\displaystyle 2 \sqrt{2}

29:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["[13∼14] 반지름의 길이가 ",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

1

"}}],", 중심이 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{O}

"}}],"인 원을 밑면으로 하고 높이가 ",["$","span","p0-0-t0-m5",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$96"}}],"인 원뿔이 평면 ",["$","span","p0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\alpha

"}}]," 위에 놓여있다. ","$L97","번과 ","$L98","번의 두 물음에 답하시오. (단, 원뿔의 한 모선이 평면 ","$L99","에 포함된다.)"]}],"$L9a","$L9b","$L9c"]}] 9d:T1f0c,

\displaystyle \frac{1}{2} \times \frac{3}{4} \times \frac{5}{6} \times \cdots \times \frac{2 n - 1}{2 n} \leq \frac{1}{\sqrt{3 n + 1}}

2a:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["다음은 모든 자연수 ",["$","span","p0-0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

n

"}}],"에 대하여\n ",["$","span","p0-0-0-t0-m3",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$9d"}}]," ","$L9e","","$L9f"," (★)\n이 성립함을 증명하는 과정이다."]}],"$La0","$La1"]}] a2:T688,

y = f ( x ) , y = g ( x )

2b:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["그림은 두 함수 ",["$","span","p0-0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$a2"}}],"의 그래프이다. 옳은 것만을 <보기>에서 있는 대로 고른 것은? [4점]"]}],["$","p","p0-0-1",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":[["$","img","p0-0-1-i2",{"src":"https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/420/overlay-9845-image8-FTYJzrpcwEq8gKTFCntdCZUTqt20WH.png","alt":"","className":"problem-img my-[1em] block","style":{"--img-w":"85cqw"}}]]}],["$","div","t0-1",{"className":"mb-[1.2em] overflow-x-auto","children":["$","table",null,{"className":"w-auto border-collapse text-[15px]","children":["$","tbody",null,{"children":[["$","tr","t0-1-r0",{"children":[["$","td","t0-1-r0c0",{"rowSpan":"$undefined","colSpan":2,"className":"px-3 py-1.5 align-middle text-center","style":{"borderLeft":"none","borderRight":"none","borderTop":"none","borderBottom":"1px solid #333","backgroundColor":"$undefined"},"children":[]}],["$","td","t0-1-r0c2",{"rowSpan":2,"colSpan":"$undefined","className":"px-3 py-1.5 align-middle text-center","style":{"borderLeft":"none","borderRight":"none","borderTop":"none","borderBottom":"none","backgroundColor":"$undefined"},"children":["<보 기>"]}],["$","td","t0-1-r0c3",{"rowSpan":"$undefined","colSpan":2,"className":"px-3 py-1.5 align-middle text-center","style":{"borderLeft":"none","borderRight":"none","borderTop":"none","borderBottom":"1px solid #333","backgroundColor":"$undefined"},"children":[]}]]}],["$","tr","t0-1-r1",{"children":[["$","td","t0-1-r1c0",{"rowSpan":"$undefined","colSpan":2,"className":"px-3 py-1.5 align-middle text-center","style":{"borderLeft":"1px solid #333","borderRight":"none","borderTop":"1px solid #333","borderBottom":"none","backgroundColor":"$undefined"},"children":[]}],["$","td","t0-1-r1c3",{"rowSpan":"$undefined","colSpan":2,"className":"px-3 py-1.5 align-middle text-center","style":{"borderLeft":"none","borderRight":"1px solid #333","borderTop":"1px solid #333","borderBottom":"none","backgroundColor":"$undefined"},"children":[]}]]}],"$La3","$La4"]}]}]}],"$La5"]}] a6:T509,

\displaystyle \frac{1}{26}

2c:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["그림과 같이 ",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

15

"}}],"개의 자리가 있는 일자형의 놀이기구에 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

5

"}}],"명이 타려고 할 때, ",["$","span","p0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

