https://mathjk.tistory.com/ 수학의 즐거움에 중독되다! 고등학교 수학 개념 및 문제 풀이 ko Thu, 7 May 2026 23:45:20 +0900 TISTORY 100 수악중독 https://tistory1.daumcdn.net/tistory/23799/attach/1bac5a872a5043a59cd49c144886add0 https://mathjk.tistory.com https://mathjk.tistory.com/6869 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;$8$개의 공과 숫자 $1, 2, 4, 8$이 하나씩 적혀 있는 $4$장의 카드가 있다. 숫자 $1, 2, 4, 8$이 하나씩 적혀 있는 $4$개의 빈 상자에 $8$개의 공과 $4$장의 카드를 남김없이 나누어 넣을 때, 다음 조건을 만족시키는 경우의 수를 구하시오. (단, 공끼리는 서로 구별하지 않고, 공이나 카드를 넣지 않는 상자가 있을 수 있다.)&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <div class="txc-textbox" style="background-color: #dbe8fb; padding: 10px; border: 1px solid #dbe8fb;"> <p data-ke-size="size16">(가) $1$이 적힌 상자에 들어 있는 카드의 개수는 $1$이고 $8$이 적힌 상자에 들어 있는 카드의 개수는 $2$ 이상이다.<br />(나) $n \; (n=2, 4, 8)$이 적힌 상자에는 $n$의 배수가 적힌 카드가 들어 있거나 공이 $n$개 이상 들어 있다.</p> </div> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 10.21.36.png" data-origin-width="970" data-origin-height="590"><span data-url="https://blog.kakaocdn.net/dn/bbwWIP/dJMcafNkcto/PgsoajDkW4g4b7UZp5s9jK/img.png" data-phocus="https://blog.kakaocdn.net/dn/bbwWIP/dJMcafNkcto/PgsoajDkW4g4b7UZp5s9jK/img.png"><img src="https://blog.kakaocdn.net/dn/bbwWIP/dJMcafNkcto/PgsoajDkW4g4b7UZp5s9jK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbbwWIP%2FdJMcafNkcto%2FPgsoajDkW4g4b7UZp5s9jK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="379" height="231" data-filename="Screenshot 2026-05-07 at 10.21.36.png" data-origin-width="970" data-origin-height="590"/></span></figure> </p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 $398$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 10.18.00.png" data-origin-width="1488" data-origin-height="1558"><span data-url="https://blog.kakaocdn.net/dn/7BImf/dJMcaf0NcNE/nErDKTWBMrfnGILsHGQCl0/img.png" data-phocus="https://blog.kakaocdn.net/dn/7BImf/dJMcaf0NcNE/nErDKTWBMrfnGILsHGQCl0/img.png"><img src="https://blog.kakaocdn.net/dn/7BImf/dJMcaf0NcNE/nErDKTWBMrfnGILsHGQCl0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2F7BImf%2FdJMcaf0NcNE%2FnErDKTWBMrfnGILsHGQCl0%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="600" height="628" data-filename="Screenshot 2026-05-07 at 10.18.00.png" data-origin-width="1488" data-origin-height="1558"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 10.18.31.png" data-origin-width="1502" data-origin-height="994"><span data-url="https://blog.kakaocdn.net/dn/tU8kV/dJMcacQygzP/xSumtkVrT3DEdak3FI9vhk/img.png" data-phocus="https://blog.kakaocdn.net/dn/tU8kV/dJMcacQygzP/xSumtkVrT3DEdak3FI9vhk/img.png"><img src="https://blog.kakaocdn.net/dn/tU8kV/dJMcacQygzP/xSumtkVrT3DEdak3FI9vhk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FtU8kV%2FdJMcacQygzP%2FxSumtkVrT3DEdak3FI9vhk%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="600" height="397" data-filename="Screenshot 2026-05-07 at 10.18.31.png" data-origin-width="1502" data-origin-height="994"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 10.19.05.png" data-origin-width="1422" data-origin-height="1464"><span data-url="https://blog.kakaocdn.net/dn/wAmmd/dJMcahK7cv5/A8nLkbCdyLTlIPkp5S1u01/img.png" data-phocus="https://blog.kakaocdn.net/dn/wAmmd/dJMcahK7cv5/A8nLkbCdyLTlIPkp5S1u01/img.png"><img src="https://blog.kakaocdn.net/dn/wAmmd/dJMcahK7cv5/A8nLkbCdyLTlIPkp5S1u01/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FwAmmd%2FdJMcahK7cv5%2FA8nLkbCdyLTlIPkp5S1u01%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="600" height="618" data-filename="Screenshot 2026-05-07 at 10.19.05.png" data-origin-width="1422" data-origin-height="1464"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 10.19.31.png" data-origin-width="1550" data-origin-height="838"><span data-url="https://blog.kakaocdn.net/dn/dMkoxy/dJMcaakTSwD/731BneqSrcGB3mEktNBuq1/img.png" data-phocus="https://blog.kakaocdn.net/dn/dMkoxy/dJMcaakTSwD/731BneqSrcGB3mEktNBuq1/img.png"><img src="https://blog.kakaocdn.net/dn/dMkoxy/dJMcaakTSwD/731BneqSrcGB3mEktNBuq1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FdMkoxy%2FdJMcaakTSwD%2F731BneqSrcGB3mEktNBuq1%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="600" height="324" data-filename="Screenshot 2026-05-07 at 10.19.31.png" data-origin-width="1550" data-origin-height="838"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 10.19.55.png" data-origin-width="1530" data-origin-height="2302"><span data-url="https://blog.kakaocdn.net/dn/yi8k5/dJMcacJO6CT/ph7I87rjSNzm8yzAcShKuK/img.png" data-phocus="https://blog.kakaocdn.net/dn/yi8k5/dJMcacJO6CT/ph7I87rjSNzm8yzAcShKuK/img.png"><img src="https://blog.kakaocdn.net/dn/yi8k5/dJMcacJO6CT/ph7I87rjSNzm8yzAcShKuK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fyi8k5%2FdJMcacJO6CT%2Fph7I87rjSNzm8yzAcShKuK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="600" height="903" data-filename="Screenshot 2026-05-07 at 10.19.55.png" data-origin-width="1530" data-origin-height="2302"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 10.20.17.png" data-origin-width="1454" data-origin-height="152"><span data-url="https://blog.kakaocdn.net/dn/bxINGB/dJMcabRDWJY/cdnPC8QrkSRM8LGAncnukk/img.png" data-phocus="https://blog.kakaocdn.net/dn/bxINGB/dJMcabRDWJY/cdnPC8QrkSRM8LGAncnukk/img.png"><img src="https://blog.kakaocdn.net/dn/bxINGB/dJMcabRDWJY/cdnPC8QrkSRM8LGAncnukk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbxINGB%2FdJMcabRDWJY%2FcdnPC8QrkSRM8LGAncnukk%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="599" height="63" data-filename="Screenshot 2026-05-07 at 10.20.17.png" data-origin-width="1454" data-origin-height="152"/></span></figure> </div> </div> <p data-ke-size="size16"><br /><br /></p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> 확률과 통계 - 문제풀이/경우의 수 수악중독 https://mathjk.tistory.com/6869 https://mathjk.tistory.com/6869#entry6869comment Thu, 7 May 2026 23:21:58 +0900 https://mathjk.tistory.com/6868 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">최고차항의 계수가 $1$인 삼차함수 $f(x)$가 역함수 $g(x)$를 갖는다. 함수 $h(x)$가 모든 실수에 대하여 $$g(x)h(x)=x \ln(1+3|g(x)|)$$이고 세 함수 $f(x), g(x), h(x)$가 다음 조건을 만족시킬 때, $f(3)$의 값을 구하시오.&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <div class="txc-textbox" style="background-color: #dbe8fb; padding: 10px; border: 1px solid #dbe8fb;"> <p data-ke-size="size16">(가) $g(k)=0$인 상수 $k$에 대하여 함수 $h(x)-|g(x)|$는 $x=k$에서 미분가능하다.</p> <p data-ke-size="size16">(나) $4g'(f(1))=3f(1)-4$</p> </div> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 $31$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 09.37.37.png" data-origin-width="1524" data-origin-height="2224"><span data-url="https://blog.kakaocdn.net/dn/xTGMo/dJMcadPpl0X/U60hjPfUrVHLrxtQUIFuik/img.png" data-phocus="https://blog.kakaocdn.net/dn/xTGMo/dJMcadPpl0X/U60hjPfUrVHLrxtQUIFuik/img.png"><img src="https://blog.kakaocdn.net/dn/xTGMo/dJMcadPpl0X/U60hjPfUrVHLrxtQUIFuik/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FxTGMo%2FdJMcadPpl0X%2FU60hjPfUrVHLrxtQUIFuik%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="556" height="811" data-filename="Screenshot 2026-05-07 at 09.37.37.png" data-origin-width="1524" data-origin-height="2224"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 09.38.02.png" data-origin-width="1520" data-origin-height="1550"><span data-url="https://blog.kakaocdn.net/dn/LYEiy/dJMcafNkblx/onzVFFAsBnLgcVogAQXaiK/img.png" data-phocus="https://blog.kakaocdn.net/dn/LYEiy/dJMcafNkblx/onzVFFAsBnLgcVogAQXaiK/img.png"><img src="https://blog.kakaocdn.net/dn/LYEiy/dJMcafNkblx/onzVFFAsBnLgcVogAQXaiK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FLYEiy%2FdJMcafNkblx%2FonzVFFAsBnLgcVogAQXaiK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="562" height="573" data-filename="Screenshot 2026-05-07 at 09.38.02.png" data-origin-width="1520" data-origin-height="1550"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 09.38.36.png" data-origin-width="1568" data-origin-height="2002"><span data-url="https://blog.kakaocdn.net/dn/X6Bv5/dJMcafsYgX9/2BSf5TAN95ORsNyKGAaYe1/img.png" data-phocus="https://blog.kakaocdn.net/dn/X6Bv5/dJMcafsYgX9/2BSf5TAN95ORsNyKGAaYe1/img.png"><img src="https://blog.kakaocdn.net/dn/X6Bv5/dJMcafsYgX9/2BSf5TAN95ORsNyKGAaYe1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FX6Bv5%2FdJMcafsYgX9%2F2BSf5TAN95ORsNyKGAaYe1%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="567" height="724" data-filename="Screenshot 2026-05-07 at 09.38.36.png" data-origin-width="1568" data-origin-height="2002"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 09.39.03.png" data-origin-width="1452" data-origin-height="956"><span data-url="https://blog.kakaocdn.net/dn/bNC1WJ/dJMcagrSTll/9BsI1boj86tTJx2PVzIYD1/img.png" data-phocus="https://blog.kakaocdn.net/dn/bNC1WJ/dJMcagrSTll/9BsI1boj86tTJx2PVzIYD1/img.png"><img src="https://blog.kakaocdn.net/dn/bNC1WJ/dJMcagrSTll/9BsI1boj86tTJx2PVzIYD1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbNC1WJ%2FdJMcagrSTll%2F9BsI1boj86tTJx2PVzIYD1%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="555" height="365" data-filename="Screenshot 2026-05-07 at 09.39.03.png" data-origin-width="1452" data-origin-height="956"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> 미적분 - 문제풀이/미분법 수악중독 https://mathjk.tistory.com/6868 https://mathjk.tistory.com/6868#entry6868comment Thu, 7 May 2026 22:40:41 +0900 https://mathjk.tistory.com/6867 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">두 초점이 $\mathrm{F}(c, 0), \mathrm{F}'(-c, 0) (c&gt;0)$인 쌍곡선 $x^{2}-\dfrac{y^{2}}{a^{2}}=1$ 위의 점 중 제$2$사분면에 있는 점 $\mathrm{P}$에 대하여 직선 $\mathrm{PF}$가 타원 $x^{2}+\dfrac{y^{2}}{b^{2}}=1 (0&lt;b&lt;1)$과 점 $\mathrm{Q}$에서 접한다. 점 $\mathrm{Q}$의 $x$좌표가 $b^2$이고 $\overline{\mathrm{PQ}}=\overline{\mathrm{PF}'}+b^2$일 때, $30(a^{2}+b^{2})$의 값을 구하시오. (단, $a$는 양수이다.)&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 $80$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 08.33.49.png" data-origin-width="1456" data-origin-height="2178"><span data-url="https://blog.kakaocdn.net/dn/bSjzlh/dJMcaaZu2ij/97mfKuGcC0WeRnDQIfSilK/img.png" data-phocus="https://blog.kakaocdn.net/dn/bSjzlh/dJMcaaZu2ij/97mfKuGcC0WeRnDQIfSilK/img.png"><img src="https://blog.kakaocdn.net/dn/bSjzlh/dJMcaaZu2ij/97mfKuGcC0WeRnDQIfSilK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbSjzlh%2FdJMcaaZu2ij%2F97mfKuGcC0WeRnDQIfSilK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="600" height="898" data-filename="Screenshot 2026-05-07 at 08.33.49.png" data-origin-width="1456" data-origin-height="2178"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 08.34.12.png" data-origin-width="1454" data-origin-height="1544"><span data-url="https://blog.kakaocdn.net/dn/ZYhJK/dJMcahxz85t/gqflwXkUxEm7ute2TrethK/img.png" data-phocus="https://blog.kakaocdn.net/dn/ZYhJK/dJMcahxz85t/gqflwXkUxEm7ute2TrethK/img.png"><img src="https://blog.kakaocdn.net/dn/ZYhJK/dJMcahxz85t/gqflwXkUxEm7ute2TrethK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FZYhJK%2FdJMcahxz85t%2FgqflwXkUxEm7ute2TrethK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="603" height="640" data-filename="Screenshot 2026-05-07 at 08.34.12.png" data-origin-width="1454" data-origin-height="1544"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> 기하 - 문제풀이/이차곡선 수악중독 https://mathjk.tistory.com/6867 https://mathjk.tistory.com/6867#entry6867comment Thu, 7 May 2026 21:34:45 +0900 https://mathjk.tistory.com/6866 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">함수 $f(x)=4x^{3}-3x^{2}+2$ 의 한 부정적분 $F(x)$ 에 대하여 $F(1)=5$ 일 때, $F(2)$ 의 값을 구하시오.