https://mathjk.tistory.com/ 수학의 즐거움에 중독되다! 고등학교 수학 개념 및 문제 풀이 ko Wed, 17 Jun 2026 18:39:36 +0900 TISTORY 100 수악중독 https://tistory1.daumcdn.net/tistory/23799/attach/1bac5a872a5043a59cd49c144886add0 https://mathjk.tistory.com https://mathjk.tistory.com/6920 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">세 다항식 $2x^{3}+3x^{2}+x+1$, $3x^{3}+8x^{2}+3x$, $5x^{3}+12x^{2}+3x-1$을 최고차항의 계수가 $1$인 이차다항식 $P(x)$로 나눈 나머지가 각각 $R(x)$, $2R(x)$, $3R(x)$ 이다. $P(3)$의 값은?<br /><br />①&nbsp;$1$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$2$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$3$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$4$&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="Screenshot 2026-06-09 at 12.09.48.png" data-origin-width="1528" data-origin-height="1522"><span data-url="https://blog.kakaocdn.net/dn/cS32eR/dJMcaiQ8NWn/hke1T8uIKG6m9mLhwcbKQ1/img.png" data-phocus="https://blog.kakaocdn.net/dn/cS32eR/dJMcaiQ8NWn/hke1T8uIKG6m9mLhwcbKQ1/img.png"><img src="https://blog.kakaocdn.net/dn/cS32eR/dJMcaiQ8NWn/hke1T8uIKG6m9mLhwcbKQ1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FcS32eR%2FdJMcaiQ8NWn%2Fhke1T8uIKG6m9mLhwcbKQ1%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="598" data-filename="Screenshot 2026-06-09 at 12.09.48.png" data-origin-width="1528" data-origin-height="1522"/></span></figure> <p data-ke-size="size16">&nbsp;</p> </div> </div> <p data-ke-size="size16">&nbsp;</p> (新 교육과정) 공통수학 - 문제풀이/다항식 수악중독 https://mathjk.tistory.com/6920 https://mathjk.tistory.com/6920#entry6920comment Wed, 10 Jun 2026 01:10:46 +0900 https://mathjk.tistory.com/6919 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과 같이 한 변의 길이가 $2$인 정사각형 $\mathrm{ABCD}$에서 선분 $\mathrm{BC}$의 연장선 위에 $\overline{\mathrm{BF}}=\overline{\mathrm{CG}}$가 되도록 두 점 $\mathrm{F}, \; \mathrm{G}$를 잡는다. 선분 $\mathrm{FG}$를 한 변으로 하고 점 $\mathrm{E}$를 꼭짓점으로 갖는 정삼각형 $\mathrm{EFG}$가 선분 $\mathrm{AD}$와 두 점에서 만난다.</p> <p data-ke-size="size16">선분 $\mathrm{EF}$가 선분 $\mathrm{AD}$, 선분 $\mathrm{AB}$와 만나는 점을 각각 $\mathrm{H}, \; \mathrm{I}$라 하고, 선분 $\mathrm{EG}$가 선분 $\mathrm{AD}$, 선분 $\mathrm{CD}$와 만나는 점을 각각 $\mathrm{J}, \; \mathrm{K}$라 하자.</p> <p data-ke-size="size16">삼각형 $\mathrm{EHJ}$의 넓이와 삼각형 $\mathrm{AIH}$의 넓이의 합의 최솟값은? (단, $\dfrac{2\sqrt{3}}{3} -1 &lt; \overline{\mathrm{BF}} &lt; \dfrac{2\sqrt{3}}{3}$)</p> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-09 at 12.04.46.png" data-origin-width="886" data-origin-height="808"><span data-url="https://blog.kakaocdn.net/dn/mnul8/dJMcajvLjfE/DJTvJPLwAUkkfgL71yy1v1/img.png" data-phocus="https://blog.kakaocdn.net/dn/mnul8/dJMcajvLjfE/DJTvJPLwAUkkfgL71yy1v1/img.png"><img src="https://blog.kakaocdn.net/dn/mnul8/dJMcajvLjfE/DJTvJPLwAUkkfgL71yy1v1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fmnul8%2FdJMcajvLjfE%2FDJTvJPLwAUkkfgL71yy1v1%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="407" height="371" data-filename="Screenshot 2026-06-09 at 12.04.46.png" data-origin-width="886" data-origin-height="808"/></span></figure> </p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16"><br />① $\dfrac{\sqrt{3}}{6}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;② $\dfrac{\sqrt{3}}{3}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ③ $\dfrac{\sqrt{3}}{2}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ④ $\dfrac{2\sqrt{3}}{3}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ⑤ $\dfrac{5\sqrt{3}}{6}$</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 ②</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-09 at 12.06.18.png" data-origin-width="1526" data-origin-height="1838"><span data-url="https://blog.kakaocdn.net/dn/bLmzIS/dJMcaijjRvt/UkfIZhhDVks2TUpzjjRJx0/img.png" data-phocus="https://blog.kakaocdn.net/dn/bLmzIS/dJMcaijjRvt/UkfIZhhDVks2TUpzjjRJx0/img.png"><img src="https://blog.kakaocdn.net/dn/bLmzIS/dJMcaijjRvt/UkfIZhhDVks2TUpzjjRJx0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbLmzIS%2FdJMcaijjRvt%2FUkfIZhhDVks2TUpzjjRJx0%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="723" data-filename="Screenshot 2026-06-09 at 12.06.18.png" data-origin-width="1526" data-origin-height="1838"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-09 at 12.06.48.png" data-origin-width="1504" data-origin-height="944"><span data-url="https://blog.kakaocdn.net/dn/bHl86w/dJMcahScUi9/WUxOd4pl6zTKiFpe0lv4z1/img.png" data-phocus="https://blog.kakaocdn.net/dn/bHl86w/dJMcahScUi9/WUxOd4pl6zTKiFpe0lv4z1/img.png"><img src="https://blog.kakaocdn.net/dn/bHl86w/dJMcahScUi9/WUxOd4pl6zTKiFpe0lv4z1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbHl86w%2FdJMcahScUi9%2FWUxOd4pl6zTKiFpe0lv4z1%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="377" data-filename="Screenshot 2026-06-09 at 12.06.48.png" data-origin-width="1504" data-origin-height="944"/></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> (新 교육과정) 공통수학 - 문제풀이/방정식과 부등식 수악중독 https://mathjk.tistory.com/6919 https://mathjk.tistory.com/6919#entry6919comment Wed, 10 Jun 2026 01:07:53 +0900 https://mathjk.tistory.com/6918 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">이차함수 $y = x^{2}$의 그래프 위의 두 점 $\mathrm{A}\left (-t, \; t^{2} \right )$, $\mathrm{B}\left (t, \; t^{2} \right )$ $(t&gt;0, \; t \ne 2)$에 대하여 선분 $\mathrm{AB}$를 한 변으로 하고 두 점 $\mathrm{C}, \; \mathrm{D}$를 꼭짓점으로 갖는 정사각형 $\mathrm{ACDB}$가 있다. 삼각형 $\mathrm{AOB}$의 넓이를 $S_{1}$, 삼각형 $\mathrm{COD}$의 넓이를 $S_{2}$라 하자. $S_{1} : S_{2} = 5 : 1$을 만족시키는 모든 실수 $t$의 값의 합은? (단, $\mathrm{O}$는 원점이다.)&nbsp;<br /><br />① $\dfrac{25}{6}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;② $\dfrac{13}{3}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③ $\dfrac{9}{2}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④ $\dfrac{14}{3}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤ $\dfrac{29}{6}$</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 ①</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-09 at 11.59.01.png" data-origin-width="1384" data-origin-height="2172"><span data-url="https://blog.kakaocdn.net/dn/GeOSN/dJMcahLt35f/Z9Ti3l4YkY5xnmMBZH1NX0/img.png" data-phocus="https://blog.kakaocdn.net/dn/GeOSN/dJMcahLt35f/Z9Ti3l4YkY5xnmMBZH1NX0/img.png"><img src="https://blog.kakaocdn.net/dn/GeOSN/dJMcahLt35f/Z9Ti3l4YkY5xnmMBZH1NX0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FGeOSN%2FdJMcahLt35f%2FZ9Ti3l4YkY5xnmMBZH1NX0%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="942" data-filename="Screenshot 2026-06-09 at 11.59.01.png" data-origin-width="1384" data-origin-height="2172"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> (新 교육과정) 공통수학 - 문제풀이/방정식과 부등식 수악중독 https://mathjk.tistory.com/6918 https://mathjk.tistory.com/6918#entry6918comment Wed, 10 Jun 2026 01:01:06 +0900 https://mathjk.tistory.com/6917 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">$1 \le |m| \le 5$, $1 \le n \le 10$ 인 두 정수 $m, \; n$ 에 대하여 $x$ 에 대한 연립부등식 $$\begin{cases} (mx - 3)(x + m) \ge 0 \\ (x - n)(x - 3) &lt; 0 \end{cases}$$을 만족시키는 정수 $x$ 의 개수가 $1$ 이 되도록 하는 $m, \; n$ 의 모든 순서쌍 $(m, \; n)$의 개수는?</p> <p data-ke-size="size16"><br />①&nbsp;$17$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$20$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$23$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$26$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$29$</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="Screenshot 2026-06-09 at 11.54.16.png" data-origin-width="1494" data-origin-height="2054"><span data-url="https://blog.kakaocdn.net/dn/JPWpT/dJMcadPMMNw/rnFKhKflfTvE9WGmQkGKyK/img.png" data-phocus="https://blog.kakaocdn.net/dn/JPWpT/dJMcadPMMNw/rnFKhKflfTvE9WGmQkGKyK/img.png"><img src="https://blog.kakaocdn.net/dn/JPWpT/dJMcadPMMNw/rnFKhKflfTvE9WGmQkGKyK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FJPWpT%2FdJMcadPMMNw%2FrnFKhKflfTvE9WGmQkGKyK%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="825" data-filename="Screenshot 2026-06-09 at 11.54.16.png" data-origin-width="1494" data-origin-height="2054"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-09 at 11.54.44.png" data-origin-width="1498" data-origin-height="2152"><span data-url="https://blog.kakaocdn.net/dn/becxXg/dJMcagsgAcN/rxMUk6Nzw58UApkK8E4p50/img.png" data-phocus="https://blog.kakaocdn.net/dn/becxXg/dJMcagsgAcN/rxMUk6Nzw58UApkK8E4p50/img.png"><img src="https://blog.kakaocdn.net/dn/becxXg/dJMcagsgAcN/rxMUk6Nzw58UApkK8E4p50/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbecxXg%2FdJMcagsgAcN%2FrxMUk6Nzw58UApkK8E4p50%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="862" data-filename="Screenshot 2026-06-09 at 11.54.44.png" data-origin-width="1498" data-origin-height="2152"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-09 at 11.55.11.png" data-origin-width="1422" data-origin-height="144"><span data-url="https://blog.kakaocdn.net/dn/CJOtH/dJMcagMCLIM/eMM6XXuvy6Zz1oMeHibUsK/img.png" data-phocus="https://blog.kakaocdn.net/dn/CJOtH/dJMcagMCLIM/eMM6XXuvy6Zz1oMeHibUsK/img.png"><img src="https://blog.kakaocdn.net/dn/CJOtH/dJMcagMCLIM/eMM6XXuvy6Zz1oMeHibUsK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FCJOtH%2FdJMcagMCLIM%2FeMM6XXuvy6Zz1oMeHibUsK%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="601" height="61" data-filename="Screenshot 2026-06-09 at 11.55.11.png" data-origin-width="1422" data-origin-height="144"/></span></figure> <p data-ke-size="size16">&nbsp;</p> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> (新 교육과정) 공통수학 - 문제풀이/방정식과 부등식 수악중독 https://mathjk.tistory.com/6917 https://mathjk.tistory.com/6917#entry6917comment Wed, 10 Jun 2026 00:55:59 +0900 https://mathjk.tistory.com/6916 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">삼차다항식 $A(x)$ 와 이차다항식 $B(x)$ 는 최고차항의 계수가 모두 $1$ 이고 다음 조건을 만족시킨다.</p> <div class="txc-textbox" style="background-color: #dbe8fb; padding: 10px; border: 1px solid #dbe8fb;"> <p data-ke-size="size16">(가) $A(x)B(x)$ 는 $x^{2}-2x+1$ 로 나누어떨어진다.&nbsp;&nbsp;<br />(나) $(B(x))^{2}$ 을 $x^{2}-3x+2$ 로 나눈 몫은 $Q(x)$ 이고 나머지는 $16x-16$ 이다.&nbsp;&nbsp;<br />(다) $B(2)&gt;0$</p> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">$A(x)$ 는 $Q(x)$ 로 나누어떨어진 때, $A(3)$ 의 값은?&nbsp;<br /><br />①&nbsp;$68$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$70$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$72$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$74$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$76$</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&nbsp;</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-09 at 11.50.32.png" data-origin-width="1386" data-origin-height="1818"><span data-url="https://blog.kakaocdn.net/dn/b2Vy48/dJMcadPMMMW/gypqMAlkq10GMIlGoSVYP0/img.png" data-phocus="https://blog.kakaocdn.net/dn/b2Vy48/dJMcadPMMMW/gypqMAlkq10GMIlGoSVYP0/img.png"><img src="https://blog.kakaocdn.net/dn/b2Vy48/dJMcadPMMMW/gypqMAlkq10GMIlGoSVYP0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fb2Vy48%2FdJMcadPMMMW%2FgypqMAlkq10GMIlGoSVYP0%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="787" data-filename="Screenshot 2026-06-09 at 11.50.32.png" data-origin-width="1386" data-origin-height="1818"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-09 at 11.50.57.png" data-origin-width="1442" data-origin-height="722"><span data-url="https://blog.kakaocdn.net/dn/dYBPzW/dJMcagMCLIs/ntXPIThJR4ekHxqQVCfiOk/img.png" data-phocus="https://blog.kakaocdn.net/dn/dYBPzW/dJMcagMCLIs/ntXPIThJR4ekHxqQVCfiOk/img.png"><img src="https://blog.kakaocdn.net/dn/dYBPzW/dJMcagMCLIs/ntXPIThJR4ekHxqQVCfiOk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FdYBPzW%2FdJMcagMCLIs%2FntXPIThJR4ekHxqQVCfiOk%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="300" data-filename="Screenshot 2026-06-09 at 11.50.57.png" data-origin-width="1442" data-origin-height="722"/></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> (新 교육과정) 공통수학 - 문제풀이/다항식 수악중독 https://mathjk.tistory.com/6916 https://mathjk.tistory.com/6916#entry6916comment Wed, 10 Jun 2026 00:52:16 +0900 https://mathjk.tistory.com/6915 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">다항식&nbsp;$x^{3}&nbsp;+&nbsp;(a+2)x^{2}&nbsp;+&nbsp;(a^{2}-3a+2)x&nbsp;+&nbsp;b$&nbsp;는&nbsp;$(x+1)(x^{2}+(a+1)x+b)$&nbsp;로&nbsp;인수분해되고,&nbsp;이차방정식&nbsp;$x^{2}+(a+1)x+b=0$&nbsp;의&nbsp;두&nbsp;근을&nbsp;$\alpha,&nbsp;\beta$&nbsp;라&nbsp;하자.&nbsp;$\alpha^{2}+\beta^{2}=24$&nbsp;일&nbsp;때,&nbsp;$a+b$&nbsp;의&nbsp;값을&nbsp;구하시오.&nbsp;(단,&nbsp;$a,&nbsp;b$&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 $11$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-08 at 11.13.50.png" data-origin-width="1332" data-origin-height="1564"><span data-url="https://blog.kakaocdn.net/dn/zmmqL/dJMcaip4mvd/ElpsM7kEk4RObywRrooWMk/img.png" data-phocus="https://blog.kakaocdn.net/dn/zmmqL/dJMcaip4mvd/ElpsM7kEk4RObywRrooWMk/img.png"><img src="https://blog.kakaocdn.net/dn/zmmqL/dJMcaip4mvd/ElpsM7kEk4RObywRrooWMk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FzmmqL%2FdJMcaip4mvd%2FElpsM7kEk4RObywRrooWMk%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="705" data-filename="Screenshot 2026-06-08 at 11.13.50.png" data-origin-width="1332" data-origin-height="1564"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> (新 교육과정) 공통수학 - 문제풀이/방정식과 부등식 수악중독 https://mathjk.tistory.com/6915 https://mathjk.tistory.com/6915#entry6915comment Tue, 9 Jun 2026 00:14:43 +0900 https://mathjk.tistory.com/6914 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과&nbsp;같이&nbsp;직선&nbsp;$y=k$&nbsp;가&nbsp;이차함수&nbsp;$f(x)=x^{2}-2x+2$&nbsp;의&nbsp;그래프와&nbsp;서로&nbsp;다른&nbsp;두&nbsp;점&nbsp;$\mathrm{A},&nbsp;\mathrm{B}$&nbsp;에서&nbsp;만나고,&nbsp;직선&nbsp;$y=k$&nbsp;가&nbsp;이차함수&nbsp;$g(x)=-x^{2}+8x-6$&nbsp;의&nbsp;그래프와&nbsp;서로&nbsp;다른&nbsp;두&nbsp;점&nbsp;$\mathrm{C},&nbsp;\mathrm{D}$&nbsp;에서&nbsp;만난다.&nbsp;$\mathrm{AB}=2\,\mathrm{CD}$&nbsp;를&nbsp;만족시키는&nbsp;실수&nbsp;$k$&nbsp;에&nbsp;대하여&nbsp;$10k$&nbsp;의&nbsp;값을&nbsp;구하시오.