5

"}}],"명이 어느 누구와도 서로 이웃하지 않게 탈 확률은? [4점]"]}],["$","p","p0-1",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":[["$","img","p0-1-i2",{"src":"https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/420/image9-ULob3Dj4QzRegAtdkYDaBZdGMUfWAx.jpg","alt":"","className":"problem-img my-[1em] block","style":{"--img-w":"90cqw"}}]]}],["$","p","p0-2",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["① ",["$","span","p0-2-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$a6"}}],"\n② ","$La7","\n③ ","$La8","\n④ ","$La9","\n⑤ ","$Laa",""]}]]}] ab:T444,

f' ( x )

2d:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["실수 전체의 집합에서 함수 ",["$","span","p0-0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

f ( x )

"}}],"가 미분가능하고 도함수\n",["$","span","p0-0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$ab"}}],"가 연속이다. ",["$","span","p0-0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

x

"}}],"축과의 교점의 ",["$","span","p0-0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

x

"}}],"좌표가 ",["$","span","p0-0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

b

"}}],", ","$Lac",", ","$Lad","뿐인 함수 ","$Lae","의 그래프가 그림과 같을 때, 옳은 것만을 <보기>에서 있는 대로 고른 것은? [4점]"]}],"$Laf","$Lb0","$Lb1","$Lb2"]}] b3:Td6d,

\displaystyle \overline{\mathrm{AB}} = 2 , \overline{\mathrm{AD}} = 3 , \overline{\mathrm{AE}} = 4

2e:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["그림과 같이 ",["$","span","p0-0-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$b3"}}]," 인 직육면체\n","$Lb4","에서 평면 ","$Lb5","와 평면 ","$Lb6","의 교선을 ","$Lb7","이라 하자. 직선 ","$Lb8","과 평면 ","$Lb9","가 이루는 예각의 크기를 ","$Lba","라 할 때, ","$Lbb","의 값은? [4점]"]}],"$Lbc","$Lbd"]}] be:T14c8,

\displaystyle A = {\begin{pmatrix} a & b \\ c & d \end{pmatrix}} , B = {\begin{pmatrix} d & b \\ c & a \end{pmatrix}}

2f:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["두 이차정사각행렬 ",["$","span","p0-0-0-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$be"}}],"에 대하여\n\t\t\t","$Lbf","\n가 성립한다고 할 때, 항상 옳은 것만을 <보기>에서 있는 대로 고른 것은? (단, ","$Lc0","는 단위행렬이다.) [4점]"]}],"$Lc1","$Lc2"]}] c3:T405,

C _{1}

c4:T405,

C _{1}

30:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["그림과 같이 길이가 ",["$","span","p0-0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

2

"}}],"인 선분 ",["$","span","p0-0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{AB}

"}}],"를 지름으로 하고 중심이 점 ",["$","span","p0-0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{O}

"}}],"인 원 ",["$","span","p0-0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$c3"}}],"이 있다. 원 ",["$","span","p0-0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$c4"}}]," 위의 점 ","$Lc5","에 대하여 ","$Lc6","라 하고, 선분 ","$Lc7","에 접하고 중심이 점 ","$Lc8","인 원 ","$Lc9","를 그린다. 원 ","$Lca","와 선분 ","$Lcb","의 교점을 점 ","$Lcc","라 할 때, ","$Lcd","의 값은?\n","$Lce","단, ","$Lcf","","$Ld0"," [4점]"]}],"$Ld1","$Ld2","$Ld3"]}] d4:T1130,

\displaystyle f \left( x \right) = 200 x - \frac{3}{2} x ^{2} - \frac{1}{3} x ^{3}

31:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["함수 ",["$","span","p0-0-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$d4"}}],"에 대하여 ","$Ld5","의 값을 구하시오. [3점]"]}]]}] d6:Ta5b,

\displaystyle \left( x ^{2} - \frac{2}{x} \right) ^{6}

32:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["",["$","span","p0-0-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$d6"}}],"의 전개식에서 상수항을 구하시오. [3점]"]}]]}] d7:T6c3,

