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imagewidth (px) 2
5.73k
| material_type
stringclasses 2
values | latex
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13
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P | [
"$\\displaystyle (1)$ $\\displaystyle 50$",
"κΆ μ΄νμΈ νμμ $\\displaystyle (3)$",
"$\\displaystyle 2$ μ",
"ν μ’
λ₯μ μμ",
" λ νμ΅ μκ°,"
] |
|
P | [
"μ°μ΅ κ²½κΈ°μμ λ£μ",
" λ΄μ¬ νλμ",
"$\\displaystyle 90$ $\\displaystyle 5$",
"$\\displaystyle 9$ $\\displaystyle 90$",
"$\\displaystyle 18$ $\\displaystyle y$"
] |
|
P | [
"$\\displaystyle C$ $\\displaystyle 17$",
"(2) λ€μμ μν¬λ€ λ° νμλ€μ΄",
"γ μλ
μ μ½μ μ±
μ κΆμκ° κ°μ₯ μ μ νμμ΄ μ¬ν΄ μ½μ μ±
μ κΆμλ $\\displaystyle x$",
"$\\displaystyle 1$ $\\displaystyle 23$",
"λͺ
μ€μ $\\displaystyle 14$"
] |
|
P | [
"$\\displaystyle 17$ $\\displaystyle 70$",
" κ°μμ ν©μ΄",
"μ κ°μ΄ 컀μ§μ λ°λΌ λ€ νμ μ€",
"γ£ μλ
κ³Ό μ¬ν΄ μ½μ μ±
μ κΆμμ λ³νκ° μλ νμμ $\\displaystyle 2$",
"$\\displaystyle x,y$ $\\displaystyle A,B,C,D,E \\; 5$"
] |
|
P | [
"$\\displaystyle x,y$ μμμ",
"μ₯ ν° νμμ ν±κ±Έμ΄μ νμλ³΄λ€ νκ΅½νν΄κΈ°μ νμκ° μλμ μΌλ‘ κ°μ₯ λ§μ",
"λͺ
μ€μ $\\displaystyle A,B,C,D,E \\; 5$",
"κ° μ΄μ λ£μ νμμ μ΄ $\\displaystyle 60$",
"μ κ°μ΄ 컀μ§μλ‘ $\\displaystyle \\therefore $"
] |
|
P | [
"λ€μμ μν¬λ€ λ° νμ ",
"μ μ΄νμΈ νμμ κ° μ΄μ",
"μ μ΄μ $\\displaystyle B$",
"(2) $\\displaystyle 8$",
"$\\displaystyle y$ $\\displaystyle 7$"
] |
|
P | [
"$\\displaystyle 6$ μ΄νμΈ νμμ",
"$\\displaystyle 10$ λΌ ν λ,",
"μ",
"μ£Όμ΄μ§ μ°μ λλ $\\displaystyle 6$",
"γ‘ μλ
μ μ½μ μ±
μ κΆμκ° λͺ
μ"
] |
|
P | [
"λͺ
μ μ§λ λ¬κ³Ό μ΄λ² λ¬μ λ΄μ¬ νλ μκ°μ μ‘°μ¬νμ¬ λνλΈ μ°μ λμ΄λ€. μ§λ λ¬κ³Ό μ΄λ² λ¬ μ€μμ μ μ΄λ ν λ¬μ λ΄μ¬ νλμ $\\displaystyle \\frac{5}{7}$",
"λͺ
μ νμ μ€ νμ΅μκ°μ λΉν΄ μ±μ μ΄ κ°μ₯ μ μ’μ νμμ $\\displaystyle \\frac{5}{7}$",
"μ΄νμΈ νμμ $\\displaystyle A,B,C,D,E \\; 5$",
" κΆμκ°",
"$\\displaystyle 80$ $\\displaystyle 6$"
] |
|
P | [
"$\\displaystyle 17$ $\\displaystyle y$",
"$\\displaystyle x,y$ μ μλ₯Ό",
