2023 math

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data/json/2023/math.json

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+{"id":1,"name":"1","problem":"1. \\left( \\frac{4}{2^{\\sqrt{2}}} \\right)^{2 + \\sqrt{2}} \\text{\uc758 \uac12\uc740? [2\uc810]}\n\n\\begin{itemize}\n    \\item[1] $\\frac{1}{4}$\n    \\item[2] $\\frac{1}{2}$\n    \\item[3] $1$\n    \\item[4] $2$\n    \\item[5] $4$\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":2,"name":"2","problem":"2. \\lim_{x \\to \\infty} \\frac{\\sqrt{x^2 - 2 + 3x}}{x + 5} \\text{\uc758 \uac12\uc740? [2\uc810]}\n\n\\begin{itemize}\n    \\item[1] 1\n    \\item[2] 2\n    \\item[3] 3\n    \\item[4] 4\n    \\item[5] 5\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":3,"name":"3","problem":"3. \\text{\uacf5\ube44\uac00 \uc591\uc218\uc778 \ub4f1\ube44\uc218\uc5f4 } \\{a_n\\}\\text{\uc774}\n\n\\[ a_2 + a_4 = 30, \\quad a_4 + a_6 = \\frac{15}{2} \\]\n\\text{\ub97c \ub9cc\uc871\uc2dc\ud0ac \ub54c, } a_1 \\text{\uc758 \uac12\uc740? [3\uc810]}\n\n\\begin{itemize}\n    \\item[1] 48\n    \\item[2] 56\n    \\item[3] 64\n    \\item[4] 72\n    \\item[5] 80\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":4,"name":"4","problem":"4. \\text{\ub2e4\ud56d\ud568\uc218 } f(x) \\text{\uc5d0 \ub300\ud558\uc5ec \ud568\uc218 } g(x) \\text{\ub97c}\n\n\\[ g(x) = x^2 f(x) \\]\n\\text{\ub77c \ud558\uc790. } f(2) = 1, \\ f'(2) = 3 \\text{\uc77c \ub54c, } g'(2) \\text{\uc758 \uac12\uc740? [3\uc810]}\n\n\\begin{itemize}\n    \\item[1] 12\n    \\item[2] 14\n    \\item[3] 16\n    \\item[4] 18\n    \\item[5] 20\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":5,"name":"5","problem":"5. \\tan \\theta < 0 \\text{\uc774\uace0} \\cos \\left( \\frac{\\pi}{2} + \\theta \\right) = \\frac{\\sqrt{5}}{5} \\text{\uc77c \ub54c, } \\cos \\theta \\text{\uc758 \uac12\uc740? [3\uc810]}\n\n\\begin{itemize}\n    \\item[1] - \\frac{2 \\sqrt{5}}{5}\n    \\item[2] - \\frac{\\sqrt{5}}{5}\n    \\item[3] 0\n    \\item[4] \\frac{\\sqrt{5}}{5}\n    \\item[5] \\frac{2 \\sqrt{5}}{5}\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":6,"name":"6","problem":"6. \\text{\ud568\uc218 } f(x) = 2x^3 - 9x^2 + ax + 5 \\text{\ub294 } x = 1 \\text{\uc5d0\uc11c \uadf9\ub300\uc774\uace0, } x = b \\text{\uc5d0\uc11c \uadf9\uc18c\uc774\ub2e4. } a + b \\text{\uc758 \uac12\uc740? (\ub2e8, } a, b \\text{\ub294 \uc0c1\uc218\uc774\ub2e4.) [3\uc810]}\n\n\\begin{itemize}\n    \\item[1] 12\n    \\item[2] 14\n    \\item[3] 16\n    \\item[4] 18\n    \\item[5] 20\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":7,"name":"7","problem":"7. \\text{\ubaa8\ub4e0 \ud56d\uc774 \uc591\uc218\uc774\uace0 \uccab\uc9f8\ud56d\uacfc \uacf5\ucc28\uac00 \uac19\uc740 \ub4f1\ucc28\uc218\uc5f4 } \\{a_n\\}\\text{\uc774}\n\n\\[ \\sum_{k=1}^{15} \\frac{1}{\\sqrt{a_k} + \\sqrt{a_{k+1}}} = 2 \\]\n\\text{\ub97c \ub9cc\uc871\uc2dc\ud0ac \ub54c, } a_4 \\text{\uc758 \uac12\uc740? [3\uc810]}\n\n\\begin{itemize}\n    \\item[1] 6\n    \\item[2] 7\n    \\item[3] 8\n    \\item[4] 9\n    \\item[5] 10\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":8,"name":"8","problem":"8. \\text{\uc810 } (0, 4) \\text{\uc5d0\uc11c \uace1\uc120 } y = x^3 - x + 2 \\text{\uc5d0 \uadf8\uc740 \uc811\uc120\uc758 } x \\text{\uc808\ud3b8\uc740? [3\uc810]}\n\n\\begin{itemize}\n    \\item[1] -\\frac{1}{2}\n    \\item[2] -1\n    \\item[3] -\\frac{3}{2}\n    \\item[4] -2\n    \\item[5] -\\frac{5}{2}\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":9,"name":"9","problem":"9. \\text{\ud568\uc218}\n\n\\[ f(x) = a - \\sqrt{3} \\tan 2x \\]\n\\text{\uac00 \ub2eb\ud78c\uad6c\uac04} \\left[ -\\frac{\\pi}{6}, b \\right] \\text{\uc5d0\uc11c \ucd5c\ub300\uac12 7, \ucd5c\uc19f\uac12 3\uc744 \uac00\uc9c8 \ub54c, } a \\times b \\text{\uc758 \uac12\uc740? (\ub2e8, } a, b \\text{\ub294 \uc0c1\uc218\uc774\ub2e4.) [4\uc810]}\n\n\\begin{itemize}\n    \\item[1] \\frac{\\pi}{2}\n    \\item[2] \\frac{5\\pi}{12}\n    \\item[3] \\frac{\\pi}{3}\n    \\item[4] \\frac{\\pi}{4}\n    \\item[5] \\frac{\\pi}{6}\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":10,"name":"10","problem":"10. \\text{\ub450 \uace1\uc120 } y = x^3 + x^2, \\ y = -x^2 + k \\text{\uc640 } y \\text{\ucd95\uc73c\ub85c \ub458\ub7ec\uc2f8\uc778 \ubd80\ubd84\uc758 \ub113\uc774\ub97c } A, \\text{ \ub450 \uace1\uc120 } y = x^3 + x^2, \\ y = -x^2 + k \\text{\uc640 \uc9c1\uc120 } x = 2 \\text{\ub85c \ub458\ub7ec\uc2f8\uc778 \ubd80\ubd84\uc758 \ub113\uc774\ub97c } B \\text{\ub77c \ud558\uc790.} A = B \\text{\uc77c \ub54c, \uc0c1\uc218 } k \\text{\uc758 \uac12\uc740? (\ub2e8, } 4 < k < 5) [4\uc810]}\n\n\\begin{itemize}\n    \\item[1] \\frac{25}{6}\n    \\item[2] \\frac{13}{3}\n    \\item[3] \\frac{9}{2}\n    \\item[4] \\frac{14}{3}\n    \\item[5] \\frac{29}{6}\n\\end{itemize}\n","answer":-1,"score":-1,"review":1.0}