\displaystyle y = \pm \frac{3}{4} x

33:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["점근선의 방정식이 ",["$","span","p0-0-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$d7"}}],"이고, 한 초점의 좌표가\n",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

( 10 , 0 )

"}}],"인 쌍곡선의 주축의 길이를 구하시오. [3점]"]}]]}] d8:T4b4,

\left\{ a _{n} \right\}

d9:T4b4,

\left\{ b _{n} \right\}

da:T504,

a _{9} = 100

34:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["수열 ",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$d8"}}],"의 계차수열을 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$d9"}}],"이라 할 때,\n ",["$","span","p0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$da"}}],", ","$Ldb","\n이다. ","$Ldc","의 값을 구하시오. [3점]"]}]]}] dd:T824,

\displaystyle y = \sqrt{x}

de:T428,

y = x - 2

35:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["곡선 ",["$","span","p0-0-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$dd"}}],"와 직선 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$de"}}]," 및 ","$Ldf","축으로 둘러싸인 부분을 ","$Le0","축 둘레로 회전시켜 생기는 회전체의 부피를 ","$Le1","라 할 때,\n","$Le2","의 값을 구하시오. [4점]"]}]]}] 36:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["남학생 ",["$","span","p0-0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

4

"}}],"명, 여학생 ",["$","span","p0-0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

2

"}}],"명이 그림과 같이 ",["$","span","p0-0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

9

"}}],"개의 자리가 있는 원탁에 다음 두 조건에 따라 앉으려고 할 때, 앉을 수 있는 모든 경우의 수를 구하시오. (단, 회전하여 일치하는 것은 같은 것으로 본다.) [4점]"]}],["$","div","t0-1",{"className":"mb-[1.2em] overflow-x-auto","children":["$","table",null,{"className":"w-auto border-collapse text-[15px]","children":["$","tbody",null,{"children":[["$","tr","t0-1-r0",{"children":[["$","td","t0-1-r0c0",{"rowSpan":"$undefined","colSpan":3,"className":"px-3 py-1.5 align-middle text-center","style":{"borderLeft":"1px solid #333","borderRight":"1px solid #333","borderTop":"1px solid #333","borderBottom":"none","backgroundColor":"$undefined"},"children":[]}]]}],["$","tr","t0-1-r1",{"children":[["$","td","t0-1-r1c0",{"rowSpan":"$undefined","colSpan":"$undefined","className":"px-3 py-1.5 align-middle text-center","style":{"borderLeft":"1px solid #333","borderRight":"none","borderTop":"none","borderBottom":"none","backgroundColor":"$undefined"},"children":[]}],["$","td","t0-1-r1c1",{"rowSpan":"$undefined","colSpan":"$undefined","className":"px-3 py-1.5 align-middle text-left whitespace-pre-wrap","style":{"borderLeft":"none","borderRight":"none","borderTop":"none","borderBottom":"none","backgroundColor":"$undefined"},"children":["(가) 남학생, 여학생 모두 같은 성별끼리 ",["$","span","t0-1-r1c1-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

2

"}}],"명씩 조를 만든다.\n(나) 서로 다른 두 개의 조 사이에 반드시 한 자리를 비워둔다."]}],["$","td","t0-1-r1c2",{"rowSpan":"$undefined","colSpan":"$undefined","className":"px-3 py-1.5 align-middle text-center","style":{"borderLeft":"none","borderRight":"1px solid #333","borderTop":"none","borderBottom":"none","backgroundColor":"$undefined"},"children":[]}]]}],["$","tr","t0-1-r2",{"children":[["$","td","t0-1-r2c0",{"rowSpan":"$undefined","colSpan":3,"className":"px-3 py-1.5 align-middle text-center","style":{"borderLeft":"1px solid #333","borderRight":"1px solid #333","borderTop":"none","borderBottom":"1px solid #333","backgroundColor":"$undefined"},"children":[]}]]}]]}]}]}],"$Le3"]}] e4:T116e,

\displaystyle \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1

2013년-07월-고3-수리(B형)