</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 $15$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="17.png" data-origin-width="1286" data-origin-height="412"><span data-url="https://blog.kakaocdn.net/dn/8asfD/dJMcadheOaa/IMT4b3HVvHyCKVJKAn0q4k/img.png" data-phocus="https://blog.kakaocdn.net/dn/8asfD/dJMcadheOaa/IMT4b3HVvHyCKVJKAn0q4k/img.png"><img src="https://blog.kakaocdn.net/dn/8asfD/dJMcadheOaa/IMT4b3HVvHyCKVJKAn0q4k/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2F8asfD%2FdJMcadheOaa%2FIMT4b3HVvHyCKVJKAn0q4k%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="1286" height="412" data-filename="17.png" data-origin-width="1286" data-origin-height="412"/></span></figure> </div> </div> 수학2 - 문제풀이/적분 수악중독 https://mathjk.tistory.com/6866 https://mathjk.tistory.com/6866#entry6866comment Sun, 5 Apr 2026 00:14:02 +0900 https://mathjk.tistory.com/6865 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">삼각형 $\mathrm{ABC}$ 에서 $\overline{\mathrm{AB}}=6, \overline{\mathrm{AC}}=8$ 이고 $\cos A = -\dfrac{1}{4}$ 일 때, $\overline{\mathrm{BC}}^{2}$ 의 값을 구하시오.&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 $124$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="18.png" data-origin-width="1400" data-origin-height="204"><span data-url="https://blog.kakaocdn.net/dn/b9ggqF/dJMcajn9rAu/RanCkWyNX3j0mRkxfnBoEK/img.png" data-phocus="https://blog.kakaocdn.net/dn/b9ggqF/dJMcajn9rAu/RanCkWyNX3j0mRkxfnBoEK/img.png"><img src="https://blog.kakaocdn.net/dn/b9ggqF/dJMcajn9rAu/RanCkWyNX3j0mRkxfnBoEK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fb9ggqF%2FdJMcajn9rAu%2FRanCkWyNX3j0mRkxfnBoEK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="564" height="82" data-filename="18.png" data-origin-width="1400" data-origin-height="204"/></span></figure> </div> </div> 수학1- 문제풀이/삼각함수 수악중독 https://mathjk.tistory.com/6865 https://mathjk.tistory.com/6865#entry6865comment Sun, 5 Apr 2026 00:12:30 +0900 https://mathjk.tistory.com/6864 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">서로 다른 종류의 연필 $4$ 자루가 있다. 이 $4$ 자루의 연필을 세 명의 학생 $\mathrm{A,\; B,\; C}$ 에게 남김없이 나누어 주는 경우의 수는? (단, 연필을 받지 못하는 학생이 있을 수 있다.)&nbsp;<br /><br />① $72$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;② $75$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③ $78$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④ $81$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤ $84$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ④</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="확통24.png" data-origin-width="1034" data-origin-height="1286"><span data-url="https://blog.kakaocdn.net/dn/IrV5K/dJMcabjsjVG/E8HjO9k4PuPBuaPWswb8Q1/img.png" data-phocus="https://blog.kakaocdn.net/dn/IrV5K/dJMcabjsjVG/E8HjO9k4PuPBuaPWswb8Q1/img.png"><img src="https://blog.kakaocdn.net/dn/IrV5K/dJMcabjsjVG/E8HjO9k4PuPBuaPWswb8Q1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FIrV5K%2FdJMcabjsjVG%2FE8HjO9k4PuPBuaPWswb8Q1%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="434" height="540" data-filename="확통24.png" data-origin-width="1034" data-origin-height="1286"/></span></figure> </div> </div> 확률과 통계 - 문제풀이/경우의 수 수악중독 https://mathjk.tistory.com/6864 https://mathjk.tistory.com/6864#entry6864comment Sun, 5 Apr 2026 00:10:20 +0900 https://mathjk.tistory.com/6863 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">숫자 $1, \;1,\; 1,\; 2,\; 2,\; 3, \;3$ 이 하나씩 적혀 있는 $7$ 장의 카드가 있다. 이 $7$ 장의 카드를 모두 한 번씩 사용하여 일렬로 나열할 때, 양 끝에 놓인 카드에 적힌 두 수의 합이 $4$ 가 되도록 나열하는 경우의 수는? (단, 같은 숫자가 적혀 있는 카드끼리는 서로 구별하지 않는다.)&nbsp;<br /><br />①&nbsp;$70$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$75$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$80$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$85$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$90$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ①</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="확통25.png" data-origin-width="1240" data-origin-height="986"><span data-url="https://blog.kakaocdn.net/dn/KACuR/dJMb99MEiz5/CFLclRTa1rCuOpuk7kdnY0/img.png" data-phocus="https://blog.kakaocdn.net/dn/KACuR/dJMb99MEiz5/CFLclRTa1rCuOpuk7kdnY0/img.png"><img src="https://blog.kakaocdn.net/dn/KACuR/dJMb99MEiz5/CFLclRTa1rCuOpuk7kdnY0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FKACuR%2FdJMb99MEiz5%2FCFLclRTa1rCuOpuk7kdnY0%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="521" height="414" data-filename="확통25.png" data-origin-width="1240" data-origin-height="986"/></span></figure> </div> </div> 확률과 통계 - 문제풀이/경우의 수 수악중독 https://mathjk.tistory.com/6863 https://mathjk.tistory.com/6863#entry6863comment Sun, 5 Apr 2026 00:08:24 +0900 https://mathjk.tistory.com/6862 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">다음 조건을 만족시키는 음이 아닌 정수 $a,\; b,\; c,\; d$ 의 모든 순서쌍 $(a, \;b, \;c, \;d)$ 의 개수는?&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <div class="txc-textbox" style="background-color: #dbe8fb; padding: 10px; border: 1px solid #dbe8fb;"> <p data-ke-size="size16">$a+b+c+|d-1|=4$</p> </div> <p data-ke-size="size16"><br />① $35$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;② $40$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③ $45$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④ $50$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤ $55$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ③</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="확통26.png" data-origin-width="1196" data-origin-height="844"><span data-url="https://blog.kakaocdn.net/dn/cAUcrt/dJMcac3Gff0/V55P0VLnc7tfdl5kZPnKUK/img.png" data-phocus="https://blog.kakaocdn.net/dn/cAUcrt/dJMcac3Gff0/V55P0VLnc7tfdl5kZPnKUK/img.png"><img src="https://blog.kakaocdn.net/dn/cAUcrt/dJMcac3Gff0/V55P0VLnc7tfdl5kZPnKUK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FcAUcrt%2FdJMcac3Gff0%2FV55P0VLnc7tfdl5kZPnKUK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="502" height="354" data-filename="확통26.png" data-origin-width="1196" data-origin-height="844"/></span></figure> </div> </div> 확률과 통계 - 문제풀이/경우의 수 수악중독 https://mathjk.tistory.com/6862 https://mathjk.tistory.com/6862#entry6862comment Sun, 5 Apr 2026 00:06:36 +0900 https://mathjk.tistory.com/6861 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">두 수열 $\{a_{n}\}, \{\mathrm{b}_{n}\}$ 에 대하 $\displaystyle{\lim_{n \to \infty} (3n+2)a_{n} = 6, \lim_{n \to \infty} \dfrac{\mathrm{b}_{n}}{n} = 2}$ 일 때, $\displaystyle{\lim_{n \to \infty} a_{n}\mathrm{b}_{n}}$ 의 값은?&nbsp;<br /><br />①&nbsp;$1$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$2$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$3$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$4$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$5$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ④</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="미적24.png" data-origin-width="1112" data-origin-height="906"><span data-url="https://blog.kakaocdn.net/dn/c6J0gN/dJMcaiJzuJe/gjylk1kDgdalCKvzoAGEU1/img.png" data-phocus="https://blog.kakaocdn.net/dn/c6J0gN/dJMcaiJzuJe/gjylk1kDgdalCKvzoAGEU1/img.png"><img src="https://blog.kakaocdn.net/dn/c6J0gN/dJMcaiJzuJe/gjylk1kDgdalCKvzoAGEU1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fc6J0gN%2FdJMcaiJzuJe%2Fgjylk1kDgdalCKvzoAGEU1%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="468" height="381" data-filename="미적24.png" data-origin-width="1112" data-origin-height="906"/></span></figure> </div> </div> 미적분 - 문제풀이/수열의 극한 수악중독 https://mathjk.tistory.com/6861 https://mathjk.tistory.com/6861#entry6861comment Sat, 4 Apr 2026 00:22:02 +0900 https://mathjk.tistory.com/6860 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">수열 $\{a_{n}\}$ 이 모든 자연수 $n$ 에 대하여 $\displaystyle{\sum_{k=1}^{n} a_{k} }= \sqrt{n+2}$ 를 만족시킬 때, $\displaystyle{\lim_{n \to \infty} \sqrt{n}a_{n}}$ 의 값은?&nbsp;<br /><br />① $\dfrac{1}{2}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;② $1$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ③ $\dfrac{3}{2}$ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;④ $2$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤ $\dfrac{5}{2}$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ①</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="미적25.png" data-origin-width="1074" data-origin-height="560"><span data-url="https://blog.kakaocdn.net/dn/MQIf7/dJMcabRfb1R/7uYFjcC4OAjQwG25ISi9oK/img.png" data-phocus="https://blog.kakaocdn.net/dn/MQIf7/dJMcabRfb1R/7uYFjcC4OAjQwG25ISi9oK/img.png"><img src="https://blog.kakaocdn.net/dn/MQIf7/dJMcabRfb1R/7uYFjcC4OAjQwG25ISi9oK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FMQIf7%2FdJMcabRfb1R%2F7uYFjcC4OAjQwG25ISi9oK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="448" height="234" data-filename="미적25.png" data-origin-width="1074" data-origin-height="560"/></span></figure> </div> </div> 미적분 - 문제풀이/수열의 극한 수악중독 https://mathjk.tistory.com/6860 https://mathjk.tistory.com/6860#entry6860comment Sat, 4 Apr 2026 00:19:50 +0900 https://mathjk.tistory.com/6859 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">자연수 $a$ 에 대하여 $\displaystyle {\lim_{n \to \infty} \dfrac{5a^{2n} + (2a)^{n+1}}{a^{2n} + (2a)^{n}} }= a+1$ 을 만족시키는 모든 자연수 $a$ 의 값의 합은?&nbsp;<br /><br />①&nbsp;$4$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$5$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$6$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$7$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$8$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ②</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="미적26.png" data-origin-width="880" data-origin-height="1234"><span data-url="https://blog.kakaocdn.net/dn/xFZbq/dJMcabKwxG2/ofMvPFLHYKVSX9WikuUXZ1/img.png" data-phocus="https://blog.kakaocdn.net/dn/xFZbq/dJMcabKwxG2/ofMvPFLHYKVSX9WikuUXZ1/img.png"><img src="https://blog.kakaocdn.net/dn/xFZbq/dJMcabKwxG2/ofMvPFLHYKVSX9WikuUXZ1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FxFZbq%2FdJMcabKwxG2%2FofMvPFLHYKVSX9WikuUXZ1%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="314" height="440" data-filename="미적26.png" data-origin-width="880" data-origin-height="1234"/></span></figure> </div> </div> 미적분 - 문제풀이/수열의 극한 수악중독 https://mathjk.tistory.com/6859 https://mathjk.tistory.com/6859#entry6859comment Sat, 4 Apr 2026 00:16:46 +0900 https://mathjk.tistory.com/6858 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">타원 $\dfrac{x^{2}}{a^{2}} + \dfrac{y^{2}}{b^{2}} = 1$ 의 단축의 길이가 $6$ 일 때, 이 타원의 두 초점 사이의 거리는? (단, $a$ 는 양수이다.)&nbsp;<br /><br />① $4$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;② $6$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③ $8$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④ $10$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤ $12$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ③</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="기하24.png" data-origin-width="1106" data-origin-height="430"><span data-url="https://blog.kakaocdn.net/dn/sonSx/dJMcaiJzuB5/InMLnXmCeoUwXEHgXxXFI1/img.png" data-phocus="https://blog.kakaocdn.net/dn/sonSx/dJMcaiJzuB5/InMLnXmCeoUwXEHgXxXFI1/img.png"><img src="https://blog.kakaocdn.net/dn/sonSx/dJMcaiJzuB5/InMLnXmCeoUwXEHgXxXFI1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FsonSx%2FdJMcaiJzuB5%2FInMLnXmCeoUwXEHgXxXFI1%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="473" height="184" data-filename="기하24.png" data-origin-width="1106" data-origin-height="430"/></span></figure> </div> </div> 기하 - 문제풀이/이차곡선 수악중독 https://mathjk.tistory.com/6858 https://mathjk.tistory.com/6858#entry6858comment Sat, 4 Apr 2026 00:14:16 +0900 https://mathjk.tistory.com/6857 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">쌍곡선 $\dfrac{x^{2}}{5a^{2}} - \dfrac{y^{2}}{a^{2}+1} = 1$ 의 한 점근선의 방정식이 $y = -\dfrac{1}{2}x$ 일 때, 이 쌍곡선의 주축의 길이는? (단, $a$ 는 양수이다.)