b _{9} - b _{3} = 27

80:["$","span","p0-0-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$f1"}}] f2:T8df,

\displaystyle \sum\limits _{k = 1} ^{10} a _{k}

81:["$","span","p0-0-t0-m13",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$f2"}}] 82:["$","span","p0-0-t0-m15",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

100

"}}] 83:["$","span","p0-0-t0-m17",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

145

"}}] 84:["$","span","p0-0-t0-m19",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

190

"}}] 85:["$","span","p0-0-t0-m21",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

235

"}}] 86:["$","span","p0-0-t0-m23",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

280

"}}] f3:T1660,

\displaystyle g \left( x \right) = \begin{cases} f \left( x + a \right) + b & & \left( x < 0 \right) \\ f \left( x \right) & & \left( x \geq 0 \right) \end{cases}

88:["$","span","p0-0-t0-m7",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$f3"}}] 89:["$","span","p0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

t

"}}] f4:T464,

y = g \left( x \right)

8a:["$","span","p0-0-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$f4"}}] 8b:["$","span","p0-0-t0-m13",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

y = t

"}}] 8c:["$","span","p0-0-t0-m15",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

h \\left( t \\right)

"}}] f5:T1436,

\displaystyle \left| \lim\limits _{t \rightarrow k +} h \left( t \right) - \lim\limits _{t \rightarrow k -} h \left( t \right) \right| = 2

8d:["$","span","p0-0-t0-m17",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$f5"}}] 8e:["$","span","p0-0-t0-m19",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

k

"}}] 8f:["$","span","p0-0-t0-m21",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

1

"}}] 90:["$","span","p0-0-t0-m23",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

4

"}}] 91:["$","span","p0-0-t0-m25",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

5

"}}] 92:["$","span","p0-0-t0-m27",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

g \\left( - 4 \\right)

"}}] 93:["$","span","p0-0-t0-m29",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

9

"}}] 94:["$","span","p0-0-t0-m31",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

10

"}}] 95:["$","span","p0-0-t0-m33",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

11

"}}] 96:["$","span","p0-0-t0-m35",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

12

"}}] 97:["$","span","p0-0-t0-m37",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

13

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

l

"}}] 9a:["$","span","p0-0-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

m

"}}] 9b:["$","span","p0-0-t0-m13",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

l

"}}] 9c:["$","span","p0-0-t0-m15",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

m

"}}] 9d:["$","span","p0-0-t0-m17",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

O

"}}] 9e:["$","span","p0-0-t0-m19",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{B}}

"}}] 9f:["$","span","p0-0-t0-m21",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{C}}

"}}] a0:["$","span","p0-0-t0-m23",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{B}}

"}}] a1:["$","span","p0-0-t0-m25",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

l

"}}] a2:["$","span","p0-0-t0-m27",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

O

"}}] a3:["$","span","p0-0-t0-m29",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{B}}

"}}] a4:["$","span","p0-0-t0-m31",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{P}}

"}}] a5:["$","span","p0-0-t0-m33",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{AP}}

"}}] a6:["$","span","p0-0-t0-m35",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

O

"}}] a7:["$","span","p0-0-t0-m37",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{P}}

"}}] a8:["$","span","p0-0-t0-m39",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{Q}}

"}}] f6:T54e,

\displaystyle {\overline{\mathrm{AB}}} = 12

a9:["$","span","p0-0-t0-m41",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$f6"}}] f7:T978,

\sin \left( \angle {\mathrm{BPQ}} \right) : \sin \left( \angle {\mathrm{QPC}} \right) = 3 : 1

aa:["$","span","p0-0-t0-m43",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$f7"}}] ab:["$","span","p0-0-t0-m45",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{BQC}}

"}}] ac:["$","p","p0-1",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":[["$","img","p0-1-i2",{"src":"https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/138/image5-1IUdKdNR6oFWD8dcv1DTio0lvKQaFB.png","alt":"","className":"problem-img my-[1em] block","style":{"--img-w":"82cqw"}}]]}] f8:Ta1a,

\displaystyle \frac{14 \sqrt{2}}{3}

f9:Ta1a,

\displaystyle \frac{16 \sqrt{2}}{3}

ad:["$","p","p0-2",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["① ",["$","span","p0-2-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$f8"}}],"\n② ",["$","span","p0-2-t0-m3",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$f9"}}],"\n③ ","$Lfa","\n④ ","$Lfb","\n⑤ ","$Lfc",""]}] fd:T422,

g \left( x \right) = 0

b0:["$","p","p0-1",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["(가) 함수 ",["$","span","p0-1-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

g \\left( x \\right)

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

x = b

"}}],"에서만 미분가능하지 않다.\n(나) 방정식 ",["$","span","p0-1-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$fd"}}],"은 음의 실근을 갖는다."]}] fe:T975,

\displaystyle g \left( - \frac{1}{2} \right) + g \left( 3 \right)

b1:["$","p","p0-2",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["",["$","span","p0-2-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$fe"}}],"의 값은? (단, ",["$","span","p0-2-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

a

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

b

"}}],"는 상수이다.) [4점]\n① ","$Lff","\n② ","$L100","\n③ ","$L101","\n④ ","$L102","\n⑤ ","$L103",""]}] b3:["$","span","p0-0-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

x

"}}] 104:T417,

f \left( 0 \right) = 2

b5:["$","span","p0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$104"}}] b6:["$","span","p0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

f \\left( 1 \\right)

"}}] 105:Te7c,

\displaystyle \sum\limits _{k = 1} ^{19} \left( a _{k + 1} + b _{k} \right) = 330

ba:["$","span","p0-0-t0-m7",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$105"}}] 106:T4fe,

a _{1} = 3

bb:["$","span","p0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$106"}}] 107:T8df,

\displaystyle \sum\limits _{k = 1} ^{20} a _{k}

bc:["$","span","p0-0-t0-m11",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$107"}}] be:["$","span","p0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

f \\left( x \\right)

"}}] bf:["$","span","p0-0-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

x = 2

"}}] c0:["$","span","p0-0-t0-m13",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

- 6

"}}] c1:["$","span","p0-0-t0-m15",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

f \\left( x \\right)

"}}] c4:["$","span","p0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

x

"}}] c5:["$","span","p0-0-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

2025년-07월-고3-수학문제(공통)