&nbsp;(단,&nbsp;$1&lt;k&lt;10$)</p> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-08 at 11.08.52.png" data-origin-width="710" data-origin-height="830"><span data-url="https://blog.kakaocdn.net/dn/PHyQc/dJMcadIYCIj/3bXPaPCb67R49LbbHKIvbk/img.png" data-phocus="https://blog.kakaocdn.net/dn/PHyQc/dJMcadIYCIj/3bXPaPCb67R49LbbHKIvbk/img.png"><img src="https://blog.kakaocdn.net/dn/PHyQc/dJMcadIYCIj/3bXPaPCb67R49LbbHKIvbk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FPHyQc%2FdJMcadIYCIj%2F3bXPaPCb67R49LbbHKIvbk%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="339" height="396" data-filename="Screenshot 2026-06-08 at 11.08.52.png" data-origin-width="710" data-origin-height="830"/></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 $82$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-08 at 11.09.37.png" data-origin-width="1516" data-origin-height="1312"><span data-url="https://blog.kakaocdn.net/dn/cY1WsX/dJMcaci2O25/uSyzZiOhKSoYRhPHdyWIS0/img.png" data-phocus="https://blog.kakaocdn.net/dn/cY1WsX/dJMcaci2O25/uSyzZiOhKSoYRhPHdyWIS0/img.png"><img src="https://blog.kakaocdn.net/dn/cY1WsX/dJMcaci2O25/uSyzZiOhKSoYRhPHdyWIS0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FcY1WsX%2FdJMcaci2O25%2FuSyzZiOhKSoYRhPHdyWIS0%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="519" data-filename="Screenshot 2026-06-08 at 11.09.37.png" data-origin-width="1516" data-origin-height="1312"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> (新 교육과정) 공통수학 - 문제풀이/방정식과 부등식 수악중독 https://mathjk.tistory.com/6914 https://mathjk.tistory.com/6914#entry6914comment Tue, 9 Jun 2026 00:11:59 +0900 https://mathjk.tistory.com/6913 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">다항식&nbsp;$\mathrm{A}(x)$&nbsp;와&nbsp;최고차항의&nbsp;계수가&nbsp;$1$&nbsp;인&nbsp;일차다항식&nbsp;$\mathrm{B}(x)$&nbsp;가&nbsp;다음&nbsp;조건을&nbsp;만족시킨다.</p> <div class="txc-textbox" style="background-color: #dbe8fb; padding: 10px; border: 1px solid #dbe8fb;"> <p data-ke-size="size16">(가) $mathrm{A}(x) = (\mathrm{B}(x))^{4} - 2(\mathrm{B}(x))^{3} - (\mathrm{B}(x))^{2} + 2\mathrm{B}(x)$</p> <p data-ke-size="size16">(나) $\mathrm{A}(1)=24,\; \mathrm{A}(2)=0$</p> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">$\mathrm{A}(x)$&nbsp;를&nbsp;$x^{2}-7x-1$&nbsp;로&nbsp;나눈&nbsp;나머지를&nbsp;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 $143$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-08 at 11.06.48.png" data-origin-width="1446" data-origin-height="1602"><span data-url="https://blog.kakaocdn.net/dn/cRIKBY/dJMcadCb9MI/whccYN6n7HI8OKVsuLAHp1/img.png" data-phocus="https://blog.kakaocdn.net/dn/cRIKBY/dJMcadCb9MI/whccYN6n7HI8OKVsuLAHp1/img.png"><img src="https://blog.kakaocdn.net/dn/cRIKBY/dJMcadCb9MI/whccYN6n7HI8OKVsuLAHp1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FcRIKBY%2FdJMcadCb9MI%2FwhccYN6n7HI8OKVsuLAHp1%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="665" data-filename="Screenshot 2026-06-08 at 11.06.48.png" data-origin-width="1446" data-origin-height="1602"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> (新 교육과정) 공통수학 - 문제풀이/다항식 수악중독 https://mathjk.tistory.com/6913 https://mathjk.tistory.com/6913#entry6913comment Tue, 9 Jun 2026 00:07:40 +0900 https://mathjk.tistory.com/6912 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">최고차항의 계수가 $1$ 인 두 다항식 $\mathrm{A}(x), \; \mathrm{B}(x)$ 가 다음 조건을 만족시킨다.</p> <div class="txc-textbox" style="background-color: #dbe8fb; padding: 10px; border: 1px solid #dbe8fb;"> <p data-ke-size="size16">(가)&nbsp;$\mathrm{A}(x)$&nbsp;를&nbsp;$\mathrm{B}(x)$&nbsp;로&nbsp;나눈&nbsp;몫은&nbsp;$\mathrm{B}(x)+x$&nbsp;이고&nbsp;나머지는&nbsp;$\mathrm{B}(x)-x^{2}$&nbsp;이다.&nbsp;&nbsp;<br />(나)&nbsp;$\mathrm{A}(x)$&nbsp;는&nbsp;$\mathrm{B}(x)-x$&nbsp;로&nbsp;나누어떨어진다.</p> </div> <p data-ke-size="size16"><br />$\mathrm{A}(2)$&nbsp;의&nbsp;값을&nbsp;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 $84$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-08 at 11.03.15.png" data-origin-width="1468" data-origin-height="2326"><span data-url="https://blog.kakaocdn.net/dn/vQ50m/dJMcaaS7AHY/uJjCBAquyolyKxkGMRPZ11/img.png" data-phocus="https://blog.kakaocdn.net/dn/vQ50m/dJMcaaS7AHY/uJjCBAquyolyKxkGMRPZ11/img.png"><img src="https://blog.kakaocdn.net/dn/vQ50m/dJMcaaS7AHY/uJjCBAquyolyKxkGMRPZ11/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FvQ50m%2FdJMcaaS7AHY%2FuJjCBAquyolyKxkGMRPZ11%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="951" data-filename="Screenshot 2026-06-08 at 11.03.15.png" data-origin-width="1468" data-origin-height="2326"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-08 at 11.03.32.png" data-origin-width="1448" data-origin-height="596"><span data-url="https://blog.kakaocdn.net/dn/JoyGN/dJMcabdmrwJ/1K75zcCg7MWFVLvQHaFyd0/img.png" data-phocus="https://blog.kakaocdn.net/dn/JoyGN/dJMcabdmrwJ/1K75zcCg7MWFVLvQHaFyd0/img.png"><img src="https://blog.kakaocdn.net/dn/JoyGN/dJMcabdmrwJ/1K75zcCg7MWFVLvQHaFyd0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FJoyGN%2FdJMcabdmrwJ%2F1K75zcCg7MWFVLvQHaFyd0%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="247" data-filename="Screenshot 2026-06-08 at 11.03.32.png" data-origin-width="1448" data-origin-height="596"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> (新 교육과정) 공통수학 - 문제풀이/다항식 수악중독 https://mathjk.tistory.com/6912 https://mathjk.tistory.com/6912#entry6912comment Tue, 9 Jun 2026 00:04:14 +0900 https://mathjk.tistory.com/6911 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">두 함수 $f(x)=x^{2}-5x$, $g(x)=-\dfrac{1}{2}x+\dfrac{5}{2}$ 가 있다. 실수 $a$ 에 대하여 직선 $y=x+k$ 가 $x &lt; a$ 에서 함수 $y=f(x)$ 의 그래프와 만나는 서로 다른 점의 개수를 $m$, $x \ge a$ 에서 함수 $y=g(x)$ 의 그래프와 만나는 서로 다른 점의 개수를 $n$ 이라 하자. $m+n=3$ 인 실수 $k$ 가 존재하도록 하는 모든 $a$ 의 값의 범위는 $p &lt; a &lt; q$ 이다. $p \times q$ 의 값을 구하시오. (단, $p, \;q$ 는 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 $23$</b></span></p> <p data-ke-size="size16">&nbsp;</p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-08 at 08.49.56.png" data-origin-width="1450" data-origin-height="1558"><span data-url="https://blog.kakaocdn.net/dn/GShlp/dJMcacwDU3A/YcW0NmFrajJhvw4nBEr2Kk/img.png" data-phocus="https://blog.kakaocdn.net/dn/GShlp/dJMcacwDU3A/YcW0NmFrajJhvw4nBEr2Kk/img.png"><img src="https://blog.kakaocdn.net/dn/GShlp/dJMcacwDU3A/YcW0NmFrajJhvw4nBEr2Kk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FGShlp%2FdJMcacwDU3A%2FYcW0NmFrajJhvw4nBEr2Kk%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="645" data-filename="Screenshot 2026-06-08 at 08.49.56.png" data-origin-width="1450" data-origin-height="1558"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-08 at 08.50.15.png" data-origin-width="1420" data-origin-height="1056"><span data-url="https://blog.kakaocdn.net/dn/ncDaT/dJMcahksc1c/oYEVXDij7OQs82nNfAiMb0/img.png" data-phocus="https://blog.kakaocdn.net/dn/ncDaT/dJMcahksc1c/oYEVXDij7OQs82nNfAiMb0/img.png"><img src="https://blog.kakaocdn.net/dn/ncDaT/dJMcahksc1c/oYEVXDij7OQs82nNfAiMb0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FncDaT%2FdJMcahksc1c%2FoYEVXDij7OQs82nNfAiMb0%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="446" data-filename="Screenshot 2026-06-08 at 08.50.15.png" data-origin-width="1420" data-origin-height="1056"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> (新 교육과정) 공통수학 - 문제풀이/방정식과 부등식 수악중독 https://mathjk.tistory.com/6911 https://mathjk.tistory.com/6911#entry6911comment Tue, 9 Jun 2026 00:00:16 +0900 https://mathjk.tistory.com/6910 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과 같이 $0 \le x \le 8$에서 정의된 함수 $f(x)=2 \sqrt{3} \sin \dfrac{\pi x}{4}$ 가 있다. 곡선 $y=f(x)$가 직선 $y=k$와 만나는 두 점을 $y$축에서 가까운 순서대로 $\mathrm{A, \; B}$라 하고, 곡선 $y=f(x)$가 직선 $y=-k$와 만나는 두 점을 $y$축에서 가까운 순서대로 $\mathrm{C, \; D}$라 하자.</p> <p data-ke-size="size16">직선 $\mathrm{AC}$의 기울기가 $-\dfrac{3}{2}$일 때, 사각형 $\mathrm{ACDB}$의 넓이는? (단, $0&lt;k&lt;2\sqrt{3})</p> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-07 at 14.19.29.png" data-origin-width="1036" data-origin-height="862"><span data-url="https://blog.kakaocdn.net/dn/4N1eJ/dJMcacXFZu0/IKUPq2JWKxraCxwKFPemtk/img.png" data-phocus="https://blog.kakaocdn.net/dn/4N1eJ/dJMcacXFZu0/IKUPq2JWKxraCxwKFPemtk/img.png"><img src="https://blog.kakaocdn.net/dn/4N1eJ/dJMcacXFZu0/IKUPq2JWKxraCxwKFPemtk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2F4N1eJ%2FdJMcacXFZu0%2FIKUPq2JWKxraCxwKFPemtk%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="509" height="424" data-filename="Screenshot 2026-06-07 at 14.19.29.png" data-origin-width="1036" data-origin-height="862"/></span></figure> </p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">① $\dfrac{13}{2}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ② $7$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ③ $\dfrac{15}{2}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ④ $8$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ⑤ $\dfrac{17}{2}$</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 ④</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-07 at 14.20.43.png" data-origin-width="1304" data-origin-height="2232"><span data-url="https://blog.kakaocdn.net/dn/nB2uH/dJMcadoGhBo/QYCYre2Y5ZhwxOeZKMXE7K/img.png" data-phocus="https://blog.kakaocdn.net/dn/nB2uH/dJMcadoGhBo/QYCYre2Y5ZhwxOeZKMXE7K/img.png"><img src="https://blog.kakaocdn.net/dn/nB2uH/dJMcadoGhBo/QYCYre2Y5ZhwxOeZKMXE7K/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FnB2uH%2FdJMcadoGhBo%2FQYCYre2Y5ZhwxOeZKMXE7K%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="1027" data-filename="Screenshot 2026-06-07 at 14.20.43.png" data-origin-width="1304" data-origin-height="2232"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> (新 교육과정) 대수 - 개념 및 유형정리/삼각함수 수악중독 https://mathjk.tistory.com/6910 https://mathjk.tistory.com/6910#entry6910comment Mon, 8 Jun 2026 03:21:11 +0900 https://mathjk.tistory.com/6909 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과 같이 두 원 $C_1$, $C_2$가 서로 다른 두 점 $\mathrm{P}$, $\mathrm{Q}$에서 만나고, 직선 $l$이 이 두 원과 동시에 접한다. 직선 $l$과 두 원 $C_1$, $C_2$의 접점을 각각 $\mathrm{A}$, $\mathrm{B}$라 할 때, $\angle \mathrm{QAB} = \theta_1$, $\angle \mathrm{QBA} = \theta_2$라 하자.</p> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-07 at 13.22.29.png" data-origin-width="1116" data-origin-height="758"><span data-url="https://blog.kakaocdn.net/dn/vQh3W/dJMcaiDBbI2/p7qd1kKCrp60clhx9bu8nK/img.png" data-phocus="https://blog.kakaocdn.net/dn/vQh3W/dJMcaiDBbI2/p7qd1kKCrp60clhx9bu8nK/img.png"><img src="https://blog.kakaocdn.net/dn/vQh3W/dJMcaiDBbI2/p7qd1kKCrp60clhx9bu8nK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FvQh3W%2FdJMcaiDBbI2%2Fp7qd1kKCrp60clhx9bu8nK%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="321" data-filename="Screenshot 2026-06-07 at 13.22.29.png" data-origin-width="1116" data-origin-height="758"/></span></figure> </p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">다음은 $\overline{\mathrm{AB}}=2$, $\sin\theta_1 : \sin\theta_2 = \sqrt{3} : \sqrt{2}$이고, 삼각형 $\mathrm{PAB}$의 외접원의 반지름의 길이가 $\dfrac{3\sqrt{3}}{5}$일 때, 선분 $\mathrm{QA}$의 길이를 구하는 과정이다. (단, $\angle \mathrm{APB} \le \angle \mathrm{AQB}$)</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">원의 성질에 의하여&nbsp;&nbsp;$\angle \mathrm{APQ} = \angle \mathrm{QAB}$, $\angle \mathrm{BPQ} = \angle \mathrm{QBA}$ 이므로 $\angle \mathrm{APB} = \theta_1 + \theta_2$이다. $\angle \mathrm{AQB} = \pi - (\theta_1 + \theta_2)$ 이고 $\angle \mathrm{APB} &lt; \angle \mathrm{AQB}$이므로 $\theta_1 + \theta_2 &lt; \frac{\pi}{2}$이다.&nbsp;&nbsp;<br />$\overline{\mathrm{AB}} = 2$이고 삼각형 $\mathrm{PAB}$의 접점원의 반지름의 길이가 $\frac{3\sqrt{3}}{5}$이므로 삼각형 $\mathrm{PAB}$ 에서 사인법칙에 의하여&nbsp;&nbsp;$$\sin(\theta_1 + \theta_2) = \boxed{\text{ (가) }}$$이다.&nbsp;&nbsp;<br />$\sin\theta_1 : \sin\theta_2 = \sqrt{3} : \sqrt{2}$이므로 삼각형 $\mathrm{QAB}$에서 사인법칙에 의하여 $$\overline{\mathrm{QB}} = \boxed{\text{ (나) }} \times \overline{\mathrm{QA}}$$이다.&nbsp;&nbsp;<br />$\angle \mathrm{AQB} = \pi - (\theta_1 + \theta_2)$, $\overline{\mathrm{AB}}=2$이므로 삼각형 $\mathrm{QAB}$에서 코사인법칙에 의하여 $$\overline{\mathrm{QA}} = \boxed{\text{ (다) }}$$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, $p \times q \times r^2$의 값은?&nbsp;<br /><br />① $\dfrac{20 \sqrt{2}}{19}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;② $\dfrac{21 \sqrt{2}}{19}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③ $\dfrac{22 \sqrt{2}}{19}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④ $\dfrac{23\sqrt{2}}{19}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤ $\dfrac{24\sqrt{2}}{19}$<br /><br /><br /></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="Screenshot 2026-06-07 at 13.46.20.png" data-origin-width="1376" data-origin-height="1704"><span data-url="https://blog.kakaocdn.net/dn/WJbFd/dJMcaci12Qe/HmyKnA9pmb69bkfmcPhOvK/img.png" data-phocus="https://blog.kakaocdn.net/dn/WJbFd/dJMcaci12Qe/HmyKnA9pmb69bkfmcPhOvK/img.png"><img src="https://blog.kakaocdn.net/dn/WJbFd/dJMcaci12Qe/HmyKnA9pmb69bkfmcPhOvK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FWJbFd%2FdJMcaci12Qe%2FHmyKnA9pmb69bkfmcPhOvK%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="743" data-filename="Screenshot 2026-06-07 at 13.46.20.png" data-origin-width="1376" data-origin-height="1704"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> (新 교육과정) 대수 - 개념 및 유형정리/삼각함수 수악중독 https://mathjk.tistory.com/6909 https://mathjk.tistory.com/6909#entry6909comment Mon, 8 Jun 2026 02:47:50 +0900 https://mathjk.tistory.com/6908 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">좌표평면에서 원 $x^2 + y^2 = 4$ 위의 두 점 $\mathrm{A}$, $\mathrm{B}$에 대하여 두 동경 $\mathrm{OA}$, $\mathrm{OB}$가 나타내는 각의 크기를 각각 $\alpha$, $\beta$라 하면 $$0 \le \alpha \le \beta \le \pi, \quad \overline{\mathrm{AB}} = 2\sqrt{2}, \quad \cos\alpha \times \sin\beta = \dfrac{1}{5}$$이다. 두 점 $\mathrm{A}$, $\mathrm{B}$에서 $x$축에 내린 수선의 발을 각각 $\mathrm{C}$, $\mathrm{D}$라 할 때, 사각형 $\mathrm{ABDC}$의 넓이는?