"$\\displaystyle y$ ",
"$\\displaystyle 16$ $\\displaystyle 7$",
"νκ΅μ λκ΅¬λΆ νμ (2)"
] |
|
P | [
"μ°¨λ³΄λ€ γ£",
"μ² μλ€ λ° νμ μ€ μ μ΄λ ν λ¬μ λ΄μ¬ νλμ λ",
" ν μ’
λ₯μ μμ",
"(2) μ μ§λ¦¬ μμ΄",
"μ μ§λ¦¬ μ μ€ μ μ΄λ ν μ’
λ₯μ μμ $\\displaystyle A$"
] |
|
P | [
"μ£Όμ΄μ§ μ°μ λλ μλλ μκΆμ μ",
"νκΈ°μ $\\displaystyle 2$",
"μλλ μκΆμ μ μ°¨ μ μκ° κ°μ νμμ",
" κ²½κΈ°μμ λ£μ",
"μ κ°μ΄ 컀μ§μ λ°λΌ $\\displaystyle A,B,C,D,E \\; 5$"
] |
|
P | [
"μμ λͺ
μ μ§λ λ¬κ³Ό μ΄λ² λ¬μ λ΄μ¬ νλ μκ°μ μ‘°μ¬νμ¬ λνλΈ μ°μ λμ΄λ€. μ§λ λ¬κ³Ό μ΄λ² λ¬ μ€μμ μ μ΄λ ν λ¬μ λ΄μ¬ νλμ",
"γ μλ
μ μ½μ μ±
μ κΆμκ° κ°μ₯ μ μ νμμ΄ μ¬ν΄ μ½μ μ±
μ κΆμλ $\\displaystyle 17$",
"γ’ μν μ μκ° $\\displaystyle 80$",
"$\\displaystyle 80$ $\\displaystyle 70$",
"$\\displaystyle E$ $\\displaystyle \\therefore $"
] |
|
P | [
"μμΈ νμ μ:",
"μ°¨ μ μκ° κ°μ νμμ λ€μμ μ² μλ€ λ° νμ",
"λ‘",
" λνμ μ°Έκ°ν",
", 2μ°¨ μ μλ₯Ό"
] |
|
P | [
"μ΄",
"λμ΄λ€.",
"μ½μ μ±
μ κΆμκ° κ°μ₯ μ μ νμμ΄ μ¬ν΄ μ½μ μ±
μ κΆμλ",
"$\\displaystyle \\therefore $ $\\displaystyle 10$",
"."
] |
|
P | [
"λ ν μ’
λ₯μ μμ",
"$\\displaystyle A$ μ€μ",
"$\\displaystyle 30$ μ΄μ ν νμμ",
"κΆμκ° κ°μ₯ μ μ νμμ΄ μ¬ν΄ μ½μ μ±
μ κΆμλ",
"$\\displaystyle (x,y)$ $\\displaystyle A,B,C,D$"
] |
|
P | [
"$\\displaystyle 35$ κ³Όν μ μκ°",
"μ°¨ μ μκ° λ λμΌλ―λ‘ μ°¨μ μ μκ°",
"$\\displaystyle 17$ $\\displaystyle 9$",
"$\\displaystyle 80$ $\\displaystyle 8$",
"γ’ μλ
κ³Ό μ¬ν΄ μ½μ μ±
μ κΆμκ° λͺ¨λ $\\displaystyle 90$"
] |
|
P | [
"κΆ μ΄μμΈ νμλ€μ΄ μ¬ν΄ μ½μ μ±
μ κΆμμ νκ· μ $\\displaystyle B$",
"γ’ μν μ μκ° μ μ§λ¦¬ μκ³Ό",
"ν μ μκ°",
"μ μ±
μ κΆμμ λ³νκ° μλ νμμ",
"μ μ΄νμΈ νμμ κ²½κΈ° λμ μ°μ΅ κ²½κΈ°μμ λ£μ"
] |
|
P | [
"$\\displaystyle 17$ $\\displaystyle 7$",
"γ‘ μλ
μ μ½μ μ±
μ κΆμκ° $\\displaystyle \\frac{5}{7}$",
"μ°¨μ μ±κ³΅ν μ κΈ°μ°¨κΈ°μ κ°μμ ν©μ΄ μ μ΄μμΈ νμμ",
"κΆ μ΄μμΈ νμλ€μ΄ μ¬ν΄ μ½μ μ±
μ κΆμμ νκ· μ $\\displaystyle B$",
" μ°¨ μ μλ₯Ό"
] |
|
P | [
"γ‘ μλ
μ μ½μ μ±
μ κΆμκ° $\\displaystyle 18$",
"$\\displaystyle 10$ $\\displaystyle 70$",
"$\\displaystyle x$ $\\displaystyle 4$",
"μ°μ λμ΄λ€.",