&nbsp;<br /><br />①&nbsp;$2\sqrt{5}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$4\sqrt{5}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$6\sqrt{5}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$8\sqrt{5}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$10\sqrt{5}$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ②</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="기하25.png" data-origin-width="1296" data-origin-height="398"><span data-url="https://blog.kakaocdn.net/dn/Ynak7/dJMcahqpMm8/5ROV07bJiFTOakgxZxatsK/img.png" data-phocus="https://blog.kakaocdn.net/dn/Ynak7/dJMcahqpMm8/5ROV07bJiFTOakgxZxatsK/img.png"><img src="https://blog.kakaocdn.net/dn/Ynak7/dJMcahqpMm8/5ROV07bJiFTOakgxZxatsK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FYnak7%2FdJMcahqpMm8%2F5ROV07bJiFTOakgxZxatsK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="534" height="164" data-filename="기하25.png" data-origin-width="1296" data-origin-height="398"/></span></figure> </div> </div> 기하 - 문제풀이/이차곡선 수악중독 https://mathjk.tistory.com/6857 https://mathjk.tistory.com/6857#entry6857comment Sat, 4 Apr 2026 00:12:18 +0900 https://mathjk.tistory.com/6856 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">포물선 $y^{2}=4px$ ($p&gt;0$)의 초점을 지나고 기울기가 $\dfrac{4}{3}$인 직선이 이 포물선과 만나는 점 중 제$1$사분면에 있는 점을 $\mathrm{P}$ 라 하자. 점 $\mathrm{P}$ 와 이 포물선의 준선 사이의 거리가 $20$ 일 때, $p$ 의 값은?&nbsp;<br /><br />①&nbsp;$1$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$2$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$3$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$4$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$5$</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답&nbsp;</b>④</span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="기하26.png" data-origin-width="1294" data-origin-height="798"><span data-url="https://blog.kakaocdn.net/dn/bqWmtE/dJMcadaofpj/eyl7fu1WYTRIeSJFfrwDTK/img.png" data-phocus="https://blog.kakaocdn.net/dn/bqWmtE/dJMcadaofpj/eyl7fu1WYTRIeSJFfrwDTK/img.png"><img src="https://blog.kakaocdn.net/dn/bqWmtE/dJMcadaofpj/eyl7fu1WYTRIeSJFfrwDTK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbqWmtE%2FdJMcadaofpj%2Feyl7fu1WYTRIeSJFfrwDTK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="505" height="311" data-filename="기하26.png" data-origin-width="1294" data-origin-height="798"/></span></figure> </div> </div> 기하 - 문제풀이/이차곡선 수악중독 https://mathjk.tistory.com/6856 https://mathjk.tistory.com/6856#entry6856comment Fri, 3 Apr 2026 00:14:32 +0900 https://mathjk.tistory.com/6855 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">함수&nbsp;$f(x)=x^{3}-6x^{2}+ax+b$&nbsp;는&nbsp;$x=1$&nbsp;에서&nbsp;극대이다.&nbsp;함수&nbsp;$f(x)$&nbsp;의&nbsp;극솟값이&nbsp;$5$&nbsp;일&nbsp;때,&nbsp;$a+b$&nbsp;의&nbsp;값을&nbsp;구하시오.&nbsp;(단,&nbsp;$a$&nbsp;와&nbsp;$b$&nbsp;는&nbsp;상수이다.)</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 $14$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="19.png" data-origin-width="1316" data-origin-height="682"><span data-url="https://blog.kakaocdn.net/dn/s5yja/dJMcacP9gek/Tstp4aO7pU3mq3eGN7Thg0/img.png" data-phocus="https://blog.kakaocdn.net/dn/s5yja/dJMcacP9gek/Tstp4aO7pU3mq3eGN7Thg0/img.png"><img src="https://blog.kakaocdn.net/dn/s5yja/dJMcacP9gek/Tstp4aO7pU3mq3eGN7Thg0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fs5yja%2FdJMcacP9gek%2FTstp4aO7pU3mq3eGN7Thg0%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="579" height="300" data-filename="19.png" data-origin-width="1316" data-origin-height="682"/></span></figure> </div> </div> 수학2 - 문제풀이/미분 수악중독 https://mathjk.tistory.com/6855 https://mathjk.tistory.com/6855#entry6855comment Fri, 3 Apr 2026 00:11:19 +0900 https://mathjk.tistory.com/6854 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">전체집합 $\mathrm{U}=\{-4, -2, -1, 1, 2, 4\}$ 의 두 부분집합 $\mathrm{A, B}$ 에 대하여 다음 조건을 만족시키는 집합 $\mathrm{A, B}$ 의 모든 순서쌍 $(\mathrm{A, B})$ 의 개수는?&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <div class="txc-textbox" style="background-color: #dbe8fb; padding: 10px; border: 1px solid #dbe8fb;"> <p data-ke-size="size16">(가) $n(A \cap B) \ge 2$<br />(나) 집합 $A \cap B$ 의 모든 원소의 합은 $0$ 이다.</p> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">① $259$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;② $262$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③ $265$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④ $268$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤ $271$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ⑤</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="확통27.png" data-origin-width="1392" data-origin-height="1474"><span data-url="https://blog.kakaocdn.net/dn/sKn1x/dJMcaf69X0z/QObqmEVa1GB0cnuZpLWUFK/img.png" data-phocus="https://blog.kakaocdn.net/dn/sKn1x/dJMcaf69X0z/QObqmEVa1GB0cnuZpLWUFK/img.png"><img src="https://blog.kakaocdn.net/dn/sKn1x/dJMcaf69X0z/QObqmEVa1GB0cnuZpLWUFK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FsKn1x%2FdJMcaf69X0z%2FQObqmEVa1GB0cnuZpLWUFK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="556" height="589" data-filename="확통27.png" data-origin-width="1392" data-origin-height="1474"/></span></figure> </div> </div> 확률과 통계 - 문제풀이/경우의 수 수악중독 https://mathjk.tistory.com/6854 https://mathjk.tistory.com/6854#entry6854comment Fri, 3 Apr 2026 00:09:12 +0900 https://mathjk.tistory.com/6853 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">모든&nbsp;항이&nbsp;양수인&nbsp;수열&nbsp;$\{a_{n}\}$&nbsp;이&nbsp;모든&nbsp;자연수&nbsp;$n$&nbsp;에&nbsp;대하여&nbsp;다음&nbsp;조건을&nbsp;만족시킨다.&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <div class="txc-textbox" style="background-color: #dbe8fb; padding: 10px; border: 1px solid #dbe8fb;"> <p data-ke-size="size16">좌표평면에서&nbsp;원점을&nbsp;지나고&nbsp;기울기가&nbsp;$a_{n}$&nbsp;인&nbsp;직선이&nbsp;점&nbsp;$(2n-1,&nbsp;0)$&nbsp;을&nbsp;중심으로&nbsp;하고&nbsp;반지름의&nbsp;길이가&nbsp;$n$&nbsp;인&nbsp;원과&nbsp;서로&nbsp;다른&nbsp;두&nbsp;점에서&nbsp;만나고,&nbsp;점&nbsp;$(2n+1,&nbsp;0)$&nbsp;을&nbsp;중심으로&nbsp;하고&nbsp;반지름의&nbsp;길이가&nbsp;$n+1$&nbsp;인&nbsp;원과&nbsp;만나지&nbsp;않는다.&nbsp;</p> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">$\displaystyle {\lim_{n \to \infty} n \left (3 - \dfrac{1}{a_{n}^{2}} \right )}$ 의 값은?&nbsp;<br /><br />①&nbsp;$2$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$\dfrac{5}{2}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$3$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$\dfrac{7}{2}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$4$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ⑤</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="미적27.png" data-origin-width="1458" data-origin-height="2124"><span data-url="https://blog.kakaocdn.net/dn/bpzSum/dJMcaiJyrKz/W29V6nxgv7VPblC5K91VJk/img.png" data-phocus="https://blog.kakaocdn.net/dn/bpzSum/dJMcaiJyrKz/W29V6nxgv7VPblC5K91VJk/img.png"><img src="https://blog.kakaocdn.net/dn/bpzSum/dJMcaiJyrKz/W29V6nxgv7VPblC5K91VJk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbpzSum%2FdJMcaiJyrKz%2FW29V6nxgv7VPblC5K91VJk%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="602" height="877" data-filename="미적27.png" data-origin-width="1458" data-origin-height="2124"/></span></figure> </div> </div> 미적분 - 문제풀이/수열의 극한 수악중독 https://mathjk.tistory.com/6853 https://mathjk.tistory.com/6853#entry6853comment Fri, 3 Apr 2026 00:05:02 +0900 https://mathjk.tistory.com/6852 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">두 점 $\mathrm{F}(c, 0), \mathrm{F}^{\prime}(-c, 0)$ ($c&gt;0$)을 초점으로 하고 장축의 길이가 $8$ 인 타원이 있다. 점 $\mathrm{F}$ 를 지나고 기울기가 양수인 직선이 이 타원과 만나는 점 중 $y$ 좌표가 양수인 점을 $\mathrm{P}$, $y$ 좌표가 음수인 점을 $\mathrm{Q}$ 라 하자. $\overline{\mathrm{FP}} : \overline{\mathrm{FQ}} = 1 : 2, \overline{\mathrm{F}^{\prime}\mathrm{P}} : \overline{\mathrm{F}^{\prime}\mathrm{Q}} = 3 : 2$ 일 때, $c$ 의 값은?&nbsp;<br /><br />①&nbsp;$\dfrac{2\sqrt{3}}{3}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$\dfrac{5\sqrt{3}}{6}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$\sqrt{3}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$\dfrac{7\sqrt{3}}{6}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$\dfrac{4\sqrt{3}}{3}$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ⑤</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="기하27.png" data-origin-width="1412" data-origin-height="1640"><span data-url="https://blog.kakaocdn.net/dn/DBz0T/dJMcahxavJh/3LgJQOg9l8RuDSu28aBQ3k/img.png" data-phocus="https://blog.kakaocdn.net/dn/DBz0T/dJMcahxavJh/3LgJQOg9l8RuDSu28aBQ3k/img.png"><img src="https://blog.kakaocdn.net/dn/DBz0T/dJMcahxavJh/3LgJQOg9l8RuDSu28aBQ3k/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FDBz0T%2FdJMcahxavJh%2F3LgJQOg9l8RuDSu28aBQ3k%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="616" height="715" data-filename="기하27.png" data-origin-width="1412" data-origin-height="1640"/></span></figure> </div> </div> 기하 - 문제풀이/이차곡선 수악중독 https://mathjk.tistory.com/6852 https://mathjk.tistory.com/6852#entry6852comment Fri, 3 Apr 2026 00:01:29 +0900 https://mathjk.tistory.com/6851 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">상자&nbsp;$\mathrm{A}$에는&nbsp;숫자&nbsp;$1,&nbsp;2,&nbsp;3,&nbsp;4,&nbsp;5,&nbsp;6$이&nbsp;하나씩&nbsp;적혀&nbsp;있는&nbsp;$6$개의&nbsp;공이&nbsp;들어&nbsp;있고,&nbsp;상자&nbsp;$\mathrm{B}$에는&nbsp;숫자&nbsp;$7,&nbsp;8,&nbsp;9$가&nbsp;하나씩&nbsp;적혀&nbsp;있는&nbsp;$3$개의&nbsp;공이&nbsp;들어&nbsp;있다.&nbsp;두&nbsp;상자&nbsp;$\mathrm{A,&nbsp;B}$에서&nbsp;각각&nbsp;공을&nbsp;임의로&nbsp;한&nbsp;개씩&nbsp;꺼낼&nbsp;때,&nbsp;꺼낸&nbsp;공에&nbsp;적혀&nbsp;있는&nbsp;두&nbsp;자연수가&nbsp;서로소일&nbsp;확률은?&nbsp;<br /><br />①&nbsp;$\dfrac{11}{18}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$\dfrac{2}{3}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$\dfrac{13}{18}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$\dfrac{7}{9}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$\dfrac{5}{6}$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ③</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고1 14.png" data-origin-width="1236" data-origin-height="700"><span data-url="https://blog.kakaocdn.net/dn/bJFfbP/dJMcaciiUqR/qaoEL7HpbWsgM18mGzyvwK/img.png" data-phocus="https://blog.kakaocdn.net/dn/bJFfbP/dJMcaciiUqR/qaoEL7HpbWsgM18mGzyvwK/img.png"><img src="https://blog.kakaocdn.net/dn/bJFfbP/dJMcaciiUqR/qaoEL7HpbWsgM18mGzyvwK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbJFfbP%2FdJMcaciiUqR%2FqaoEL7HpbWsgM18mGzyvwK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="569" height="322" data-filename="고1 14.png" data-origin-width="1236" data-origin-height="700"/></span></figure> </div> </div> 수악중독 https://mathjk.tistory.com/6851 https://mathjk.tistory.com/6851#entry6851comment Thu, 2 Apr 2026 07:12:28 +0900 https://mathjk.tistory.com/6850 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">둘레의 길이가 $400\mathrm{m}$인 원 모양의 산책로를 두 학생 $\mathrm{A, B}$가 각자 일정한 속력으로 뛰려고 한다. 두 학생 $\mathrm{A, B}$가 같은 지점에서 동시에 출발하여 서로 반대 방향으로 뛰면 출발한 시각으로부터 $1$분 $30$초 후에 처음으로 다시 만나고, 서로 같은 방향으로 뛰면 출발한 시각으로부터 $12$분 후에 처음으로 다시 만난다. 학생 $\mathrm{A}$의 속력이 학생 $\mathrm{B}$의 속력보다 클 때, 학생 $\mathrm{A}$가 산책로를 한 바퀴 뛰는 데 걸리는 시간은?&nbsp;<br /><br />①&nbsp;$2$분&nbsp;$10$초&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$2$분&nbsp;$20$초&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$2$분&nbsp;$30$초&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$2$분&nbsp;$40$초&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$2$분&nbsp;$50$초</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ④</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고1 15.png" data-origin-width="1340" data-origin-height="730"><span data-url="https://blog.kakaocdn.net/dn/RNl5Q/dJMcaax1TCq/ncmpzPkuaGdXxUunSM8Bv1/img.png" data-phocus="https://blog.kakaocdn.net/dn/RNl5Q/dJMcaax1TCq/ncmpzPkuaGdXxUunSM8Bv1/img.png"><img src="https://blog.kakaocdn.net/dn/RNl5Q/dJMcaax1TCq/ncmpzPkuaGdXxUunSM8Bv1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FRNl5Q%2FdJMcaax1TCq%2FncmpzPkuaGdXxUunSM8Bv1%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="565" height="308" data-filename="고1 15.png" data-origin-width="1340" data-origin-height="730"/></span></figure> </div> </div> 수악중독 https://mathjk.tistory.com/6850 https://mathjk.tistory.com/6850#entry6850comment Thu, 2 Apr 2026 07:10:07 +0900 https://mathjk.tistory.com/6849 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과&nbsp;같이&nbsp;한&nbsp;변의&nbsp;길이가&nbsp;$1$인&nbsp;두&nbsp;정육각형&nbsp;$\mathrm{ABCDEF,&nbsp;AGHIJK}$가&nbsp;있다.