&nbsp;<br /><br />①&nbsp;$\dfrac{16}{5}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$\dfrac{33}{10}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$\dfrac{17}{5}$&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;$\dfrac{18}{5}$</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 ⑤</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-07 at 13.20.26.png" data-origin-width="1542" data-origin-height="1728"><span data-url="https://blog.kakaocdn.net/dn/blXNW7/dJMcabLi8Nj/yTGcBH1uTIvwkHnjyuEAk1/img.png" data-phocus="https://blog.kakaocdn.net/dn/blXNW7/dJMcabLi8Nj/yTGcBH1uTIvwkHnjyuEAk1/img.png"><img src="https://blog.kakaocdn.net/dn/blXNW7/dJMcabLi8Nj/yTGcBH1uTIvwkHnjyuEAk1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FblXNW7%2FdJMcabLi8Nj%2FyTGcBH1uTIvwkHnjyuEAk1%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="672" data-filename="Screenshot 2026-06-07 at 13.20.26.png" data-origin-width="1542" data-origin-height="1728"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> (新 교육과정) 대수 - 개념 및 유형정리/삼각함수 수악중독 https://mathjk.tistory.com/6908 https://mathjk.tistory.com/6908#entry6908comment Mon, 8 Jun 2026 02:20:51 +0900 https://mathjk.tistory.com/6907 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">$n \ge 2$인 자연수 $n$에 대하여 $n- \sqrt{401}$의 $n$제곱근 중 실수인 것의 개수를 $f(n)$이라 할 때, $$\log_2 \dfrac{15}{n \times (f(n)+3)}$$의 값이 정수가 되도록 하는 $50$ 이하의 모든 $n$의 값의 합은?</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">① $108$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ② $111$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ③ $114$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ④ $117$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ⑤ $120$</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="Screenshot 2026-06-07 at 12.01.39.png" data-origin-width="1356" data-origin-height="1780"><span data-url="https://blog.kakaocdn.net/dn/bNdAqX/dJMcad3iO43/KMRKTKMFUDapq1dUK3vGrK/img.png" data-phocus="https://blog.kakaocdn.net/dn/bNdAqX/dJMcad3iO43/KMRKTKMFUDapq1dUK3vGrK/img.png"><img src="https://blog.kakaocdn.net/dn/bNdAqX/dJMcad3iO43/KMRKTKMFUDapq1dUK3vGrK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbNdAqX%2FdJMcad3iO43%2FKMRKTKMFUDapq1dUK3vGrK%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="788" data-filename="Screenshot 2026-06-07 at 12.01.39.png" data-origin-width="1356" data-origin-height="1780"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-07 at 12.01.56.png" data-origin-width="1318" data-origin-height="1088"><span data-url="https://blog.kakaocdn.net/dn/NJcYY/dJMcahEEhmp/iEocv1kao0Ky21vFvQy19K/img.png" data-phocus="https://blog.kakaocdn.net/dn/NJcYY/dJMcahEEhmp/iEocv1kao0Ky21vFvQy19K/img.png"><img src="https://blog.kakaocdn.net/dn/NJcYY/dJMcahEEhmp/iEocv1kao0Ky21vFvQy19K/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FNJcYY%2FdJMcahEEhmp%2FiEocv1kao0Ky21vFvQy19K%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="495" data-filename="Screenshot 2026-06-07 at 12.01.56.png" data-origin-width="1318" data-origin-height="1088"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> (新 교육과정) 대수 - 개념 및 유형정리/지수함수와 로그함수 수악중독 https://mathjk.tistory.com/6907 https://mathjk.tistory.com/6907#entry6907comment Mon, 8 Jun 2026 01:02:21 +0900 https://mathjk.tistory.com/6906 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과 같이 집합 $\{x|0 \le x \le 4\pi, \; x \ne 2\pi\}$에서 정의된 함수 $$f(x)= 3 \tan \dfrac{x}{4} + \left | \tan \dfrac{x}{4} \right |$$의 그래프와 한 점 $\mathrm{P}(4 \pi, \; 0)$이 있다. 두 점 $\mathrm{A}(a, \; f(a))$, $\mathrm{B}(b, \; 0)$을 지나고 기울기가 음수인 직선이 함수 $y=f(x)$의 그래프와 만나는 점 중 $\mathrm{A}$가 아닌 점을 $\mathrm{C}$라 하자.&nbsp;</p> <p data-ke-size="size16">세 점 $\mathrm{A, \; B, \; C}$가 다음 조건을 만족시킬 때, $a+b$의 값은? (단, $\mathrm{O}$는 원점이고, $0&lt;a&lt;2\pi, \; 0&lt;b&lt;4\pi$이다.)</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) 두 점 $\mathrm{A, \; C}$의 $x$좌표의 합은 $4\pi$이다.</p> <p data-ke-size="size16">(나) 삼각형 $\mathrm{AOB}$와 삼각형 $\mathrm{BCP}$의 넓이의 비는 $7:3$이다.</p> </div> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-07 at 11.26.10.png" data-origin-width="1154" data-origin-height="1300"><span data-url="https://blog.kakaocdn.net/dn/dOExTB/dJMcacKccCO/WpsLIuvAHX1vjgkhBU1TK0/img.png" data-phocus="https://blog.kakaocdn.net/dn/dOExTB/dJMcacKccCO/WpsLIuvAHX1vjgkhBU1TK0/img.png"><img src="https://blog.kakaocdn.net/dn/dOExTB/dJMcacKccCO/WpsLIuvAHX1vjgkhBU1TK0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FdOExTB%2FdJMcacKccCO%2FWpsLIuvAHX1vjgkhBU1TK0%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="499" height="562" data-filename="Screenshot 2026-06-07 at 11.26.10.png" data-origin-width="1154" data-origin-height="1300"/></span></figure> </p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">① $\dfrac{47}{13}\pi$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ② $\dfrac{48}{13}\pi$ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;③ $\dfrac{49}{13}\pi$ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;④ $\dfrac{50}{13}\pi$ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;⑤ $\dfrac{51}{13}\pi$</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="Screenshot 2026-06-07 at 11.27.31.png" data-origin-width="1322" data-origin-height="1688"><span data-url="https://blog.kakaocdn.net/dn/xYh7Q/dJMcaaewlW0/LX6pE4xHKqKEucc1R4gOKK/img.png" data-phocus="https://blog.kakaocdn.net/dn/xYh7Q/dJMcaaewlW0/LX6pE4xHKqKEucc1R4gOKK/img.png"><img src="https://blog.kakaocdn.net/dn/xYh7Q/dJMcaaewlW0/LX6pE4xHKqKEucc1R4gOKK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FxYh7Q%2FdJMcaaewlW0%2FLX6pE4xHKqKEucc1R4gOKK%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="766" data-filename="Screenshot 2026-06-07 at 11.27.31.png" data-origin-width="1322" data-origin-height="1688"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-07 at 11.27.47.png" data-origin-width="1216" data-origin-height="1468"><span data-url="https://blog.kakaocdn.net/dn/cz1nnJ/dJMcacKccDf/fSdm2RLn8QFDzowDnckwLK/img.png" data-phocus="https://blog.kakaocdn.net/dn/cz1nnJ/dJMcacKccDf/fSdm2RLn8QFDzowDnckwLK/img.png"><img src="https://blog.kakaocdn.net/dn/cz1nnJ/dJMcacKccDf/fSdm2RLn8QFDzowDnckwLK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fcz1nnJ%2FdJMcacKccDf%2FfSdm2RLn8QFDzowDnckwLK%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="724" data-filename="Screenshot 2026-06-07 at 11.27.47.png" data-origin-width="1216" data-origin-height="1468"/></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> 수학1- 문제풀이/삼각함수 수악중독 https://mathjk.tistory.com/6906 https://mathjk.tistory.com/6906#entry6906comment Mon, 8 Jun 2026 00:29:03 +0900 https://mathjk.tistory.com/6905 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">함수 $$f(x) = \begin{cases} 2^{x+1} &amp; (x \le 1) \\ 4-2 \log_2 x &amp; (x&gt;1) \end{cases}$$ 에 대하여 다음 조건을 만족시키는 모든 양수 $k$ 의 값의 집합이 $$\{ k | 0&lt;k \le \alpha \text{ 또는 } \beta &lt;k&lt;\gamma\}$$일 때, $\alpha+\beta+\gamma$ 의 값은? (단, $\alpha, \; \beta, \; \gamma$는 상수이다.)</p> <p data-ke-size="size16">&nbsp;</p> <div class="txc-textbox" style="background-color: #dbe8fb; padding: 10px; border: 1px solid #dbe8fb;">함수 $y=|f(x)-k|$의 그래프가. 두 직선 $y=p$, $y=2p$와 만나는 점의 개수가 각각 $3$, $2$가 되도록 하는 양수 $p$가 존재한다.</div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">① $8$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ② $9$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ③ $10$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ④ $11$&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 ①</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-06 at 13.54.59.png" data-origin-width="1172" data-origin-height="1230"><span data-url="https://blog.kakaocdn.net/dn/k8J8B/dJMcabqW0yH/IuBAMP697bJceV9xrD2LCk/img.png" data-phocus="https://blog.kakaocdn.net/dn/k8J8B/dJMcabqW0yH/IuBAMP697bJceV9xrD2LCk/img.png"><img src="https://blog.kakaocdn.net/dn/k8J8B/dJMcabqW0yH/IuBAMP697bJceV9xrD2LCk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fk8J8B%2FdJMcabqW0yH%2FIuBAMP697bJceV9xrD2LCk%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="630" data-filename="Screenshot 2026-06-06 at 13.54.59.png" data-origin-width="1172" data-origin-height="1230"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-06 at 13.55.14.png" data-origin-width="1308" data-origin-height="1194"><span data-url="https://blog.kakaocdn.net/dn/RhBNT/dJMcahYXVCy/nPQXgLcrF4uOuW5euSh7ek/img.png" data-phocus="https://blog.kakaocdn.net/dn/RhBNT/dJMcahYXVCy/nPQXgLcrF4uOuW5euSh7ek/img.png"><img src="https://blog.kakaocdn.net/dn/RhBNT/dJMcahYXVCy/nPQXgLcrF4uOuW5euSh7ek/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FRhBNT%2FdJMcahYXVCy%2FnPQXgLcrF4uOuW5euSh7ek%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="548" data-filename="Screenshot 2026-06-06 at 13.55.14.png" data-origin-width="1308" data-origin-height="1194"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-06 at 13.55.33.png" data-origin-width="1280" data-origin-height="958"><span data-url="https://blog.kakaocdn.net/dn/LANBT/dJMb99NmTPf/OxMgK7SnUyWRT9jfCcYWLk/img.png" data-phocus="https://blog.kakaocdn.net/dn/LANBT/dJMb99NmTPf/OxMgK7SnUyWRT9jfCcYWLk/img.png"><img src="https://blog.kakaocdn.net/dn/LANBT/dJMb99NmTPf/OxMgK7SnUyWRT9jfCcYWLk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FLANBT%2FdJMb99NmTPf%2FOxMgK7SnUyWRT9jfCcYWLk%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="449" data-filename="Screenshot 2026-06-06 at 13.55.33.png" data-origin-width="1280" data-origin-height="958"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-06 at 13.55.50.png" data-origin-width="1314" data-origin-height="514"><span data-url="https://blog.kakaocdn.net/dn/6kbqF/dJMcaiKi7MT/auksvUCM80TFvEkVBuQH11/img.png" data-phocus="https://blog.kakaocdn.net/dn/6kbqF/dJMcaiKi7MT/auksvUCM80TFvEkVBuQH11/img.png"><img src="https://blog.kakaocdn.net/dn/6kbqF/dJMcaiKi7MT/auksvUCM80TFvEkVBuQH11/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2F6kbqF%2FdJMcaiKi7MT%2FauksvUCM80TFvEkVBuQH11%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="601" height="235" data-filename="Screenshot 2026-06-06 at 13.55.50.png" data-origin-width="1314" data-origin-height="514"/></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> (新 교육과정) 대수 - 개념 및 유형정리/지수함수와 로그함수 수악중독 https://mathjk.tistory.com/6905 https://mathjk.tistory.com/6905#entry6905comment Sun, 7 Jun 2026 02:56:13 +0900 https://mathjk.tistory.com/6904 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">양수 $a$에 대하여 곡선 $y = \log_2 (x - a)$ 위의 점 $\mathrm{A}$를 지나고 $y$축에 평행한 직선이 곡선 $y = \log_2 x$와 만나는 점을 $\mathrm{B}$, 점 $\mathrm{B}$를 지나고 $x$축에 평행한 직선이 곡선 $y = \log_2 (x - a)$와 만나는 점을 $\mathrm{C}$라 하자. $\overline{\mathrm{AB}} = \overline{\mathrm{BC}}$가 되도록 하는 점 $\mathrm{A}$의 $x$좌표를 $f(a)$라 할 때, $f(a) \le \dfrac{64}{63}$를 만족시키는 $a$의 최솟값을 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 $6$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-06 at 13.32.48.png" data-origin-width="1152" data-origin-height="1020"><span data-url="https://blog.kakaocdn.net/dn/xouZ0/dJMcajia7Ce/G6q0S4kea3f1texfBv9jR1/img.png" data-phocus="https://blog.kakaocdn.net/dn/xouZ0/dJMcajia7Ce/G6q0S4kea3f1texfBv9jR1/img.png"><img src="https://blog.kakaocdn.net/dn/xouZ0/dJMcajia7Ce/G6q0S4kea3f1texfBv9jR1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FxouZ0%2FdJMcajia7Ce%2FG6q0S4kea3f1texfBv9jR1%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="531" data-filename="Screenshot 2026-06-06 at 13.32.48.png" data-origin-width="1152" data-origin-height="1020"/></span></figure> <p data-ke-size="size16">&nbsp;</p> </div> </div> <p data-ke-size="size16">&nbsp;</p> (新 교육과정) 대수 - 개념 및 유형정리/지수함수와 로그함수 수악중독 https://mathjk.tistory.com/6904 https://mathjk.tistory.com/6904#entry6904comment Sun, 7 Jun 2026 02:33:38 +0900 https://mathjk.tistory.com/6903 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과 같이 $\overline{\mathrm{AB}}=2\sqrt{5}$, $\overline{\mathrm{AC}}=\overline{\mathrm{BC}}=5$인 삼각형 $\mathrm{ABC}$에 대하여 선분 $\mathrm{BC}$를 지름으로 하는 반원이 선분 $\mathrm{AC}$와 만나는 점 중 $\mathrm{C}$가 아닌 점을 $\mathrm{D}$라 하자. 호 $\mathrm{CD}$ 위에 점 $\mathrm{E}$를 삼각형 $\mathrm{DCE}$의 넓이가 $\dfrac{3}{5}$가 되도록 잡는다. 선분 $\mathrm{CE}$의 길이를 $k$라 할 때, $60k^2$의 값을 구하시오. (단, $\overline{\mathrm{CE}} &lt;\overline{\mathrm{DE}}$)</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 $48$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-06 at 13.22.41.png" data-origin-width="1330" data-origin-height="1454"><span data-url="https://blog.kakaocdn.net/dn/pIJm6/dJMcajbkOdD/S8wjAhtGhs0IGK12szvZAk/img.png" data-phocus="https://blog.kakaocdn.net/dn/pIJm6/dJMcajbkOdD/S8wjAhtGhs0IGK12szvZAk/img.png"><img src="https://blog.kakaocdn.net/dn/pIJm6/dJMcajbkOdD/S8wjAhtGhs0IGK12szvZAk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FpIJm6%2FdJMcajbkOdD%2FS8wjAhtGhs0IGK12szvZAk%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="656" data-filename="Screenshot 2026-06-06 at 13.22.41.png" data-origin-width="1330" data-origin-height="1454"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-06 at 13.23.05.png" data-origin-width="1326" data-origin-height="2046"><span data-url="https://blog.kakaocdn.net/dn/cIa1rU/dJMcahLr6fu/SrNcwmkkZQBBLsHLK8brC0/img.png" data-phocus="https://blog.kakaocdn.net/dn/cIa1rU/dJMcahLr6fu/SrNcwmkkZQBBLsHLK8brC0/img.png"><img src="https://blog.kakaocdn.net/dn/cIa1rU/dJMcahLr6fu/SrNcwmkkZQBBLsHLK8brC0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FcIa1rU%2FdJMcahLr6fu%2FSrNcwmkkZQBBLsHLK8brC0%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="926" data-filename="Screenshot 2026-06-06 at 13.23.05.png" data-origin-width="1326" data-origin-height="2046"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> (新 교육과정) 대수 - 개념 및 유형정리/삼각함수 수악중독 https://mathjk.tistory.com/6903 https://mathjk.tistory.com/6903#entry6903comment Sun, 7 Jun 2026 02:24:03 +0900 https://mathjk.tistory.com/6902 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과 같이 $a &gt; 2$, $b &gt; 0$인 두 실수 $a$, $b$에 대하여 곡선 $y = a^x + b$와 $y$축이 만나는 점을 지나고 $x$축에 평행한 직선을 $l$ 이라 하자. 직선 $l$ 위의 점 $\mathrm{A}$를 지나고 기울기가 $-1$인 직선이 두 곡선 $y = \log_a x + b$, $y = a^x + b$와 만나는 점을 각각 $\mathrm{B}$, $\mathrm{C}$ 라 하고, $y$축과 만나는 점을 $\mathrm{D}$라 하자.<br />$\overline{\mathrm{AB}} : \overline{\mathrm{BC}} : \overline{\mathrm{CD}} = 1 : 3 : 3$ 이고 삼각형 $\mathrm{OBC}$ 의 넓이가 $\dfrac{9}{2}$일 때, $20(a^3 + b)$의 값을 구하시오. (단, $\mathrm{O}$는 원점이고, 점 $\mathrm{A}$의 $x$좌표는 $a$보다 크다.)