+{"id":11,"name":"11","problem":"11. \\text{\uadf8\ub9bc\uacfc \uac19\uc774 \uc0ac\uac01\ud615 } ABCD \\text{\uac00 \ud55c \uc6d0\uc5d0 \ub0b4\uc811\ud558\uace0}\n\n\\[ \\overline{AB} = 5, \\quad \\overline{AC} = 3 \\sqrt{5}, \\quad \\overline{AD} = 7, \\quad \\angle BAC = \\angle CAD \\]\n\\text{\uc77c \ub54c, \uc774 \uc6d0\uc758 \ubc18\uc9c0\ub984\uc758 \uae38\uc774\ub294? [4\uc810]}\n\n\\begin{itemize}\n    \\item[1] \\frac{5 \\sqrt{2}}{2}\n    \\item[2] \\frac{8 \\sqrt{5}}{5}\n    \\item[3] \\frac{5 \\sqrt{5}}{3}\n    \\item[4] \\frac{8 \\sqrt{2}}{3}\n    \\item[5] \\frac{9 \\sqrt{3}}{4}\n\\end{itemize}\n","answer":-1,"score":-1,"review":1.0}
+{"id":12,"name":"12","problem":"12. \\text{\uc2e4\uc218 \uc804\uccb4\uc758 \uc9d1\ud569\uc5d0\uc11c \uc5f0\uc18d\uc778 \ud568\uc218 } f(x) \\text{\uac00 \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a8\ub2e4.}\n\n\\[ n - 1 \\leq x < n \\text{\uc77c \ub54c, } |f(x)| = |6(x - n + 1)(x - n)| \\text{\uc774\ub2e4. (\ub2e8, } n \\text{\uc740 \uc790\uc5f0\uc218\uc774\ub2e4.)} \\]\n\n\\text{\uc5f4\ub9b0\uad6c\uac04 } (0, 4) \\text{\uc5d0\uc11c \uc815\uc758\ub41c \ud568\uc218} \n\\[ g(x) = \\int_0^x f(t) dt - \\int_x^4 f(t) dt \\]\n\\text{\uac00 } x = 2 \\text{\uc5d0\uc11c \ucd5c\uc19f\uac12 0\uc744 \uac00\uc9c8 \ub54c, } \\int_{\\frac{1}{2}}^4 f(x) dx \\text{\uc758 \uac12\uc740? [4\uc810]}\n\n\\begin{itemize}\n    \\item[1] -\\frac{3}{2}\n    \\item[2] -\\frac{1}{2}\n    \\item[3] \\frac{1}{2}\n    \\item[4] \\frac{3}{2}\n    \\item[5] \\frac{5}{2}\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":13,"name":"13","problem":"13. \\text{\uc790\uc5f0\uc218 } m(m \\geq 2) \\text{\uc5d0 \ub300\ud558\uc5ec } m^{12} \\text{\uc758 } n \\text{\uc81c\uacf1\uadfc \uc911\uc5d0\uc11c \uc815\uc218\uac00 \uc874\uc7ac\ud558\ub3c4\ub85d \ud558\ub294 2 \uc774\uc0c1\uc758 \uc790\uc5f0\uc218 } n \\text{\uc758 \uac1c\uc218\ub97c } f(m) \\text{\uc774\ub77c \ud560 \ub54c,} \n\\[ \\sum_{m=2}^{9} f(m) \\text{\uc758 \uac12\uc740? [4\uc810]} \\]\n\n\\begin{itemize}\n    \\item[1] 37\n    \\item[2] 42\n    \\item[3] 47\n    \\item[4] 52\n    \\item[5] 57\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":14,"name":"14","problem":"14. \\text{\ub2e4\ud56d\ud568\uc218 } f(x) \\text{\uc5d0 \ub300\ud558\uc5ec \ud568\uc218 } g(x) \\text{\ub97c \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.}\n\n\\[ g(x) = \\begin{cases} x & (x < -1 \\text{ \ub610\ub294 } x > 1) \\\\ f(x) & (-1 \\leq x \\leq 1) \\end{cases} \\]\n\\text{\ud568\uc218 } h(x) = \\lim_{t \\to 0^+} g(x+t) \\times \\lim_{t \\to 2^+} g(x+t) \\text{\uc5d0 \ub300\ud558\uc5ec} \n\\text{\ubcf4\uae30\uc5d0\uc11c \uc633\uc740 \uac83\ub9cc\uc744 \uc788\ub294 \ub300\ub85c \uace0\ub978 \uac83\uc740? [4\uc810]}\n\n\\<\ubcf4\uae30>\n\n\u3131. h(1) = 3 \n\n\u3134. \ud568\uc218 h(x)\ub294 \uc2e4\uc218 \uc804\uccb4\uc758 \uc9d1\ud569\uc5d0\uc11c \uc5f0\uc18d\uc774\ub2e4. \n\n\u3137. \ud568\uc218 g(x)\uac00 \ub2eb\ud78c\uad6c\uac04 \\([-1, 1]\\)\uc5d0\uc11c \uac10\uc18c\ud558\uace0 \\(g(-1) = -2\\)\uc774\uba74 \ud568\uc218 h(x)\ub294 \uc2e4\uc218 \uc804\uccb4\uc758 \uc9d1\ud569\uc5d0\uc11c \ucd5c\uc19f\uac12\uc744 \uac16\ub294\ub2e4.\n\n\\begin{itemize}\n    \\item[1] \u3131\n    \\item[2] \u3134\n    \\item[3] \u3131, \u3134\n    \\item[4] \u3131, \u3137\n    \\item[5] \u3134, \u3137\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":15,"name":"15","problem":"15. \\text{\ubaa8\ub4e0 \ud56d\uc774 \uc790\uc5f0\uc218\uc774\uace0 \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \ubaa8\ub4e0 \uc218\uc5f4 } \\{a_n\\} \\text{\uc5d0 \ub300\ud558\uc5ec } a_9 \\text{\uc758 \ucd5c\ub300\uac12\uacfc \ucd5c\uc19f\uac12\uc744 \uac01\uac01 } M, m \\text{\uc774\ub77c \ud560 \ub54c, } M + m \\text{\uc758 \uac12\uc740? [4\uc810]}\n\n\\text{(\uac00) } a_7 = 40 \n\n\\text{(\ub098) \ubaa8\ub4e0 \uc790\uc5f0\uc218 } n \\text{\uc5d0 \ub300\ud558\uc5ec}\n\\[ a_{n+2} = \\begin{cases} a_{n+1} + a_n & (a_{n+1}\\text{\uc774 } 3 \\text{\uc758 \ubc30\uc218\uac00 \uc544\ub2cc \uacbd\uc6b0}) \\\\ \\frac{1}{3} a_{n+1} & (a_{n+1}\\text{\uc774 } 3 \\text{\uc758 \ubc30\uc218\uc778 \uacbd\uc6b0}) \\end{cases} \\]\n\n\\begin{itemize}\n    \\item[1] 216\n    \\item[2] 218\n    \\item[3] 220\n    \\item[4] 222\n    \\item[5] 224\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":16,"name":"16","problem":"16. \\text{\ubc29\uc815\uc2dd}\n\n\\[ \\log_2(3x + 2) = 2 + \\log_2(x - 2) \\]\n\\text{\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc2e4\uc218 } x \\text{\uc758 \uac12\uc744 \uad6c\ud558\uc2dc\uc624. [3\uc810]}\n","answer":-1,"score":-1,"review":null}
+{"id":17,"name":"17","problem":"17. \\text{\ud568\uc218 } f(x) \\text{\uc5d0 \ub300\ud558\uc5ec } f'(x) = 4x^3 - 2x \\text{\uc774\uace0 } f(0) = 3 \\text{\uc77c \ub54c, } f(2) \\text{\uc758 \uac12\uc744 \uad6c\ud558\uc2dc\uc624. [3\uc810]}\n","answer":-1,"score":-1,"review":null}
+{"id":18,"name":"18","problem":"18. \\text{\ub450 \uc218\uc5f4 } \\{a_n\\}, \\{b_n\\} \\text{\uc5d0 \ub300\ud558\uc5ec}\n\n\\[ \\sum_{k=1}^{5} (3a_k + 5) = 55, \\quad \\sum_{k=1}^{5} (a_k + b_k) = 32 \\]\n\\text{\uc77c \ub54c, } \\sum_{k=1}^{5} b_k \\text{\uc758 \uac12\uc744 \uad6c\ud558\uc2dc\uc624. [3\uc810]}\n","answer":-1,"score":-1,"review":null}
+{"id":19,"name":"19","problem":"19. \\text{\ubc29\uc815\uc2dd } 2x^3 - 6x^2 + k = 0 \\text{\uc758 \uc11c\ub85c \ub2e4\ub978 \uc591\uc758 \uc2e4\uadfc\uc758 \uac1c\uc218\uac00 2\uac00 \ub418\ub3c4\ub85d \ud558\ub294 \uc815\uc218 } k \\text{\uc758 \uac1c\uc218\ub97c \uad6c\ud558\uc2dc\uc624. [3\uc810]}\n","answer":-1,"score":-1,"review":null}
