diff --git a/dsRagAnything/T4_Recognize.py b/dsRagAnything/T4_Recognize.py index 5e256058..39c1dacf 100644 --- a/dsRagAnything/T4_Recognize.py +++ b/dsRagAnything/T4_Recognize.py @@ -23,9 +23,7 @@ logger.addHandler(handler) async def main(): # 要处理的文件路径 - # file_path = "static/Txt/化学方程式_CHEMISTRY_1.docx" - # file_path = "static/Txt/小学数学教学中的若干问题_MATH_1.docx" - file_path = "static/Txt/Math.png" + file_path = "TesT/Ocr/Docx/《动能定理》巩固练习.docx" WORKING_DIR = "./Topic/MathOcr" # 删除output目录下的所有文件 @@ -78,6 +76,17 @@ async def main(): doc_id=None, # 可选的文档ID ) + """ + 修正一下MinerU生成的Latex中，如果是数字加圆圈的样式 \textcircled{1}，无法在Typora或者PyCharm中显示的问题,改成兼容性更强的 \enclose{circle}{1} + """ + + finalName = r'D:\dsWork\dsProject\dsRagAnything\output\《动能定理》巩固练习\auto\《动能定理》巩固练习.md' + with open(finalName, 'r', encoding='utf-8') as f: + content = f.read() + content = content.replace(r'\textcircled{', r'\enclose{circle}{') + with open(finalName, 'w', encoding='utf-8') as f: + f.write(content) + if __name__ == "__main__": asyncio.run(main()) diff --git a/dsRagAnything/Test/Ocr/Res/Images/media/image1.png b/dsRagAnything/Test/Ocr/Res/Images/media/image1.png deleted file mode 100644 index 9e0e4c51..00000000 Binary files a/dsRagAnything/Test/Ocr/Res/Images/media/image1.png and /dev/null differ diff --git a/dsRagAnything/Test/Ocr/Res/Images/media/image10.tiff b/dsRagAnything/Test/Ocr/Res/Images/media/image10.tiff deleted file mode 100644 index afa8029e..00000000 Binary files a/dsRagAnything/Test/Ocr/Res/Images/media/image10.tiff and /dev/null differ diff --git a/dsRagAnything/Test/Ocr/Res/Images/media/image2.png b/dsRagAnything/Test/Ocr/Res/Images/media/image2.png deleted file mode 100644 index b0a5aac5..00000000 Binary files a/dsRagAnything/Test/Ocr/Res/Images/media/image2.png and /dev/null differ diff --git a/dsRagAnything/Test/Ocr/Res/Images/media/image3.png b/dsRagAnything/Test/Ocr/Res/Images/media/image3.png deleted file mode 100644 index e1fc7a3b..00000000 Binary files a/dsRagAnything/Test/Ocr/Res/Images/media/image3.png and /dev/null differ diff --git a/dsRagAnything/Test/Ocr/Res/Images/media/image4.png