</p> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-06 at 11.40.46.png" data-origin-width="1014" data-origin-height="910"><span data-url="https://blog.kakaocdn.net/dn/6Llyw/dJMcaaMjrVv/iEvADAREJzCUC9ZtGpTCck/img.png" data-phocus="https://blog.kakaocdn.net/dn/6Llyw/dJMcaaMjrVv/iEvADAREJzCUC9ZtGpTCck/img.png"><img src="https://blog.kakaocdn.net/dn/6Llyw/dJMcaaMjrVv/iEvADAREJzCUC9ZtGpTCck/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2F6Llyw%2FdJMcaaMjrVv%2FiEvADAREJzCUC9ZtGpTCck%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="479" data-filename="Screenshot 2026-06-06 at 11.40.46.png" data-origin-width="1014" data-origin-height="910"/></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 $210$</b></span></p> <p data-ke-size="size16">&nbsp;</p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-06 at 11.42.19.png" data-origin-width="1394" data-origin-height="2240"><span data-url="https://blog.kakaocdn.net/dn/brzzkk/dJMcadPKMoY/LfsJoIK9cvGagYkftIq8V1/img.png" data-phocus="https://blog.kakaocdn.net/dn/brzzkk/dJMcadPKMoY/LfsJoIK9cvGagYkftIq8V1/img.png"><img src="https://blog.kakaocdn.net/dn/brzzkk/dJMcadPKMoY/LfsJoIK9cvGagYkftIq8V1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fbrzzkk%2FdJMcadPKMoY%2FLfsJoIK9cvGagYkftIq8V1%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="964" data-filename="Screenshot 2026-06-06 at 11.42.19.png" data-origin-width="1394" data-origin-height="2240"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-06 at 11.42.36.png" data-origin-width="1362" data-origin-height="1456"><span data-url="https://blog.kakaocdn.net/dn/13VVI/dJMcahYXT6K/xOpsHkVuvJrtaaOK90iK1K/img.png" data-phocus="https://blog.kakaocdn.net/dn/13VVI/dJMcahYXT6K/xOpsHkVuvJrtaaOK90iK1K/img.png"><img src="https://blog.kakaocdn.net/dn/13VVI/dJMcahYXT6K/xOpsHkVuvJrtaaOK90iK1K/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2F13VVI%2FdJMcahYXT6K%2FxOpsHkVuvJrtaaOK90iK1K%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="641" data-filename="Screenshot 2026-06-06 at 11.42.36.png" data-origin-width="1362" data-origin-height="1456"/></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> (新 교육과정) 대수 - 개념 및 유형정리/지수함수와 로그함수 수악중독 https://mathjk.tistory.com/6902 https://mathjk.tistory.com/6902#entry6902comment Sun, 7 Jun 2026 00:43:35 +0900 https://mathjk.tistory.com/6901 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">양수 $a$와 이차함수 $f(x)$에 대하여 $x \ge 0$에서 정의된 함수 $$g(x) = \begin{cases} \sin \dfrac{3\pi x}{a} &amp; (0 \le x &lt; a) \\&nbsp;<br />f(x) - f(a) &amp; (x \ge a) \end{cases}$$가 다음 조건을 만족시킬 때, $g(10)$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)&nbsp;$x&nbsp;\ge&nbsp;0$인&nbsp;모든&nbsp;실수&nbsp;$x$에&nbsp;대하여&nbsp;$g(x)&nbsp;\ge&nbsp;g(4)$이다.<br />(나) 자연수 $n$에 대하여 $x$에 대한 방정식 $g(x) = g(n)$의 서로 다른 실근의 개수를 $h(n)$이라 할 때,$$\{h(1), \; h(2), \; h(3), \;&nbsp; h(4), \; h(5)\} = \{1, \; 2, \; 3, \; 4, \; 5\}$$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 224$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-06 at 10.51.42.png" data-origin-width="1342" data-origin-height="2038"><span data-url="https://blog.kakaocdn.net/dn/bPNxu9/dJMcacciChc/Yg1KGuPsV29aVouxsgYOSk/img.png" data-phocus="https://blog.kakaocdn.net/dn/bPNxu9/dJMcacciChc/Yg1KGuPsV29aVouxsgYOSk/img.png"><img src="https://blog.kakaocdn.net/dn/bPNxu9/dJMcacciChc/Yg1KGuPsV29aVouxsgYOSk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbPNxu9%2FdJMcacciChc%2FYg1KGuPsV29aVouxsgYOSk%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="911" data-filename="Screenshot 2026-06-06 at 10.51.42.png" data-origin-width="1342" data-origin-height="2038"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-06 at 10.52.00.png" data-origin-width="1316" data-origin-height="1676"><span data-url="https://blog.kakaocdn.net/dn/bj7o3x/dJMcagZ1Z3q/VEQBb8WTVkAVzvYI3DOOck/img.png" data-phocus="https://blog.kakaocdn.net/dn/bj7o3x/dJMcagZ1Z3q/VEQBb8WTVkAVzvYI3DOOck/img.png"><img src="https://blog.kakaocdn.net/dn/bj7o3x/dJMcagZ1Z3q/VEQBb8WTVkAVzvYI3DOOck/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fbj7o3x%2FdJMcagZ1Z3q%2FVEQBb8WTVkAVzvYI3DOOck%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="764" data-filename="Screenshot 2026-06-06 at 10.52.00.png" data-origin-width="1316" data-origin-height="1676"/></span></figure> </div> </div> <p data-ke-size="size16"><br /><br /><br /><br /></p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> (新 교육과정) 대수 - 개념 및 유형정리/삼각함수 수악중독 https://mathjk.tistory.com/6901 https://mathjk.tistory.com/6901#entry6901comment Sun, 7 Jun 2026 00:04:50 +0900 https://mathjk.tistory.com/6900 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">두 다항함수 $f(x)$와 $g(x)$가 모든 실수 $x$에 대하여 $f(x) &gt; g(x)$를 만족시키고, $f(1) = g(1) + 1$이다. 양수 $t$에 대하여 두 곡선 $y=f(x)$, $y=g(x)$와 두 직선 $x=0$, $x=t$로 둘러싸인 도형의 넓이를 $S(t)$라 할 때, $$S'(t)=t^2-2t+a$$이다. &lt;보기&gt;에서 옳은 것만을 있는 대로 고른 것은? (단, $a$는 상수이다.)</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;$a=1$&nbsp;&nbsp;<br />ㄴ.&nbsp;$S(3)=6$&nbsp;&nbsp;<br />ㄷ. 두 곡선 $y=f(x)$, $y=g(x)$와 두 직선 $x=-2$, $x=2$로 둘러싸인 도형의 넓이는 $S(4)$의 값과 같다.</p> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">① ㄴ&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;② ㄷ&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ③ ㄱ, ㄴ&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ④ ㄱ, ㄷ&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ⑤ 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="13번.png" data-origin-width="1408" data-origin-height="2238"><span data-url="https://blog.kakaocdn.net/dn/mxLiL/dJMcagyYUV0/5mK9oFnrNJKz8T0fTYelp1/img.png" data-phocus="https://blog.kakaocdn.net/dn/mxLiL/dJMcagyYUV0/5mK9oFnrNJKz8T0fTYelp1/img.png"><img src="https://blog.kakaocdn.net/dn/mxLiL/dJMcagyYUV0/5mK9oFnrNJKz8T0fTYelp1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FmxLiL%2FdJMcagyYUV0%2F5mK9oFnrNJKz8T0fTYelp1%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="954" data-filename="13번.png" data-origin-width="1408" data-origin-height="2238"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> 수학2 - 문제풀이/적분 수악중독 https://mathjk.tistory.com/6900 https://mathjk.tistory.com/6900#entry6900comment Sat, 6 Jun 2026 00:28:09 +0900 https://mathjk.tistory.com/6899 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과 같이 $1$보다 큰 실수 $b$에 대하여 두 함수 $f(x)=b^x$과 $g(x)=-\log_b x$의 그래프가 제$1$사분면에서 만나는 점 $\mathrm{P}$의 좌표를 $(\alpha, \; \beta)$라 하자.</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-05 at 11.18.17.png" data-origin-width="852" data-origin-height="920"><span data-url="https://blog.kakaocdn.net/dn/cgi3D0/dJMcaaevyZv/dFwOAsksoeMrZRAiQucIg0/img.png" data-phocus="https://blog.kakaocdn.net/dn/cgi3D0/dJMcaaevyZv/dFwOAsksoeMrZRAiQucIg0/img.png"><img src="https://blog.kakaocdn.net/dn/cgi3D0/dJMcaaevyZv/dFwOAsksoeMrZRAiQucIg0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fcgi3D0%2FdJMcaaevyZv%2FdFwOAsksoeMrZRAiQucIg0%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="320" height="346" data-filename="Screenshot 2026-06-05 at 11.18.17.png" data-origin-width="852" data-origin-height="920"/></span></figure> </p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">다음은 $\alpha \beta^3 = 1$일 때, 직선 $\mathrm{OP}$의 기울기 $m$에 대하여 $g(m)$의 값을 구하는 과정이다. (단, $\mathrm{O}$는 원점이다.)</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">제$1$사분면에 있는 점 $\mathrm{P}(\alpha, \; \beta)$는 두 곡선 $$y=f(x), \quad y=g(x)$$ 위의 점이므로, 두 양수 $\alpha$, $\beta$가 $$\beta = b^{\alpha}, \quad \beta = -\log_b \alpha$$ 를 만족시킨다.<br />$\alpha \beta^3 = 1$이고 $\alpha = \log_b \beta$, $\beta = -\log_b \alpha$이므로 $$3\alpha - \beta = 3\log_b \beta + \log_b \alpha = \log_b (\alpha \beta^3) = 0$$ 이다. 그러므로 $m = \dfrac{\beta}{\alpha} = \boxed{\text{ (가) }}$이다.<br />$\beta^4 = m \alpha \beta^3 = m$이므로 $\beta = \boxed{\text{ (나) }}$이다.<br />$b = \alpha^{-\frac{1}{\beta}}$이고 $\alpha = \dfrac{\beta}{m}$ 이므로 $$g(m) = -\log_b m = \dfrac{\beta}{\log_m \alpha} = \dfrac{\beta}{-1 + \log_m \beta} = \boxed{\text{ (다) }}$$이다.</p> </div> <p data-ke-size="size16"><br />위의 (가), (나), (다)에 알맞은 수를 각각 $p$, $q$, $r$이라 할 때, $(p \times q \times r)^2$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 $48$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="20-1.png" data-origin-width="1548" data-origin-height="1660"><span data-url="https://blog.kakaocdn.net/dn/bPzATu/dJMcaayOn9m/ReK37sJROsm9P1BpSG1NQ0/img.png" data-phocus="https://blog.kakaocdn.net/dn/bPzATu/dJMcaayOn9m/ReK37sJROsm9P1BpSG1NQ0/img.png"><img src="https://blog.kakaocdn.net/dn/bPzATu/dJMcaayOn9m/ReK37sJROsm9P1BpSG1NQ0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbPzATu%2FdJMcaayOn9m%2FReK37sJROsm9P1BpSG1NQ0%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="643" data-filename="20-1.png" data-origin-width="1548" data-origin-height="1660"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="20-2.png" data-origin-width="1552" data-origin-height="1634"><span data-url="https://blog.kakaocdn.net/dn/bGJfFx/dJMcahxVe4x/ffDwCjhH27ATzsGYUx1PsK/img.png" data-phocus="https://blog.kakaocdn.net/dn/bGJfFx/dJMcahxVe4x/ffDwCjhH27ATzsGYUx1PsK/img.png"><img src="https://blog.kakaocdn.net/dn/bGJfFx/dJMcahxVe4x/ffDwCjhH27ATzsGYUx1PsK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbGJfFx%2FdJMcahxVe4x%2FffDwCjhH27ATzsGYUx1PsK%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="632" data-filename="20-2.png" data-origin-width="1552" data-origin-height="1634"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> 수학1- 문제풀이/지수함수와 로그함수 수악중독 https://mathjk.tistory.com/6899 https://mathjk.tistory.com/6899#entry6899comment Sat, 6 Jun 2026 00:24:44 +0900 https://mathjk.tistory.com/6898 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">앞면에 숫자 $1, \; 2, \; 3, \; 4, \; 5, \; 6$이 하나씩 적혀 있는 카드 $6$장이 있다. 각 카드의 뒷면에는 앞면에 적힌 숫자와 같은 숫자가 적혀 있다. 이 $6$장의 카드가 다음과 같이 놓여 있다.</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">숫자 $1, \; 6$이 적힌 카드는 뒷면이 보이도록 놓여 있고, 숫자 $2, \; 3, \; 4, \; 5$가 적힌 카드는 앞면이 보이도록 놓여 있다.</p> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;이 $6$장의 카드와 한 개의 주사위를 사용하여 다음 시행을 한다.</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">주사위를 한 번 던져 나온 눈의 수가 $k$일 때,</p> <p data-ke-size="size16">$k$가 홀수이면 $k$ 이하의 수가 적힌 카드를 모두 한 번씩 뒤집고,</p> <p data-ke-size="size16">$k$가 짝수이면 $k$ 이상의 수가 적힌 카드를 모두 한 번씩 뒤집는다.</p> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">이 시행을 $4$번 반복한 후 $6$장의 카드가 모두 앞면이 보이도록 놓여 있을 확률은?&nbsp;</p> <p data-ke-size="size16"><br />① $\dfrac{19}{162}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ② $\dfrac{13}{108}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ③ $\dfrac{10}{81}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ④ $\dfrac{41}{324}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ⑤ $\dfrac{7}{54}$<br /><br /></p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-05 at 11.15.00.png" data-origin-width="1188" data-origin-height="284"><span data-url="https://blog.kakaocdn.net/dn/CLFl2/dJMcaftjtHQ/5I42nPizlnMEDR88a6nEF0/img.png" data-phocus="https://blog.kakaocdn.net/dn/CLFl2/dJMcaftjtHQ/5I42nPizlnMEDR88a6nEF0/img.png"><img src="https://blog.kakaocdn.net/dn/CLFl2/dJMcaftjtHQ/5I42nPizlnMEDR88a6nEF0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FCLFl2%2FdJMcaftjtHQ%2F5I42nPizlnMEDR88a6nEF0%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="597" height="143" data-filename="Screenshot 2026-06-05 at 11.15.00.png" data-origin-width="1188" data-origin-height="284"/></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 ③&nbsp;</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="확통28-1.png" data-origin-width="1432" data-origin-height="1576"><span data-url="https://blog.kakaocdn.net/dn/TUuHA/dJMcabYNlK6/dlo2OnVYe9olTgmJROt7Xk/img.png" data-phocus="https://blog.kakaocdn.net/dn/TUuHA/dJMcabYNlK6/dlo2OnVYe9olTgmJROt7Xk/img.png"><img src="https://blog.kakaocdn.net/dn/TUuHA/dJMcabYNlK6/dlo2OnVYe9olTgmJROt7Xk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FTUuHA%2FdJMcabYNlK6%2Fdlo2OnVYe9olTgmJROt7Xk%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="660" data-filename="확통28-1.png" data-origin-width="1432" data-origin-height="1576"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="확통28-2.png" data-origin-width="1456" data-origin-height="1414"><span data-url="https://blog.kakaocdn.net/dn/IKsTE/dJMcadCaEI2/m5b0Y4KtiTgxD3j4DIADuk/img.png" data-phocus="https://blog.kakaocdn.net/dn/IKsTE/dJMcadCaEI2/m5b0Y4KtiTgxD3j4DIADuk/img.png"><img src="https://blog.kakaocdn.net/dn/IKsTE/dJMcadCaEI2/m5b0Y4KtiTgxD3j4DIADuk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FIKsTE%2FdJMcadCaEI2%2Fm5b0Y4KtiTgxD3j4DIADuk%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="583" data-filename="확통28-2.png" data-origin-width="1456" data-origin-height="1414"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="확통28-3.png" data-origin-width="1414" data-origin-height="1688"><span data-url="https://blog.kakaocdn.net/dn/zBwpG/dJMcacKboFO/uyhDjxJUbSLqgtx9MTmye1/img.png" data-phocus="https://blog.kakaocdn.net/dn/zBwpG/dJMcacKboFO/uyhDjxJUbSLqgtx9MTmye1/img.png"><img src="https://blog.kakaocdn.net/dn/zBwpG/dJMcacKboFO/uyhDjxJUbSLqgtx9MTmye1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FzBwpG%2FdJMcacKboFO%2FuyhDjxJUbSLqgtx9MTmye1%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="716" data-filename="확통28-3.png" data-origin-width="1414" data-origin-height="1688"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="확통28-4.png" data-origin-width="1450" data-origin-height="2288"><span data-url="https://blog.kakaocdn.net/dn/dxQLLW/dJMcahYXvs5/JGhhPYdyaV23kuGxbNklBk/img.png" data-phocus="https://blog.kakaocdn.net/dn/dxQLLW/dJMcahYXvs5/JGhhPYdyaV23kuGxbNklBk/img.png"><img src="https://blog.kakaocdn.net/dn/dxQLLW/dJMcahYXvs5/JGhhPYdyaV23kuGxbNklBk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FdxQLLW%2FdJMcahYXvs5%2FJGhhPYdyaV23kuGxbNklBk%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="947" data-filename="확통28-4.png" data-origin-width="1450" data-origin-height="2288"/></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> 확률과 통계 - 문제풀이/확률 수악중독 https://mathjk.tistory.com/6898 https://mathjk.tistory.com/6898#entry6898comment Sat, 6 Jun 2026 00:17:01 +0900 https://mathjk.tistory.com/6897 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">좌표평면에서 양수 $t$에 대하여 직선 $y=t$가 두 곡선 $y=e^{2x}-e^{-x}+1$, $y=e^{2x}$과 만나는 점을 각각 $\mathrm{P}$, $\mathrm{Q}$라 하자. 