\mathrm{OA} _{1} B _{2}

9c:["$","span","p0-0-t0-m15",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$107"}}] 9d:["$","img","p0-0-i2",{"src":"https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/100/image5-OJNocJPm9hLfNO8qJNWoDSYJG0dwgg.png","alt":"","className":"inline-block align-middle","style":{"height":"1.75em"}}] 108:T405,

R _{1}

9e:["$","span","p0-0-t3-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$108"}}] 109:T405,

R _{1}

9f:["$","span","p0-0-t3-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$109"}}] a0:["$","span","p0-0-t3-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{B} _{2}

"}}] 10a:T68d,

\mathrm{A} _{1} B _{1}

a1:["$","span","p0-0-t3-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$10a"}}] 10b:T432,

\mathrm{OA} _{1}

a2:["$","span","p0-0-t3-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$10b"}}] 10c:T436,

\mathrm{A} _{2} ,

a3:["$","span","p0-0-t3-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$10c"}}] a4:["$","span","p0-0-t3-m13",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{O}

"}}] 10d:T63a,

\displaystyle \mathrm{\overline{OA}} _{2}

a5:["$","span","p0-0-t3-m15",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$10d"}}] 10e:T432,

\mathrm{OB} _{2}

a6:["$","span","p0-0-t3-m17",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$10e"}}] a7:["$","span","p0-0-t3-m19",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{B} _{3}

"}}] 10f:T6c5,

\mathrm{OA} _{2} B _{2}

a8:["$","span","p0-0-t3-m21",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$10f"}}] 110:T6c5,

\mathrm{OA} _{2} B _{3}

a9:["$","span","p0-0-t3-m23",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$110"}}] aa:["$","img","p0-0-i5",{"src":"https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/100/image5-OJNocJPm9hLfNO8qJNWoDSYJG0dwgg.png","alt":"","className":"inline-block align-middle","style":{"height":"1.75em"}}] 111:T405,

R _{2}

ab:["$","span","p0-0-t6-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$111"}}] ac:["$","span","p0-0-t6-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

n

"}}] 112:T410,

R _{n}

ad:["$","span","p0-0-t6-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$112"}}] 113:T410,

S _{n}

ae:["$","span","p0-0-t6-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$113"}}] 114:T806,

\displaystyle \lim\limits _{n \rightarrow \infty} {S _{n}}

af:["$","span","p0-0-t6-m9",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$114"}}] b0:["$","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/100/image6-W1WzYBKHCohXUQB5RqtzmCCNujGgac.png","alt":"","className":"problem-img my-[1em] block","style":{"--img-w":"90cqw"}}]]}] 115:T55b,

\displaystyle \frac{3}{2} \pi

116:T55b,

\displaystyle \frac{5}{3} \pi

117:T55e,

\displaystyle \frac{11}{6} \pi

b1:["$","p","p0-2",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["① ",["$","span","p0-2-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$115"}}],"\n② ",["$","span","p0-2-t0-m3",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$116"}}],"\n③ ",["$","span","p0-2-t0-m5",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$117"}}],"\n④ ","$L118","\n⑤ ","$L119",""]}] 11a:T489,

x = 6 , x = 9

b4:["$","p","p0-2",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["함수 ",["$","span","p0-2-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

f ( x )

"}}],"의 그래프와 ",["$","span","p0-2-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

x

"}}],"축 및 두 직선 ",["$","span","p0-2-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$11a"}}],"로 둘러싸인 부분의 넓이는? [4점]\n① ",["$","span","p0-2-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

9

"}}],"\n② ",["$","span","p0-2-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

12

"}}],"\n③ ","$L11b","\n④ ","$L11c","\n⑤ ","$L11d",""]}] b5:["$","p","p0-2",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["위의 시행을 반복하여 점 ",["$","span","p0-2-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{A}

"}}],"의 ",["$","span","p0-2-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

x

"}}],"좌표 또는 ",["$","span","p0-2-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

y

"}}],"좌표가 처음으로 ",["$","span","p0-2-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

3

"}}],"이 되면 이 시행을 멈춘다. 점 ",["$","span","p0-2-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{A}

"}}],"의 ",["$","span","p0-2-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

y

"}}],"좌표가 처음으로 ",["$","span","p0-2-t0-m13",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

3

"}}],"이 되었을 때, 점 ","$L11e","의 ","$L11f","좌표가 ","$L120","일 확률은? [4점]\n① ","$L121","\n② ","$L122","\n③ ","$L123","\n④ ","$L124","\n⑤ ","$L125",""]}] b8:["$","span","p0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

5

"}}] b9:["$","span","p0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

f

"}}] ba:["$","p","p0-1",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["함수 ",["$","span","p0-1-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

f

"}}],"와 함수 ",["$","span","p0-1-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

f \\circ f

"}}],"의 치역을 각각 ",["$","span","p0-1-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

A

"}}],"와 ",["$","span","p0-1-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

B

"}}]," 라 하자.\n",["$","span","p0-1-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

n ( A ) = 6

"}}],"이면 함수 ","$L126","는 일대일 대응이고, 함수 ","$L127","도 일대일 대응이므로 ","$L128","이다.\n또한 ","$L129","이면 ","$L12a","이므로 ","$L12b","이다.\n그러므로 ","$L12c"," 즉 ","$L12d","인 경우만 생각하면 된다."]}] bb:["$","p","p0-2",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["(ⅰ) ",["$","span","p0-2-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

n ( A ) = 5

"}}],"인 ",["$","span","p0-2-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

X

"}}],"의 부분집합 ",["$","span","p0-2-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