b/dsRagAnything/Test/Ocr/Res/Images/media/image4.png deleted file mode 100644 index a3badd10..00000000 Binary files a/dsRagAnything/Test/Ocr/Res/Images/media/image4.png and /dev/null differ diff --git a/dsRagAnything/Test/Ocr/Res/Images/media/image5.png b/dsRagAnything/Test/Ocr/Res/Images/media/image5.png deleted file mode 100644 index e84f07ab..00000000 Binary files a/dsRagAnything/Test/Ocr/Res/Images/media/image5.png and /dev/null differ diff --git a/dsRagAnything/Test/Ocr/Res/Images/media/image6.png b/dsRagAnything/Test/Ocr/Res/Images/media/image6.png deleted file mode 100644 index 5a108144..00000000 Binary files a/dsRagAnything/Test/Ocr/Res/Images/media/image6.png and /dev/null differ diff --git a/dsRagAnything/Test/Ocr/Res/Images/media/image7.tiff b/dsRagAnything/Test/Ocr/Res/Images/media/image7.tiff deleted file mode 100644 index 46fd9549..00000000 Binary files a/dsRagAnything/Test/Ocr/Res/Images/media/image7.tiff and /dev/null differ diff --git a/dsRagAnything/Test/Ocr/Res/Images/media/image8.tiff b/dsRagAnything/Test/Ocr/Res/Images/media/image8.tiff deleted file mode 100644 index 0f916e1d..00000000 Binary files a/dsRagAnything/Test/Ocr/Res/Images/media/image8.tiff and /dev/null differ diff --git a/dsRagAnything/Test/Ocr/Res/Images/media/image9.tiff b/dsRagAnything/Test/Ocr/Res/Images/media/image9.tiff deleted file mode 100644 index 7a40df29..00000000 Binary files a/dsRagAnything/Test/Ocr/Res/Images/media/image9.tiff and /dev/null differ diff --git a/dsRagAnything/Test/Ocr/Res/《动能定理》巩固练习.md b/dsRagAnything/Test/Ocr/Res/《动能定理》巩固练习.md deleted file mode 100644 index ddc7343a..00000000 --- a/dsRagAnything/Test/Ocr/Res/《动能定理》巩固练习.md +++ /dev/null @@ -1,343 +0,0 @@ -《动能定理》巩固练习 - -【题型】不定项选择 - -【题文】如图所示，固定斜面倾角为*θ*，整个斜面分为*AB*、*BC*两段，*AB*＝2*BC*.小物块*P*(可视为质点)与*AB*、*BC*两段斜面间的动摩擦因数分别为*μ*~1~、*μ*~2~.已知*P*由静止开始从*A*点释放，恰好能滑动到*C*点而停下，那么*θ*、*μ*~1~、*μ*~2~间应满足的关系是(　　) - -![5-40.tif](./Res/Images/media/image1.png){width="0.9847222222222223in" -height="0.6979166666666666in"}A．tan*θ*＝ B．tan*θ*＝ - -C．tan*θ*＝2*μ*~1~－*μ*~2~ D．