+{"id":20,"name":"20","problem":"20. \\text{\uc218\uc9c1\uc120 \uc704\ub97c \uc6c0\uc9c1\uc774\ub294 \uc810 P\uc758 \uc2dc\uac01 } t(t \\geq 0) \\text{\uc5d0\uc11c\uc758 \uc18d\ub3c4 } v(t) \\text{\uc640 \uac00\uc18d\ub3c4 } a(t) \\text{\uac00 \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a8\ub2e4.}\n\n\\text{(\uac00) } 0 \\leq t \\leq 2 \\text{\uc77c \ub54c, } v(t) = 2t^3 - 8t \\text{\uc774\ub2e4.}\n\\text{(\ub098) } t \\geq 2 \\text{\uc77c \ub54c, } a(t) = 6t + 4 \\text{\uc774\ub2e4.}\n\n\\text{\uc2dc\uac01 } t = 0 \\text{\uc5d0\uc11c } t = 3 \\text{\uae4c\uc9c0 \uc810 P\uac00 \uc6c0\uc9c1\uc778 \uac70\ub9ac\ub97c \uad6c\ud558\uc2dc\uc624. [4\uc810]}\n","answer":-1,"score":-1,"review":null}
+{"id":21,"name":"21","problem":"21. \\text{\uc790\uc5f0\uc218 } n \\text{\uc5d0 \ub300\ud558\uc5ec \ud568\uc218 } f(x) \\text{\ub97c}\n\n\\[ f(x) = \\begin{cases} |3^x + 2 - n| & (x < 0) \\\\ |\\log_2(x + 4) - n| & (x \\geq 0) \\end{cases} \\]\n\\text{\uc774\ub77c \ud558\uc790. \uc2e4\uc218 } t \\text{\uc5d0 \ub300\ud558\uc5ec } x \\text{\uc5d0 \ub300\ud55c \ubc29\uc815\uc2dd } f(x) = t \\text{\uc758 \uc11c\ub85c \ub2e4\ub978 \uc2e4\uadfc\uc758 \uac1c\uc218\ub97c } g(t) \\text{\ub77c \ud560 \ub54c, \ud568\uc218 } g(t) \\text{\uc758 \ucd5c\ub313\uac12\uc774 4\uac00 \ub418\ub3c4\ub85d \ud558\ub294 \ubaa8\ub4e0 \uc790\uc5f0\uc218 } n \\text{\uc758 \uac12\uc758 \ud569\uc744 \uad6c\ud558\uc2dc\uc624. [4\uc810]}\n","answer":-1,"score":-1,"review":null}
+{"id":22,"name":"22","problem":"22. \\text{\ucd5c\uace0\ucc28\ud56d\uc758 \uacc4\uc218\uac00 1\uc778 \uc0bc\ucc28\ud568\uc218 } f(x) \\text{\uc640 \uc2e4\uc218 \uc804\uccb4\uc758 \uc9d1\ud569\uc5d0\uc11c \uc5f0\uc18d\uc778 \ud568\uc218 } g(x) \\text{\uac00 \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0ac \ub54c, } f(4) \\text{\uc758 \uac12\uc744 \uad6c\ud558\uc2dc\uc624. [4\uc810]}\n\n\\text{(\uac00) \ubaa8\ub4e0 \uc2e4\uc218 } x \\text{\uc5d0 \ub300\ud558\uc5ec } f(x) = f(1) + (x - 1)f'(g(x)) \\text{\uc774\ub2e4.}\n\\text{(\ub098) \ud568\uc218 } g(x) \\text{\uc758 \ucd5c\uc19f\uac12\uc740 } \\frac{5}{2} \\text{\uc774\ub2e4.}\n\\text{(\ub2e4) } f(0) = -3, \\quad f(g(1)) = 6 \n","answer":-1,"score":-1,"review":null}
+{"id":23,"name":"23_prob","problem":"23. \\( (x^3 + 3)^5 \\)\uc758 \uc804\uac1c\uc2dd\uc5d0\uc11c \\(x^9\\)\uc758 \uacc4\uc218\ub294? [2\uc810]\n\\begin{itemize}\n    \\item[1] 30\n    \\item[2] 60\n    \\item[3] 90\n    \\item[4] 120\n    \\item[5] 150\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":24,"name":"24_prob","problem":"24. \\text{\uc22b\uc790 } 1, 2, 3, 4, 5 \\text{ \uc911\uc5d0\uc11c \uc911\ubcf5\uc744 \ud5c8\ub77d\ud558\uc5ec 4\uac1c\ub97c \ud0dd\ud574 \uc77c\ub82c\ub85c \ub098\uc5f4\ud558\uc5ec \ub9cc\ub4e4 \uc218 \uc788\ub294 \ub124 \uc790\ub9ac\uc758 \uc790\uc5f0\uc218 \uc911 4000 \uc774\uc0c1\uc778 \ud640\uc218\uc758 \uac1c\uc218\ub294? [3\uc810]}\n\n\\begin{itemize}\n    \\item[1] 125\n    \\item[2] 150\n    \\item[3] 175\n    \\item[4] 200\n    \\item[5] 225\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":25,"name":"25_prob","problem":"25. \\text{\ud770\uc0c9 \ub9c8\uc2a4\ud06c 5\uac1c, \uac80\uc740\uc0c9 \ub9c8\uc2a4\ud06c 9\uac1c\uac00 \ub4e4\uc5b4 \uc788\ub294 \uc0c1\uc790\uac00 \uc788\ub2e4. \uc774 \uc0c1\uc790\uc5d0\uc11c \uc784\uc758\ub85c 3\uac1c\uc758 \ub9c8\uc2a4\ud06c\ub97c \ub3d9\uc2dc\uc5d0 \uaebc\ub0bc \ub54c, \uaebc\ub0b8 3\uac1c\uc758 \ub9c8\uc2a4\ud06c \uc911\uc5d0\uc11c \uc801\uc5b4\ub3c4 \ud55c \uac1c\uac00 \ud770\uc0c9 \ub9c8\uc2a4\ud06c\uc77c \ud655\ub960\uc740? [3\uc810]}\n\n\\begin{itemize}\n    \\item[1] \\frac{8}{13}\n    \\item[2] \\frac{17}{26}\n    \\item[3] \\frac{9}{13}\n    \\item[4] \\frac{19}{26}\n    \\item[5] \\frac{10}{13}\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":26,"name":"26_prob","problem":"26. \\text{\uc8fc\uba38\ub2c8\uc5d0 1\uc774 \uc801\ud78c \ud770 \uacf5 1\uac1c, 2\uac00 \uc801\ud78c \ud770 \uacf5 1\uac1c, 1\uc774 \uc801\ud78c \uac80\uc740 \uacf5 1\uac1c, 2\uac00 \uc801\ud78c \uac80\uc740 \uacf5 3\uac1c\uac00 \ub4e4\uc5b4 \uc788\ub2e4. \uc774 \uc8fc\uba38\ub2c8\uc5d0\uc11c \uc784\uc758\ub85c 3\uac1c\uc758 \uacf5\uc744 \ub3d9\uc2dc\uc5d0 \uaebc\ub0b4\ub294 \uc2dc\ud589\uc744 \ud55c\ub2e4. \uc774 \uc2dc\ud589\uc5d0\uc11c \uaebc\ub0b8 3\uac1c\uc758 \uacf5 \uc911\uc5d0\uc11c \ud770 \uacf5\uc774 1\uac1c\uc774\uace0 \uac80\uc740 \uacf5\uc774 2\uac1c\uc778 \uc0ac\uac74\uc744 } A, \\text{ \uaebc\ub0b8 3\uac1c\uc758 \uacf5\uc5d0 \uc801\ud600 \uc788\ub294 \uc218\ub97c \ubaa8\ub450 \uacf1\ud55c \uac12\uc774 8\uc778 \uc0ac\uac74\uc744 } B \\text{\ub77c \ud560 \ub54c, } P(A \\cup B) \\text{\uc758 \uac12\uc740? [3\uc810]}\n\n\\begin{itemize}\n    \\item[1] \\frac{11}{20}\n    \\item[2] \\frac{3}{5}\n    \\item[3] \\frac{13}{20}\n    \\item[4] \\frac{7}{10}\n    \\item[5] \\frac{3}{4}\n\\end{itemize}\n","answer":-1,"score":-1,"review":1.0}