&nbsp;점&nbsp;$\mathrm{G}$가&nbsp;정육각형&nbsp;$\mathrm{ABCDEF}$의&nbsp;내부에&nbsp;있고&nbsp;$\angle&nbsp;\mathrm{BAG}=45^{\circ}$일&nbsp;때,&nbsp;사각형&nbsp;$\mathrm{AGEF}$의&nbsp;넓이는?&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-04-01 at 18.05.55.png" data-origin-width="1056" data-origin-height="786"><span data-url="https://blog.kakaocdn.net/dn/9BCJo/dJMcahYcJNt/QEYFOaGUDH0tLK3Kbnc3p0/img.png" data-phocus="https://blog.kakaocdn.net/dn/9BCJo/dJMcahYcJNt/QEYFOaGUDH0tLK3Kbnc3p0/img.png"><img src="https://blog.kakaocdn.net/dn/9BCJo/dJMcahYcJNt/QEYFOaGUDH0tLK3Kbnc3p0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2F9BCJo%2FdJMcahYcJNt%2FQEYFOaGUDH0tLK3Kbnc3p0%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="387" height="288" data-filename="Screenshot 2026-04-01 at 18.05.55.png" data-origin-width="1056" data-origin-height="786"/></span></figure> </p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">① $\dfrac{2+\sqrt{3}}{4}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;② $\dfrac{\sqrt{3}+\sqrt{6}}{4}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③ $\dfrac{2+\sqrt{6}}{4}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④ $\dfrac{2\sqrt{2}+\sqrt{3}}{4}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤ $\dfrac{2\sqrt{2}+\sqrt{6}}{4}$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ②</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고1 16.png" data-origin-width="1404" data-origin-height="1004"><span data-url="https://blog.kakaocdn.net/dn/qGsuh/dJMcacCCbzH/Zf5kaFq6kREc9lcOHcYeuk/img.png" data-phocus="https://blog.kakaocdn.net/dn/qGsuh/dJMcacCCbzH/Zf5kaFq6kREc9lcOHcYeuk/img.png"><img src="https://blog.kakaocdn.net/dn/qGsuh/dJMcacCCbzH/Zf5kaFq6kREc9lcOHcYeuk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FqGsuh%2FdJMcacCCbzH%2FZf5kaFq6kREc9lcOHcYeuk%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="565" height="404" data-filename="고1 16.png" data-origin-width="1404" data-origin-height="1004"/></span></figure> </div> </div> 수악중독 https://mathjk.tistory.com/6849 https://mathjk.tistory.com/6849#entry6849comment Thu, 2 Apr 2026 07:08:23 +0900 https://mathjk.tistory.com/6848 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과 같이 직선 $y=\dfrac{2}{3}x-5$가 $y$축과 만나는 점을 $\mathrm{A}$, 직선 $y=-x$와 만나는 점을 $\mathrm{B}$라 하자. 원점 $\mathrm{O}$와 제$3$사분면에 있는 점 $\mathrm{C}$에 대하여 사각형 $\mathrm{OCAB}$가 사다리꼴이고 넓이가 $\dfrac{25}{2}$가 되도록 하는 모든 점 $\mathrm{C}$의 $y$좌표의 곱은? (단, 점 $\mathrm{C}$의 $y$좌표는 $-5$보다 크다.)&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-04-01 at 18.03.40.png" data-origin-width="904" data-origin-height="700"><span data-url="https://blog.kakaocdn.net/dn/cSaT02/dJMcafzk97C/z6dkLIWwCPJnBcY8gLvRu0/img.png" data-phocus="https://blog.kakaocdn.net/dn/cSaT02/dJMcafzk97C/z6dkLIWwCPJnBcY8gLvRu0/img.png"><img src="https://blog.kakaocdn.net/dn/cSaT02/dJMcafzk97C/z6dkLIWwCPJnBcY8gLvRu0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FcSaT02%2FdJMcafzk97C%2Fz6dkLIWwCPJnBcY8gLvRu0%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="358" height="277" data-filename="Screenshot 2026-04-01 at 18.03.40.png" data-origin-width="904" data-origin-height="700"/></span></figure> </p> <p data-ke-size="size16"><br /><br />①&nbsp;$\dfrac{8}{3}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$3$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$\dfrac{10}{3}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$\dfrac{11}{3}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$4$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ⑤</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고1 17.png" data-origin-width="1310" data-origin-height="1368"><span data-url="https://blog.kakaocdn.net/dn/PoF1m/dJMcaarf9pH/a5ZO97phWj4H7nyqlxr4zK/img.png" data-phocus="https://blog.kakaocdn.net/dn/PoF1m/dJMcaarf9pH/a5ZO97phWj4H7nyqlxr4zK/img.png"><img src="https://blog.kakaocdn.net/dn/PoF1m/dJMcaarf9pH/a5ZO97phWj4H7nyqlxr4zK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FPoF1m%2FdJMcaarf9pH%2Fa5ZO97phWj4H7nyqlxr4zK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="515" height="538" data-filename="고1 17.png" data-origin-width="1310" data-origin-height="1368"/></span></figure> </div> </div> 수악중독 https://mathjk.tistory.com/6848 https://mathjk.tistory.com/6848#entry6848comment Thu, 2 Apr 2026 07:05:27 +0900 https://mathjk.tistory.com/6847 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과 같이 $\overline{\mathrm{AB}}=7$인 삼각형 $\mathrm{ABC}$의 내심을 $\mathrm{I}$라 할 때, 점 $\mathrm{I}$에서 선분 $\mathrm{AC}$에 내린 수선의 발을 $\mathrm{D}$라 하자. $\overline{\mathrm{AD}}=2, \angle \mathrm{AIB}=120^{\circ}$일 때, 삼각형 $\mathrm{ABC}$의 둘레의 길이는?&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-04-01 at 18.01.46.png" data-origin-width="942" data-origin-height="588"><span data-url="https://blog.kakaocdn.net/dn/FT9HI/dJMcadBqIgF/XjByuECDkuiiuTtHbiubwK/img.png" data-phocus="https://blog.kakaocdn.net/dn/FT9HI/dJMcadBqIgF/XjByuECDkuiiuTtHbiubwK/img.png"><img src="https://blog.kakaocdn.net/dn/FT9HI/dJMcadBqIgF/XjByuECDkuiiuTtHbiubwK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FFT9HI%2FdJMcadBqIgF%2FXjByuECDkuiiuTtHbiubwK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="375" height="234" data-filename="Screenshot 2026-04-01 at 18.01.46.png" data-origin-width="942" data-origin-height="588"/></span></figure> </p> <p data-ke-size="size16"><br /><br />①&nbsp;$18$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$19$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$20$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$21$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$22$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ③</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고1 18.png" data-origin-width="1440" data-origin-height="1680"><span data-url="https://blog.kakaocdn.net/dn/eh4Xnz/dJMcaaEN9Yd/w62oSAZjg0xM4pChBB60mk/img.png" data-phocus="https://blog.kakaocdn.net/dn/eh4Xnz/dJMcaaEN9Yd/w62oSAZjg0xM4pChBB60mk/img.png"><img src="https://blog.kakaocdn.net/dn/eh4Xnz/dJMcaaEN9Yd/w62oSAZjg0xM4pChBB60mk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Feh4Xnz%2FdJMcaaEN9Yd%2Fw62oSAZjg0xM4pChBB60mk%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="585" height="683" data-filename="고1 18.png" data-origin-width="1440" data-origin-height="1680"/></span></figure> </div> </div> 수악중독 https://mathjk.tistory.com/6847 https://mathjk.tistory.com/6847#entry6847comment Thu, 2 Apr 2026 07:03:12 +0900 https://mathjk.tistory.com/6846 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">한&nbsp;변의&nbsp;길이가&nbsp;$4\mathrm{cm}$인&nbsp;정사각형&nbsp;모양의&nbsp;종이를&nbsp;다음과&nbsp;같이&nbsp;차례로&nbsp;접는다.&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-03-31 at 12.21.19.png" data-origin-width="960" data-origin-height="812"><span data-url="https://blog.kakaocdn.net/dn/dUsqNo/dJMcaadH9pY/xgAAYbBRZGSIIcmt9isRhk/img.png" data-phocus="https://blog.kakaocdn.net/dn/dUsqNo/dJMcaadH9pY/xgAAYbBRZGSIIcmt9isRhk/img.png"><img src="https://blog.kakaocdn.net/dn/dUsqNo/dJMcaadH9pY/xgAAYbBRZGSIIcmt9isRhk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FdUsqNo%2FdJMcaadH9pY%2FxgAAYbBRZGSIIcmt9isRhk%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="526" height="445" data-filename="Screenshot 2026-03-31 at 12.21.19.png" data-origin-width="960" data-origin-height="812"/></span></figure> </p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">선분 $\mathrm{CG}$의 길이가 $a\mathrm{cm}$일 때, $a$의 값은? (단, 종이의 두께는 고려하지 않는다.)&nbsp;<br /><br />①&nbsp;$\dfrac{8\sqrt{14}}{7}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$\dfrac{17\sqrt{14}}{14}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$\dfrac{9\sqrt{14}}{7}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$\dfrac{19\sqrt{14}}{14}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$\dfrac{10\sqrt{14}}{7}$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ①</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고1 19.png" data-origin-width="1374" data-origin-height="1064"><span data-url="https://blog.kakaocdn.net/dn/xA25h/dJMcaibKHCU/CYWJu5I2o0qFgSLoV4uGw1/img.png" data-phocus="https://blog.kakaocdn.net/dn/xA25h/dJMcaibKHCU/CYWJu5I2o0qFgSLoV4uGw1/img.png"><img src="https://blog.kakaocdn.net/dn/xA25h/dJMcaibKHCU/CYWJu5I2o0qFgSLoV4uGw1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FxA25h%2FdJMcaibKHCU%2FCYWJu5I2o0qFgSLoV4uGw1%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="531" height="411" data-filename="고1 19.png" data-origin-width="1374" data-origin-height="1064"/></span></figure> </div> </div> 수악중독 https://mathjk.tistory.com/6846 https://mathjk.tistory.com/6846#entry6846comment Wed, 1 Apr 2026 01:22:42 +0900 https://mathjk.tistory.com/6845 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과 같이 제$4$사분면에 있는 점 $\mathrm{A}$를 꼭짓점으로 하고 원점 $\mathrm{O}$를 지나는 이차함수 $y=f(x)$의 그래프가 있다. 점 $\mathrm{A}$에서 $x$축에 내린 수선의 발을 $\mathrm{B}$라 하자. 최고차항의 계수가 음수인 이차함수 $y=g(x)$의 그래프는 꼭짓점 $\mathrm{C}$가 $y$축 위에 있고 점 $\mathrm{B}$를 지난다. 이차함수 $y=g(x)$의 그래프가 $x$축과 만나는 점 중 $\mathrm{B}$가 아닌 점을 $\mathrm{D}$라 할 때, 점 $\mathrm{D}$의 $x$좌표는 $-2$이다. 두 직선 $\mathrm{BC, \;OA}$는 점 $\mathrm{E}$에서 만나고, 점 $\mathrm{E}$에서 $x$축에 내린 수선의 발은 $\mathrm{D}$이다. 사각형 $\mathrm{OABC}$의 넓이가 $9$일 때, $f(-4)+g(-4)$의 값은?&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-03-31 at 12.17.36.png" data-origin-width="650" data-origin-height="688"><span data-url="https://blog.kakaocdn.net/dn/cCK7zS/dJMb990bU5i/gtKWoVR9gRJtUCnC5OVhHK/img.png" data-phocus="https://blog.kakaocdn.net/dn/cCK7zS/dJMb990bU5i/gtKWoVR9gRJtUCnC5OVhHK/img.png"><img src="https://blog.kakaocdn.net/dn/cCK7zS/dJMb990bU5i/gtKWoVR9gRJtUCnC5OVhHK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FcCK7zS%2FdJMb990bU5i%2FgtKWoVR9gRJtUCnC5OVhHK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="319" height="338" data-filename="Screenshot 2026-03-31 at 12.17.36.png" data-origin-width="650" data-origin-height="688"/></span></figure> </p> <p data-ke-size="size16"><br />①&nbsp;$33$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$35$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$37$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$39$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$41$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ④</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고1 20.png" data-origin-width="1330" data-origin-height="1346"><span data-url="https://blog.kakaocdn.net/dn/vfi04/dJMcagkFmKp/QCNEqQaMpRJRkafEPk366K/img.png" data-phocus="https://blog.kakaocdn.net/dn/vfi04/dJMcagkFmKp/QCNEqQaMpRJRkafEPk366K/img.png"><img src="https://blog.kakaocdn.net/dn/vfi04/dJMcagkFmKp/QCNEqQaMpRJRkafEPk366K/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fvfi04%2FdJMcagkFmKp%2FQCNEqQaMpRJRkafEPk366K%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="530" height="536" data-filename="고1 20.png" data-origin-width="1330" data-origin-height="1346"/></span></figure> </div> </div> 수악중독 https://mathjk.tistory.com/6845 https://mathjk.tistory.com/6845#entry6845comment Wed, 1 Apr 2026 01:19:40 +0900 https://mathjk.tistory.com/6844 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과 같이 $\angle \mathrm{B}=90^{\circ}$인 직각삼각형 $\mathrm{ABC}$에서 선분 $\mathrm{AB}$ 위의 점 $\mathrm{D}$와 선분 $\mathrm{AC}$ 위의 점 $\mathrm{E}$에 대하여 $\overline{\mathrm{BC}}=\overline{\mathrm{BE}}=\overline{\mathrm{BD}}$이다. 