"λ€μ μ€ νμ΅μκ°κ³Ό μ±μ μ¬μ΄μ μκ΄κ΄κ³λ₯Ό λνλ΄λ μ°μ λλ₯Ό κ³ λ₯΄μμ€. ( λ¨, $\\displaystyle 80$"
] |
|
P | [
"ν΄ μ½μ μ±
μ κΆμμ νκ· μ",
" λͺΈλ¬΄κ²λ λ§μ΄ λκ°λ νμμ",
"γ£ $\\displaystyle E$",
"λ€μμ μ΄λ μ΄λ±νκ΅ νμλ€μ νμ΅μκ°κ³Ό μ±μ μ μ‘°μ¬νμ¬ λνλΈ μ°μ λμ΄λ€. $\\displaystyle \\therefore $",
"$\\displaystyle 70$ $\\displaystyle 9$"
] |
|
P | [
"λ€μμ μ² μλ€ λ° νμ $\\displaystyle A,B,C,D$",
"$\\displaystyle 90$ κ°μ΄ 컀μ§μλ‘",
"$\\displaystyle 90$ $\\displaystyle A,B,C,D,E \\; 5$",
" $\\displaystyle 50$",
"$\\displaystyle 2$ λ λ³λ"
] |
|
P | [
"γ μν μ μκ° μ°¨λ³΄λ€",
":",
"$\\displaystyle 9$ $\\displaystyle 50$",
"$\\displaystyle 16$ $\\displaystyle 8$",
" κ°μμ ν©μ΄"
] |
|
P | [
"μ°¨μ μ μκ° λͺ¨λ $\\displaystyle (2)$",
"γ μλ
μ μ½μ μ±
μ κΆμκ° κ°μ₯ μ μ νμμ΄ μ¬ν΄ μ½μ μ±
μ κΆμλ $\\displaystyle 7$",
"μ μ§λ¦¬ μκ³Ό μ°¨ μ μλ₯Ό",
" νμμ ν±κ±Έμ΄μ νμλ³΄λ€ νκ΅½νν΄κΈ°μ νμκ° μλμ μΌλ‘ κ°μ₯ λ§μ",
"$\\displaystyle A,B,C,D$ $\\displaystyle (3)$"
] |
|
P | [
" λνλΈ μ°μ λμ΄λ€.",
"μ λλ₯Ό κ³ λ₯΄μμ€. ( λ¨, 차보λ€",
"γ‘ μλ
μ μ½μ μ±
μ κΆμκ° $\\displaystyle 35$",
"νκ΅μ λκ΅¬λΆ νμ μ°¨μ μ μκ° λͺ¨λ",
"λ νμ΅ μκ°, μ°¨ μ μμ λΉν΄"
] |
|
P | [
"$\\displaystyle 8$ $\\displaystyle 1$",
" κ°μλ₯Ό μ‘°μ¬νμ¬ λνλΈ μ°μ λμ΄λ€.",
"$\\displaystyle (2)$ μ μ μκ°",
"γ£ μν μ μμ κ³Όν μ μκ° λͺ¨λ μλλ μκΆμ μ",
"$\\displaystyle 50$ $\\displaystyle \\therefore $"
] |
|
P | [
"$\\displaystyle 90$ μ μλ₯Ό",
" νμλ³΄λ€ νκ΅½νν΄κΈ°μ νμκ° μλμ μΌλ‘ κ°μ₯ λ§μ γ‘",
"μ°¨ μ μκ° λ λμΌλ―λ‘ μ μ΄νμΈ νμ μ:",
"μ°¨μ μ μκ° λͺ¨λ κ°, λμ μ κ°μλ₯Ό",
"μ°¨λ³΄λ€ $\\displaystyle 23$"
] |
|
P | [
"λ€μμ μν¬λ€ λ° νμλ€μ΄ γ μμμ",
"(1) $\\displaystyle A,B,C,D$",
"μ΄λ ν λ¬μ λ΄μ¬ νλμ",
"μ μ΄μ 차보λ€",
"λ€μμ μ΄λ λ° νμ λ νμ΅ μκ°,"
] |
|
P | [
"$\\displaystyle (x,y)$ $\\displaystyle 4$",
"$\\displaystyle 5$ μ΄νμΈ νμμ",
"κ°λΌ ν λ, κ° μ΄μ",
"$\\displaystyle x$ $\\displaystyle 23$",
"$\\displaystyle 16$ μ΄μμΈ μ°Έκ°μλ"
] |
|
P | [
"$\\displaystyle 90$ $\\displaystyle 16$",
"γ’ $\\displaystyle A,B,C,D,E \\; 5$",
"μ°¨ μ μλ₯Ό κ²½κΈ° λμ μ°μ΅ κ²½κΈ°μμ λ£μ",
