¯<span class="red b">æ¸å°</span><br />
ã\(\,\color{blue}{x\,ï¼\,0}\,\)ã®ç¯å²ã§ã¯\(\,x\,\)ãå¢å ããã°\(\,y\,\)ã¯<span class="blue b">å¢å </span><br />
ãã¦ãã¾ãã</p>
<p><span class="red b">æ£ãããªã</span>ã</p>
<p>çãã\(\,\underline{ãã¤ãã¨ãã¨ã}\,\)</p>
<h4>è¦åã¨æ´æ°ã®æ§è³ª</h4>
<p>(11)ã\(\color{red}{\fbox{ãå¦æ ¡é¸æåé¡ã®1ã®(8)ã}}\)</p>
<p>ãã®åé¡ã¯è¦åæ§ã®åé¡ã¨é£ç«æ¹ç¨å¼ã¨è¦ããããæ´æ°åé¡ã§ãã<br />
å¸ã®ææ°ã¯æ´æ°ãªã®ã§æ°ãã¦ããã°â ã®çãã¯åºã¦ããã§ãããã</p>
<p>åé¡ã®æ¡ä»¶ãæ´çãã¦ããã¾ãããã</p>
<p>ãé·ã\(\,\mathrm{50\,cm}\,\)ã¨é·ã\(\,\mathrm{30\,cm}\,\)ãéãã¦\(\,\mathrm{5\,m}\,\)ã«ããã<br />
ãå¹ ã¯\(\,\mathrm{5\,cm}\,\)éããã<br />
<img src="https://arakannotie.com/wp-content/uploads/2019/03/2019saitama010.jpg" alt="" width="327" height="74" class="aligncenter size-full wp-image-13181" />é£ãåãå¸ã\(\,\mathrm{5\,cm}\,\)éãªãããã«ã¤ãªããã¨ãããã¨ã§ãã<br />
縦ã®é·ãã¯é¢ä¿ããã¾ããã</p>
<p>ãããããªèãæ¹ãã§ãã¾ãã®ã§è§£æ³ãããããã¨åºã¦ããã§ãããã<br />
ããã¤ãç´¹ä»ãã¦ããã¾ãã解çä¾ã«éãã¾ããã®ã§ãèªåã®è§£æ³ã§åã£ã¦ãããã¯å¦æ ¡ã®å çã«ã§ãèãã¦ä¸ããã</p>
<p>â <br />
\(\,\mathrm{50\,cm}\,\)ã®é·ãã®å¸ã ãã使ã£ã¦\(\,\mathrm{5\,m}\,\)ã«ãã¾ãã<br />
\(\,\mathrm{5\,m}\,\)ã¯\(\,\mathrm{500\,cm}\,\)ã§ãã</p>
<p>åä½ãããããã®ã§å¾ã¯åä½æãã§æ¸ãåºãã¾ãã</p>
<p>éããå¹ ã¯\(\,5\,\)ãªã®ã§<br />
ã\(\,1\,\)æã§\(\,50\,\)<br />
ã\(\,2\,\)æã§\(\,50+45\,\)<br />
ã\(\,3\,\)æã§\(\,50+45+45\,\)<br />
<img src="https://arakannotie.com/wp-content/uploads/2019/03/2019saitama009.jpg" alt="" width="206" height="121" class="aligncenter size-full wp-image-13180" /><br />
ã¨è¦ãã¨ã<br />
ã\(\,50+45\times 10=500\,\)<br />
ã¨ãªãã®ã§å ããææ°ã\(\,10\,\)æãªã®ã§\(\,\underline{ã11ã}\,\)æ</p>
<p>ãããä¸è¬çã«è¡¨ãã¨\(\,n\,\)æã®å¸ãç¶ãã¨ããã¨ã足ããã\(\,45\,\)ã¯\(\,(\,n-1\,)\,\)æãªã®ã§<br />
<img src="https://arakannotie.com/wp-content/uploads/2019/03/2019saitama011.jpg" alt="" width="306" height="95" class="aligncenter size-full wp-image-13182" /><br />
ã\(\,50+(n-1)45=500\,\)<br />
ã解ãã°åºã¦ãã¾ãã</p>
<p>ã¾ãã¯ã<br />
ã\(\,50\,\)ã®é·ãã\(\,n\,\)æéãããã¦ããªãã¨ãã®é·ãã¯\(\,50n\,\)<br />
<img src="https://arakannotie.com/wp-content/uploads/2019/03/2019saitama012.jpg" alt="" width="281" height="97" class="aligncenter size-full wp-image-13183" /><br />
ãéãªã\(\,5\,\)ã¯\(\,(\,n-1\,)\,\)åããã®ã§å ¨ä½ã®é·ãã¯\(\,5(n-1)\,\)æ¸ãã®ã§<br />
<img src="https://arakannotie.com/wp-content/uploads/2019/03/2019saitama013.jpg" alt="" width="231" height="142" class="aligncenter size-full wp-image-13184" />å ¨ä½ã®é·ãã¯<br />
ã\(\hspace{10pt}50n-5(n-1)\\<br />
=50n-5n+5\\<br />
=45n+5\)</p>
<p>ã¨è¡¨ããã®ã§<br />
ã\(\begin{eqnarray}<br />
45n+5&#038;=&#038;500\\<br />
45n&#038;=&#038;500-5\\<br />
&#038;=&#038;495\\<br />
n&#038;=&#038;\underline{ã11ã}<br />
\end{eqnarray}\)</p>
<p>â¡<br />
ä»åº¦ã¯\(\,50\,\)ã¨\(\,30\,\)ã両æ¹ä½¿ã£ã¦\(\,500\,\)ã«ãã¾ãã</p>