삼각형 $\mathrm{EAD}$의 넓이가 $16$이고 삼각형 $\mathrm{CED}$의 넓이가 $4$일 때, 삼각형 $\mathrm{CEB}$의 둘레의 길이는? (단, 점 $\mathrm{E}$는 점 $\mathrm{C}$가 아니다.)</p> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-03-31 at 12.15.15.png" data-origin-width="852" data-origin-height="372"><span data-url="https://blog.kakaocdn.net/dn/XPfyl/dJMcagrrkVz/cnFMRcqnQRTR07KgPIkjzk/img.png" data-phocus="https://blog.kakaocdn.net/dn/XPfyl/dJMcagrrkVz/cnFMRcqnQRTR07KgPIkjzk/img.png"><img src="https://blog.kakaocdn.net/dn/XPfyl/dJMcagrrkVz/cnFMRcqnQRTR07KgPIkjzk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FXPfyl%2FdJMcagrrkVz%2FcnFMRcqnQRTR07KgPIkjzk%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="465" height="203" data-filename="Screenshot 2026-03-31 at 12.15.15.png" data-origin-width="852" data-origin-height="372"/></span></figure> </p> <p data-ke-size="size16"><br /><br />①&nbsp;$\sqrt{5}+2\sqrt{10}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$3\sqrt{2}+2\sqrt{5}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$2\sqrt{5}+2\sqrt{10}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$2\sqrt{2}+4\sqrt{5}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$4\sqrt{5}+\sqrt{10}$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ④</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고1 21.png" data-origin-width="1370" data-origin-height="1846"><span data-url="https://blog.kakaocdn.net/dn/bvVxv7/dJMcabjoTws/FRJ5HKnorAGrCvWRYklp2K/img.png" data-phocus="https://blog.kakaocdn.net/dn/bvVxv7/dJMcabjoTws/FRJ5HKnorAGrCvWRYklp2K/img.png"><img src="https://blog.kakaocdn.net/dn/bvVxv7/dJMcabjoTws/FRJ5HKnorAGrCvWRYklp2K/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbvVxv7%2FdJMcabjoTws%2FFRJ5HKnorAGrCvWRYklp2K%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="565" height="761" data-filename="고1 21.png" data-origin-width="1370" data-origin-height="1846"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> 수악중독 https://mathjk.tistory.com/6844 https://mathjk.tistory.com/6844#entry6844comment Wed, 1 Apr 2026 01:16:46 +0900 https://mathjk.tistory.com/6843 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">다음은&nbsp;어느&nbsp;날&nbsp;$6$개&nbsp;지역의&nbsp;일일&nbsp;최저&nbsp;기온을&nbsp;조사하여&nbsp;나타낸&nbsp;자료이다.&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <div class="txc-textbox" style="background-color: #dbe8fb; padding: 10px; border: 1px solid #dbe8fb;"> <p data-ke-size="size16">$$2, \; 1,\;&nbsp; 7,\; 6,\; -3,\; a$$</p> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">자료의 중앙값이 $2$일 때, 분산을 구하시오. (단, $a$는 실수이다.)</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답&nbsp;</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고1 26.png" data-origin-width="954" data-origin-height="896"><span data-url="https://blog.kakaocdn.net/dn/bd1lvV/dJMcagdVDFB/v51lNQHzd9KPfnVvArrBck/img.png" data-phocus="https://blog.kakaocdn.net/dn/bd1lvV/dJMcagdVDFB/v51lNQHzd9KPfnVvArrBck/img.png"><img src="https://blog.kakaocdn.net/dn/bd1lvV/dJMcagdVDFB/v51lNQHzd9KPfnVvArrBck/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fbd1lvV%2FdJMcagdVDFB%2Fv51lNQHzd9KPfnVvArrBck%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="431" height="405" data-filename="고1 26.png" data-origin-width="954" data-origin-height="896"/></span></figure> </div> </div> 수악중독 https://mathjk.tistory.com/6843 https://mathjk.tistory.com/6843#entry6843comment Wed, 1 Apr 2026 01:13:52 +0900 https://mathjk.tistory.com/6842 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과 같이 정육각형 $\mathrm{ABCDEF}$에 대하여 변 $\mathrm{AB}$를 한 변으로 하는 정사각형과 변 $\mathrm{EF}$를 한 변으로 하는 정오각형이 있다. 이 정사각형에서 꼭짓점 $\mathrm{A}$와 이웃한 꼭짓점 중 $\mathrm{B}$가 아닌 점을 $\mathrm{G}$, 이 정오각형에서 꼭짓점 $\mathrm{F}$와 이웃한 꼭짓점 중 $\mathrm{E}$가 아닌 점을 $\mathrm{H}$라 하자. 두 선분 $\mathrm{AH, FG}$가 만나는 점을 $\mathrm{I}$라 할 때, $\angle \mathrm{AIF}=x^{\mathrm{o}}$이다. $x^{\mathrm{o}}$의 값을 구하시오. (단, 점 $\mathrm{G}$와 점 $\mathrm{H}$는 정육각형 $\mathrm{ABCDEF}$의 외부에 있다.)</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-03-31 at 12.09.11.png" data-origin-width="908" data-origin-height="652"><span data-url="https://blog.kakaocdn.net/dn/cV6k1x/dJMb990bUZr/mAFa9hgacZs5KG7Vz1NSFK/img.png" data-phocus="https://blog.kakaocdn.net/dn/cV6k1x/dJMb990bUZr/mAFa9hgacZs5KG7Vz1NSFK/img.png"><img src="https://blog.kakaocdn.net/dn/cV6k1x/dJMb990bUZr/mAFa9hgacZs5KG7Vz1NSFK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FcV6k1x%2FdJMb990bUZr%2FmAFa9hgacZs5KG7Vz1NSFK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="534" height="383" data-filename="Screenshot 2026-03-31 at 12.09.11.png" data-origin-width="908" data-origin-height="652"/></span></figure> </p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 $141$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고1 27.png" data-origin-width="1004" data-origin-height="1332"><span data-url="https://blog.kakaocdn.net/dn/cPcUvD/dJMcaco3jY7/fsaAUUIuqvSNcqCiWkYvv0/img.png" data-phocus="https://blog.kakaocdn.net/dn/cPcUvD/dJMcaco3jY7/fsaAUUIuqvSNcqCiWkYvv0/img.png"><img src="https://blog.kakaocdn.net/dn/cPcUvD/dJMcaco3jY7/fsaAUUIuqvSNcqCiWkYvv0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FcPcUvD%2FdJMcaco3jY7%2FfsaAUUIuqvSNcqCiWkYvv0%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="447" height="593" data-filename="고1 27.png" data-origin-width="1004" data-origin-height="1332"/></span></figure> </div> </div> 수악중독 https://mathjk.tistory.com/6842 https://mathjk.tistory.com/6842#entry6842comment Wed, 1 Apr 2026 01:11:43 +0900 https://mathjk.tistory.com/6841 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과&nbsp;같이&nbsp;양수&nbsp;$a$에&nbsp;대하여&nbsp;두&nbsp;반비례&nbsp;관계&nbsp;$y=\dfrac{a}{x},&nbsp;y=-\dfrac{2a}{x}$의&nbsp;그래프가&nbsp;있다.&nbsp;양수&nbsp;$m$에&nbsp;대하여&nbsp;정비례&nbsp;관계&nbsp;$y=mx$의&nbsp;그래프가&nbsp;$y=\dfrac{a}{x}$의&nbsp;그래프와&nbsp;제$1$사분면에서&nbsp;만나는&nbsp;점을&nbsp;$\mathrm{A}$라&nbsp;하고,&nbsp;점&nbsp;$\mathrm{A}$를&nbsp;지나고&nbsp;$x$축에&nbsp;수직인&nbsp;직선이&nbsp;$y=-\dfrac{2a}{x}$의&nbsp;그래프와&nbsp;만나는&nbsp;점을&nbsp;$\mathrm{B}$라&nbsp;하자.&nbsp;$y=mx$의&nbsp;그래프&nbsp;위의&nbsp;점&nbsp;중&nbsp;$x$좌표가&nbsp;점&nbsp;$\mathrm{A}$의&nbsp;$x$좌표의&nbsp;$\dfrac{1}{2}$배인&nbsp;점을&nbsp;$\mathrm{C}$라&nbsp;하고,&nbsp;점&nbsp;$\mathrm{C}$를&nbsp;지나고&nbsp;$x$축에&nbsp;수직인&nbsp;직선이&nbsp;$y=-\dfrac{2a}{x}$의&nbsp;그래프와&nbsp;만나는&nbsp;점을&nbsp;$\mathrm{D}$라&nbsp;하자.&nbsp;사각형&nbsp;$\mathrm{ACDB}$의&nbsp;넓이가&nbsp;$45$일&nbsp;때,&nbsp;$a$의&nbsp;값을&nbsp;구하시오.</p> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-03-30 at 11.31.42.png" data-origin-width="1306" data-origin-height="1010"><span data-url="https://blog.kakaocdn.net/dn/cvhdBY/dJMcacJmmWK/Grz2U3m3KICvhgUolUnidK/img.png" data-phocus="https://blog.kakaocdn.net/dn/cvhdBY/dJMcacJmmWK/Grz2U3m3KICvhgUolUnidK/img.png"><img src="https://blog.kakaocdn.net/dn/cvhdBY/dJMcacJmmWK/Grz2U3m3KICvhgUolUnidK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FcvhdBY%2FdJMcacJmmWK%2FGrz2U3m3KICvhgUolUnidK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="460" height="356" data-filename="Screenshot 2026-03-30 at 11.31.42.png" data-origin-width="1306" data-origin-height="1010"/></span></figure> </p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 $24$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고1 28.png" data-origin-width="1400" data-origin-height="646"><span data-url="https://blog.kakaocdn.net/dn/kMoC2/dJMcaf67hPo/RdaeBVdmbELI8ti4wBRMDk/img.png" data-phocus="https://blog.kakaocdn.net/dn/kMoC2/dJMcaf67hPo/RdaeBVdmbELI8ti4wBRMDk/img.png"><img src="https://blog.kakaocdn.net/dn/kMoC2/dJMcaf67hPo/RdaeBVdmbELI8ti4wBRMDk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FkMoC2%2FdJMcaf67hPo%2FRdaeBVdmbELI8ti4wBRMDk%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="647" height="299" data-filename="고1 28.png" data-origin-width="1400" data-origin-height="646"/></span></figure> </div> </div> 수악중독 https://mathjk.tistory.com/6841 https://mathjk.tistory.com/6841#entry6841comment Tue, 31 Mar 2026 00:33:18 +0900 https://mathjk.tistory.com/6840 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;$0$이 아닌 실수 $a$에 대하여 이차함수 $$f(x)=ax^{2}-3ax-4a^{2}-8a-2$$가 있다. 이차함수 $y=f(x)$의 그래프의 꼭짓점을 $\mathrm{A}$라 하고, 이 그래프가 $y$축과 만나는 점을 $\mathrm{B}$라 하자. 세 점 $\mathrm{O, A, B}$를 꼭짓점으로 하는 삼각형의 넓이가 $\dfrac{3}{2}$이 되도록 하는 모든 $f(x)$에 대하여 $f(1)$의 값의 합을 구하시오. (단, $\mathrm{O}$는 원점이고, 점 $\mathrm{B}$는 점 $\mathrm{O}$가 아니다.)</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 $6$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고1 29.png" data-origin-width="1374" data-origin-height="1512"><span data-url="https://blog.kakaocdn.net/dn/uACKd/dJMcagSvSEt/2eRPaupE2xGHqC9lSXZzj0/img.png" data-phocus="https://blog.kakaocdn.net/dn/uACKd/dJMcagSvSEt/2eRPaupE2xGHqC9lSXZzj0/img.png"><img src="https://blog.kakaocdn.net/dn/uACKd/dJMcagSvSEt/2eRPaupE2xGHqC9lSXZzj0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FuACKd%2FdJMcagSvSEt%2F2eRPaupE2xGHqC9lSXZzj0%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="659" height="725" data-filename="고1 29.png" data-origin-width="1374" data-origin-height="1512"/></span></figure> </div> </div> 수악중독 https://mathjk.tistory.com/6840 https://mathjk.tistory.com/6840#entry6840comment Tue, 31 Mar 2026 00:31:01 +0900 https://mathjk.tistory.com/6839 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과 같이 $\overline{\mathrm{AB}}=16, \overline{\mathrm{BC}}=15, \angle \mathrm{B} &lt; 90^{\circ}$인 평행사변형 $\mathrm{ABCD}$의 변 $\mathrm{CD}$ 위에 $\overline{\mathrm{CE}}=6$인 점 $\mathrm{E}$가 있다. 직선 $\mathrm{BC}$와 직선 $\mathrm{AE}$의 교점을 $\mathrm{F}$라 할 때, $\overline{\mathrm{EF}}=9$이다. 삼각형 $\mathrm{ABF}$의 내심을 $\mathrm{I}$, 선분 $\mathrm{DF}$의 수직이등분선과 직선 $\mathrm{CD}$의 교점을 $\mathrm{J}$라 할 때, 선분 $\mathrm{AE}$ 위의 점 $\mathrm{K}$는 $\overline{\mathrm{IJ}}=\overline{\mathrm{KJ}}$를 만족시킨다. $\tan(\angle \mathrm{FKD}) = \dfrac{q\sqrt{2}}{p}$일 때, $p+q$의 값을 구하시오. (단, $p$와 $q$는 서로소인 자연수이다.)&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-03-30 at 11.26.45.png" data-origin-width="1286" data-origin-height="906"><span data-url="https://blog.kakaocdn.net/dn/cpBsAH/dJMcaco2n7w/DKwVJKgPYBi4rQzPBvBlMk/img.png" data-phocus="https://blog.kakaocdn.net/dn/cpBsAH/dJMcaco2n7w/DKwVJKgPYBi4rQzPBvBlMk/img.png"><img src="https://blog.kakaocdn.net/dn/cpBsAH/dJMcaco2n7w/DKwVJKgPYBi4rQzPBvBlMk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FcpBsAH%2FdJMcaco2n7w%2FDKwVJKgPYBi4rQzPBvBlMk%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="463" height="326" data-filename="Screenshot 2026-03-30 at 11.26.45.png" data-origin-width="1286" data-origin-height="906"/></span></figure> </p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 $25$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고1 30.png" data-origin-width="1490" data-origin-height="2122"><span data-url="https://blog.kakaocdn.net/dn/bdvnuJ/dJMcacCAdnY/KQMmrM0szHPkB9EoKQLVak/img.png" data-phocus="https://blog.kakaocdn.net/dn/bdvnuJ/dJMcacCAdnY/KQMmrM0szHPkB9EoKQLVak/img.png"><img src="https://blog.kakaocdn.net/dn/bdvnuJ/dJMcacCAdnY/KQMmrM0szHPkB9EoKQLVak/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbdvnuJ%2FdJMcacCAdnY%2FKQMmrM0szHPkB9EoKQLVak%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="1490" height="2122" data-filename="고1 30.png" data-origin-width="1490" data-origin-height="2122"/></span></figure> </div> </div> 수악중독 https://mathjk.tistory.com/6839 https://mathjk.tistory.com/6839#entry6839comment Tue, 31 Mar 2026 00:28:26 +0900 https://mathjk.tistory.com/6838 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과&nbsp;같이&nbsp;좌표평면&nbsp;위에&nbsp;원&nbsp;$\mathrm{C}&nbsp;:&nbsp;(x-7)^{2}+(y-3)^{2}=2$와&nbsp;점&nbsp;$\mathrm{A}(2,&nbsp;0)$이&nbsp;있다.&nbsp;원&nbsp;$\mathrm{C}$&nbsp;위의&nbsp;점&nbsp;$\mathrm{P}$,&nbsp;직선&nbsp;$y=x$&nbsp;위의&nbsp;점&nbsp;$\mathrm{Q}$에&nbsp;대하여&nbsp;$\overline{\mathrm{AQ}}+\overline{\mathrm{QP}}$의&nbsp;최솟값은?