+{"id":27,"name":"27_prob","problem":"27. \\text{\uc5b4\ub290 \ud68c\uc0ac\uc5d0\uc11c \uc0dd\uc0b0\ud558\ub294 \uc0f4\ud478 1\uac1c\uc758 \uc6a9\ub7c9\uc740 \uc815\uaddc\ubd84\ud3ec } N(m, \\sigma^2) \\text{\uc744 \ub530\ub978\ub2e4\uace0 \ud55c\ub2e4. \uc774 \ud68c\uc0ac\uc5d0\uc11c \uc0dd\uc0b0\ud558\ub294 \uc0f4\ud478 \uc911\uc5d0\uc11c 16\uac1c\ub97c \uc784\uc758\ucd94\ucd9c\ud558\uc5ec \uc5bb\uc740 \ud45c\ubcf8\ud3c9\uade0\uc744 \uc774\uc6a9\ud558\uc5ec \uad6c\ud55c } m \\text{\uc5d0 \ub300\ud55c \uc2e0\ub8b0\ub3c4 95%\uc758 \uc2e0\ub8b0\uad6c\uac04\uc774 } 746.1 \\leq m \\leq 755.9 \\text{\uc774\ub2e4. \uc774 \ud68c\uc0ac\uc5d0\uc11c \uc0dd\uc0b0\ud558\ub294 \uc0f4\ud478 \uc911\uc5d0\uc11c } n \\text{\uac1c\ub97c \uc784\uc758\ucd94\ucd9c\ud558\uc5ec \uc5bb\uc740 \ud45c\ubcf8\ud3c9\uade0\uc744 \uc774\uc6a9\ud558\uc5ec \uad6c\ud558\ub294 } m \\text{\uc5d0 \ub300\ud55c \uc2e0\ub8b0\ub3c4 99%\uc758 \uc2e0\ub8b0\uad6c\uac04\uc774 } a \\leq m \\leq b \\text{\uc77c \ub54c, } b - a \\text{\uc758 \uac12\uc774 6 \uc774\ud558\uac00 \ub418\uae30 \uc704\ud55c \uc790\uc5f0\uc218 } n \\text{\uc758 \ucd5c\uc19f\uac12\uc740? (\ub2e8, \uc6a9\ub7c9\uc758 \ub2e8\uc704\ub294 mL\uc774\uace0, } Z \\text{\uac00 \ud45c\uc900\uc815\uaddc\ubd84\ud3ec\ub97c \ub530\ub974\ub294 \ud655\ub960\ubcc0\uc218\uc77c \ub54c, } P(|Z| \\leq 1.96) = 0.95, P(|Z| \\leq 2.58) = 0.99 \\text{\ub85c \uacc4\uc0b0\ud55c\ub2e4.) [3\uc810]}\n\n\\begin{itemize}\n    \\item[1] 70\n    \\item[2] 74\n    \\item[3] 78\n    \\item[4] 82\n    \\item[5] 86\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":28,"name":"28_prob","problem":"28. \\text{\uc5f0\uc18d\ud655\ub960\ubcc0\uc218 } X \\text{\uac00 \uac16\ub294 \uac12\uc758 \ubc94\uc704\ub294 } 0 \\leq X \\leq a \\text{\uc774\uace0, } X \\text{\uc758 \ud655\ub960\ubc00\ub3c4\ud568\uc218\uc758 \uadf8\ub798\ud504\uac00 \uadf8\ub9bc\uacfc \uac19\ub2e4.}\n\n\\[ P(X \\leq b) - P(X \\geq b) = \\frac{1}{4}, \\quad P(X \\leq \\sqrt{5}) = \\frac{1}{2} \\]\n\\text{\uc77c \ub54c, } a + b + c \\text{\uc758 \uac12\uc740? (\ub2e8, } a, b, c \\text{\ub294 \uc0c1\uc218\uc774\ub2e4.) [4\uc810]}\n\n\\begin{itemize}\n    \\item[1] \\frac{11}{2}\n    \\item[2] 6\n    \\item[3] \\frac{13}{2}\n    \\item[4] 7\n    \\item[5] \\frac{15}{2}\n\\end{itemize}\n","answer":-1,"score":-1,"review":2.0}
+{"id":29,"name":"29_prob","problem":"29. \\text{\uc55e\uba74\uc5d0\ub294 1\ubd80\ud130 6\uae4c\uc9c0\uc758 \uc790\uc5f0\uc218\uac00 \ud558\ub098\uc529 \uc801\ud600 \uc788\uace0, \ub4b7\uba74\uc5d0\ub294 \ubaa8\ub450 0\uc774 \ud558\ub098\uc529 \uc801\ud600 \uc788\ub294 6\uc7a5\uc758 \uce74\ub4dc\uac00 \uc788\ub2e4. \uc774 6\uc7a5\uc758 \uce74\ub4dc\uac00 \uadf8\ub9bc\uacfc \uac19\uc774 6 \uc774\ud558\uc758 \uc790\uc5f0\uc218 } k \\text{\uc5d0 \ub300\ud558\uc5ec } k \\text{\ubc88\uc9f8 \uc790\ub9ac\uc5d0 \uc790\uc5f0\uc218 } k \\text{\uac00 \ubcf4\uc774\ub3c4\ub85d \ub193\uc5ec \uc788\ub2e4.}\n\n\\text{\uc774 6\uc7a5\uc758 \uce74\ub4dc\uc640 \ud55c \uac1c\uc758 \uc8fc\uc0ac\uc704\ub97c \uc0ac\uc6a9\ud558\uc5ec \ub2e4\uc74c \uc2dc\ud589\uc744 \ud55c\ub2e4.}\n\n\\[ \\text{\uc8fc\uc0ac\uc704\ub97c \ud55c \ubc88 \ub358\uc838 \ub098\uc628 \ub208\uc758 \uc218\uac00 } k \\text{\uc774\uba74 } k \\text{\ubc88\uc9f8 \uc790\ub9ac\uc5d0 \ub193\uc5ec \uc788\ub294 \uce74\ub4dc\ub97c \ud55c \ubc88 \ub4a4\uc9d1\uc5b4 \uc81c\uc790\ub9ac\uc5d0 \ub193\ub294\ub2e4.} \\]\n\n\\text{\uc704\uc758 \uc2dc\ud589\uc744 3\ubc88 \ubc18\ubcf5\ud55c \ud6c4 6\uc7a5\uc758 \uce74\ub4dc\uc5d0 \ubcf4\uc774\ub294 \ubaa8\ub4e0 \uc218\uc758 \ud569\uc774 \uc9dd\uc218\uc77c \ub54c, \uc8fc\uc0ac\uc704\uc758 1\uc758 \ub208\uc774 \ud55c \ubc88\ub9cc \ub098\uc654\uc744 \ud655\ub960\uc740 } \\frac{q}{p} \\text{\uc774\ub2e4. } p + q \\text{\uc758 \uac12\uc744 \uad6c\ud558\uc2dc\uc624. (\ub2e8, } p \\text{\uc640 } q \\text{\ub294 \uc11c\ub85c\uc18c\uc778 \uc790\uc5f0\uc218\uc774\ub2e4.) [4\uc810]}\n","answer":-1,"score":-1,"review":1.0}
+{"id":30,"name":"30_prob","problem":"30. \\text{\uc9d1\ud569 } X = \\{x | x \\text{\ub294 10 \uc774\ud558\uc758 \uc790\uc5f0\uc218}\\} \\text{\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \ud568\uc218 } f: X \\to X \\text{\uc758 \uac1c\uc218\ub97c \uad6c\ud558\uc2dc\uc624. [4\uc810]}\n\n\\text{(\uac00) 9 \uc774\ud558\uc758 \ubaa8\ub4e0 \uc790\uc5f0\uc218 } x \\text{\uc5d0 \ub300\ud558\uc5ec } f(x) \\leq f(x+1) \\text{\uc774\ub2e4.}\n\\text{(\ub098) } 1 \\leq x \\leq 5 \\text{\uc77c \ub54c } f(x) \\leq x \\text{\uc774\uace0, } 6 \\leq x \\leq 10 \\text{\uc77c \ub54c } f(x) \\geq x \\text{\uc774\ub2e4.}\n\\text{(\ub2e4) } f(6) = f(5) + 6\n","answer":-1,"score":-1,"review":null}