tan*θ*＝2*μ*~2~－*μ*~1~ - -【答案】　B - -【解析】设斜面的长度为*l*，小物块从斜面顶端下滑到斜面底端的全过程由动能定理得： - -*mgl*sin*θ*－*μ*~1~*mg*cos*θ*－*μ*~2~*mg*cos*θ*＝0， - -解得tan*θ*＝，故B正确． - -【知识点】动能定理 - -【难度】中 - -【题型】不定项选择 - -在有大风的情况下，一小球自*A*点竖直上抛，其运动轨迹如图9所示(小球的运动可看做竖直方向的竖直上抛运动和水平方向的初速度为零的匀加速直线运动的合运动)，小球运动轨迹上的*A*、*B*两点在同一水平直线上，*M*点为轨迹的最高点．若风力的大小恒定，方向水平向右，小球在*A*点抛出时的动能为4 -J，在*M*点时它的动能为2 -J，落回到*B*点时动能记为*E*~k*B*~，小球上升时间记为*t*~1~，下落时间记为*t*~2~，不计其他阻力，则(　　) - -A．*x*~1~∶*x*~2~＝1∶3 B．*t*~1~＜*t*~2~ - -![5-46.tif](./Res/Images/media/image2.png){width="1.3020833333333333in" -height="1.0055555555555555in"}C．*E*~k*B*~＝6 J D．*E*~k*B*~＝12 J - -【答案】AD - -【解析】由小球上升与下落时间相等即*t*~1~＝*t*~2~， - -*x*~1~∶(*x*~1~＋*x*~2~)＝1∶2^2^＝1∶4， - -即*x*~1~∶*x*~2~＝1∶3.*A*→*M*应用动能定理得 - -－*mgh*＋*W*~1~＝*mv~M~*^2^－*mv*^2^， ① - -竖直方向有*v*^2^＝2*gh* ② - -①②式联立得*W*~1~＝2 J - -*A*→*B*风力做功*W*~2~＝4*W*~1~＝8 J， - -*A*→*B*由动能定理*W*~2~＝*E*~k*B*~－*E*~k*A*~， - -可求得*E*~k*B*~＝12 J，A、D正确． - -【知识点】运动学、动能定理 - -【难度】难 - -【题型】不定项选择 - -如图所示，一个质量为*m*的圆环套在一根固定的水平长直杆上，环与杆的动摩擦因数为*μ*.现给环一个向右的初速度*v*~0~，同时对环施加一个竖直向上的作用力*F*，并使*F*的大小随环的速度的大小变化，两者关系为*F*＝*kv*，其中*k*为常数，则环在运动过程中克服摩擦所做的功的大小不可能为(　　) - -![j5](./Res/Images/media/image3.png){width="1.3020833333333333in" -height="1.2083333333333333in"} - -A. B．0 - -C.＋ D.－ - -【答案】　C - -【解析】　若圆环最终静止，则－*W~f~*＝0－，*W~f~*＝，A可能；若圆环刚开始运动时，*mg*＝*F*＝*kv*~0~，圆环一直做匀速运动，克服摩擦所做的功为零，B可能；若圆环最终做匀速运动，*mg*＝*F*＝*kv*，*v*＝，则－*W~f~*＝－，化简得*W~f~*＝－，D可能，C不可能． - -【知识点】物体的平衡、牛顿第二定律、动能定理 - -【难度】中 - -【题型】不定项选择物体在合外力作用下做直线运动的*v*－*t*图象如图所示．下列表述正确的是(　　) - -![wl165](./Res/Images/media/image4.png){width="1.25in" -height="0.8958333333333334in"} - -A．在0～2s内，合外力总是做负功 - -B．在1～2s内，合外力不做功 - -C．在0～3s内，合外力做功为零 - -D．在0～1s内比1～3s内合外力做功快 - -【答案】　CD - -【解析】根据物体的速度图象和动能定理可知在0～2s内物体先加速后减速，合外力先做正功后做负功，A错；根据动能定理得0～3s内合外力做功为零，1～2s内合外力做负功，C对，B错；在0～1s -内比1～3s内合外力做功快，D对． - -【知识点】v-t图像、动能定理 - -【难度】易 - -![l210](./Res/Images/media/image5.png){width="1.0902777777777777in" -height="0.7777777777777778in"}【题型】不定项选择如右图所示，质量为*m*的物体用细绳经过光滑小孔牵引在光滑水平面上做匀速圆周运动，拉力为某个值*F*时，转动半径为*R*，当拉力逐渐减小到时，物体仍做匀速圆周运动，半径为2*R*，则外力对物体所做的功大小是(　　) - -A.　　　 B.　　 　 C.　　 　 D．