"(2) μκ°",
"λͺ
μ€μ $\\displaystyle A,B,C,D,E \\; 5$"
] |
|
P | [
"γ μλ
μ μ½μ μ±
μ κΆμκ° κ°μ₯ μ μ νμμ΄ μ¬ν΄ μ½μ μ±
μ κΆμλ $\\displaystyle E$",
"μ¬ν΄ μ½μ μ±
μ κΆμμ νκ· μ",
"$\\displaystyle 17$ $\\displaystyle y$",
"γ’ μλ
κ³Ό μ¬ν΄ μ½μ μ±
μ κΆμκ° λͺ¨λ $\\displaystyle (2)$",
"λ‘μ μ°¨κ° κ°μ₯ ν° νμμ ν±κ±Έμ΄μ νμλ³΄λ€ νκ΅½νν΄κΈ°μ νμκ° μλμ μΌλ‘ κ°μ₯ λ§μ"
] |
|
P | [
"$\\displaystyle 80$ $\\displaystyle 30$",
"μ‘μ΄ κ°μ₯ λ§μ μ§μμ",
"γ‘ κ³Όν μ μκ° λͺ
μ",
"λ€ νμ μ€ νκ΅μ λκ΅¬λΆ νμ",
"μ°¨ μ μμ λΉν΄ $\\displaystyle E$"
] |
|
P | [
"$\\displaystyle 60$ , λμ μ κ°μλ₯Ό",
"(2) λΆ μ΄μ ν νμμ",
"μ°¨λ³΄λ€ $\\displaystyle 8$",
"$\\displaystyle (1)$ ()",
" λͺΈλ¬΄κ²λ λ§μ΄ λκ°λ νμμ"
] |
|
P | [
"μ κ°μ΄ 컀μ§μλ‘ μ°¨ ,",
"μ°¨μ μ μκ° λͺ¨λ μ°¨ μ μκ° λ λμΌλ―λ‘",
"μ°¨ μ μλ₯Ό γ€",
"$\\displaystyle (x,y)$ $\\displaystyle 50$",
"μ λλ₯Ό κ³ λ₯΄μμ€. ( λ¨, μ£Όμ΄μ§ μ°μ λλ"
] |
|
P | [
"γ μλ
μ μ½μ μ±
μ κΆμκ° κ°μ₯ μ μ νμμ΄ μ¬ν΄ μ½μ μ±
μ κΆμλ $\\displaystyle x,y$",
"γ£ μν μ μμ κ³Όν μ μκ° λͺ¨λ $\\displaystyle 11$",
"$\\displaystyle 1$ $\\displaystyle 50$",
"γ‘ κ³Όν μ μκ° $\\displaystyle \\frac{5}{7}$",
"$\\displaystyle 50$ "
] |
|
P | [
"μ°¨μ μ μκ° λͺ¨λ γ‘ κ³Όν μ μκ°",
" λ¬μ λ΄μ¬ νλ μκ°μ μ‘°μ¬νμ¬ λνλΈ μ°μ λμ΄λ€. μ§λ λ¬κ³Ό μ΄λ² λ¬ μ€μμ μ μ΄λ ν λ¬μ λ΄μ¬ νλμ",
"$\\displaystyle 23$ $\\displaystyle A$",
" νμλ³΄λ€ νκ΅½νν΄κΈ°μ νμκ° μλμ μΌλ‘ κ°μ₯ λ§μ μ μ΄μ",
"γ£ μν μ μμ κ³Όν μ μκ° λͺ¨λ $\\displaystyle 11$"
] |
|
P | [
"μ",
"γ μλ
μ μ½μ μ±
μ κΆμκ° κ°μ₯ μ μ νμμ΄ μ¬ν΄ μ½μ μ±
μ κΆμλ $\\displaystyle A,B,C,D,E \\; 5$",
"$\\displaystyle 20$ $\\displaystyle A,B,C,D,E \\; 5$",
"$\\displaystyle 8$ $\\displaystyle 14$",
"μ°¨, $\\displaystyle 90$"
] |
|
P | [
" κΆμκ°",
"γ€ $\\displaystyle 80$",
"μμ μ΄λ νκ΅ νμλ€μ ν κ΅½ν ν΄κΈ° νμμ ν±κ±Έμ΄ νμλ₯Ό μ‘°μ¬νμ¬ λνλΈ μ°μ λμ΄λ€.",
"γ‘ κ³Όν μ μκ° λͺ
μ΄",
"$\\displaystyle (3)$ μμμ"
] |
|
P | [
"νκΈ°μ $\\displaystyle 9$",
"$\\displaystyle 30$ $\\displaystyle 20$",
"γ’ μν μ μκ° μ κ°μ΄ 컀μ§μλ‘",
"νμ μ°Έκ°ν",
"$\\displaystyle E$ $\\displaystyle 7$"