<p>éãªãã¯åã\(\,5\,\)ãªã®ã§ãéãªãã®ãªãé·ãããéãªããå¼ãæ¹åã§è§£çãã¾ãã</p>
<p>ã\(\,50\,\)ã\(\,x\,\)æã\(\,30\,\)ã\(\,y\,\)æ使ã£ã¦\(\,500\,\)ã«ããã¨ããã¨,</p>
<p>éãªããèããªãå ´åã®é·ãã¯<br />
<img src="https://arakannotie.com/wp-content/uploads/2019/03/2019saitama014.jpg" alt="" width="291" height="173" class="aligncenter size-full wp-image-13185" /><br />
ã\(\color{red}{50x}+\color{blue}{30y}\)</p>
<p>å ¨ä½ã®ææ°ã¯\(\,x+y\,\)ãªã®ã§éãªãã¯\(\,x+y-1\,\)åããã¾ãã</p>
<p><img src="https://arakannotie.com/wp-content/uploads/2019/03/2019saitama015.jpg" alt="" width="178" height="109" class="aligncenter size-full wp-image-13186" /><br />
\(\,1\,\)åã®éãªãã¯\(\,5\,\)ã ãã\(\,(x+y-1)\,\)åã®éãªãã§æ¸ãé·ãã¯</p>
<p>ã\(\,\color{magenta}{5(x+y-1)}\,\)</p>
<p>éãªãé¨åãå¼ããå ¨ä½ã®é·ãã¯</p>
<p>ã\(\hspace{10pt}50x+30y-5(x+y-1)\\<br />
=50x+30y-5x-5y+5\\<br />
=45x+25y+5\)</p>
<p>ããã\(\,500\,\)ã«ãªãã®ã§</p>
<p>ã\(\begin{eqnarray}<br />
45x+25y+5&#038;=&#038;500\\<br />
45x+25y&#038;=&#038;495\\<br />
9x+5y&#038;=&#038;99<br />
\end{eqnarray}\)</p>
<p>ãããæºããæ´æ°\(\,x,y\,\)ãæ¢ãã¨ã<br />
ã\(\,x=1\,\)ã®ã¨ã\(\,y=18\,\)<br />
ã\(\,x=6\,\)ã®ã¨ã\(\,y=9\,\)<br />
ãã£ã¦<br />
ã\(\,\underline{ã赤ãå¸\,1\,æã¨ç½ãå¸\,18\,æã}\,\)<br />
ã¨<br />
ã\(\,\underline{ã赤ãå¸\,6\,æã¨ç½ãå¸\,9\,æã}\,\)<br />
ã®çµã ãã§ãã</p>
<p>\(\,x=11,y=0\,\)ãæ¹ç¨å¼ã¯æºããã¾ããã<br />
ã両æ¹ä½¿ããã®ã§\(\,y=0\,\)ã¯æ¡ä»¶ãæºããã¾ããã</p>
<p>æåã2ã¤ããã®ã§é£ç«æ¹ç¨å¼ã ã¨æãã¾ãããä»ã«æ¡ä»¶ã¯ããã¾ããã<br />
ããã®ã¯ææ°ã¨ãããæ´æ°ãã§ãããã¨ã ãã§ãã</p>
<p>æ´æ°ã¨ããå ´åã¯<span class="red b">調ã¹å°½ãã</span>ãã¨ããã¤ã³ãã«ãªãã¾ãã</p>
<p>ã\(\begin{eqnarray}<br />
9x+5y&#038;=&#038;99\\<br />
5y&#038;=&#038;99-9x\\<br />
y&#038;=&#038;\frac{9(11-x)}{5}<br />
\end{eqnarray}\)</p>
<p>ã¨å¤å½¢ã§ããã°\(\,y\,\)ãæ´æ°ãªã®ã§ã<br />
ã<span class="red b">\(\,11-x\,\)ã\(\,5\,\)ã®åæ°</span><br />
ã¨çµããã¨ã¯ã§ãã¾ããããã¹ã¦èª¿ã¹ã¦ãããã¦ãã¾ãã</p>
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<p>⇒ã<a href="https://arakannotie.com/13197.html" rel="noopener" target="_blank">2019å¹´(å¹³æ31å¹´)度å¼ççå ¬ç«é«æ ¡å ¥è©¦æ°å¦ç¬¬2åã®è§£èª¬</a></p>
<p>\(\large{2\})ã¯æ¨æ¬èª¿æ»ã¨ä½ç©åé¡ãä½å³ã¨è¨¼æã§ãã<br />
æ¬å½ã¯ããã¾ã§ãååã¨ãããã£ãã®ã§ããã¡ãã£ã¨é·ããªãã¾ããã</p>
<p>ããã¨ã\(\large{1}\,\)ã ãã§é ç¹ã¯\(51\)ç¹ããã¾ãã<br />
ååã¨ããã«ã¯ã¡ããã©è¯ãã®ã§ã¯ãªãã§ãããããç¬<br />
ï¼ããã©ããããªã£ãããã§ã¯ããã¾ããããï¼</p>
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<p>2019年度å¼ççå ¬ç«é«æ ¡å ¥è©¦ æ°å¦ç¬¬3åã»4å(åå¦æ ¡é¸æåé¡)ã®ãªãªã¸ãã«è§£èª¬ã«ãªãã¾ãã</p>
<p>ã⇒ã<a href="https://arakannotie.com/12656.html" rel="noopener" target="_blank">å¼ççå ¬ç«é«æ ¡å ¥è©¦(å¹³æ30年度)ã®æ°å¦éå»åé¡ã®è§£èª¬ã¨å¯¾ç</a></p>
<p>\(2018\)å¹´ã®åé¡ã§ã詳ãã解説ãã¦ãã¾ãã®ã§è¦ã¦ããã¨è¯ãã§ãã
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