+{"id":31,"name":"23_calc","problem":"23. \\lim_{x \\to 0} \\frac{\\ln(x+1)}{\\sqrt{x+4} - 2} \\text{\uc758 \uac12\uc740? [2\uc810]}\n\n\\begin{itemize}\n    \\item[1] 1\n    \\item[2] 2\n    \\item[3] 3\n    \\item[4] 4\n    \\item[5] 5\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":32,"name":"24_calc","problem":"24. \\lim_{n \\to \\infty} \\frac{1}{n} \\sum_{k=1}^{n} \\sqrt{1 + \\frac{3k}{n}} \\text{\uc758 \uac12\uc740? [3\uc810]}\n\n\\begin{itemize}\n    \\item[1] \\frac{4}{3}\n    \\item[2] \\frac{13}{9}\n    \\item[3] \\frac{14}{9}\n    \\item[4] \\frac{5}{3}\n    \\item[5] \\frac{16}{9}\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":33,"name":"25_calc","problem":"25. \\text{\ub4f1\ube44\uc218\uc5f4 } \\{a_n\\} \\text{\uc5d0 \ub300\ud558\uc5ec } \\lim_{n \\to \\infty} \\frac{a_n + 1}{3^n + 2^{2n-1}} = 3 \\text{\uc77c \ub54c, } a_2 \\text{\uc758 \uac12\uc740? [3\uc810]}\n\n\\begin{itemize}\n    \\item[1] 16\n    \\item[2] 18\n    \\item[3] 20\n    \\item[4] 22\n    \\item[5] 24\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":34,"name":"26_calc","problem":"26. \\text{\uadf8\ub9bc\uacfc \uac19\uc774 \uace1\uc120 } y = \\sqrt{\\sec^2 x} + \\tan x \\left(0 \\leq x \\leq \\frac{\\pi}{3}\\right) \\text{\uc640 } x \\text{\ucd95, } y \\text{\ucd95 \ubc0f \uc9c1\uc120 } x = \\frac{\\pi}{3} \\text{\ub85c \ub458\ub7ec\uc2f8\uc778 \ubd80\ubd84\uc744 \ubc11\uba74\uc73c\ub85c \ud558\ub294 \uc785\uccb4\ub3c4\ud615\uc774 \uc788\ub2e4. \uc774 \uc785\uccb4\ub3c4\ud615\uc744 } x \\text{\ucd95\uc5d0 \uc218\uc9c1\uc778 \ud3c9\uba74\uc73c\ub85c \uc790\ub978 \ub2e8\uba74\uc774 \ubaa8\ub450 \uc815\uc0ac\uac01\ud615\uc77c \ub54c, \uc774 \uc785\uccb4\ub3c4\ud615\uc758 \ubd80\ud53c\ub294? [3\uc810]}\n\n\\begin{itemize}\n    \\item[1] \\frac{\\sqrt{3}}{2} + \\frac{\\ln 2}{2}\n    \\item[2] \\frac{\\sqrt{3}}{2} + \\ln 2\n    \\item[3] \\sqrt{3} + \\frac{\\ln 2}{2}\n    \\item[4] \\sqrt{3} + \\ln 2\n    \\item[5] \\sqrt{3} + 2\\ln 2\n\\end{itemize}\n","answer":-1,"score":-1,"review":1.0}
+{"id":35,"name":"27_prob","problem":"27. \\text{\uadf8\ub9bc\uacfc \uac19\uc774 \uc911\uc2ec\uc774 } O, \\text{\ubc18\uc9c0\ub984\uc758 \uae38\uc774\uac00 1\uc774\uace0 \uc911\uc2ec\uac01\uc758 \ud06c\uae30\uac00 } \\frac{\\pi}{2} \\text{\uc778 \ubd80\ucc44\uaf34 } OA_1B_1 \\text{\uc774 \uc788\ub2e4. \ud638 } A_1B_1 \\text{ \uc704\uc5d0 \uc810 } P_1, \\text{\uc120\ubd84 } OA_1 \\text{ \uc704\uc5d0 \uc810 } C_1, \\text{\uc120\ubd84 } OB_1 \\text{ \uc704\uc5d0 \uc810 } D_1 \\text{\uc744 \uc0ac\uac01\ud615 } OC_1P_1D_1 \\text{\uc774 } OC_1 : OD_1 = 3:4 \\text{\uc778 \uc9c1\uc0ac\uac01\ud615\uc774 \ub418\ub3c4\ub85d \uc7a1\ub294\ub2e4.}\n\n\\text{\ubd80\ucc44\uaf34 } OA_1B_1 \\text{\uc758 \ub0b4\ubd80\uc5d0 \uc810 } Q_1 \\text{\uc744 } PQ_1 = AQ_1, \\angle PQ_1A_1 = \\frac{\\pi}{2} \\text{\uac00 \ub418\ub3c4\ub85d \uc7a1\uace0, \uc774\ub4f1\ubcc0\uc0bc\uac01\ud615 } P_1Q_1A_1 \\text{\uc5d0 \uc0c9\uce60\ud558\uc5ec \uc5bb\uc740 \uadf8\ub9bc\uc744 } R_1 \\text{\uc774\ub77c \ud558\uc790.}\n\\text{\uadf8\ub9bc } R_1 \\text{\uc5d0\uc11c \uc120\ubd84 } OA_1 \\text{ \uc704\uc758 \uc810 } A_2 \\text{\uc640 \uc120\ubd84 } OB_1 \\text{ \uc704\uc758 \uc810 } B_2 \\text{\ub97c } OQ_1 = OA_2 = OB_2 \\text{\uac00 \ub418\ub3c4\ub85d \uc7a1\uace0, \uc911\uc2ec\uc774 } O, \\text{\ubc18\uc9c0\ub984\uc758 \uae38\uc774\uac00 } OQ_1, \\text{\uc911\uc2ec\uac01\uc758 \ud06c\uae30\uac00 } \\frac{\\pi}{2} \\text{\uc778 \ubd80\ucc44\uaf34 } OA_2B_2 \\text{\ub97c \uadf8\ub9b0\ub2e4. \uadf8\ub9b0 } R_1 \\text{\uc744 \uc5bb\uc740 \uac83\uacfc \uac19\uc740 \ubc29\ubc95\uc73c\ub85c \ub124 \uc810 } P_2, C_2, D_2, Q_2 \\text{\ub97c \uc7a1\uace0, \uc774\ub4f1\ubcc0\uc0bc\uac01\ud615 } P_2Q_2A_2 \\text{\uc5d0 \uc0c9\uce60\ud558\uc5ec \uc5bb\uc740 \uadf8\ub9bc\uc744 } R_2 \\text{\ub77c \ud558\uc790. \uc774\uc640 \uac19\uc740 \uacfc\uc815\uc744 \uacc4\uc18d\ud558\uc5ec } n \\text{\ubc88\uc9f8 \uc5bb\uc740 \uadf8\ub9bc } R_n \\text{\uc5d0 \uc0c9\uce60\ub418\uc5b4 \uc788\ub294 \ubd80\ubd84\uc758 \ub113\uc774\ub97c } S_n \\text{\uc774\ub77c \ud560 \ub54c, } \\lim_{n \\to \\infty} S_n \\text{\uc758 \uac12\uc740? [3\uc810]}\n\n\\begin{itemize}\n    \\item[1] \\frac{9}{40}\n    \\item[2] \\frac{1}{4}\n    \\item[3] \\frac{11}{40}\n    \\item[4] \\frac{3}{10}\n    \\item[5] \\frac{13}{40}\n\\end{itemize}\n","answer":-1,"score":-1,"review":1.0}
+{"id":36,"name":"28_prob","problem":"28. \\text{\uadf8\ub9bc\uacfc \uac19\uc774 \uc911\uc2ec\uc774 } O \\text{\uc774\uace0 \uae38\uc774\uac00 2\uc778 \uc120\ubd84 } AB \\text{\ub97c \uc9c0\ub984\uc73c\ub85c \ud558\ub294 \ubc18\uc6d0 \uc704\uc5d0 } \\angle AOC = \\frac{\\pi}{2} \\text{\uc778 \uc810 } C \\text{\uac00 \uc788\ub2e4.}\n\\text{\ud638 } BC \\text{ \uc704\uc5d0 \uc810 } P \\text{\uc640 \ud638 } CA \\text{ \uc704\uc5d0 \uc810 } Q \\text{\ub97c } PB = QC \\text{\uac00 \ub418\ub3c4\ub85d \uc7a1\uace0, \uc120\ubd84 } AP \\text{ \uc704\uc5d0 \uc810 } R \\text{\uc744 } \\angle CQR = \\frac{\\pi}{2} \\text{\uac00 \ub418\ub3c4\ub85d \uc7a1\ub294\ub2e4.}\n\\text{\uc120\ubd84 } AP \\text{\uc640 \uc120\ubd84 } CO \\text{\uc758 \uad50\uc810\uc744 } S \\text{\ub77c \ud558\uc790. } \\angle PAB = \\theta \\text{\uc77c \ub54c, \uc0bc\uac01\ud615 } POB \\text{\uc758 \ub113\uc774\ub97c } f(\\theta), \\text{\uc0ac\uac01\ud615 } CQRS \\text{\uc758 \ub113\uc774\ub97c } g(\\theta) \\text{\ub77c \ud558\uc790.}\n\n\\lim_{\\theta \\to 0^+} \\frac{3f(\\theta) - 2g(\\theta)}{\\theta^2} \\text{\uc758 \uac12\uc740? (\ub2e8, } 0 < \\theta < \\frac{\\pi}{4} \\text{) [4\uc810]}\n\n\\begin{itemize}\n    \\item[1] 1\n    \\item[2] 2\n    \\item[3] 3\n    \\item[4] 4\n    \\item[5] 5\n\\end{itemize}\n","answer":-1,"score":-1,"review":1.0}