] |
|
P | [
"μ‘°μ¬νμ¬ λνλΈ μ°μ λμ΄λ€.",
"$\\displaystyle 1$ μ΄μ ν νμμ",
"$\\displaystyle (2)$ μ§λ¦¬ μκ³Ό",
"$\\displaystyle 2$ $\\displaystyle 3$",
"λ€μμ μ΄λ νκ΅ νμλ€μ ν κ΅½ν ν΄κΈ° νμμ ν±κ±Έμ΄ νμλ₯Ό μ‘°μ¬νμ¬ λνλΈ μ°μ λμ΄λ€. $\\displaystyle E$"
] |
|
P | [
" μ‘°μ¬νμ¬ λνλΈ νμ΄λ€. μν
μ κ°μλ₯Ό γ‘",
"λͺ
μ΄ $\\displaystyle 16$",
"γ μλ
μ μ½μ μ±
μ κΆμκ° κ°μ₯ μ μ νμμ΄ μ¬ν΄ μ½μ μ±
μ κΆμλ $\\displaystyle 1$",
"μ°¨μ μ μκ° λ λμ νμ μ: γ£",
"μ°¨ μ μμ λΌκ³ ν λ,"
] |
|
P | [
" λ€μμ μν¬λ€ λ° νμλ€μ΄",
"μ°¨, $\\displaystyle 60$",
"γ μμμ μ μ΄μμΈ νμμ",
"$\\displaystyle (3)$ ",
"μ μ§λ¦¬ μμ΄ μ°¨ ,"
] |
|
P | [
"(2) μ°¨μ",
"μ°¨μ μ±κ³΅ν μ κΈ°μ°¨κΈ°μ κ°μμ ν©μ΄ γ’ μν μ μκ°",
"$\\displaystyle 50$ νμ΅ μκ°,",
"$\\displaystyle 3$ $\\displaystyle 30$",
"(1) $\\displaystyle 70$"
] |
|
P | [
" λ³νκ° μλ νμμ",
"$\\displaystyle (1)$ μ΄μ",
"$\\displaystyle 11$ μ μλ₯Ό",
"λ€μμ μ΄λ νκ΅ νμλ€μ ν κ΅½ν ν΄κΈ° νμμ ν±κ±Έμ΄ νμλ₯Ό μ‘°μ¬νμ¬ λνλΈ μ°μ λμ΄λ€. $\\displaystyle 17$",
"μ κΆμκ°"
] |
|
P | [
"μ μ΄νμΈ νμμ $\\displaystyle \\therefore $",
"νμ μ:",
"(1) μ°¨ μ μμ λΉν΄",
"$\\displaystyle 14$ ",
"λ€ νμ μ€ $\\displaystyle 20$"
] |
|
P | [
"$\\displaystyle C$ κΈ°μ",
"$\\displaystyle 7$ $\\displaystyle (x,y)$",
"κ° μ΄μμΈ μ°Έκ°μλ $\\displaystyle 1$",
"γ€ $\\displaystyle 30$",
" μ°¨μ μ μκ° λͺ¨λ"
] |
|
P | [
"μ°¨ μ μκ° λ€μμ λ―Όμλ€ λ° νμ",
"μ°¨μ μ μκ° $\\displaystyle 11$",
"λͺ
μ νμ μ€ νμ΅μκ°μ λΉν΄ μ±μ μ΄ κ°μ₯ μ μ’μ νμμ $\\displaystyle (x,y)$",
"$\\displaystyle x,y$ $\\displaystyle 23$",
"$\\displaystyle 10$ $\\displaystyle 80$"
] |
|
P | [
"γ’ λ€μμ μ κΈ°μ°¨κΈ° λνμ μ°Έκ°ν",
"$\\displaystyle (3)$ λ λ³λ",
"(1) $\\displaystyle (3)$",
" κΆμκ° κ°μ₯ μ μ νμμ΄ μ¬ν΄ μ½μ μ±
μ κΆμλ",
"$\\displaystyle C$ νμΈ νμμ"
] |
|
P | [
"λ€ νμ μ€ $\\displaystyle 2$",
"μ°¨ μ μλ₯Ό κ° μ΄μμΈ μ°Έκ°μλ",
"$\\displaystyle B$ $\\displaystyle y$",
"λΌκ³ ν λ, $\\displaystyle 35$",
"$\\displaystyle (x,y)$ $\\displaystyle \\therefore $"
] |
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