점 $\mathrm{P}$를 지나고 $x$축에 수직인 직선이 곡선 $y=e^{2x}$과 만나는 점의 $y$좌표를 $f(t)$, 점 $\mathrm{Q}$를 지나고 $x$축에 수직인 직선이 곡선 $y=e^{2x}-e^{-x}+1$과 만나는 점의 $y$좌표를 $g(t)$라 할 때, 두 함수 $f(t)$, $g(t)$는 구간 $(0,\; \infty)$에서 미분가능한 함수이다. $\lim \limits_{t \to 1} \dfrac{9f'(t)-4g'(t)}{t-1}$의 값은?</p> <p data-ke-size="size16">&nbsp;&nbsp;<br />① $1$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ② $3$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ③ $5$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ④ $7$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ⑤ $9$</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="미적분28-1.png" data-origin-width="1424" data-origin-height="1934"><span data-url="https://blog.kakaocdn.net/dn/Ukc4q/dJMcada79NQ/byor5j0kroA9l5shvyaKnK/img.png" data-phocus="https://blog.kakaocdn.net/dn/Ukc4q/dJMcada79NQ/byor5j0kroA9l5shvyaKnK/img.png"><img src="https://blog.kakaocdn.net/dn/Ukc4q/dJMcada79NQ/byor5j0kroA9l5shvyaKnK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FUkc4q%2FdJMcada79NQ%2Fbyor5j0kroA9l5shvyaKnK%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="815" data-filename="미적분28-1.png" data-origin-width="1424" data-origin-height="1934"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="미적분28-2.png" data-origin-width="1356" data-origin-height="2014"><span data-url="https://blog.kakaocdn.net/dn/bcW51B/dJMcada79N3/rDtaB2WiMYgeuIBFaakWoK/img.png" data-phocus="https://blog.kakaocdn.net/dn/bcW51B/dJMcada79N3/rDtaB2WiMYgeuIBFaakWoK/img.png"><img src="https://blog.kakaocdn.net/dn/bcW51B/dJMcada79N3/rDtaB2WiMYgeuIBFaakWoK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbcW51B%2FdJMcada79N3%2FrDtaB2WiMYgeuIBFaakWoK%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="891" data-filename="미적분28-2.png" data-origin-width="1356" data-origin-height="2014"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="미적분28-3.png" data-origin-width="1440" data-origin-height="1152"><span data-url="https://blog.kakaocdn.net/dn/cwJ7rw/dJMcag6PeTE/KihR76dy9SbOQ0gx4TsrF1/img.png" data-phocus="https://blog.kakaocdn.net/dn/cwJ7rw/dJMcag6PeTE/KihR76dy9SbOQ0gx4TsrF1/img.png"><img src="https://blog.kakaocdn.net/dn/cwJ7rw/dJMcag6PeTE/KihR76dy9SbOQ0gx4TsrF1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FcwJ7rw%2FdJMcag6PeTE%2FKihR76dy9SbOQ0gx4TsrF1%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="480" data-filename="미적분28-3.png" data-origin-width="1440" data-origin-height="1152"/></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> 미적분 - 문제풀이/미분법 수악중독 https://mathjk.tistory.com/6897 https://mathjk.tistory.com/6897#entry6897comment Sat, 6 Jun 2026 00:11:59 +0900 https://mathjk.tistory.com/6896 <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 타원 $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$이 있다. 이 타원 위에 있는 제$1$사분면 위의 점 $\mathrm{P}$와 이 타원 위에 있는 제$4$사분면 위의 점 $\mathrm{Q}$에 대하여 점 $\mathrm{F}$가 선분 $\mathrm{PQ}$ 위에 있고 $$\dfrac{\overline{\mathrm{PF}}}{\overline{\mathrm{QF}}}=\dfrac{1}{2}, \quad \dfrac{\overline{\mathrm{PF}}}{\overline{\mathrm{FF'}}}=\dfrac{\sqrt{6}}{16}$$이다. 삼각형 $\mathrm{FF'Q}$의 넓이가 $4\sqrt{5}$일 때, $b^2$의 값은? (단, $a$와 $b$는 양수이다.)&nbsp;&nbsp;</p> <p data-ke-size="size16"><br />① $\dfrac{13}{2}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ② $7$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ③ $\dfrac{15}{2}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ④ $8$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ⑤ $\dfrac{17}{2}$</p> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-05 at 08.29.51.png" data-origin-width="1210" data-origin-height="792"><span data-url="https://blog.kakaocdn.net/dn/dyLVXw/dJMcaaFBlee/QrnJwKPlyH1rAmswf5X8v1/img.png" data-phocus="https://blog.kakaocdn.net/dn/dyLVXw/dJMcaaFBlee/QrnJwKPlyH1rAmswf5X8v1/img.png"><img src="https://blog.kakaocdn.net/dn/dyLVXw/dJMcaaFBlee/QrnJwKPlyH1rAmswf5X8v1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FdyLVXw%2FdJMcaaFBlee%2FQrnJwKPlyH1rAmswf5X8v1%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="338" data-filename="Screenshot 2026-06-05 at 08.29.51.png" data-origin-width="1210" data-origin-height="792"/></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 ④</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-05 at 08.47.13.png" data-origin-width="1434" data-origin-height="1828"><span data-url="https://blog.kakaocdn.net/dn/bziXxf/dJMcacQSa0J/3kkGKrZY9yrBHBOvwaVK11/img.png" data-phocus="https://blog.kakaocdn.net/dn/bziXxf/dJMcacQSa0J/3kkGKrZY9yrBHBOvwaVK11/img.png"><img src="https://blog.kakaocdn.net/dn/bziXxf/dJMcacQSa0J/3kkGKrZY9yrBHBOvwaVK11/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbziXxf%2FdJMcacQSa0J%2F3kkGKrZY9yrBHBOvwaVK11%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="765" data-filename="Screenshot 2026-06-05 at 08.47.13.png" data-origin-width="1434" data-origin-height="1828"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-05 at 08.47.38.png" data-origin-width="1404" data-origin-height="2194"><span data-url="https://blog.kakaocdn.net/dn/dNbI8o/dJMcacpRqU7/BLIr51llXFNdshGkxkXzX1/img.png" data-phocus="https://blog.kakaocdn.net/dn/dNbI8o/dJMcacpRqU7/BLIr51llXFNdshGkxkXzX1/img.png"><img src="https://blog.kakaocdn.net/dn/dNbI8o/dJMcacpRqU7/BLIr51llXFNdshGkxkXzX1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FdNbI8o%2FdJMcacpRqU7%2FBLIr51llXFNdshGkxkXzX1%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="938" data-filename="Screenshot 2026-06-05 at 08.47.38.png" data-origin-width="1404" data-origin-height="2194"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-05 at 08.48.05.png" data-origin-width="1482" data-origin-height="522"><span data-url="https://blog.kakaocdn.net/dn/cH4yAe/dJMcadIWX8m/TCkUcEMmbkNH9OpkQ1eE51/img.png" data-phocus="https://blog.kakaocdn.net/dn/cH4yAe/dJMcadIWX8m/TCkUcEMmbkNH9OpkQ1eE51/img.png"><img src="https://blog.kakaocdn.net/dn/cH4yAe/dJMcadIWX8m/TCkUcEMmbkNH9OpkQ1eE51/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FcH4yAe%2FdJMcadIWX8m%2FTCkUcEMmbkNH9OpkQ1eE51%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="212" data-filename="Screenshot 2026-06-05 at 08.48.05.png" data-origin-width="1482" data-origin-height="522"/></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/6896 https://mathjk.tistory.com/6896#entry6896comment Sat, 6 Jun 2026 00:06:50 +0900 https://mathjk.tistory.com/6895 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">양수 $a$ 와 자연수 $b$ 에 대하여 $0 \le x \le 2$ 일 때 $x$ 에 대한 방정식 $$ \left( \cos(b\pi x) - \dfrac{1}{2} \right) \left( a \cos(b\pi x) + \dfrac{a+2}{2} \right) = 0$$의 서로 다른 실근의 개수는 $15$이다. $a+b$의 값은?&nbsp;<br />① $6$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ② $\dfrac{13}{2}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ③ $7$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ④ $\dfrac{15}{2}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ⑤ $8$</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 ③</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 21.40.15.png" data-origin-width="1396" data-origin-height="1206"><span data-url="https://blog.kakaocdn.net/dn/bpoUmK/dJMcad3hdQc/YOD0cUeZ8SvyplgElUrfW0/img.png" data-phocus="https://blog.kakaocdn.net/dn/bpoUmK/dJMcad3hdQc/YOD0cUeZ8SvyplgElUrfW0/img.png"><img src="https://blog.kakaocdn.net/dn/bpoUmK/dJMcad3hdQc/YOD0cUeZ8SvyplgElUrfW0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbpoUmK%2FdJMcad3hdQc%2FYOD0cUeZ8SvyplgElUrfW0%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="518" data-filename="Screenshot 2026-06-04 at 21.40.15.png" data-origin-width="1396" data-origin-height="1206"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 21.40.34.png" data-origin-width="1462" data-origin-height="1922"><span data-url="https://blog.kakaocdn.net/dn/bjwcom/dJMcajh9PDc/yKbAKKoNzRe3L5sBKvj3g1/img.png" data-phocus="https://blog.kakaocdn.net/dn/bjwcom/dJMcajh9PDc/yKbAKKoNzRe3L5sBKvj3g1/img.png"><img src="https://blog.kakaocdn.net/dn/bjwcom/dJMcajh9PDc/yKbAKKoNzRe3L5sBKvj3g1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fbjwcom%2FdJMcajh9PDc%2FyKbAKKoNzRe3L5sBKvj3g1%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="789" data-filename="Screenshot 2026-06-04 at 21.40.34.png" data-origin-width="1462" data-origin-height="1922"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> 수학1- 문제풀이/삼각함수 수악중독 https://mathjk.tistory.com/6895 https://mathjk.tistory.com/6895#entry6895comment Fri, 5 Jun 2026 10:41:00 +0900 https://mathjk.tistory.com/6894 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">상수항이 $0$인 삼차함수 $f(x)$가 다음 조건을 만족시킨다.&nbsp;&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) $\displaystyle \int_{p}^{p+3}&nbsp; \left | f(x) \right | \; dx = \left | \int_{p}^{p+3} f(x)\; dx \right |$가 되도록 하는 모든 실수 $p$의 값의 범위는 $0 &lt; p &lt; 3$이다.&nbsp;&nbsp;<br />(나) $\displaystyle\int_{0}^{3} \left |f(x) + q \right | \, dx =&nbsp; \left |\int_{0}^{3} (f(x) + q)\,dx \right |$&nbsp; 되도록 하는 모든 실수 $q$의 값의 범위는 $0 &lt; q &lt; 1$이다.&nbsp;&nbsp;</p> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">$f(6)$의 값은?&nbsp; &nbsp;<br />① $18$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ② $21$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ③ $24$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ④ $27$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ⑤ $30$</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="Screenshot 2026-06-04 at 21.23.45.png" data-origin-width="1500" data-origin-height="1296"><span data-url="https://blog.kakaocdn.net/dn/cm6RwA/dJMcacXEiPO/iVmOhHzCs39njX5bSMrS51/img.png" data-phocus="https://blog.kakaocdn.net/dn/cm6RwA/dJMcacXEiPO/iVmOhHzCs39njX5bSMrS51/img.png"><img src="https://blog.kakaocdn.net/dn/cm6RwA/dJMcacXEiPO/iVmOhHzCs39njX5bSMrS51/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fcm6RwA%2FdJMcacXEiPO%2FiVmOhHzCs39njX5bSMrS51%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="518" data-filename="Screenshot 2026-06-04 at 21.23.45.png" data-origin-width="1500" data-origin-height="1296"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 21.24.04.png" data-origin-width="1430" data-origin-height="1958"><span data-url="https://blog.kakaocdn.net/dn/QOYwl/dJMcahYWGN0/lnXokwJcpKb9c2mwaL3utK/img.png" data-phocus="https://blog.kakaocdn.net/dn/QOYwl/dJMcahYWGN0/lnXokwJcpKb9c2mwaL3utK/img.png"><img src="https://blog.kakaocdn.net/dn/QOYwl/dJMcahYWGN0/lnXokwJcpKb9c2mwaL3utK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FQOYwl%2FdJMcahYWGN0%2FlnXokwJcpKb9c2mwaL3utK%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="822" data-filename="Screenshot 2026-06-04 at 21.24.04.png" data-origin-width="1430" data-origin-height="1958"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> 수학2 - 문제풀이/적분 수악중독 https://mathjk.tistory.com/6894 https://mathjk.tistory.com/6894#entry6894comment Fri, 5 Jun 2026 10:25:39 +0900 https://mathjk.tistory.com/6893 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">서로&nbsp;다른&nbsp;다섯&nbsp;개의&nbsp;주사위를&nbsp;동시에&nbsp;던져&nbsp;나온&nbsp;다섯&nbsp;개의&nbsp;눈의&nbsp;수의&nbsp;곱이&nbsp;홀수일&nbsp;때,&nbsp;이&nbsp;다섯&nbsp;개의&nbsp;눈의&nbsp;수의&nbsp;합이&nbsp;$15$일&nbsp;확률은&nbsp;$\dfrac{p}{q}$이다.&nbsp;$p+q$의&nbsp;값을&nbsp;구하시오.&nbsp;(단,&nbsp;$p$와&nbsp;$q$는&nbsp;서로소인&nbsp;자연수이다.)</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 $98$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 18.41.44.png" data-origin-width="1464" data-origin-height="1158"><span data-url="https://blog.kakaocdn.net/dn/k4Hn4/dJMcabkbKQM/K4Jm2tUc9hb9jXkDMS7XrK/img.png" data-phocus="https://blog.kakaocdn.net/dn/k4Hn4/dJMcabkbKQM/K4Jm2tUc9hb9jXkDMS7XrK/img.png"><img src="https://blog.kakaocdn.net/dn/k4Hn4/dJMcabkbKQM/K4Jm2tUc9hb9jXkDMS7XrK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fk4Hn4%2FdJMcabkbKQM%2FK4Jm2tUc9hb9jXkDMS7XrK%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="601" height="475" data-filename="Screenshot 2026-06-04 at 18.41.44.png" data-origin-width="1464" data-origin-height="1158"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> 확률과 통계 - 문제풀이/확률 수악중독 https://mathjk.tistory.com/6893 https://mathjk.tistory.com/6893#entry6893comment Fri, 5 Jun 2026 07:42:41 +0900 https://mathjk.tistory.com/6892 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">모든 항이 정수인 등차수열 $\{a_n\}$과 모든 항이 양수인 등비수열 $\{b_n\}$이 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;$a_1&nbsp;=&nbsp;b_1$,&nbsp;$a_2&nbsp;=&nbsp;b_2$&nbsp;&nbsp;<br />(나)&nbsp;어떤&nbsp;자연수&nbsp;$k$에&nbsp;대하여&nbsp;$a_k&nbsp;=&nbsp;b_3$이다.