+{"id":37,"name":"29_prob","problem":"29. \\text{\uc138 \uc0c1\uc218 } a, b, c \\text{\uc5d0 \ub300\ud558\uc5ec \ud568\uc218 } f(x) = ae^{2x} + be^x + c \\text{\uac00 \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a8\ub2e4.}\n\n\\text{(\uac00) } \\lim_{x \\to -\\infty} \\frac{f(x) + 6}{e^x} = 1\n\\text{(\ub098) } f(\\ln 2) = 0\n\n\\text{\ud568\uc218 } f(x) \\text{\uc758 \uc5ed\ud568\uc218\ub97c } g(x) \\text{\ub77c \ud560 \ub54c,}\n\\[ \\int_0^{14} g(x) dx = p + q \\ln 2 \\text{\uc774\ub2e4. } p + q \\text{\uc758 \uac12\uc744 \uad6c\ud558\uc2dc\uc624.}\n\\text{(\ub2e8, } p, q \\text{\ub294 \uc720\ub9ac\uc218\uc774\uace0, } \\ln 2 \\text{\ub294 \ubb34\ub9ac\uc218\uc774\ub2e4.) [4\uc810]}\n","answer":-1,"score":-1,"review":null}
+{"id":38,"name":"30_prob","problem":"30. \\text{\ucd5c\uace0\ucc28\ud56d\uc758 \uacc4\uc218\uac00 \uc591\uc218\uc778 \uc0bc\ucc28\ud568\uc218 } f(x) \\text{\uc640 \ud568\uc218 } g(x) = e^{\\sin \\pi x} - 1 \\text{\uc5d0 \ub300\ud558\uc5ec \uc2e4\uc218 \uc804\uccb4\uc758 \uc9d1\ud569\uc5d0\uc11c \uc815\uc758\ub41c \ud569\uc131\ud568\uc218 } h(x) = g(f(x)) \\text{\uac00 \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a8\ub2e4.}\n\n\\text{(\uac00) \ud568\uc218 } h(x) \\text{\ub294 } x = 0 \\text{\uc5d0\uc11c \uadf9\ub313\uac12 0\uc744 \uac16\ub294\ub2e4.}\n\\text{(\ub098) \uc5f4\ub9b0\uad6c\uac04 } (0, 3) \\text{\uc5d0\uc11c \ubc29\uc815\uc2dd } h(x) = 1 \\text{\uc758 \uc11c\ub85c \ub2e4\ub978 \uc2e4\uadfc\uc758 \uac1c\uc218\ub294 7\uc774\ub2e4.}\n\nf(3) = \\frac{1}{2}, f'(3) = 0 \\text{\uc77c \ub54c, } f(2) = \\frac{q}{p} \\text{\uc774\ub2e4. } p + q \\text{\uc758 \uac12\uc744 \uad6c\ud558\uc2dc\uc624. (\ub2e8, } p \\text{\uc640 } q \\text{\ub294 \uc11c\ub85c\uc18c\uc778 \uc790\uc5f0\uc218\uc774\ub2e4.) [4\uc810]}\n","answer":-1,"score":-1,"review":null}
+{"id":39,"name":"23_geom","problem":"23. \\text{\uc88c\ud45c\uacf5\uac04\uc758 \uc810 } A(2, 2, -1) \\text{\uc744 } x \\text{\ucd95\uc5d0 \ub300\ud558\uc5ec \ub300\uce6d\uc774\ub3d9\ud55c \uc810\uc744 } B \\text{\ub77c \ud558\uc790. \uc810 } C(-2, 1, 1) \\text{\uc5d0 \ub300\ud558\uc5ec \uc120\ubd84 BC\uc758 \uae38\uc774\ub294? [2\uc810]}\n\n\\begin{itemize}\n    \\item[1] 1\n    \\item[2] 2\n    \\item[3] 3\n    \\item[4] 4\n    \\item[5] 5\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":40,"name":"24_geom","problem":"24. \\text{\ucd08\uc810\uc774 } F\\left(\\frac{1}{3}, 0\\right) \\text{\uc774\uace0 \uc900\uc120\uc774 } x = -\\frac{1}{3} \\text{\uc778 \ud3ec\ubb3c\uc120\uc774 \uc810 } (a, 2) \\text{\ub97c \uc9c0\ub0a0 \ub54c, } a \\text{\uc758 \uac12\uc740? [3\uc810]}\n\n\\begin{itemize}\n    \\item[1] 1\n    \\item[2] 2\n    \\item[3] 3\n    \\item[4] 4\n    \\item[5] 5\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":41,"name":"25_geom","problem":"25. \\text{\ud0c0\uc6d0 } \\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 \\text{ \uc704\uc758 \uc810 } (2, 1) \\text{\uc5d0\uc11c\uc758 \uc811\uc120\uc758 \uae30\uc6b8\uae30\uac00 } -\\frac{1}{2} \\text{\uc77c \ub54c, \uc774 \ud0c0\uc6d0\uc758 \ub450 \ucd08\uc810 \uc0ac\uc774\uc758 \uac70\ub9ac\ub294? (\ub2e8, } a, b \\text{\ub294 \uc591\uc218\uc774\ub2e4.) [3\uc810]}\n\n\\begin{itemize}\n    \\item[1] 2\\sqrt{3}\n    \\item[2] 4\n    \\item[3] 2\\sqrt{5}\n    \\item[4] 2\\sqrt{6}\n    \\item[5] 2\\sqrt{7}\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":42,"name":"26_geom","problem":"26. \\text{\uc88c\ud45c\ud3c9\uba74\uc5d0\uc11c \uc138 \ubca1\ud130 } \\vec{a} = (2, 4), \\vec{b} = (2, 8), \\vec{c} = (1, 0) \\text{\uc5d0 \ub300\ud558\uc5ec \ub450 \ubca1\ud130 } \\vec{p}, \\vec{q} \\text{\uac00}\n\n(\\vec{p} - \\vec{a}) \\cdot (\\vec{p} - \\vec{b}) = 0, \\quad \\vec{q} = \\frac{1}{2} \\vec{a} + t \\vec{c} \\quad (t \\text{\ub294 \uc2e4\uc218}) \\text{\ub97c \ub9cc\uc871\uc2dc\ud0ac \ub54c, } |\\vec{p} - \\vec{q}| \\text{\uc758 \ucd5c\uc19f\uac12\uc740? [3\uc810]}\n\n\\begin{itemize}\n    \\item[1] \\frac{3}{2}\n    \\item[2] 2\n    \\item[3] \\frac{5}{2}\n    \\item[4] 3\n    \\item[5] \\frac{7}{2}\n\\end{itemize}\n","answer":-1,"score":-1,"review":null}
+{"id":43,"name":"27_geom","problem":"27. \\text{\uc88c\ud45c\uacf5\uac04\uc5d0 \uc9c1\uc120 AB\ub97c \ud3ec\ud568\ud558\ub294 \ud3c9\uba74 } \\alpha \\text{\uac00 \uc788\ub2e4. \ud3c9\uba74 } \\alpha \\text{ \uc704\uc5d0 \uc788\uc9c0 \uc54a\uc740 \uc810 C\uc5d0 \ub300\ud558\uc5ec \uc9c1\uc120 AB\uc640 \uc9c1\uc120 AC\uac00 \uc774\ub8e8\ub294 \uc608\uac01\uc758 \ud06c\uae30\ub97c } \\theta_1 \\text{\uc774\ub77c \ud560 \ub54c } \\sin \\theta_1 = \\frac{4}{5} \\text{\uc774\uace0, \uc9c1\uc120 AC\uc640 \ud3c9\uba74 } \\alpha \\text{\uac00 \uc774\ub8e8\ub294 \uc608\uac01\uc758 \ud06c\uae30\ub294 } \\frac{\\pi}{2} - \\theta_1 \\text{\uc774\ub2e4. \ud3c9\uba74 ABC\uc640 \ud3c9\uba74 } \\alpha \\text{\uac00 \uc774\ub8e8\ub294 \uc608\uac01\uc758 \ud06c\uae30\ub97c } \\theta_2 \\text{\ub77c \ud560 \ub54c, } \\cos \\theta_2 \\text{\uc758 \uac12\uc740? [3\uc810]}\n\n\\begin{itemize}\n    \\item[1] \\frac{\\sqrt{7}}{4}\n    \\item[2] \\frac{\\sqrt{7}}{5}\n    \\item[3] \\frac{\\sqrt{7}}{6}\n    \\item[4] \\frac{\\sqrt{7}}{7}\n    \\item[5] \\frac{\\sqrt{7}}{8}\n\\end{itemize}\n","answer":-1,"score":-1,"review":1.0}