&nbsp;$[4\mathrm{점}]$</p> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-03-30 at 11.24.24.png" data-origin-width="958" data-origin-height="764"><span data-url="https://blog.kakaocdn.net/dn/oVZoH/dJMcafF4pSH/PB6NAQnNGRODm78T0WIAB1/img.png" data-phocus="https://blog.kakaocdn.net/dn/oVZoH/dJMcafF4pSH/PB6NAQnNGRODm78T0WIAB1/img.png"><img src="https://blog.kakaocdn.net/dn/oVZoH/dJMcafF4pSH/PB6NAQnNGRODm78T0WIAB1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FoVZoH%2FdJMcafF4pSH%2FPB6NAQnNGRODm78T0WIAB1%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="468" height="373" data-filename="Screenshot 2026-03-30 at 11.24.24.png" data-origin-width="958" data-origin-height="764"/></span></figure> </p> <p data-ke-size="size16"><br />①&nbsp;$3\sqrt{2}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$4\sqrt{2}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$5\sqrt{2}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$6\sqrt{2}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$7\sqrt{2}$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ②</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고2 14.png" data-origin-width="1416" data-origin-height="972"><span data-url="https://blog.kakaocdn.net/dn/qk1dh/dJMcadOW1GH/6augqdcEP6WTN8QUpcsK2k/img.png" data-phocus="https://blog.kakaocdn.net/dn/qk1dh/dJMcadOW1GH/6augqdcEP6WTN8QUpcsK2k/img.png"><img src="https://blog.kakaocdn.net/dn/qk1dh/dJMcadOW1GH/6augqdcEP6WTN8QUpcsK2k/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fqk1dh%2FdJMcadOW1GH%2F6augqdcEP6WTN8QUpcsK2k%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="578" height="397" data-filename="고2 14.png" data-origin-width="1416" data-origin-height="972"/></span></figure> </div> </div> (新 교육과정) 공통수학 - 문제풀이/도형의 방정식 수악중독 https://mathjk.tistory.com/6838 https://mathjk.tistory.com/6838#entry6838comment Tue, 31 Mar 2026 00:25:56 +0900 https://mathjk.tistory.com/6837 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;$x$에&nbsp;대한&nbsp;연립부등식<br />$$\begin{cases}&nbsp;x^{2}-2x-3&nbsp;\ge&nbsp;0&nbsp;\\&nbsp;(x+a)(x-a+2)&nbsp;&lt;&nbsp;0&nbsp;\end{cases}$$<br />을 만족시키는 정수 $x$의 개수가 $6$이 되도록 하는 모든 정수 $a$의 값의 합은?&nbsp;<br /><br />①&nbsp;$-2$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$-1$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$0$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$1$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$2$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답&nbsp;</b>⑤</span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고2 15.png" data-origin-width="1376" data-origin-height="2012"><span data-url="https://blog.kakaocdn.net/dn/cFR5c3/dJMcadOW1El/0BiMM5mKiBNSHZHT23t0y0/img.png" data-phocus="https://blog.kakaocdn.net/dn/cFR5c3/dJMcadOW1El/0BiMM5mKiBNSHZHT23t0y0/img.png"><img src="https://blog.kakaocdn.net/dn/cFR5c3/dJMcadOW1El/0BiMM5mKiBNSHZHT23t0y0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FcFR5c3%2FdJMcadOW1El%2F0BiMM5mKiBNSHZHT23t0y0%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="572" height="836" data-filename="고2 15.png" data-origin-width="1376" data-origin-height="2012"/></span></figure> </div> </div> (新 교육과정) 공통수학 - 문제풀이/방정식과 부등식 수악중독 https://mathjk.tistory.com/6837 https://mathjk.tistory.com/6837#entry6837comment Tue, 31 Mar 2026 00:21:11 +0900 https://mathjk.tistory.com/6836 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">서로 다른 동화책 $3$권, 서로 다른 시집 $3$권이 있다. 이 $6$권의 책을 다음 규칙에 따라 $1$학년 학생 $2$명과 $2$학년 학생 $3$명에게 남김없이 나누어 주는 경우의 수는? (단, $5$명의 학생 중 책을 한 권도 받지 못하는 학생은 없다.)&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <div class="txc-textbox" style="background-color: #dbe8fb; padding: 10px; border: 1px solid #dbe8fb;"> <p data-ke-size="size16">(가)&nbsp;동화책은&nbsp;$2$학년&nbsp;학생에게만&nbsp;나누어&nbsp;준다.<br />(나)&nbsp;시집을&nbsp;$2$권&nbsp;이상&nbsp;받는&nbsp;학생은&nbsp;없다.</p> </div> <p data-ke-size="size16"><br />①&nbsp;$168$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$180$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$192$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$204$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$216$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ⑤</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고2 16.png" data-origin-width="1554" data-origin-height="650"><span data-url="https://blog.kakaocdn.net/dn/n7vnh/dJMb99Z9521/tViSdkBd82VPs8pnXrTuak/img.png" data-phocus="https://blog.kakaocdn.net/dn/n7vnh/dJMb99Z9521/tViSdkBd82VPs8pnXrTuak/img.png"><img src="https://blog.kakaocdn.net/dn/n7vnh/dJMb99Z9521/tViSdkBd82VPs8pnXrTuak/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fn7vnh%2FdJMb99Z9521%2FtViSdkBd82VPs8pnXrTuak%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="562" height="235" data-filename="고2 16.png" data-origin-width="1554" data-origin-height="650"/></span></figure> </div> </div> (新 교육과정) 공통수학 - 문제풀이/경우의 수 수악중독 https://mathjk.tistory.com/6836 https://mathjk.tistory.com/6836#entry6836comment Mon, 30 Mar 2026 00:59:54 +0900 https://mathjk.tistory.com/6835 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과 같이 좌표평면 위에 원 $\mathrm{C} : (x-3)^{2}+(y-3)^{2}=9$와 직선 $y=mx$ ($0 &lt; m &lt; 1$)이 있다. 원 $\mathrm{C}$의 중심을 $\mathrm{A}$, 점 $\mathrm{A}$에서 직선 $y=mx$에 내린 수선의 발을 $\mathrm{H}$, 직선 $y=mx$가 원 $\mathrm{C}$와 만나는 두 점 중 원점 $\mathrm{O}$에 가까운 점을 $\mathrm{B}$라 할 때, $\overline{\mathrm{OH}} : \overline{\mathrm{BH}} = \sqrt{3} : 1$이다. 상수 $m$의 값은?&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-03-29 at 11.55.16.png" data-origin-width="1026" data-origin-height="818"><span data-url="https://blog.kakaocdn.net/dn/7lqcI/dJMcaaELiYE/HQvmE9W02KlBJj8U2bkvE0/img.png" data-phocus="https://blog.kakaocdn.net/dn/7lqcI/dJMcaaELiYE/HQvmE9W02KlBJj8U2bkvE0/img.png"><img src="https://blog.kakaocdn.net/dn/7lqcI/dJMcaaELiYE/HQvmE9W02KlBJj8U2bkvE0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2F7lqcI%2FdJMcaaELiYE%2FHQvmE9W02KlBJj8U2bkvE0%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="419" height="334" data-filename="Screenshot 2026-03-29 at 11.55.16.png" data-origin-width="1026" data-origin-height="818"/></span></figure> </p> <p data-ke-size="size16"><br /><br />① $-5+3\sqrt{3}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;② $- \dfrac{3}{2}-3\sqrt{3}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③ $2-\sqrt{3}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④ $\dfrac{11}{2}-3\sqrt{3}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤ $3-\dfrac{3\sqrt{3}}{2}$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ③</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고2 17.png" data-origin-width="1514" data-origin-height="1548"><span data-url="https://blog.kakaocdn.net/dn/yZxBq/dJMcabXXamU/QlMpmuU7qzxytGfH3LdPe0/img.png" data-phocus="https://blog.kakaocdn.net/dn/yZxBq/dJMcabXXamU/QlMpmuU7qzxytGfH3LdPe0/img.png"><img src="https://blog.kakaocdn.net/dn/yZxBq/dJMcabXXamU/QlMpmuU7qzxytGfH3LdPe0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FyZxBq%2FdJMcabXXamU%2FQlMpmuU7qzxytGfH3LdPe0%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="538" height="550" data-filename="고2 17.png" data-origin-width="1514" data-origin-height="1548"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> (新 교육과정) 공통수학 - 문제풀이/도형의 방정식 수악중독 https://mathjk.tistory.com/6835 https://mathjk.tistory.com/6835#entry6835comment Mon, 30 Mar 2026 00:57:54 +0900 https://mathjk.tistory.com/6834 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">최고차항의&nbsp;계수가&nbsp;$1$인&nbsp;이차함수&nbsp;$f(x)$가&nbsp;있다.&nbsp;$x$에&nbsp;대한&nbsp;방정식<br />$$f(x) \times \left( f(x)+\dfrac{1}{3}f(t)\right)=0$$<br />의 서로 다른 실근의 개수가 $3$이 되도록 하는 모든 실수 $t$의 값이 $-1, 7$일 때, $f(10)$의 값은?&nbsp;<br /><br />①&nbsp;$45$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$50$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$55$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$60$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$65$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ①</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고2 18.png" data-origin-width="1490" data-origin-height="1394"><span data-url="https://blog.kakaocdn.net/dn/bjFhuD/dJMcaaxY4Av/VPG8V90nEUX1g4DyZ95gcK/img.png" data-phocus="https://blog.kakaocdn.net/dn/bjFhuD/dJMcaaxY4Av/VPG8V90nEUX1g4DyZ95gcK/img.png"><img src="https://blog.kakaocdn.net/dn/bjFhuD/dJMcaaxY4Av/VPG8V90nEUX1g4DyZ95gcK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbjFhuD%2FdJMcaaxY4Av%2FVPG8V90nEUX1g4DyZ95gcK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="554" height="518" data-filename="고2 18.png" data-origin-width="1490" data-origin-height="1394"/></span></figure> </div> </div> (新 교육과정) 공통수학 - 문제풀이/방정식과 부등식 수악중독 https://mathjk.tistory.com/6834 https://mathjk.tistory.com/6834#entry6834comment Mon, 30 Mar 2026 00:53:14 +0900 https://mathjk.tistory.com/6833 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">집합 $X=\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$이 있다. 다음 조건을 만족시키는 집합 $X$의 두 부분집합 $A, \;&nbsp; B$에 대하여 집합 $B-A$의 모든 원소의 합의 최댓값은?&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <div class="txc-textbox" style="background-color: #dbe8fb; padding: 10px; border: 1px solid #dbe8fb;"> <p data-ke-size="size16">(가) $n(A \cap B)=2, n(B-A)=3$<br />(나) $p \in A \cap B$이면 $\dfrac{p+2}{3} \in B-A$이다.<br />(다) $q \in B-A$이면 $q+3 \in A$이다.</p> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16"><br />① $8$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;② $10$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③ $12$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④ $14$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤ $16$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ③</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고2 19.png" data-origin-width="1402" data-origin-height="2118"><span data-url="https://blog.kakaocdn.net/dn/AKJ0c/dJMcahX9ZKO/aTHILkYnjtco8EtMrpYZ21/img.png" data-phocus="https://blog.kakaocdn.net/dn/AKJ0c/dJMcahX9ZKO/aTHILkYnjtco8EtMrpYZ21/img.png"><img src="https://blog.kakaocdn.net/dn/AKJ0c/dJMcahX9ZKO/aTHILkYnjtco8EtMrpYZ21/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FAKJ0c%2FdJMcahX9ZKO%2FaTHILkYnjtco8EtMrpYZ21%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="543" height="820" data-filename="고2 19.png" data-origin-width="1402" data-origin-height="2118"/></span></figure> </div> </div> (新 교육과정) 공통수학 - 문제풀이/집합과 명제 수악중독 https://mathjk.tistory.com/6833 https://mathjk.tistory.com/6833#entry6833comment Mon, 30 Mar 2026 00:49:33 +0900 https://mathjk.tistory.com/6832 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">최고차항의&nbsp;계수가&nbsp;$1$인&nbsp;서로&nbsp;다른&nbsp;세&nbsp;이차다항식&nbsp;$f(x),&nbsp;g(x),&nbsp;h(x)$가&nbsp;다음&nbsp;조건을&nbsp;만족시킨다.</p> <p data-ke-size="size16">&nbsp;</p> <div class="txc-textbox" style="background-color: #dbe8fb; padding: 10px; border: 1px solid #dbe8fb;"> <p data-ke-size="size16">(가) 다항식 $f(x)g(x)$는 다항식 $(x-1)h(x)$로 나누어떨어진다.<br />(나)&nbsp;다항식&nbsp;$g(x)h(x)$는&nbsp;다항식&nbsp;$(x-2)f(x)$로&nbsp;나누어떨어진다.</p> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">$f(-1)+g(-1)=18$일 때, $h(0)$의 값은?&nbsp;<br /><br />① $4$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;② $6$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③ $8$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④ $10$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤ $12$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ④</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고2 20.png" data-origin-width="1576" data-origin-height="1760"><span data-url="https://blog.kakaocdn.net/dn/2MmZJ/dJMcaiW1Z3V/tkB3kvtY44UulVjcJccvfK/img.png" data-phocus="https://blog.kakaocdn.net/dn/2MmZJ/dJMcaiW1Z3V/tkB3kvtY44UulVjcJccvfK/img.png"><img src="https://blog.kakaocdn.net/dn/2MmZJ/dJMcaiW1Z3V/tkB3kvtY44UulVjcJccvfK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2F2MmZJ%2FdJMcaiW1Z3V%2FtkB3kvtY44UulVjcJccvfK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="637" height="711" data-filename="고2 20.png" data-origin-width="1576" data-origin-height="1760"/></span></figure> </div> </div> (新 교육과정) 공통수학 - 문제풀이/다항식 수악중독 https://mathjk.tistory.com/6832 https://mathjk.tistory.com/6832#entry6832comment Mon, 30 Mar 2026 00:44:05 +0900 https://mathjk.tistory.com/6831 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">실수 전체의 집합에서 정의되고 역함수를 갖는 두 함수 $f(x), g(x)$가 모든 실수 $x$에 대하여 $$g(f(x))=x-2$$를 만족시킨다. 