&nbsp;&nbsp;</p> </div> <p data-ke-size="size16"><br />급수 $\sum \limits_{n=1}^{\infty} b_n$이 수렴할 때, $\left | \sum \limits_{n=1}^{\infty} (b_n \cos(a_n \pi)) \right |$의 최솟값을 $m$이라 하자. $10 \times m$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 $54$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 18.31.54.png" data-origin-width="1368" data-origin-height="1438"><span data-url="https://blog.kakaocdn.net/dn/Of1XC/dJMcaaS49AE/oshF4su6RuuJbZe5FmM3u1/img.png" data-phocus="https://blog.kakaocdn.net/dn/Of1XC/dJMcaaS49AE/oshF4su6RuuJbZe5FmM3u1/img.png"><img src="https://blog.kakaocdn.net/dn/Of1XC/dJMcaaS49AE/oshF4su6RuuJbZe5FmM3u1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FOf1XC%2FdJMcaaS49AE%2FoshF4su6RuuJbZe5FmM3u1%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="631" data-filename="Screenshot 2026-06-04 at 18.31.54.png" data-origin-width="1368" data-origin-height="1438"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 18.32.13.png" data-origin-width="1496" data-origin-height="1638"><span data-url="https://blog.kakaocdn.net/dn/bSxKOD/dJMcada7h8q/6uo5MV9ikO6Lk2x99YkLSk/img.png" data-phocus="https://blog.kakaocdn.net/dn/bSxKOD/dJMcada7h8q/6uo5MV9ikO6Lk2x99YkLSk/img.png"><img src="https://blog.kakaocdn.net/dn/bSxKOD/dJMcada7h8q/6uo5MV9ikO6Lk2x99YkLSk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbSxKOD%2FdJMcada7h8q%2F6uo5MV9ikO6Lk2x99YkLSk%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="657" data-filename="Screenshot 2026-06-04 at 18.32.13.png" data-origin-width="1496" data-origin-height="1638"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 18.32.37.png" data-origin-width="1346" data-origin-height="2212"><span data-url="https://blog.kakaocdn.net/dn/KYYTv/dJMcada7h8x/XKQHBC8lemWmpOP7CYePC1/img.png" data-phocus="https://blog.kakaocdn.net/dn/KYYTv/dJMcada7h8x/XKQHBC8lemWmpOP7CYePC1/img.png"><img src="https://blog.kakaocdn.net/dn/KYYTv/dJMcada7h8x/XKQHBC8lemWmpOP7CYePC1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FKYYTv%2FdJMcada7h8x%2FXKQHBC8lemWmpOP7CYePC1%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="986" data-filename="Screenshot 2026-06-04 at 18.32.37.png" data-origin-width="1346" data-origin-height="2212"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 18.33.06.png" data-origin-width="1424" data-origin-height="240"><span data-url="https://blog.kakaocdn.net/dn/TTyeR/dJMcagFNIHM/4zgN8Hjd8GqDauAQ21lHB0/img.png" data-phocus="https://blog.kakaocdn.net/dn/TTyeR/dJMcagFNIHM/4zgN8Hjd8GqDauAQ21lHB0/img.png"><img src="https://blog.kakaocdn.net/dn/TTyeR/dJMcagFNIHM/4zgN8Hjd8GqDauAQ21lHB0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FTTyeR%2FdJMcagFNIHM%2F4zgN8Hjd8GqDauAQ21lHB0%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="101" data-filename="Screenshot 2026-06-04 at 18.33.06.png" data-origin-width="1424" data-origin-height="240"/></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> 미적분 - 문제풀이/수열의 극한 수악중독 https://mathjk.tistory.com/6892 https://mathjk.tistory.com/6892#entry6892comment Fri, 5 Jun 2026 07:34:30 +0900 https://mathjk.tistory.com/6891 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">두 초점이 $\mathrm{F}(3, \; 0)$, $\mathrm{F}'(-3, \; 0)$인 쌍곡선 $C_1$이 있다. 쌍곡선 $C_1$의 두 꼭짓점 중 $x$좌표가 음수인 점을 $\mathrm{A}(-a, \; 0)$ ($a&gt;0$)이라 하고, 초점이 $\mathrm{F}$이고 꼭짓점이 $\mathrm{A}$인 포물선을 $C_2$, 이 포물선의 준선을 $l$이라 하자. 쌍곡선 $C_1$과 포물선 $C_2$가 만나는 점 중 제$1$사분면 위의 점의 $y$좌표와 쌍곡선 $C_1$과 직선 $l$이 만나는 점 중 제$2$사분면 위의 점의 $y$좌표가 같을 때, $a^2$의 값이 $\dfrac{q}{p}$이다. $p+q$의 값을 구하시오. (단, $p$와 $q$는 서로소인 자연수이다.)</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="Screenshot 2026-06-04 at 18.27.07.png" data-origin-width="1444" data-origin-height="2016"><span data-url="https://blog.kakaocdn.net/dn/b2s3Rb/dJMcacchkdb/wFohwDfmJxeEWxr7R8bys0/img.png" data-phocus="https://blog.kakaocdn.net/dn/b2s3Rb/dJMcacchkdb/wFohwDfmJxeEWxr7R8bys0/img.png"><img src="https://blog.kakaocdn.net/dn/b2s3Rb/dJMcacchkdb/wFohwDfmJxeEWxr7R8bys0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fb2s3Rb%2FdJMcacchkdb%2FwFohwDfmJxeEWxr7R8bys0%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="838" data-filename="Screenshot 2026-06-04 at 18.27.07.png" data-origin-width="1444" data-origin-height="2016"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 18.27.32.png" data-origin-width="1460" data-origin-height="646"><span data-url="https://blog.kakaocdn.net/dn/rEh1B/dJMcabRV4n1/wcHUb9kPDp5zcE3zgi0Kn1/img.png" data-phocus="https://blog.kakaocdn.net/dn/rEh1B/dJMcabRV4n1/wcHUb9kPDp5zcE3zgi0Kn1/img.png"><img src="https://blog.kakaocdn.net/dn/rEh1B/dJMcabRV4n1/wcHUb9kPDp5zcE3zgi0Kn1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FrEh1B%2FdJMcabRV4n1%2FwcHUb9kPDp5zcE3zgi0Kn1%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="601" height="266" data-filename="Screenshot 2026-06-04 at 18.27.32.png" data-origin-width="1460" data-origin-height="646"/></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/6891 https://mathjk.tistory.com/6891#entry6891comment Fri, 5 Jun 2026 07:28:43 +0900 https://mathjk.tistory.com/6890 <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 있다. 실수 $t$에 대하여 $f(\alpha) =f'(t) - 4t^2 + 4$ 를 만족시키는 실수 $\alpha$ 의 최댓값을 $g(t)$라 하자. 함수 $g(t)$가 $t=3$에서만 불연속이고 $g(3)=1$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 $11$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 10.10.52.png" data-origin-width="1532" data-origin-height="2122"><span data-url="https://blog.kakaocdn.net/dn/blPmXl/dJMcacXD8cs/kSY9YlYfvJAVdmWHKG3TV1/img.png" data-phocus="https://blog.kakaocdn.net/dn/blPmXl/dJMcacXD8cs/kSY9YlYfvJAVdmWHKG3TV1/img.png"><img src="https://blog.kakaocdn.net/dn/blPmXl/dJMcacXD8cs/kSY9YlYfvJAVdmWHKG3TV1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FblPmXl%2FdJMcacXD8cs%2FkSY9YlYfvJAVdmWHKG3TV1%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="831" data-filename="Screenshot 2026-06-04 at 10.10.52.png" data-origin-width="1532" data-origin-height="2122"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 10.11.17.png" data-origin-width="1350" data-origin-height="1690"><span data-url="https://blog.kakaocdn.net/dn/uoU1K/dJMcadWxsqa/C5dobDxha3dmLeoMWB5Oj0/img.png" data-phocus="https://blog.kakaocdn.net/dn/uoU1K/dJMcadWxsqa/C5dobDxha3dmLeoMWB5Oj0/img.png"><img src="https://blog.kakaocdn.net/dn/uoU1K/dJMcadWxsqa/C5dobDxha3dmLeoMWB5Oj0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FuoU1K%2FdJMcadWxsqa%2FC5dobDxha3dmLeoMWB5Oj0%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="751" data-filename="Screenshot 2026-06-04 at 10.11.17.png" data-origin-width="1350" data-origin-height="1690"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> 수학2 - 문제풀이/미분 수악중독 https://mathjk.tistory.com/6890 https://mathjk.tistory.com/6890#entry6890comment Thu, 4 Jun 2026 23:11:40 +0900 https://mathjk.tistory.com/6889 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">수열 $\{a_n\}$은 $a_1=1$, $a_2=4$이고, 모든 자연수 $n$에 대하여 $$a_{2n} = a_n + 1, \quad a_{4n+3} = a_{4n+1} = a_n + 4$$ 를 만족시킨다. $a_k = 10$을 만족시키는 자연수 $k$의 개수를 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 $32$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 09.34.59.png" data-origin-width="1358" data-origin-height="1322"><span data-url="https://blog.kakaocdn.net/dn/df8Hg4/dJMcagyXSoM/pyQ1dS4KAsETCOm2xh5mx0/img.png" data-phocus="https://blog.kakaocdn.net/dn/df8Hg4/dJMcagyXSoM/pyQ1dS4KAsETCOm2xh5mx0/img.png"><img src="https://blog.kakaocdn.net/dn/df8Hg4/dJMcagyXSoM/pyQ1dS4KAsETCOm2xh5mx0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fdf8Hg4%2FdJMcagyXSoM%2FpyQ1dS4KAsETCOm2xh5mx0%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="584" data-filename="Screenshot 2026-06-04 at 09.34.59.png" data-origin-width="1358" data-origin-height="1322"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 09.35.17.png" data-origin-width="1334" data-origin-height="1112"><span data-url="https://blog.kakaocdn.net/dn/b1uF6y/dJMcahR9BlE/YNgLoPKJ4elKRhMaDXoo8K/img.png" data-phocus="https://blog.kakaocdn.net/dn/b1uF6y/dJMcahR9BlE/YNgLoPKJ4elKRhMaDXoo8K/img.png"><img src="https://blog.kakaocdn.net/dn/b1uF6y/dJMcahR9BlE/YNgLoPKJ4elKRhMaDXoo8K/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fb1uF6y%2FdJMcahR9BlE%2FYNgLoPKJ4elKRhMaDXoo8K%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="500" data-filename="Screenshot 2026-06-04 at 09.35.17.png" data-origin-width="1334" data-origin-height="1112"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> 수학1- 문제풀이/수열 수악중독 https://mathjk.tistory.com/6889 https://mathjk.tistory.com/6889#entry6889comment Thu, 4 Jun 2026 22:35:54 +0900 https://mathjk.tistory.com/6888 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">노란색 공 <span>4</span>개, 보라색 공 <span>4</span>개, 검은색 공 <span>4</span>개가 있다. 이 <span>12</span>개의 공을 모두 일렬로 나열할 때, 노란색 공이 보라색 공과 이웃하지 않게 나열하는 경우의 수를 구하시오. (단, 같은 색 공끼리는 서로 구별하지 않는다.)</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 $780$</b></span></p> <p data-ke-size="size16">&nbsp;</p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 09.10.43.png" data-origin-width="1420" data-origin-height="2234"><span data-url="https://blog.kakaocdn.net/dn/b3TETI/dJMcacchcvI/Y22K0LuSOwZ3krsJOmIkp0/img.png" data-phocus="https://blog.kakaocdn.net/dn/b3TETI/dJMcacchcvI/Y22K0LuSOwZ3krsJOmIkp0/img.png"><img src="https://blog.kakaocdn.net/dn/b3TETI/dJMcacchcvI/Y22K0LuSOwZ3krsJOmIkp0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fb3TETI%2FdJMcacchcvI%2FY22K0LuSOwZ3krsJOmIkp0%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="944" data-filename="Screenshot 2026-06-04 at 09.10.43.png" data-origin-width="1420" data-origin-height="2234"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 09.11.08.png" data-origin-width="1500" data-origin-height="1452"><span data-url="https://blog.kakaocdn.net/dn/w77UZ/dJMb997GOLL/MeJuU6i3wDKDA5E9HglMTK/img.png" data-phocus="https://blog.kakaocdn.net/dn/w77UZ/dJMb997GOLL/MeJuU6i3wDKDA5E9HglMTK/img.png"><img src="https://blog.kakaocdn.net/dn/w77UZ/dJMb997GOLL/MeJuU6i3wDKDA5E9HglMTK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fw77UZ%2FdJMb997GOLL%2FMeJuU6i3wDKDA5E9HglMTK%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="581" data-filename="Screenshot 2026-06-04 at 09.11.08.png" data-origin-width="1500" data-origin-height="1452"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> 확률과 통계 - 문제풀이/경우의 수 수악중독 https://mathjk.tistory.com/6888 https://mathjk.tistory.com/6888#entry6888comment Thu, 4 Jun 2026 22:11:56 +0900 https://mathjk.tistory.com/6887 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">최고차항의 계수가 $1$인 삼차함수 $f(x)$에 대하여 함수 $g(x)$는 $$g(x) = \sqrt[3]{x \left (f(x) \right )^2}$$ 이다. 함수 $g(x)$가 실수 전체의 집합에서 미분가능하고 $x = \dfrac{19}{7}$와 $x = 3$에서 극값을 가질 때, $f(5)$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 $20$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 08.40.28.png" data-origin-width="1450" data-origin-height="2116"><span data-url="https://blog.kakaocdn.net/dn/v8QdM/dJMcaf06SLc/Q9M5ukgXr8XkPKAorTkO9K/img.png" data-phocus="https://blog.kakaocdn.net/dn/v8QdM/dJMcaf06SLc/Q9M5ukgXr8XkPKAorTkO9K/img.png"><img src="https://blog.kakaocdn.net/dn/v8QdM/dJMcaf06SLc/Q9M5ukgXr8XkPKAorTkO9K/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fv8QdM%2FdJMcaf06SLc%2FQ9M5ukgXr8XkPKAorTkO9K%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="876" data-filename="Screenshot 2026-06-04 at 08.40.28.png" data-origin-width="1450" data-origin-height="2116"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 08.40.46.png" data-origin-width="1444" data-origin-height="1884"><span data-url="https://blog.kakaocdn.net/dn/bhIfGN/dJMcaayNik9/mgkKxVvUzYyh49NXrmNdq1/img.png" data-phocus="https://blog.kakaocdn.net/dn/bhIfGN/dJMcaayNik9/mgkKxVvUzYyh49NXrmNdq1/img.png"><img src="https://blog.kakaocdn.net/dn/bhIfGN/dJMcaayNik9/mgkKxVvUzYyh49NXrmNdq1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbhIfGN%2FdJMcaayNik9%2FmgkKxVvUzYyh49NXrmNdq1%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="783" data-filename="Screenshot 2026-06-04 at 08.40.46.png" data-origin-width="1444" data-origin-height="1884"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> 미적분 - 문제풀이/미분법 수악중독 https://mathjk.tistory.com/6887 https://mathjk.tistory.com/6887#entry6887comment Thu, 4 Jun 2026 21:42:49 +0900 https://mathjk.tistory.com/6886 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">좌표평면에서 $\overline{\mathrm{AB}} = \overline{\mathrm{AC}} = 2$, $\angle \mathrm{CAB} &gt; \dfrac{\pi}{2}$인 이등변삼각형의 세 꼭짓점 $\mathrm{A}$, $\mathrm{B}$, $\mathrm{C}$와 선분 $\mathrm{AB}$의 수직이등분선 위의 점 $\mathrm{D}$가 $$\overrightarrow{\mathrm{BA}} \cdot \overrightarrow{\mathrm{BC}} = \overrightarrow{\mathrm{CB}} \cdot \overrightarrow{\mathrm{CD}}, \quad 2 \overrightarrow{\mathrm{AC}} \cdot \overrightarrow{\mathrm{AD}} = \overrightarrow{\mathrm{DA}} \cdot \overrightarrow{\mathrm{DB}}$$ 를 만족시킨다. 선분 $\mathrm{AB}$를 지름으로 하는 원 위를 움직이는 점 $\mathrm{X}$에 대하여 $\overrightarrow{\mathrm{DX}} \cdot \overrightarrow{\mathrm{BC}}$의 최댓값을 $M$, 최솟값을 $m$이라 하자. $|M \times m| = \dfrac{q}{p}$ 일 때, $p+q$의 값을 구하시오. (단, $p$와 $q$는 서로소인 자연수이다.)</p> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 07.15.35.png" data-origin-width="996" data-origin-height="506"><span data-url="https://blog.kakaocdn.net/dn/UsR2x/dJMcaiwNunL/sP64YHYqljtKHXLr7Gg0kk/img.png" data-phocus="https://blog.kakaocdn.net/dn/UsR2x/dJMcaiwNunL/sP64YHYqljtKHXLr7Gg0kk/img.png"><img src="https://blog.kakaocdn.net/dn/UsR2x/dJMcaiwNunL/sP64YHYqljtKHXLr7Gg0kk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FUsR2x%2FdJMcaiwNunL%2FsP64YHYqljtKHXLr7Gg0kk%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="417" height="212" data-filename="Screenshot 2026-06-04 at 07.15.35.png" data-origin-width="996" data-origin-height="506"/></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 $29$</b></span></p> <p data-ke-size="size16">&nbsp;</p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 07.57.29.png" data-origin-width="1532" data-origin-height="1508"><span data-url="https://blog.kakaocdn.net/dn/cwsSAu/dJMcafNFnbY/vyGNRIKF5ftoiIb3BkEYx1/img.png" data-phocus="https://blog.kakaocdn.net/dn/cwsSAu/dJMcafNFnbY/vyGNRIKF5ftoiIb3BkEYx1/img.png"><img src="https://blog.kakaocdn.net/dn/cwsSAu/dJMcafNFnbY/vyGNRIKF5ftoiIb3BkEYx1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FcwsSAu%2FdJMcafNFnbY%2FvyGNRIKF5ftoiIb3BkEYx1%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="591" data-filename="Screenshot 2026-06-04 at 07.57.29.png" data-origin-width="1532" data-origin-height="1508"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 07.58.14.png" data-origin-width="1494" data-origin-height="1238"><span data-url="https://blog.kakaocdn.net/dn/bWFelt/dJMcajh9BlF/31fttkWt61WThZXRbKjSsK/img.png" data-phocus="https://blog.kakaocdn.net/dn/bWFelt/dJMcajh9BlF/31fttkWt61WThZXRbKjSsK/img.png"><img src="https://blog.kakaocdn.net/dn/bWFelt/dJMcajh9BlF/31fttkWt61WThZXRbKjSsK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbWFelt%2FdJMcajh9BlF%2F31fttkWt61WThZXRbKjSsK%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="497" data-filename="Screenshot 2026-06-04 at 07.58.14.png" data-origin-width="1494" data-origin-height="1238"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-06-04 at 07.58.34.png" data-origin-width="1444" data-origin-height="1166"><span data-url="https://blog.kakaocdn.net/dn/yGHWT/dJMcaftip2i/p0mZ1UwzmA3BcswJciwRc1/img.png" data-phocus="https://blog.kakaocdn.net/dn/yGHWT/dJMcaftip2i/p0mZ1UwzmA3BcswJciwRc1/img.png"><img src="https://blog.kakaocdn.net/dn/yGHWT/dJMcaftip2i/p0mZ1UwzmA3BcswJciwRc1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FyGHWT%2FdJMcaftip2i%2Fp0mZ1UwzmA3BcswJciwRc1%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="484" data-filename="Screenshot 2026-06-04 at 07.58.34.png" data-origin-width="1444" data-origin-height="1166"/></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> 기하 - 문제풀이/평면벡터 수악중독 https://mathjk.tistory.com/6886 https://mathjk.tistory.com/6886#entry6886comment Thu, 4 Jun 2026 20:59:33 +0900 https://mathjk.tistory.com/6885 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">다항함수 $f(x)$에 대하여 함수 $g(x)$를 $$g(x)=\left( x^2+x \right ) f(x)$$라 하자. $\lim \limits_{h \to 0} \dfrac{g(1+h)-4}{h}=9$일 때, $f(1) \times f'(1)$의 값은?