+{"id":44,"name":"28_geom","problem":"28. \\text{\ub450 \ucd08\uc810\uc774 } F(c, 0), F'(-c, 0) \\text{(} c > 0 \\text{)\uc778 \uc30d\uace1\uc120 } C \\text{\uc640 } y \\text{\ucd95 \uc704\uc758 \uc810 } A \\text{\uac00 \uc788\ub2e4. \uc30d\uace1\uc120 } C \\text{\uac00 \uc120\ubd84 } AF \\text{\uc640 \ub9cc\ub098\ub294 \uc810\uc744 } P, \\text{\uc120\ubd84 } AF' \\text{\uacfc \ub9cc\ub098\ub294 \uc810\uc744 } P' \\text{\uc774\ub77c \ud558\uc790. \uc9c1\uc120 } AF \\text{\ub294 \uc30d\uace1\uc120 } C \\text{\uc758 \ud55c \uc811\uadfc\uc120\uacfc \ud3c9\ud589\ud558\uace0 }\n\\frac{AP}{PP'} = \\frac{5}{6}, PF = 1 \\text{\uc77c \ub54c, \uc30d\uace1\uc120 } C \\text{\uc758 \uc8fc\ucd95\uc758 \uae38\uc774\ub294? [4\uc810]}\n\n\\begin{itemize}\n    \\item[1] \\frac{13}{6}\n    \\item[2] \\frac{9}{4}\n    \\item[3] \\frac{7}{3}\n    \\item[4] \\frac{29}{12}\n    \\item[5] \\frac{5}{2}\n\\end{itemize}\n","answer":-1,"score":-1,"review":1.0}
+{"id":45,"name":"29_geom","problem":"29. \\text{\ud3c9\uba74 } \\alpha \\text{ \uc704\uc5d0 } \\overline{AB} = \\overline{CD} = \\overline{AD} = 2, \\quad \\angle ABC = \\angle BCD = \\frac{\\pi}{3} \\text{\uc778 \uc0ac\ub2e4\ub9ac\uaf34 ABCD\uac00 \uc788\ub2e4. \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \ud3c9\uba74 } \\alpha \\text{ \uc704\uc758 \ub450 \uc810 P, Q\uc5d0 \ub300\ud558\uc5ec } \\overrightarrow{CP} \\cdot \\overrightarrow{DQ} \\text{\uc758 \uac12\uc744 \uad6c\ud558\uc2dc\uc624. [4\uc810]}\n\n\\text{(\uac00) } \\overrightarrow{AC} = 2(\\overrightarrow{AD} + \\overrightarrow{BP})\n\\text{(\ub098) } \\overrightarrow{AC} \\cdot \\overrightarrow{PQ} = 6\n\\text{(\ub2e4) } 2 \\times \\angle BQA = \\angle PBQ < \\frac{\\pi}{2}\n","answer":-1,"score":-1,"review":2.0}
+{"id":46,"name":"30_geom","problem":"30. \\text{\uc88c\ud45c\uacf5\uac04\uc5d0 \uc815\uc0ac\uba74\uccb4 ABCD\uac00 \uc788\ub2e4. \uc815\uc0bc\uac01\ud615 BCD\uc758 \uc678\uc2ec\uc744 \uc911\uc2ec\uc73c\ub85c \ud558\uace0 \uc810 B\ub97c \uc9c0\ub098\ub294 \uad6c\ub97c } S \\text{\ub77c \ud558\uc790.}\n\\text{\uad6c } S \\text{\uc640 \uc120\ubd84 AB\uac00 \ub9cc\ub098\ub294 \uc810 \uc911 B\uac00 \uc544\ub2cc \uc810\uc744 P,}\n\\text{\uad6c } S \\text{\uc640 \uc120\ubd84 AC\uac00 \ub9cc\ub098\ub294 \uc810 \uc911 C\uac00 \uc544\ub2cc \uc810\uc744 Q,}\n\\text{\uad6c } S \\text{\uc640 \uc120\ubd84 AD\uac00 \ub9cc\ub098\ub294 \uc810 \uc911 D\uac00 \uc544\ub2cc \uc810\uc744 R\ub77c \ud558\uace0, \uc810 P\uc5d0\uc11c \uad6c } S \\text{\uc5d0 \uc811\ud558\ub294 \ud3c9\uba74\uc744 } \\alpha \\text{\ub77c \ud558\uc790.}\n\\text{\uad6c } S \\text{\uc758 \ubc18\uc9c0\ub984\uc758 \uae38\uc774\uac00 6\uc77c \ub54c, \uc0bc\uac01\ud615 PQR\uc758 \ud3c9\uba74 } \\alpha \\text{\uc704\ub85c\uc758 \uc815\uc0ac\uc601\uc758 \ub113\uc774\ub294 } k \\alpha \\text{\uc774\ub2e4. } k^2 \\text{\uc758 \uac12\uc744 \uad6c\ud558\uc2dc\uc624. [4\uc810]}\n","answer":-1,"score":-1,"review":null}

test_dataset.ipynb

@@ -0,0 +1,36 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from datasets import load_dataset\n",
+    "\n",
+    "ds = load_dataset(\"cfpark00/KoreanSAT\")\n",
+    "ds[\"2024_math\"].to_json(\"./data/json/2024/math.json\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "venv1",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "name": "python",
+   "version": "3.8.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

to_json.ipynb

@@ -0,0 +1,499 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from datasets import load_dataset"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "dataset=load_dataset(\"json\",data_files={\"2024_math\":\"./data/json/2024/math.json\"})"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "b1cb0061e5e44907ad4e4b517a9958ec",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Uploading the dataset shards:   0%|          | 0/1 [00:00<?, ?it/s]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "36dc057254534c3c85a9f896138b6bdd",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Creating parquet from Arrow format:   0%|          | 0/1 [00:00<?, ?ba/s]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "e20e228b1acb44cda94c8deae8a11ae5",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "README.md:   0%|          | 0.00/1.06k [00:00<?, ?B/s]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "No files have been modified since last commit. Skipping to prevent empty commit.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "CommitInfo(commit_url='https://huggingface.co/datasets/cfpark00/KoreanSAT/commit/550fafbd44998c53609db2bd54d582e1cbead523', commit_message='Upload dataset', commit_description='', oid='550fafbd44998c53609db2bd54d582e1cbead523', pr_url=None, repo_url=RepoUrl('https://huggingface.co/datasets/cfpark00/KoreanSAT', endpoint='https://huggingface.co', repo_type='dataset', repo_id='cfpark00/KoreanSAT'), pr_revision=None, pr_num=None)"
+      ]
+     },