좌표평면에서 함수 $y=f(x)$의 그래프는 직선 $y=kx$ ($k &gt; 1$)와 서로 다른 두 점 $\mathrm{A, B}$에서만 만나고, 두 점 $\mathrm{A, B}$는 원 $(x-13)^{2}+(y-13)^{2}=26$ 위에 있다. $\overline{\mathrm{AB}}=2\sqrt{13}$일 때, $x$에 대한 방정식 $g(x)=\dfrac{1}{k}x-2$의 모든 실근은 $\alpha, \beta$ ($\alpha &lt; \beta$)이다. $\beta-\alpha$의 값은? (단, $k$는 상수이다.)&nbsp;<br /><br />①&nbsp;$5$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$\dfrac{11}{2}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$6$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$\dfrac{13}{2}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$7$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ③</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고2 20-1.png" data-origin-width="1440" data-origin-height="2104"><span data-url="https://blog.kakaocdn.net/dn/0WkO9/dJMcahjAvNN/sMtU5zMJX7OkbJQfDVwsGk/img.png" data-phocus="https://blog.kakaocdn.net/dn/0WkO9/dJMcahjAvNN/sMtU5zMJX7OkbJQfDVwsGk/img.png"><img src="https://blog.kakaocdn.net/dn/0WkO9/dJMcahjAvNN/sMtU5zMJX7OkbJQfDVwsGk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2F0WkO9%2FdJMcahjAvNN%2FsMtU5zMJX7OkbJQfDVwsGk%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="685" height="1001" data-filename="고2 20-1.png" data-origin-width="1440" data-origin-height="2104"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고2 20-2.png" data-origin-width="1300" data-origin-height="960"><span data-url="https://blog.kakaocdn.net/dn/dz89S8/dJMcadIa9yG/oLkrMfAH88CnzWbdzfR3J0/img.png" data-phocus="https://blog.kakaocdn.net/dn/dz89S8/dJMcadIa9yG/oLkrMfAH88CnzWbdzfR3J0/img.png"><img src="https://blog.kakaocdn.net/dn/dz89S8/dJMcadIa9yG/oLkrMfAH88CnzWbdzfR3J0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fdz89S8%2FdJMcadIa9yG%2FoLkrMfAH88CnzWbdzfR3J0%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="669" height="494" data-filename="고2 20-2.png" data-origin-width="1300" data-origin-height="960"/></span></figure> <p data-ke-size="size16">&nbsp;</p> </div> </div> (新 교육과정) 공통수학 - 문제풀이/함수와 그래프 수악중독 https://mathjk.tistory.com/6831 https://mathjk.tistory.com/6831#entry6831comment Sun, 29 Mar 2026 00:41:45 +0900 https://mathjk.tistory.com/6830 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">두 실수 $a$ ($a \ne 0$), $b$에 대하여 이차함수 $f(x)$를 $f(x)=a(x-2)^{2}+b$라 하자. 모든 실수 $k$에 대하여 $-k^2 \le x \le k^2+3$에서 함수 $f(x)$의 최댓값이 $3k^4+12k^2$일 때, $a^2+b^2$의 값을 구하시오.&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 $153$</b></span></p> <p data-ke-size="size16">&nbsp;</p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고2 26.png" data-origin-width="1252" data-origin-height="1400"><span data-url="https://blog.kakaocdn.net/dn/7ol6Q/dJMcafF24Sw/5I140UQtcbozKzB7cipgMk/img.png" data-phocus="https://blog.kakaocdn.net/dn/7ol6Q/dJMcafF24Sw/5I140UQtcbozKzB7cipgMk/img.png"><img src="https://blog.kakaocdn.net/dn/7ol6Q/dJMcafF24Sw/5I140UQtcbozKzB7cipgMk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2F7ol6Q%2FdJMcafF24Sw%2F5I140UQtcbozKzB7cipgMk%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="517" height="578" data-filename="고2 26.png" data-origin-width="1252" data-origin-height="1400"/></span></figure> </div> </div> (新 교육과정) 공통수학 - 문제풀이/방정식과 부등식 수악중독 https://mathjk.tistory.com/6830 https://mathjk.tistory.com/6830#entry6830comment Sun, 29 Mar 2026 00:38:03 +0900 https://mathjk.tistory.com/6829 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과 같이 좌석 번호가 적힌 $8$개의 의자가 배열되어 있다. 네 학생 $\mathrm{A, B, C, D}$가 다음 규칙에 따라 $8$개의 의자 중에서 서로 다른 $4$개의 의자에 앉는 경우의 수를 구하시오.&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <div class="txc-textbox" style="background-color: #dbe8fb; padding: 10px; border: 1px solid #dbe8fb;"> <p data-ke-size="size16">(가)&nbsp;$\mathrm{A}$가&nbsp;앉는&nbsp;의자의&nbsp;좌석&nbsp;번호는&nbsp;홀수이다.<br />(나)&nbsp;$\mathrm{B}$가&nbsp;앉는&nbsp;의자의&nbsp;좌석&nbsp;번호는&nbsp;$32$&nbsp;이하이다.<br />(다)&nbsp;$\mathrm{C}$와&nbsp;$\mathrm{D}$가&nbsp;앉는&nbsp;두&nbsp;의자의&nbsp;좌석&nbsp;번호는&nbsp;각각&nbsp;$31$&nbsp;이상이다.</p> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 $150$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고2 27.png" data-origin-width="1306" data-origin-height="2262"><span data-url="https://blog.kakaocdn.net/dn/b0DiYI/dJMcacbtGbW/n6aE1lgnuNhNj9pdz4rmO1/img.png" data-phocus="https://blog.kakaocdn.net/dn/b0DiYI/dJMcacbtGbW/n6aE1lgnuNhNj9pdz4rmO1/img.png"><img src="https://blog.kakaocdn.net/dn/b0DiYI/dJMcacbtGbW/n6aE1lgnuNhNj9pdz4rmO1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fb0DiYI%2FdJMcacbtGbW%2Fn6aE1lgnuNhNj9pdz4rmO1%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="646" height="1119" data-filename="고2 27.png" data-origin-width="1306" data-origin-height="2262"/></span></figure> </div> </div> (新 교육과정) 공통수학 - 문제풀이/경우의 수 수악중독 https://mathjk.tistory.com/6829 https://mathjk.tistory.com/6829#entry6829comment Sun, 29 Mar 2026 00:34:36 +0900 https://mathjk.tistory.com/6828 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">집합 $\mathrm{X}=\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$에 대하여 함수 $f : \mathrm{X} \to \mathrm{X}$는 $f(k) = (3^{k} \text{의 일의 자리의 수})$이다. 다음 조건을 만족시키는 집합 $\mathrm{A}$에 대하여 $n(\mathrm{A})$의 모든 원소의 합의 최댓값을 구하시오.</p> <p data-ke-size="size16">&nbsp;</p> <div class="txc-textbox" style="background-color: #dbe8fb; padding: 10px; border: 1px solid #dbe8fb;"> <p data-ke-size="size16">(가)&nbsp;$\mathrm{A}&nbsp;\subset&nbsp;\mathrm{X},&nbsp;n(\mathrm{A})&nbsp;\ge&nbsp;2$<br />(나)&nbsp;집합&nbsp;$\mathrm{A}$의&nbsp;임의의&nbsp;원소&nbsp;$a$에&nbsp;대하여&nbsp;$a&nbsp;\ne&nbsp;f(a)$이고,&nbsp;$(f&nbsp;\circ&nbsp;f)(a)=7$이다.<br />(다) 집합 $\mathrm{A}$의 임의의 두 원소 $x, y$에 대하여 $x &lt; y$이면 $f(x) \le f(y)$이다.</p> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 $11$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고2 28-1.png" data-origin-width="1316" data-origin-height="1182"><span data-url="https://blog.kakaocdn.net/dn/dmgtPd/dJMcabwQ8VM/vX07NlTdVDSBvz7W1p1K5k/img.png" data-phocus="https://blog.kakaocdn.net/dn/dmgtPd/dJMcabwQ8VM/vX07NlTdVDSBvz7W1p1K5k/img.png"><img src="https://blog.kakaocdn.net/dn/dmgtPd/dJMcabwQ8VM/vX07NlTdVDSBvz7W1p1K5k/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FdmgtPd%2FdJMcabwQ8VM%2FvX07NlTdVDSBvz7W1p1K5k%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="572" height="514" data-filename="고2 28-1.png" data-origin-width="1316" data-origin-height="1182"/></span></figure> <p data-ke-size="size16">&nbsp;</p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고2 28-2.png" data-origin-width="1242" data-origin-height="1640"><span data-url="https://blog.kakaocdn.net/dn/bvdv0a/dJMcaf65ZSu/SyoSqMSPwXHG9DFka2aReK/img.png" data-phocus="https://blog.kakaocdn.net/dn/bvdv0a/dJMcaf65ZSu/SyoSqMSPwXHG9DFka2aReK/img.png"><img src="https://blog.kakaocdn.net/dn/bvdv0a/dJMcaf65ZSu/SyoSqMSPwXHG9DFka2aReK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fbvdv0a%2FdJMcaf65ZSu%2FSyoSqMSPwXHG9DFka2aReK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="569" height="751" data-filename="고2 28-2.png" data-origin-width="1242" data-origin-height="1640"/></span></figure> </div> </div> (新 교육과정) 공통수학 - 문제풀이/함수와 그래프 수악중독 https://mathjk.tistory.com/6828 https://mathjk.tistory.com/6828#entry6828comment Sun, 29 Mar 2026 00:32:57 +0900 https://mathjk.tistory.com/6827 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">영행렬이 아닌 두 행 $\mathrm{A}=\begin{pmatrix} a_{11} &amp; a_{12} \\ a_{21} &amp; a_{22} \end{pmatrix}, \mathrm{B}=\begin{pmatrix} b_{11} &amp; b_{12} \\ b_{21} &amp; b_{22} \end{pmatrix}$가 $\mathrm{A}^{2}=\mathrm{B}$이고, 각 행렬의 성분은 다음 조건을 만족시킨다.</p> <p data-ke-size="size16">&nbsp;</p> <div class="txc-textbox" style="background-color: #dbe8fb; padding: 10px; border: 1px solid #dbe8fb;"> <p data-ke-size="size16">(가)&nbsp;모든&nbsp;$i,&nbsp;j$&nbsp;($i=1,&nbsp;2,&nbsp;j=1,&nbsp;2$)에&nbsp;대하여&nbsp;$a_{ij}&nbsp;\times&nbsp;b_{ij}&nbsp;=&nbsp;0$이다.<br />(나)&nbsp;모든&nbsp;$i,&nbsp;j$&nbsp;($i=1,&nbsp;2,&nbsp;j=1,&nbsp;2$)에&nbsp;대하여&nbsp;$a_{ij}&nbsp;+&nbsp;b_{ij}&nbsp;\ne&nbsp;0$이다.</p> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">행렬 $\mathrm{A}+\mathrm{B}$의 모든 성분의 합이 $-1$, 곱이 $-8$일 때, $(a_{12})^{3}+(a_{21})^{3}$의 값을 구하시오. (단, $\mathrm{A}^{2}=\mathrm{AA}$이고, 행렬 $\mathrm{A}$의 모든 성분은 실수이다.)&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 $45$</b></span></p> <figure class="imageblock alignLeft" data-ke-mobileStyle="widthOrigin" data-filename="고2 29.png" data-origin-width="1216" data-origin-height="2332"><span data-url="https://blog.kakaocdn.net/dn/pHTtM/dJMcaadF1e4/Rte8tLen6tFwB58Ycc5aO0/img.png" data-phocus="https://blog.kakaocdn.net/dn/pHTtM/dJMcaadF1e4/Rte8tLen6tFwB58Ycc5aO0/img.png"><img src="https://blog.kakaocdn.net/dn/pHTtM/dJMcaadF1e4/Rte8tLen6tFwB58Ycc5aO0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FpHTtM%2FdJMcaadF1e4%2FRte8tLen6tFwB58Ycc5aO0%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="493" height="2332" data-filename="고2 29.png" data-origin-width="1216" data-origin-height="2332"/></span></figure> </div> </div> (新 교육과정) 공통수학 - 문제풀이/행렬 수악중독 https://mathjk.tistory.com/6827 https://mathjk.tistory.com/6827#entry6827comment Sun, 29 Mar 2026 00:30:24 +0900 https://mathjk.tistory.com/6826 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">$0$이 아닌 정수 $a$와 유리수 $b$ $\left (b &gt; \dfrac{4}{a} \right )$에 대하여 함수 $f(x)$를<br />$$f(x) = \begin{cases} \left| \dfrac{ax-4}{x-b} \right| &amp; (x &lt; \dfrac{4}{a} \text{ 또는 } x &gt; b) \\ ax^{2}-4bx &amp; (\dfrac{4}{a} \le x \le b) \end{cases}$$<br />라 하자. 함수 $f(x)$가 다음 조건을 만족시키도록 하는 $a, b$의 모든 순서쌍이 $(a_{1}, b_{1}), (a_{2}, b_{2})$일 때, $a_{1} \times b_{1} \times a_{2} \times b_{2}$의 값을 구하시오. $</p> <p data-ke-size="size16">&nbsp;</p> <div class="txc-textbox" style="background-color: #dbe8fb; padding: 10px; border: 1px solid #dbe8fb;"> <p data-ke-size="size16">(가) 함수 $f(x)$는 일대일함수이다.<br />(나) $y$에 대한 방정식 $f(x)=k$의 해가 존재하지 않도록 하는 양수 $k$의 값을 $p$라 하고, 함수 $f(x)$의 최솟값을 $m$이라 할 때, $p \times m = -64$이다.</p> </div> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 $24$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고2-30-1.png" data-origin-width="1466" data-origin-height="2332"><span data-url="https://blog.kakaocdn.net/dn/Ay7NE/dJMb99Z9bTC/4KI7qalv0A1Ksv8MlbsRH0/img.png" data-phocus="https://blog.kakaocdn.net/dn/Ay7NE/dJMb99Z9bTC/4KI7qalv0A1Ksv8MlbsRH0/img.png"><img src="https://blog.kakaocdn.net/dn/Ay7NE/dJMb99Z9bTC/4KI7qalv0A1Ksv8MlbsRH0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FAy7NE%2FdJMb99Z9bTC%2F4KI7qalv0A1Ksv8MlbsRH0%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="698" height="1110" data-filename="고2-30-1.png" data-origin-width="1466" data-origin-height="2332"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고2-30-2.png" data-origin-width="1432" data-origin-height="1704"><span data-url="https://blog.kakaocdn.net/dn/3v94l/dJMcahRm5yR/cTZC5XUKRyKqxeJtVjKnm1/img.png" data-phocus="https://blog.kakaocdn.net/dn/3v94l/dJMcahRm5yR/cTZC5XUKRyKqxeJtVjKnm1/img.png"><img src="https://blog.kakaocdn.net/dn/3v94l/dJMcahRm5yR/cTZC5XUKRyKqxeJtVjKnm1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2F3v94l%2FdJMcahRm5yR%2FcTZC5XUKRyKqxeJtVjKnm1%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="693" height="825" data-filename="고2-30-2.png" data-origin-width="1432" data-origin-height="1704"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="고2-30-3.png" data-origin-width="1486" data-origin-height="1132"><span data-url="https://blog.kakaocdn.net/dn/xO4Ex/dJMcaaxYaNX/s4HkQfkVnvXTNkfjkcZK11/img.png" data-phocus="https://blog.kakaocdn.net/dn/xO4Ex/dJMcaaxYaNX/s4HkQfkVnvXTNkfjkcZK11/img.png"><img src="https://blog.kakaocdn.net/dn/xO4Ex/dJMcaaxYaNX/s4HkQfkVnvXTNkfjkcZK11/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FxO4Ex%2FdJMcaaxYaNX%2Fs4HkQfkVnvXTNkfjkcZK11%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="694" height="529" data-filename="고2-30-3.png" data-origin-width="1486" data-origin-height="1132"/></span></figure> </div> </div> <p data-ke-size="size16"><br /><br /></p> (고1) 수학 - 문제풀이/함수와 그래프 수악중독 https://mathjk.tistory.com/6826 https://mathjk.tistory.com/6826#entry6826comment Sat, 28 Mar 2026 03:47:08 +0900 https://mathjk.tistory.com/6825 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">닫힌구간 $[1, 3]$ 에서 함수 $f(x)=2x^{3}-3x^{2}-12x+k$ 가 최댓값 $\mathrm{M}$, 최솟값 $4$ 를 가질 때, $\mathrm{M}$ 의 값은? (단, $k$ 는 상수이다.)