f \left( n \right) + f \left( 2 n \right) = 1

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":["",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

2

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

n

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

n - 12

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

n

"}}],"제곱근 중 실수인 것의 개수를 ",["$","span","p0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

f \\left( n \\right)

"}}],"이라 하자. ",["$","span","p0-0-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$a2"}}],"을 만족시키는 모든 ","$La3","의 값의 합은? [4점]\n① ","$La4","\n② ","$La5","\n③ ","$La6","\n④ ","$La7","\n⑤ ","$La8",""]}]]}] a9:T417,

f \left( 1 \right) = 0

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

1

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

f \\left( x \\right)

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

g \\left( x \\right)

"}}],"가\n\t",["$","span","p0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$a9"}}],", ","$Laa","\n을 만족시킬 때, ","$Lab","의 값은? [4점]\n① ","$Lac","\n② ","$Lad","\n③ ","$Lae","\n④ ","$Laf","\n⑤ ","$Lb0",""]}]]}] b1:T4b4,

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

b2:T887,

a _{4} \times a _{5} \leq 0

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

- 2

"}}],"인 등차수열 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$b1"}}],"과 자연수 ",["$","span","p0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

k

"}}],"가\n\t",["$","span","p0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$b2"}}],", ","$Lb3","\n를 만족시킬 때, ","$Lb4","의 값은? [4점]\n① ","$Lb5","\n② ","$Lb6","\n③ ","$Lb7","\n④ ","$Lb8","\n⑤ ","$Lb9",""]}]]}] ba:T65b,

f \left( x \right) = \sin \left( x + a \right)

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":["함수 ",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$ba"}}],"가 다음 조건을 만족시키도록 하는 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

3 \\pi

"}}],"보다 작은 모든 양수 ",["$","span","p0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

a

"}}],"의 값의 합은? [4점]"]}],["$","p","p0-1",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["닫힌구간 ",["$","span","p0-1-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\left[ 0 , \\pi \\right]

"}}],"에서 함수 ","$Lbb","의 최댓값과 최솟값을 각각 ","$Lbc",", ","$Lbd","이라 할 때, ","$Lbe","이다."]}],"$Lbf"]}] c0:T495,

y = 2 ^{x}

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

1

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

l

"}}],"이 곡선 ",["$","span","p0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$c0"}}],"과 서로 다른 두 점 ",["$","span","p0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{A}}

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

{\\mathrm{B}}

"}}],"에서 만나고, 곡선 ","$Lc1","과 서로 다른 두 점 ","$Lc2",", ","$Lc3","에서 만난다. 점 ","$Lc4","가 선분 ","$Lc5","를 ","$Lc6","로 내분할 때, 점 ","$Lc7","의 ","$Lc8","좌표는? (단, 점 ","$Lc9","의 ","$Lca","좌표는 점 ","$Lcb","의 ","$Lcc","좌표보다 크고, 점 ","$Lcd","의 ","$Lce","좌표는 점 ","$Lcf","의 ","$Ld0","좌표보다 크다.) [4점]"]}],"$Ld1","$Ld2"]}] d3:T4b4,

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

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":["등비수열 ",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$d3"}}],"이 다음 조건을 만족시킬 때, ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

a _{10}

"}}],"의 값은? [4점]"]}],["$","p","p0-1",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["(가) ",["$","span","p0-1-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

2

"}}]," 이상의 모든 자연수 ",["$","span","p0-1-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

n

"}}],"에 대하여\n\t","$Ld4",", ","$Ld5","\n이다.\n(나) ","$Ld6",""]}],"$Ld7"]}] d8:T18fc,

\displaystyle f \left( x \right) = {\begin{cases} - 2 ^{x + 3} + a & & \left( x < 0 \right) \\ 2 ^{- x + 6} + a - 12 & & \left( x \geq 0 \right) \end{cases}}

2f:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["함수\n\t",["$","span","p0-0-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$d8"}}],"\n이 다음 조건을 만족시키도록 하는 모든 정수 ","$Ld9","의 값의 합은?\n[4점]"]}],"$Lda","$Ldb"]}] dc:T88f,

\log _{3} 54 - \log _{3} 2

30:["$","div",null,{"className":"math-text text-[15px] leading-[1.9]","children":[["$","p","p0-0",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$dc"}}],"의 값을 구하시오. [3점]"]}]]}] dd:T55b,

\displaystyle \frac{2}{5} \pi

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":["중심각의 크기가 ",["$","span","p0-0-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$dd"}}],"이고 호의 길이가 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

4 \\pi

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

a \\pi

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

a

"}}],"의 값을 구하시오. [3점]"]}]]}] de:T540,

y = \log \left( x - 2 \right)

df:T5cc,

y = 2 ^{x} + 5

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":["함수 ",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$de"}}],"의 그래프의 점근선과 함수 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$df"}}],"의 그래프의 점근선이 만나는 점의 좌표가 ",["$","span","p0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\left( a , b \\right)

"}}],"일 때, ","$Le0","의 값을 구하시오. [3점]"]}]]}] e1:T4b4,

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

e2:T410,

S _{n}

e3:T529,

S _{11} = 88

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":["등차수열 ",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$e1"}}],"의 첫째항부터 제 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

n

"}}],"항까지의 합을 ",["$","span","p0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$e2"}}],"이라 하자. ",["$","span","p0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$e3"}}],"이고 ","$Le4","일 때, ","$Le5","의 값을 구하시오. [3점]"]}]]}] e6:T655,

f \left( x \right) = a \left| x - 2 \right|

e7:T1bf9,

\displaystyle \lim\limits _{x \rightarrow k +} \frac{f \left( x \right) - f \left( k \right)}{x - k} - \lim\limits _{x \rightarrow k -} \frac{f \left( x \right) - f \left( k \right)}{x - k} = 6

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":["두 상수 ",["$","span","p0-0-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

a

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

k

"}}],"에 대하여 함수 ",["$","span","p0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$e6"}}],"가\n\t",["$","span","p0-0-t0-m7",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$e7"}}],"\n을 만족시킬 때, ","$Le8","의 값을 구하시오. [4점]"]}]]}] e9:T54b,

\displaystyle {\overline{\mathrm{AB}}} = 6

ea:T41f,

2 \sin A = \sin B

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":["",["$","span","p0-0-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$e9"}}],"인 삼각형 ",["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{ABC}}

"}}],"에 대하여\n\t",["$","span","p0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$ea"}}],", ","$Leb","\n일 때, 삼각형 ","$Lec","의 넓이를 구하시오. [4점]"]}]]}] ed:T7e8,

\displaystyle \frac{f \left( 0 \right)}{f \left( 2 \right)}

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

\\left[ 0 , 2 \\right]

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

f \\left( x \\right)

"}}],"가 다음 조건을 만족시킬 때, ",["$","span","p0-0-t0-m5",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$ed"}}],"의 값을 구하시오. [4점]"]}],"$Lee"]}]

2025년-10월-고2-수학영역