A

"}}],"를 선택하는 경우의 수는 ",["$","span","p0-2-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\square {( \\text{가} )}

"}}],"이다.\n(ⅱ) (ⅰ)에서 선택한 집합 ",["$","span","p0-2-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

A

"}}],"에 대하여, ","$L12e","의 원소 중\n","$L12f","에 속하지 않은 원소를 ","$L130","라 하자.\n","$L131","이므로 집합 ","$L132","에서 ","$L133","를 선택하는 경우의 수는 ","$L134","이다.\n(ⅲ) (ⅰ)에서 선택한 ","$L135","와 (ⅱ)에서 선택한 ","$L136","에 대하여, ","$L137","이며 ","$L138","이므로\n","$L139","\n이다. ","$L13a","을 만족시키는 셩우의 수는 집합 ","$L13b","에서 집합 ","$L13c","로의 일대일 대응의 개수와 같으므로\n","$L13d","이다."]}] 13e:T780,

\square {( \text{가} )} \times \square {( \text{나} )} \times \square {( \text{다} )}

bc:["$","p","p0-3",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["따라서 (ⅰ), (ⅱ), (ⅲ)에 의하여 구하는 함수 ",["$","span","p0-3-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

f

"}}],"의 개수는\n",["$","span","p0-3-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$13e"}}],"이다."]}] 13f:T44f,

p + q + r

bd:["$","p","p0-4",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["위의 (가), (나), (다)에 알맞은 수를 각각 ",["$","span","p0-4-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

p , q , r

"}}],"이라 할 때, ",["$","span","p0-4-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$13f"}}],"의 값은? [4점]\n① ",["$","span","p0-4-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

131

"}}],"\n② ",["$","span","p0-4-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

136

"}}],"\n③ ",["$","span","p0-4-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

141

"}}],"\n④ ","$L140","\n⑤ ","$L141",""]}] bf:["$","span","p0-0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

x

"}}] c0:["$","span","p0-0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

y

"}}] c1:["$","span","p0-0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{A} , B

"}}] c2:["$","p","p0-0-1",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":[["$","img","p0-0-1-i2",{"src":"https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/100/image7-y7hrPRFut5hOxvY2mVKeOblErVMwpZ.png","alt":"","className":"problem-img my-[1em] block","style":{"--img-w":"71cqw"}}]]}] c3:["$","p","p0-0-2",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["이 그래프의 두 점근선의 교점과 점 ",["$","span","p0-0-2-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{B}

"}}],"를 지나는 직선이 이 그래프와 만나는 점 중 ",["$","span","p0-0-2-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{B}

"}}],"가 아닌 점을 ",["$","span","p0-0-2-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{P}

"}}],", 점 ",["$","span","p0-0-2-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{P}

"}}],"에서 ",["$","span","p0-0-2-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

x

"}}],"축에 내린 수선의 발을 ",["$","span","p0-0-2-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{Q}

"}}],"라 할 때, <보기>에서 옳은 것만을 있는 대로 고른 것은? [4점]"]}] c4:["$","div","t0-1",{"className":"mb-[1.2em] overflow-x-auto","children":["$","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":"$undefined","className":"px-3 py-1.5 align-middle text-center","style":{"borderLeft":"none","borderRight":"none","borderTop":"none","borderBottom":"1px solid #333","backgroundColor":"$undefined"},"children":[]}],["$","td","t0-1-r0c1",{"rowSpan":2,"colSpan":"$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-r0c2",{"rowSpan":"$undefined","colSpan":"$undefined","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":"$undefined","className":"px-3 py-1.5 align-middle text-center","style":{"borderLeft":"1px solid #333","borderRight":"none","borderTop":"1px solid #333","borderBottom":"none","backgroundColor":"$undefined"},"children":[]}],["$","td","t0-1-r1c2",{"rowSpan":"$undefined","colSpan":"$undefined","className":"px-3 py-1.5 align-middle text-center","style":{"borderLeft":"none","borderRight":"1px solid #333","borderTop":"1px solid #333","borderBottom":"none","backgroundColor":"$undefined"},"children":[]}]]}],["$","tr","t0-1-r2",{"children":[["$","td","t0-1-r2c0",{"rowSpan":"$undefined","colSpan":3,"className":"px-3 py-1.5 align-middle text-left whitespace-pre-wrap","style":{"borderLeft":"1px solid #333","borderRight":"1px solid #333","borderTop":"none","borderBottom":"1px solid #333","backgroundColor":"$undefined"},"children":["ㄱ. ",["$","span","t0-1-r2c0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

k = 1

"}}],"일 때, 점 ",["$","span","t0-1-r2c0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{P}

"}}],"의 좌표는 ",["$","span","t0-1-r2c0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

( 2 , 4 )

"}}],"이다.\nㄴ. ","$L142"," 인 실수 ","$L143","에 대하여 직선 ","$L144","의 기울기와 \n직선 ","$L145","의 기울기의 합은 ","$L146","이다.\nㄷ. 사각형 ","$L147","의 넓이가 자연수일 때, 직선 ","$L148","의 \n기울기는 ","$L149","과 ","$L14a","사이의 값이다."]}]]}]]}]}]}] c5:["$","p","p2-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["① ㄱ\n② ㄱ, ㄴ\n③ ㄱ, ㄷ\n④ ㄴ, ㄷ\n⑤ ㄱ, ㄴ, ㄷ"]}] c7:["$","span","p0-1-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

g ( 0 ) = 1

"}}] 14b:T509,

\displaystyle \frac{5}{13}

14c:T509,

\displaystyle \frac{5}{14}

2019학년도 수능 수리(나형)