&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">① $3$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ② $\dfrac{9}{2}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ③ $6$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ④ $\dfrac{15}{2}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ⑤ $9$</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="9번.png" data-origin-width="1534" data-origin-height="1142"><span data-url="https://blog.kakaocdn.net/dn/lp62L/dJMcagrVNcL/eikvPltjLRHkE8IRrs94Bk/img.png" data-phocus="https://blog.kakaocdn.net/dn/lp62L/dJMcagrVNcL/eikvPltjLRHkE8IRrs94Bk/img.png"><img src="https://blog.kakaocdn.net/dn/lp62L/dJMcagrVNcL/eikvPltjLRHkE8IRrs94Bk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Flp62L%2FdJMcagrVNcL%2FeikvPltjLRHkE8IRrs94Bk%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="1534" height="446" data-filename="9번.png" data-origin-width="1534" data-origin-height="1142"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> 수학2 - 문제풀이/미분 수악중독 https://mathjk.tistory.com/6885 https://mathjk.tistory.com/6885#entry6885comment Mon, 11 May 2026 23:41:38 +0900 https://mathjk.tistory.com/6884 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">각 $\mathrm{A}$가 예각인 삼각형 $\mathrm{ABC}$가 다음 조건을 만족시킬 때, 삼각형 $\mathrm{ABC}$의 외접원의 반지름의 길이는?&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) $\overline{\mathrm{AB}}=4,&nbsp;\overline{\mathrm{AC}}=15$<br />(나) 삼각형 $\mathrm{ABC}$의 넓이는 $24$이다.</p> </div> <p data-ke-size="size16"><br />①&nbsp;$\dfrac{15}{2}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$\dfrac{65}{8}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$\dfrac{35}{4}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$\dfrac{75}{8}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$10$</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 ②&nbsp;</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="10번.png" data-origin-width="1390" data-origin-height="974"><span data-url="https://blog.kakaocdn.net/dn/bcBeUw/dJMcadu7Nju/EkZtXOreK9AEKk6DW77bx0/img.png" data-phocus="https://blog.kakaocdn.net/dn/bcBeUw/dJMcadu7Nju/EkZtXOreK9AEKk6DW77bx0/img.png"><img src="https://blog.kakaocdn.net/dn/bcBeUw/dJMcadu7Nju/EkZtXOreK9AEKk6DW77bx0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbcBeUw%2FdJMcadu7Nju%2FEkZtXOreK9AEKk6DW77bx0%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="420" data-filename="10번.png" data-origin-width="1390" data-origin-height="974"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> 수학1- 문제풀이/삼각함수 수악중독 https://mathjk.tistory.com/6884 https://mathjk.tistory.com/6884#entry6884comment Sun, 10 May 2026 04:25:50 +0900 https://mathjk.tistory.com/6883 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">다음 조건을 만족시키는 모든 수열 $\{a_{n}\}$에 대하여 $a_{1}$의 값의 합은?&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) 모든 자연수 $n$에 대하여 $$a_{n+1}=\begin{cases}-2a_{n}&amp;(a_{n}&lt;0)\\ a_{n}-3&amp;(a_{n}\ge0)\end{cases}$$이다.<br />(나) $a_{3}=a_{1}+4$</p> </div> <p data-ke-size="size16"><br />①&nbsp;$-\dfrac{2}{3}$&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;$-\dfrac{4}{3}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$-\dfrac{5}{3}$&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 ④</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="11번.png" data-origin-width="1446" data-origin-height="1954"><span data-url="https://blog.kakaocdn.net/dn/bfHSN7/dJMcaiwtN3B/9A0CU3347qqhYYUoUyljk0/img.png" data-phocus="https://blog.kakaocdn.net/dn/bfHSN7/dJMcaiwtN3B/9A0CU3347qqhYYUoUyljk0/img.png"><img src="https://blog.kakaocdn.net/dn/bfHSN7/dJMcaiwtN3B/9A0CU3347qqhYYUoUyljk0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbfHSN7%2FdJMcaiwtN3B%2F9A0CU3347qqhYYUoUyljk0%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="811" data-filename="11번.png" data-origin-width="1446" data-origin-height="1954"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> 수학1- 문제풀이/수열 수악중독 https://mathjk.tistory.com/6883 https://mathjk.tistory.com/6883#entry6883comment Sun, 10 May 2026 04:23:21 +0900 https://mathjk.tistory.com/6882 <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 $\mathrm{P}$의 시각 $t \; (t\ge0)$에서의 속도 $v(t)$가 $$v(t)=3t^{2}-11t+8$$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;$t=1$일&nbsp;때&nbsp;점&nbsp;$\mathrm{P}$의&nbsp;운동&nbsp;방향이&nbsp;바뀐다.<br />ㄴ. 점 $\mathrm{P}$의 가속도가 $1$이 되는 순간 점 $\mathrm{P}$의 위치는 $2$이다.<br />ㄷ. 시각 $t=0$에서 $t=2$까지 점 $\mathrm{P}$가 움직인 거리는 $6$이다.</p> </div> <p data-ke-size="size16"><br />① ㄱ&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;② ㄱ, ㄴ&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③ ㄱ, ㄷ&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④ ㄴ, 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 ②</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="12번.png" data-origin-width="1436" data-origin-height="1588"><span data-url="https://blog.kakaocdn.net/dn/boN65e/dJMcabc2BYk/SPqHjQ96nFDfXPtU67vxB0/img.png" data-phocus="https://blog.kakaocdn.net/dn/boN65e/dJMcabc2BYk/SPqHjQ96nFDfXPtU67vxB0/img.png"><img src="https://blog.kakaocdn.net/dn/boN65e/dJMcabc2BYk/SPqHjQ96nFDfXPtU67vxB0/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FboN65e%2FdJMcabc2BYk%2FSPqHjQ96nFDfXPtU67vxB0%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="664" data-filename="12번.png" data-origin-width="1436" data-origin-height="1588"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> 수학2 - 문제풀이/적분 수악중독 https://mathjk.tistory.com/6882 https://mathjk.tistory.com/6882#entry6882comment Sun, 10 May 2026 04:20:43 +0900 https://mathjk.tistory.com/6881 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">실수 전체의 집합에서 연속인 함수 $f(x)$가 다음 조건을 만족시킬 때, $f(28)$의 값은?</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;$0&nbsp;\le&nbsp;x&nbsp;\le&nbsp;12$인&nbsp;모든&nbsp;실수&nbsp;$x$에&nbsp;대하여&nbsp;$$(\sqrt{2x+1}-1)\times&nbsp;f(x)=ax$$이다.&nbsp;(단,&nbsp;$a$는&nbsp;상수이다.)<br />(나) 모든 실수 $k$에 대하여 함수 $f(x)$에서 $x$의 값이 $k$에서 $k+12$까지 변할 때의 평균변화율은 $\dfrac{1}{2}$이다.</p> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">①&nbsp;$16$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$18$&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;$22$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$24$</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="13번.png" data-origin-width="1472" data-origin-height="1414"><span data-url="https://blog.kakaocdn.net/dn/bVvB53/dJMcab5c36H/C4Gn87zdlfCL0TsMfngRDK/img.png" data-phocus="https://blog.kakaocdn.net/dn/bVvB53/dJMcab5c36H/C4Gn87zdlfCL0TsMfngRDK/img.png"><img src="https://blog.kakaocdn.net/dn/bVvB53/dJMcab5c36H/C4Gn87zdlfCL0TsMfngRDK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbVvB53%2FdJMcab5c36H%2FC4Gn87zdlfCL0TsMfngRDK%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="576" data-filename="13번.png" data-origin-width="1472" data-origin-height="1414"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> 수학2 - 문제풀이/미분 수악중독 https://mathjk.tistory.com/6881 https://mathjk.tistory.com/6881#entry6881comment Sun, 10 May 2026 04:17:45 +0900 https://mathjk.tistory.com/6880 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과 같이 곡선 $y=\sin x \; (0 \le x \le 2\pi)$가 직선 $y=k$와 만나는 두 점을 $\mathrm{A, \; B}$라 하고, 직선 $y=-\sqrt{1-k^{2}}$과 만나는 두 점을 $\mathrm{C, \; D}$라 하자. $\overline{\mathrm{CD}}-\overline{\mathrm{AB}}=\dfrac{2}{9}\pi$일 때, 선분 $\mathrm{AB}$의 길이는? (단, $k$는 $0&lt;k&lt;1$인 상수이다.)&nbsp;<br /><br /></p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-09 at 15.12.22.png" data-origin-width="1116" data-origin-height="464"><span data-url="https://blog.kakaocdn.net/dn/sd07O/dJMcagyFfv9/j89iJtPkmokyVzxJia3IBK/img.png" data-phocus="https://blog.kakaocdn.net/dn/sd07O/dJMcagyFfv9/j89iJtPkmokyVzxJia3IBK/img.png"><img src="https://blog.kakaocdn.net/dn/sd07O/dJMcagyFfv9/j89iJtPkmokyVzxJia3IBK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fsd07O%2FdJMcagyFfv9%2Fj89iJtPkmokyVzxJia3IBK%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="464" height="193" data-filename="Screenshot 2026-05-09 at 15.12.22.png" data-origin-width="1116" data-origin-height="464"/></span></figure> </p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">①&nbsp;$\dfrac{13}{36}\pi$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$\dfrac{3}{8}\pi$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$\dfrac{7}{18}\pi$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$\dfrac{29}{72}\pi$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$\dfrac{5}{12}\pi$</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="14번.png" data-origin-width="1322" data-origin-height="1198"><span data-url="https://blog.kakaocdn.net/dn/6VJYS/dJMcabKXrY2/HYHAypRd6b8QfcT4s2wwOk/img.png" data-phocus="https://blog.kakaocdn.net/dn/6VJYS/dJMcabKXrY2/HYHAypRd6b8QfcT4s2wwOk/img.png"><img src="https://blog.kakaocdn.net/dn/6VJYS/dJMcabKXrY2/HYHAypRd6b8QfcT4s2wwOk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2F6VJYS%2FdJMcabKXrY2%2FHYHAypRd6b8QfcT4s2wwOk%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="601" height="545" data-filename="14번.png" data-origin-width="1322" data-origin-height="1198"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> 수학1- 문제풀이/삼각함수 수악중독 https://mathjk.tistory.com/6880 https://mathjk.tistory.com/6880#entry6880comment Sun, 10 May 2026 04:15:06 +0900 https://mathjk.tistory.com/6879 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;$p&gt;1$인 상수 $p$에 대하여 함수 $f(x)=x^{2}-px$가 있다. 실수 $t \; (t&gt;-p)$에 대하여 함수 $y=|f(x)|$의 그래프와 직선 $y=x+t$가 만나는 점의 좌표 중 가장 작은 값을 $\alpha(t)$, 가장 큰 값을 $\beta(t)$라 하자. 열린구간 $(-p, \infty)$에서 정의된 함수 $$g(t)=\int_{\alpha(t)}^{\beta(t)} \{|f(x)|-(x+t)\}dx$$의 최댓값이 $\dfrac{1}{2}$일 때, $p$의 값은?&nbsp;</p> <p data-ke-size="size16"><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="15번.png" data-origin-width="1434" data-origin-height="2248"><span data-url="https://blog.kakaocdn.net/dn/bpnxHc/dJMcabYscKs/NQAbh0H9Z2sNtAKMq2Xbl1/img.png" data-phocus="https://blog.kakaocdn.net/dn/bpnxHc/dJMcabYscKs/NQAbh0H9Z2sNtAKMq2Xbl1/img.png"><img src="https://blog.kakaocdn.net/dn/bpnxHc/dJMcabYscKs/NQAbh0H9Z2sNtAKMq2Xbl1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbpnxHc%2FdJMcabYscKs%2FNQAbh0H9Z2sNtAKMq2Xbl1%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="941" data-filename="15번.png" data-origin-width="1434" data-origin-height="2248"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> 수학2 - 문제풀이/적분 수악중독 https://mathjk.tistory.com/6879 https://mathjk.tistory.com/6879#entry6879comment Sat, 9 May 2026 00:33:21 +0900 https://mathjk.tistory.com/6878 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">첫째항이 $8$인 등차수열 $\{a_{n}\}$에 대하여 수열 $\{b_{n}\}$이 다음 조건을 만족시킬 때, $\sum \limits_{k=1}^{10}b_{k}$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)&nbsp;모든&nbsp;자연수&nbsp;$n$에&nbsp;대하여&nbsp;$$b_{n}=\begin{cases}-2a_{n}&amp;(a_{n}\le0)\\&nbsp;a_{n}&amp;(a_{n}&gt;0)\end{cases}$$이다.<br />(나) $b_{3}+b_{5}=2b_{4}+6, b_{4}+b_{6}=2b_{5}$</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 $155$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="20번.png" data-origin-width="1478" data-origin-height="2128"><span data-url="https://blog.kakaocdn.net/dn/b0L3xb/dJMcaiQLpBj/w8mY70tEJIuXcP3zZm2M91/img.png" data-phocus="https://blog.kakaocdn.net/dn/b0L3xb/dJMcaiQLpBj/w8mY70tEJIuXcP3zZm2M91/img.png"><img src="https://blog.kakaocdn.net/dn/b0L3xb/dJMcaiQLpBj/w8mY70tEJIuXcP3zZm2M91/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fb0L3xb%2FdJMcaiQLpBj%2Fw8mY70tEJIuXcP3zZm2M91%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="864" data-filename="20번.png" data-origin-width="1478" data-origin-height="2128"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> 수학1- 문제풀이/수열 수악중독 https://mathjk.tistory.com/6878 https://mathjk.tistory.com/6878#entry6878comment Sat, 9 May 2026 00:30:54 +0900 https://mathjk.tistory.com/6877 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">집합 $\mathrm{X}=\{1, 2, 3, 4, 5\}$에 대하여 $\mathrm{X}$에서 $\mathrm{X}$로의 모든 일대일대응 중에서 임의로 하나를 선택할 때, 이 함수가 다음 조건을 만족시킬 확률은?&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;$f(1)&lt;f(3),&nbsp;f(2)&lt;f(4)$<br />(나) 함수의 역함수 $f^{-1}$에 대하여 $|f(1)-f(5)| \ge f^{-1}(1)$이다.