&nbsp;<br /><br />①&nbsp;$13$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$14$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$15$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$16$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$17$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ③</b></span></p> <figure class="imageblock alignLeft" data-ke-mobileStyle="widthOrigin" data-filename="9.png" data-origin-width="1210" data-origin-height="900"><span data-url="https://blog.kakaocdn.net/dn/M2s68/dJMcahKDgqz/JwkFEd7wzuaz9cUuOqMid1/img.png" data-phocus="https://blog.kakaocdn.net/dn/M2s68/dJMcahKDgqz/JwkFEd7wzuaz9cUuOqMid1/img.png"><img src="https://blog.kakaocdn.net/dn/M2s68/dJMcahKDgqz/JwkFEd7wzuaz9cUuOqMid1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FM2s68%2FdJMcahKDgqz%2FJwkFEd7wzuaz9cUuOqMid1%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="427" height="318" data-filename="9.png" data-origin-width="1210" data-origin-height="900"/></span></figure> </div> </div> 수학2 - 문제풀이/미분 수악중독 https://mathjk.tistory.com/6825 https://mathjk.tistory.com/6825#entry6825comment Sat, 28 Mar 2026 03:43:13 +0900 https://mathjk.tistory.com/6824 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">양수 $k$ 에 대하여 곡선 $y=\log_{2}(x-k)$ 가 $x$ 축과 만나는 점을 $a$ 라 하자. 직선 $y=2$ 가 곡선 $y=\log_{2}(x-k)$ 와 만나는 점을 $\mathrm{B}, y$ 축과 만나는 점을 $\mathrm{C}$ 라 하자. $\overline{\mathrm{AB}}=\overline{\mathrm{AC}}$ 일 때, 삼각형 $\mathrm{ABC}$ 의 넓이는?&nbsp;<br /><br />①&nbsp;$4$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$6$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$8$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$10$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$12$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답&nbsp;</b>②</span></p> <figure class="imageblock alignLeft" data-ke-mobileStyle="widthOrigin" data-filename="10.png" data-origin-width="1332" data-origin-height="862"><span data-url="https://blog.kakaocdn.net/dn/cBMWzh/dJMb99Mynaz/Up6fRKg4I7ngOwZVnjPpeK/img.png" data-phocus="https://blog.kakaocdn.net/dn/cBMWzh/dJMb99Mynaz/Up6fRKg4I7ngOwZVnjPpeK/img.png"><img src="https://blog.kakaocdn.net/dn/cBMWzh/dJMb99Mynaz/Up6fRKg4I7ngOwZVnjPpeK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FcBMWzh%2FdJMb99Mynaz%2FUp6fRKg4I7ngOwZVnjPpeK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="497" height="322" data-filename="10.png" data-origin-width="1332" data-origin-height="862"/></span></figure> </div> </div> 수학1- 문제풀이/지수함수와 로그함수 수악중독 https://mathjk.tistory.com/6824 https://mathjk.tistory.com/6824#entry6824comment Sat, 28 Mar 2026 03:40:30 +0900 https://mathjk.tistory.com/6823 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">시각 $t=0$ 일 때 원점을 출발하여 수직선 위를 움직이는 점 $\mathrm{P}$ 가 있다. 시각 $t$ ($t \ge 0$)일 때 점 $\mathrm{P}$ 의 속도 $v(t)$ 가<br />$$v(t)=3t^{2}-24t+36$$<br />이다. &lt;보기&gt;에서 옳은 것만을 있는 대로 고른 것은?&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <div class="txc-textbox" style="background-color: #fefeb8; padding: 10px; border: 1px solid #fefeb8;"> <p data-ke-size="size16">ㄱ.&nbsp;시각&nbsp;$t=1$&nbsp;일&nbsp;때&nbsp;점&nbsp;$\mathrm{P}$&nbsp;의&nbsp;위치는&nbsp;$25$&nbsp;이다.<br />ㄴ.&nbsp;출발한&nbsp;후&nbsp;점&nbsp;$\mathrm{P}$&nbsp;의&nbsp;운동&nbsp;방향은&nbsp;두&nbsp;번&nbsp;바뀐다.<br />ㄷ.&nbsp;시각&nbsp;$t=0$&nbsp;에서&nbsp;$t=3$&nbsp;까지&nbsp;점&nbsp;$\mathrm{P}$&nbsp;가&nbsp;움직인&nbsp;거리는&nbsp;$37$&nbsp;이다.</p> </div> <p data-ke-size="size16"><br />① ㄱ&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;② ㄴ&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③ ㄱ, ㄴ&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④ ㄱ, ㄷ&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤ ㄱ, ㄴ, ㄷ</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ⑤</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="11.png" data-origin-width="1434" data-origin-height="1276"><span data-url="https://blog.kakaocdn.net/dn/Fjhp3/dJMcagx9rKr/xKtANb4EFp6MqGnEuyJsak/img.png" data-phocus="https://blog.kakaocdn.net/dn/Fjhp3/dJMcagx9rKr/xKtANb4EFp6MqGnEuyJsak/img.png"><img src="https://blog.kakaocdn.net/dn/Fjhp3/dJMcagx9rKr/xKtANb4EFp6MqGnEuyJsak/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FFjhp3%2FdJMcagx9rKr%2FxKtANb4EFp6MqGnEuyJsak%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="529" height="471" data-filename="11.png" data-origin-width="1434" data-origin-height="1276"/></span></figure> </div> </div> 수학2 - 문제풀이/미분 수악중독 https://mathjk.tistory.com/6823 https://mathjk.tistory.com/6823#entry6823comment Sat, 28 Mar 2026 03:35:41 +0900 https://mathjk.tistory.com/6822 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">$a_{1}=3,&nbsp;a_{2}=10$&nbsp;인&nbsp;수열&nbsp;$\{a_{n}\}$&nbsp;과&nbsp;모든&nbsp;항이&nbsp;양수인&nbsp;등비수열&nbsp;$\{\mathrm{b}_{n}\}$&nbsp;이&nbsp;모든&nbsp;자연수&nbsp;$n$&nbsp;에&nbsp;대하여<br />$$\sum_{k=1}^{n}&nbsp;\dfrac{a_{k}}{\mathrm{b}_{k}+1}&nbsp;=&nbsp;n^{2}+n$$<br />을 만족시킨다. 다음은 $\displaystyle {\sum_{n=1}^{5} \dfrac{a_{n}}{n}}$ 의 값을 구하는 과정이다.</p> <p data-ke-size="size16">&nbsp;</p> <div class="txc-textbox" style="background-color: #e7fdb5; padding: 10px; border: 1px solid #e7fdb5;"> <p data-ke-size="size16">$n=1$&nbsp;일&nbsp;때&nbsp;$\dfrac{a_{1}}{\mathrm{b}_{1}+1}=2$&nbsp;에서&nbsp;$\mathrm{b}_{1}=\dfrac{1}{2}$&nbsp;이다.<br />$2$&nbsp;이상의&nbsp;모든&nbsp;자연수&nbsp;$n$&nbsp;에&nbsp;대하여<br />$\dfrac{a_{n}}{b_{n}+1} = \displaystyle {\sum_{k=1}^{n} \dfrac{a_{k}}{\mathrm{b}_{k}+1} - \sum_{k=1}^{n-1} \dfrac{a_{k}}{\mathrm{b}_{k}+1}}$ 이므로<br />$\dfrac{a_{n}}{b_{n}+1} = \text{(가)} \times n$ 이다.<br />$n=1$&nbsp;일&nbsp;때도&nbsp;이&nbsp;성립하므로&nbsp;모든&nbsp;자연수&nbsp;$n$&nbsp;에&nbsp;대하여&nbsp;$\dfrac{a_{n}}{n}&nbsp;=&nbsp;\text{(가)}&nbsp;\times&nbsp;(\mathrm{b}_{n}+1)$&nbsp;이다.<br />그러므로 등비수열 $\{b_{n}\}$ 의 공비는 (나) 이다.<br />따라서 에 의하여 $\displaystyle{\sum_{n=1}^{5} \dfrac{a_{n}}{n}} = \text{(다)}$ 이다.</p> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">위의 (가), (나), (다)에 알맞은 수를 각각 $p, q, r$ 이라 할 때, $p+q+r$ 의 값은?&nbsp;<br /><br />①&nbsp;$136$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$137$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$138$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$139$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$140$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ①</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="12.png" data-origin-width="1372" data-origin-height="1712"><span data-url="https://blog.kakaocdn.net/dn/pDUeN/dJMcaco0CeL/1xJCVKqxFwYWWhBiEN5W7k/img.png" data-phocus="https://blog.kakaocdn.net/dn/pDUeN/dJMcaco0CeL/1xJCVKqxFwYWWhBiEN5W7k/img.png"><img src="https://blog.kakaocdn.net/dn/pDUeN/dJMcaco0CeL/1xJCVKqxFwYWWhBiEN5W7k/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FpDUeN%2FdJMcaco0CeL%2F1xJCVKqxFwYWWhBiEN5W7k%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="515" height="643" data-filename="12.png" data-origin-width="1372" data-origin-height="1712"/></span></figure> </div> </div> 수학1- 문제풀이/수열 수악중독 https://mathjk.tistory.com/6822 https://mathjk.tistory.com/6822#entry6822comment Sat, 28 Mar 2026 03:33:17 +0900 https://mathjk.tistory.com/6821 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">함수 $f(x)=x^{3}-4x^{2}+6x-8$ 에 대하여 곡선 $y=f(x)$ 위의 점 $\mathrm{P}(1, -5)$ 에서의 접선이 곡선 $y=f(x)$ 와 만나는 점 중 $\mathrm{P}$ 가 아닌 점을 $\mathrm{Q}$ 라 하자. 곡선 $y=f(x)$ 위의 점 $\mathrm{Q}$ 에서의 접선과 $x$ 축, $y$ 축으로 둘러싸인 도형의 넓이는?&nbsp;<br /><br />①&nbsp;$8$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$10$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$12$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$14$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$16$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ⑤</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="13.png" data-origin-width="914" data-origin-height="1134"><span data-url="https://blog.kakaocdn.net/dn/cibX0z/dJMcad2rF5Y/ePdI6nXTozoCVQ7ZauxsJK/img.png" data-phocus="https://blog.kakaocdn.net/dn/cibX0z/dJMcad2rF5Y/ePdI6nXTozoCVQ7ZauxsJK/img.png"><img src="https://blog.kakaocdn.net/dn/cibX0z/dJMcad2rF5Y/ePdI6nXTozoCVQ7ZauxsJK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FcibX0z%2FdJMcad2rF5Y%2FePdI6nXTozoCVQ7ZauxsJK%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="914" height="1134" data-filename="13.png" data-origin-width="914" data-origin-height="1134"/></span></figure> </div> </div> 수학2 - 문제풀이/미분 수악중독 https://mathjk.tistory.com/6821 https://mathjk.tistory.com/6821#entry6821comment Fri, 27 Mar 2026 00:20:47 +0900 https://mathjk.tistory.com/6820 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">두&nbsp;상수&nbsp;$a$&nbsp;($a&nbsp;\ne&nbsp;0$),&nbsp;$b$&nbsp;에&nbsp;대하여&nbsp;닫힌구간&nbsp;$[0,&nbsp;2\pi]$&nbsp;에서&nbsp;정의된&nbsp;함수<br />$$f(x)&nbsp;=&nbsp;\begin{cases}&nbsp;3&nbsp;\sin&nbsp;x&nbsp;&amp;&nbsp;(0&nbsp;\le&nbsp;x&nbsp;&lt;&nbsp;\pi)&nbsp;\\&nbsp;a&nbsp;\cos&nbsp;x&nbsp;+&nbsp;b&nbsp;&amp;&nbsp;(\pi&nbsp;\le&nbsp;x&nbsp;\le&nbsp;2\pi)&nbsp;\end{cases}$$<br />가 있다. $0 \le t \le 2\pi$ 인 실수 $t$ 에 대하여 $x$ 에 대한 방정식 $f(x)=f(t)$ 를 만족시키는 모든 $x$ 의 값의 합이 $\dfrac{7}{4}\pi$ 가 되도록 하는 서로 다른 모든 실수 $t$ 의 개수가 $4$ 일 때, $a^{2}+b^{2}$ 의 값은?&nbsp;<br /><br />①&nbsp;$\dfrac{13}{2}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$\dfrac{27}{4}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$7$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$\dfrac{29}{4}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$\dfrac{15}{2}$</p> <p data-ke-size="size16">&nbsp;</p> <div data-ke-type="moreLess" data-text-more="풀이보기" data-text-less="풀이닫기"><a class="btn-toggle-moreless">더보기</a> <div class="moreless-content"> <p data-ke-size="size16"><span style="color: #ee2323;"><b>정답 ②</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="14.png" data-origin-width="1014" data-origin-height="2390"><span data-url="https://blog.kakaocdn.net/dn/uvsxt/dJMcaakpckc/EGy9S4oIPCTu1d6MdwzqNk/img.png" data-phocus="https://blog.kakaocdn.net/dn/uvsxt/dJMcaakpckc/EGy9S4oIPCTu1d6MdwzqNk/img.png"><img src="https://blog.kakaocdn.net/dn/uvsxt/dJMcaakpckc/EGy9S4oIPCTu1d6MdwzqNk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fuvsxt%2FdJMcaakpckc%2FEGy9S4oIPCTu1d6MdwzqNk%2Fimg.png" onerror="this.onerror=null; this.src='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png'; this.srcset='//t1.daumcdn.net/tistory_admin/static/images/no-image-v1.png';" loading="lazy" width="1014" height="2390" data-filename="14.png" data-origin-width="1014" data-origin-height="2390"/></span></figure> </div> </div> 수학1- 문제풀이/삼각함수 수악중독 https://mathjk.tistory.com/6820 https://mathjk.tistory.com/6820#entry6820comment Fri, 27 Mar 2026 00:19:21 +0900