+     "execution_count": 30,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "#save as parquet\n",
+    "dataset.push_to_hub(\"cfpark00/KoreanSAT\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "95ec444f91fb4eef82eca149345bd1a2",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Generating 2023_math split: 0 examples [00:00, ? examples/s]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "dataset=load_dataset(\"json\",data_files={\"2023_math\":\"./data/json/2023/math_temp.json\"})"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "bfd367afe6af4cb187a07e60a4689e9b",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Creating json from Arrow format:   0%|          | 0/1 [00:00<?, ?ba/s]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "33742"
+      ]
+     },
+     "execution_count": 32,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dataset[\"2023_math\"].to_json(\"./data/json/2023/math.json\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "8b94256626874d8887b20f1534fb87ad",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Generating 2023_math split: 0 examples [00:00, ? examples/s]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "dataset=load_dataset(\"json\",data_files={\"2023_math\":\"./data/json/2023/math.json\"})"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "dc80fede92f943229adc4f440f7f8539",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Uploading the dataset shards:   0%|          | 0/1 [00:00<?, ?it/s]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "1247550d08ad427488506b34981052b5",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Creating parquet from Arrow format:   0%|          | 0/1 [00:00<?, ?ba/s]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "CommitInfo(commit_url='https://huggingface.co/datasets/cfpark00/KoreanSAT/commit/0dd40e51b7b17a6e6a6dfd362fb559a46f58d84e', commit_message='Upload dataset', commit_description='', oid='0dd40e51b7b17a6e6a6dfd362fb559a46f58d84e', pr_url=None, repo_url=RepoUrl('https://huggingface.co/datasets/cfpark00/KoreanSAT', endpoint='https://huggingface.co', repo_type='dataset', repo_id='cfpark00/KoreanSAT'), pr_revision=None, pr_num=None)"
+      ]
+     },
+     "execution_count": 34,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "#save as parquet\n",
+    "dataset.push_to_hub(\"cfpark00/KoreanSAT\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'id': 1,\n",
+       " 'name': '1',\n",
+       " 'problem': '1. \\\\left( \\\\frac{4}{2^{\\\\sqrt{2}}} \\\\right)^{2 + \\\\sqrt{2}} \\\\text{의 값은? [2점]}\\n\\n\\\\begin{itemize}\\n    \\\\item[1] $\\\\frac{1}{4}$\\n    \\\\item[2] $\\\\frac{1}{2}$\\n    \\\\item[3] $1$\\n    \\\\item[4] $2$\\n    \\\\item[5] $4$\\n\\\\end{itemize}\\n',\n",
+       " 'answer': -1,\n",
+       " 'score': -1}"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dataset[\"2023_math\"][0]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "ed6870fcaa5d4641ae911c05f8d5e1a3",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Creating json from Arrow format:   0%|          | 0/1 [00:00<?, ?ba/s]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "33057"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from datasets import load_dataset\n",
+    "\n",
+    "ds = load_dataset(\"cfpark00/KoreanSAT\")\n",
+    "ds[\"2024_math\"].to_json(\"./data/json/2024/math.json\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "DatasetDict({\n",
+       "    2024_math: Dataset({\n",
+       "        features: ['id', 'name', 'problem', 'answer', 'score'],\n",
+       "        num_rows: 46\n",
+       "    })\n",
+       "})"
+      ]
+     },
+     "execution_count": 46,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ds"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "56b0357800c24f42af02e56bcd9f9133",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Creating json from Arrow format:   0%|          | 0/1 [00:00<?, ?ba/s]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "33057"
+      ]
+     },
+     "execution_count": 37,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dataset[\"2024_math\"].to_json(\"./data/json/2024/math.json\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import json\n",
+    "jsons=[]\n",
+    "for line in open(\"./data/json/2024/math.json\"):\n",
+    "    jsons.append(json.loads(line))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "16. 방정식\n",
+      "\\[\n",
+      "\\log_2{(3x+2)} = 2 + \\log_2{(x-2)}\n",
+      "\\]\n",
+      "\\text{를 만족시키는 실수 } \\( x \\) \\text{의 값을 구하시오. [3점]}\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(jsons[15][\"problem\"])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'id': 16,\n",
+       " 'name': '16',\n",
+       " 'problem': '16. 방정식\\n\\\\[\\n\\\\log_2{(3x+2)} = 2 + \\\\log_2{(x-2)}\\n\\\\]\\n\\\\text{를 만족시키는 실수 } \\\\( x \\\\) \\\\text{의 값을 구하시오. [3점]}\\n',\n",
+       " 'answer': '2',\n",
+       " 'score': 3}"
+      ]
+     },
+     "execution_count": 30,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "jsons[15]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "venv1",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}