</p> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">①&nbsp;$\dfrac{3}{20}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$\dfrac{1}{6}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$\dfrac{11}{60}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$\dfrac{1}{5}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$\dfrac{13}{60}$</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="확통28번-1.png" data-origin-width="1608" data-origin-height="1782"><span data-url="https://blog.kakaocdn.net/dn/bI2CO9/dJMcahYD75l/b0koXrJJt614suqzz8ulrK/img.png" data-phocus="https://blog.kakaocdn.net/dn/bI2CO9/dJMcahYD75l/b0koXrJJt614suqzz8ulrK/img.png"><img src="https://blog.kakaocdn.net/dn/bI2CO9/dJMcahYD75l/b0koXrJJt614suqzz8ulrK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbI2CO9%2FdJMcahYD75l%2Fb0koXrJJt614suqzz8ulrK%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="665" data-filename="확통28번-1.png" data-origin-width="1608" data-origin-height="1782"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="확통28번-2.png" data-origin-width="1436" data-origin-height="2340"><span data-url="https://blog.kakaocdn.net/dn/WaVS8/dJMcadu7ilg/0nzxwdyjIMY0UF9LXBAPsk/img.png" data-phocus="https://blog.kakaocdn.net/dn/WaVS8/dJMcadu7ilg/0nzxwdyjIMY0UF9LXBAPsk/img.png"><img src="https://blog.kakaocdn.net/dn/WaVS8/dJMcadu7ilg/0nzxwdyjIMY0UF9LXBAPsk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FWaVS8%2FdJMcadu7ilg%2F0nzxwdyjIMY0UF9LXBAPsk%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="978" data-filename="확통28번-2.png" data-origin-width="1436" data-origin-height="2340"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> 확률과 통계 - 문제풀이/확률 수악중독 https://mathjk.tistory.com/6877 https://mathjk.tistory.com/6877#entry6877comment Sat, 9 May 2026 00:27:43 +0900 https://mathjk.tistory.com/6876 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">공비가 $-\dfrac{1}{2}$인 등비수열 $\{a_{n}\}$과 수열 $\{b_{n}\}$이 다음 조건을 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">(가) 모든 자연수 $n$에 대하여 $(b_{n}-a_{n})(b_{n}-|a_{n}|)=0$이다.<br />(나) $\sum \limits_{n=k}^{\infty}(a_{2n+1}+b_{2n+1})=0$을 만족시키는 자연수 $k$의 최솟값은 $2$이다.</p> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">$b_{7}-b_{8}=3 \times a_3 +5$일 때, $\sum \limits_{n=1}^{\infty}b_{n}$의 값은?<br /><br />①&nbsp;$-\dfrac{9}{4}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;②&nbsp;$-\dfrac{3}{4}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③&nbsp;$\dfrac{3}{4}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④&nbsp;$\dfrac{9}{4}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤&nbsp;$\dfrac{15}{4}$</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="미적28번-1.png" data-origin-width="1524" data-origin-height="2016"><span data-url="https://blog.kakaocdn.net/dn/b8sBAz/dJMcafzMNWD/95fztORFtEOehwl7taOw40/img.png" data-phocus="https://blog.kakaocdn.net/dn/b8sBAz/dJMcafzMNWD/95fztORFtEOehwl7taOw40/img.png"><img src="https://blog.kakaocdn.net/dn/b8sBAz/dJMcafzMNWD/95fztORFtEOehwl7taOw40/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fb8sBAz%2FdJMcafzMNWD%2F95fztORFtEOehwl7taOw40%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="794" data-filename="미적28번-1.png" data-origin-width="1524" data-origin-height="2016"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="미적28번-2.png" data-origin-width="1470" data-origin-height="1474"><span data-url="https://blog.kakaocdn.net/dn/0SETs/dJMcadWdEyQ/36rvNAiPEBohwpiBglYke1/img.png" data-phocus="https://blog.kakaocdn.net/dn/0SETs/dJMcadWdEyQ/36rvNAiPEBohwpiBglYke1/img.png"><img src="https://blog.kakaocdn.net/dn/0SETs/dJMcadWdEyQ/36rvNAiPEBohwpiBglYke1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2F0SETs%2FdJMcadWdEyQ%2F36rvNAiPEBohwpiBglYke1%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="602" data-filename="미적28번-2.png" data-origin-width="1470" data-origin-height="1474"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="미적28번-3.png" data-origin-width="1506" data-origin-height="1522"><span data-url="https://blog.kakaocdn.net/dn/dytga0/dJMcafsZtJ6/QLlznY3CNrXF0Abghmpl30/img.png" data-phocus="https://blog.kakaocdn.net/dn/dytga0/dJMcafsZtJ6/QLlznY3CNrXF0Abghmpl30/img.png"><img src="https://blog.kakaocdn.net/dn/dytga0/dJMcafsZtJ6/QLlznY3CNrXF0Abghmpl30/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fdytga0%2FdJMcafsZtJ6%2FQLlznY3CNrXF0Abghmpl30%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="606" data-filename="미적28번-3.png" data-origin-width="1506" data-origin-height="1522"/></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> 미적분 - 문제풀이/수열의 극한 수악중독 https://mathjk.tistory.com/6876 https://mathjk.tistory.com/6876#entry6876comment Sat, 9 May 2026 00:24:01 +0900 https://mathjk.tistory.com/6875 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">점 $\mathrm{F}(3a, 4a) \; (a&gt;0)$을 초점으로 하고 준선이 $x=-5a$인 포물선을 $\mathrm{C}_{1}$, 점 $\mathrm{F}$를 초점으로 하고 준선이 $y=-5a$인 포물선을 $\mathrm{C}_{2}$라 하자. 두 포물선 $\mathrm{C}_{1}, \mathrm{C}_{2}$가 만나는 두 점을 $\mathrm{A, B} \; \left ( \overline{\mathrm{BF}}&lt;\overline{\mathrm{AF}}\right )$라 할 때, $\overline{\mathrm{OA}}=6$이다. $\overline{\mathrm{AF}}-\overline{\mathrm{BF}}$의 값은? (단, $\mathrm{O}$는 원점이다.)&nbsp;</p> <p data-ke-size="size16"><br />① $\dfrac{8}{3}\sqrt{2}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;② $3\sqrt{2}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;③ $\dfrac{10}{3}\sqrt{2}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;④ $\dfrac{11}{3}\sqrt{2}$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⑤ $4\sqrt{2}$</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="기하28번.png" data-origin-width="1446" data-origin-height="2302"><span data-url="https://blog.kakaocdn.net/dn/0yLM9/dJMb99TQzTy/FTxPAL62tKohtyLhaluHf1/img.png" data-phocus="https://blog.kakaocdn.net/dn/0yLM9/dJMb99TQzTy/FTxPAL62tKohtyLhaluHf1/img.png"><img src="https://blog.kakaocdn.net/dn/0yLM9/dJMb99TQzTy/FTxPAL62tKohtyLhaluHf1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2F0yLM9%2FdJMb99TQzTy%2FFTxPAL62tKohtyLhaluHf1%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="955" data-filename="기하28번.png" data-origin-width="1446" data-origin-height="2302"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> 기하 - 문제풀이/이차곡선 수악중독 https://mathjk.tistory.com/6875 https://mathjk.tistory.com/6875#entry6875comment Sat, 9 May 2026 00:19:51 +0900 https://mathjk.tistory.com/6874 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">$1$부터 $7$까지의 자연수가 하나씩 적혀 있는 $7$개의 의자가 있다. 이 $7$개의 의자를 일정한 간격을 두고 원형으로 배열할 때, 다음 조건을 만족시키는 경우의 수를 구하시오. (단, 회전하여 일치하는 것은 같은 것으로 본다.)</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;$6$이&nbsp;적힌&nbsp;의자와&nbsp;이웃한&nbsp;$2$개의&nbsp;의자에&nbsp;적힌&nbsp;두&nbsp;수의&nbsp;합은&nbsp;$9$이다.<br />(나) $7$이 적힌 의자와 이웃하지 않은 $4$개의 의자에 적힌 네 수의 곱은 $12$의 배수이다.</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 $68$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 16.06.18.png" data-origin-width="1440" data-origin-height="2022"><span data-url="https://blog.kakaocdn.net/dn/tbxOd/dJMcahqO0fX/8MWKlcm84rZ1w6I0jroaf1/img.png" data-phocus="https://blog.kakaocdn.net/dn/tbxOd/dJMcahqO0fX/8MWKlcm84rZ1w6I0jroaf1/img.png"><img src="https://blog.kakaocdn.net/dn/tbxOd/dJMcahqO0fX/8MWKlcm84rZ1w6I0jroaf1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FtbxOd%2FdJMcahqO0fX%2F8MWKlcm84rZ1w6I0jroaf1%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="842" data-filename="Screenshot 2026-05-07 at 16.06.18.png" data-origin-width="1440" data-origin-height="2022"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> 확률과 통계 - 문제풀이/경우의 수 수악중독 https://mathjk.tistory.com/6874 https://mathjk.tistory.com/6874#entry6874comment Fri, 8 May 2026 05:07:14 +0900 https://mathjk.tistory.com/6873 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과 같이 길이가 $2$인 선분 $\mathrm{AB}$를 지름으로 하는 반원이 있다. 호 $\mathrm{AB}$ 위에 점 $\mathrm{P}$를 $\angle\mathrm{BAP}=\theta \; \left (0&lt;\theta&lt;\dfrac{\pi}{3} \right )$가 되도록 잡고, 호 $\mathrm{AP}$ 위에 점 $\mathrm{Q}$를 $\overline{\mathrm{PQ}}=1$이 되도록 잡는다. 선분 $\mathrm{AP}$의 중점을 $\mathrm{M}$이라 할 때, 삼각형 $\mathrm{PQM}$의 넓이를 $f(\theta)$라 하자. $\overline{\mathrm{AP}}=\dfrac{6}{5}$이 되도록 하는 $\theta$의 값을 $a$라 할 때, $f'(a)=p+q\sqrt{3}$이다. $100 \times |p+q|$의 값을 구하시오. (단, $p$와 $q$는 유리수이다.)</p> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 16.00.14.png" data-origin-width="1018" data-origin-height="582"><span data-url="https://blog.kakaocdn.net/dn/wnvcy/dJMcabKVM7V/OiW2uY54KUkbFIQ1wDkfFk/img.png" data-phocus="https://blog.kakaocdn.net/dn/wnvcy/dJMcabKVM7V/OiW2uY54KUkbFIQ1wDkfFk/img.png"><img src="https://blog.kakaocdn.net/dn/wnvcy/dJMcabKVM7V/OiW2uY54KUkbFIQ1wDkfFk/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fwnvcy%2FdJMcabKVM7V%2FOiW2uY54KUkbFIQ1wDkfFk%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="362" height="207" data-filename="Screenshot 2026-05-07 at 16.00.14.png" data-origin-width="1018" data-origin-height="582"/></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 $17$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 16.01.26.png" data-origin-width="1366" data-origin-height="1884"><span data-url="https://blog.kakaocdn.net/dn/bfrkG3/dJMb990DHND/u7ddYWyJbtKbWSrVCkziKK/img.png" data-phocus="https://blog.kakaocdn.net/dn/bfrkG3/dJMb990DHND/u7ddYWyJbtKbWSrVCkziKK/img.png"><img src="https://blog.kakaocdn.net/dn/bfrkG3/dJMb990DHND/u7ddYWyJbtKbWSrVCkziKK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FbfrkG3%2FdJMb990DHND%2Fu7ddYWyJbtKbWSrVCkziKK%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="828" data-filename="Screenshot 2026-05-07 at 16.01.26.png" data-origin-width="1366" data-origin-height="1884"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 16.01.49.png" data-origin-width="1360" data-origin-height="944"><span data-url="https://blog.kakaocdn.net/dn/QviLl/dJMb997m9SA/mnwehtUG2sBRxTabFjkbh1/img.png" data-phocus="https://blog.kakaocdn.net/dn/QviLl/dJMb997m9SA/mnwehtUG2sBRxTabFjkbh1/img.png"><img src="https://blog.kakaocdn.net/dn/QviLl/dJMb997m9SA/mnwehtUG2sBRxTabFjkbh1/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FQviLl%2FdJMb997m9SA%2FmnwehtUG2sBRxTabFjkbh1%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="416" data-filename="Screenshot 2026-05-07 at 16.01.49.png" data-origin-width="1360" data-origin-height="944"/></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> 미적분 - 문제풀이/미분법 수악중독 https://mathjk.tistory.com/6873 https://mathjk.tistory.com/6873#entry6873comment Fri, 8 May 2026 05:04:46 +0900 https://mathjk.tistory.com/6872 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">그림과 같이 한 변의 길이가 $1$인 정사각형 $\mathrm{ABCD}$와 중심각의 크기가 $\dfrac{3}{2}\pi$인 부채꼴 $\mathrm{BAC}$가 있고, 선분 $\mathrm{AD}$의 중점을 $\mathrm{M}$이라 하자. 정사각형 $\mathrm{ABCD}$ 위를 움직이는 점 $\mathrm{P}$와 호 $\mathrm{AC}$ 위를 움직이는 점 $\mathrm{Q}$에 대하여 $|\overrightarrow{\mathrm{DP}}+\overrightarrow{\mathrm{MQ}}|$의 최댓값은 $\dfrac{q}{p}$이다. $p+q$의 값을 구하시오. (단, $p$와 $q$는 서로소인 자연수이다.)</p> <p data-ke-size="size16">&nbsp;</p> <p><figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 15.55.42.png" data-origin-width="896" data-origin-height="856"><span data-url="https://blog.kakaocdn.net/dn/luE3W/dJMcabKVM2U/tGb1U33x7dTUCmlNaq2y7K/img.png" data-phocus="https://blog.kakaocdn.net/dn/luE3W/dJMcabKVM2U/tGb1U33x7dTUCmlNaq2y7K/img.png"><img src="https://blog.kakaocdn.net/dn/luE3W/dJMcabKVM2U/tGb1U33x7dTUCmlNaq2y7K/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FluE3W%2FdJMcabKVM2U%2FtGb1U33x7dTUCmlNaq2y7K%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="364" height="348" data-filename="Screenshot 2026-05-07 at 15.55.42.png" data-origin-width="896" data-origin-height="856"/></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 $9$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 15.56.43.png" data-origin-width="1420" data-origin-height="2206"><span data-url="https://blog.kakaocdn.net/dn/Sb9gL/dJMcaaZvaos/kUrNPxGXvb5WqXO9FvfJFK/img.png" data-phocus="https://blog.kakaocdn.net/dn/Sb9gL/dJMcaaZvaos/kUrNPxGXvb5WqXO9FvfJFK/img.png"><img src="https://blog.kakaocdn.net/dn/Sb9gL/dJMcaaZvaos/kUrNPxGXvb5WqXO9FvfJFK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FSb9gL%2FdJMcaaZvaos%2FkUrNPxGXvb5WqXO9FvfJFK%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="932" data-filename="Screenshot 2026-05-07 at 15.56.43.png" data-origin-width="1420" data-origin-height="2206"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> 기하 - 문제풀이/평면벡터 수악중독 https://mathjk.tistory.com/6872 https://mathjk.tistory.com/6872#entry6872comment Fri, 8 May 2026 04:57:58 +0900 https://mathjk.tistory.com/6871 <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">최고차항의 계수가 $1$이고 $f(0)=0$인 삼차함수 $f(x)$가 있다. 양수 $p$와 실수 $k(k\ne0)$에 대하여 함수 $$g(x)=\begin{cases}f(x)&amp;(x&lt;p)\\ kf(x-p)&amp;(x\ge p)\end{cases}$$가 다음 조건을 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">(가)&nbsp;함수&nbsp;$g(x)$는&nbsp;실수&nbsp;전체의&nbsp;집합에서&nbsp;미분가능하다.<br />(나) $x$에 대한 방정식 $g(x)=0$의 서로 다른 모든 실근의 합이 $2p$이다.</p> </div> <p data-ke-size="size16"><br />함수 $g(x)$의 극값 중 가장 큰 값이 $\dfrac{3\sqrt{3}}{2}$일 때, $f(4)$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 $55$</b></span></p> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 12.07.23.png" data-origin-width="1506" data-origin-height="2270"><span data-url="https://blog.kakaocdn.net/dn/b4T4gE/dJMcaiccH1W/aft3ya55Y9B5dIQMAFFlkK/img.png" data-phocus="https://blog.kakaocdn.net/dn/b4T4gE/dJMcaiccH1W/aft3ya55Y9B5dIQMAFFlkK/img.png"><img src="https://blog.kakaocdn.net/dn/b4T4gE/dJMcaiccH1W/aft3ya55Y9B5dIQMAFFlkK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2Fb4T4gE%2FdJMcaiccH1W%2Faft3ya55Y9B5dIQMAFFlkK%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="904" data-filename="Screenshot 2026-05-07 at 12.07.23.png" data-origin-width="1506" data-origin-height="2270"/></span></figure> <figure class="imageblock alignCenter" data-ke-mobileStyle="widthOrigin" data-filename="Screenshot 2026-05-07 at 12.07.53.png" data-origin-width="1440" data-origin-height="1584"><span data-url="https://blog.kakaocdn.net/dn/M7hoa/dJMcadPpppw/y4uk6wIH6XOF3iQBZcQTjK/img.png" data-phocus="https://blog.kakaocdn.net/dn/M7hoa/dJMcadPpppw/y4uk6wIH6XOF3iQBZcQTjK/img.png"><img src="https://blog.kakaocdn.net/dn/M7hoa/dJMcadPpppw/y4uk6wIH6XOF3iQBZcQTjK/img.png" srcset="https://img1.daumcdn.net/thumb/R1280x0/?scode=mtistory2&fname=https%3A%2F%2Fblog.kakaocdn.net%2Fdn%2FM7hoa%2FdJMcadPpppw%2Fy4uk6wIH6XOF3iQBZcQTjK%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="660" data-filename="Screenshot 2026-05-07 at 12.07.53.png" data-origin-width="1440" data-origin-height="1584"/></span></figure> </div> </div> <p data-ke-size="size16">&nbsp;</p> <p data-ke-size="size16">&nbsp;</p> 수학2 - 문제풀이/미분 수악중독 https://mathjk.tistory.com/6871 https://mathjk.tistory.com/6871#entry6871comment Fri, 8 May 2026 01:08:48 +0900