0 - -【答案】A - -【解析】设当绳的拉力为*F*时，小球做匀速圆周运动时线速度为*v*~1~，则有 - -*F*＝*m* - -当绳的拉力减为时，小球做匀速圆周运动的线速度为*v*~2~，则有 - -*F*＝*m* - -在绳的拉力由*F*减为*F*的过程中，绳的拉力所做的功为 - -*W*＝*mv*~2~^2^－*mv*~1~^2^＝－*FR* - -所以，绳的拉力所做功的大小为*FR*. - -【知识点】圆周运动、动能定理 - -【难度】易 - -【题型】计算题 - -一质量为*M*＝2.0kg的小物块随足够长的水平传送带一起向右匀速运动，被一水平向左飞来的子弹击中，且子弹从小物块中穿过，子弹和小物块的作用时间极短，如图甲所示．地面观察者记录的小物块被击中后的速度随时间变化关系如图乙所示(图中取向右运动的方向为正方向)．已知传送带的速度保持不变，*g*取10m/s^2^.求： - -![l216](./Res/Images/media/image6.png){width="2.40625in" -height="1.15625in"} - -(1)传送带的速度*v*的大小； - -(2)小物块与传送带之间的动摩擦因数*μ*； - -(3)传送带对小物块所做的功． - -【答案】(1)2.0m/s　(2)0.2　(3)－12J - -【解析】　(1)小物块最后与传送带的运动速度相同，从图象上可读出传送带的速度*v*的大小为2.0m/s. - -(2)由速度图象可得，小物块在滑动摩擦力的作用下做匀变速运动的加速度为*a*＝Δ*v*/Δ*t*＝2.0m/s^2^ - -由牛顿第二定律得*f*＝*μMg*＝*Ma* - -得到小物块与传送带之间的动摩擦因数*μ*＝＝0.2 - -(3)从子弹离开小物块到小物块与传送带一起匀速运动的过程中，设传送带对小物块所做的功为*W*，由动能定理得： - -*W*＝Δ*E*~k~＝－ - -从速度图象可知：*v*~1~＝4.0m/s　*v*~2~＝*v*＝2.0m/s - -解得：*W*＝－12J. - -【知识点】牛顿第二定律、v-t图像、定能定理 - -【难度】中 - -【题型】计算题 - -我国将于2022年举办冬奥会，跳台滑雪是其中最具观赏性的项目之一．如图所示，质量*m*＝60 -kg的运动员从长直助滑道*AB*的*A*处由静止开始以加速度*a*＝3.6 -m/s^2^匀加速滑下，到达助滑道末端*B*时速度*v~B~*＝24 -m/s，*A*与*B*的竖直高度差*H*＝48 -m，为了改变运动员的运动方向，在助滑道与起跳台之间用一段弯曲滑道衔接，其中最低点*C*处附近是一段以*O*为圆心的圆弧．助滑道末端*B*与滑道最低点*C*的高度差*h*＝5 -m，运动员在*B*、*C*间运动时阻力做功*W*＝－1 530 J，取*g*＝10 m/s^2^. - -![\\\\张美英\\j\\张美英\\2017\\一轮\\物理\\2017 物理 人教 -通用\\X21.TIF](./Res/Images/media/image7.tiff){width="1.5333333333333334in" -height="0.8416666666666667in"} - -(1)求运动员在*AB*段下滑时受到阻力*F*~f~的大小； - -(2)若运动员能够承受的最大压力为其所受重力的6倍，则*C*点所在圆弧的半径*R*至少应为 - -多大． - -【答案】　(1)144 N　(2)12.5 m - -【解析】(1)运动员在*AB*上做初速度为零的匀加速运动，设*AB*的长度为*x*，则有*v*＝2*ax*① - -由牛顿第二定律有*mg*－*F*~f~＝*ma*② - -联立①②式，代入数据解得*F*~f~＝144 N③ - -(2)设运动员到达*C*点时的速度为*v~C~*，在由*B*到达*C*的过程中，由动能定理得 - -*mgh*＋*W*＝*mv*－*mv*④ - -设运动员在*C*点所受的支持力为*F*~N~，由牛顿第二定律有 - -*F*~N~－*mg*＝*m*⑤ - -由题意和牛顿第三定律知*F*~N~＝6*mg*⑥ - -联立④⑤⑥式，代入数据解得 - -*R*＝12.5 m. - -【知识点】圆周运动、动能定理、牛顿第二定律、运动学 - -【难度】中 - -【题型】计算题 - -如图所示为某游乐场内水上滑梯轨道示意图，整个轨道在同一竖直平面内，表面粗糙的*AB*段轨道与四分之一光滑圆弧轨道*BC*在*B*点水平相切．点*A*距水面的高度为*H*，圆弧轨道*BC*的半径为*R*，圆心*O*恰在水面．一质量为*m*的游客(视为质点)可从轨道*AB*的任意位置滑下，不计空气阻力． - -![\\\\张美英\\j\\张美英\\2017\\一轮\\物理\\2017 物理 人教 -通用\\X29.TIF](./Res/Images/media/image8.tiff){width="1.775in" -height="1.0166666666666666in"} - -(1)若游客从*A*点由静止开始滑下，到*B*点时沿切线方向滑离轨道落在水面*D*点，*OD*＝2*R*，求游客滑到*B*点时的速度*v~B~*大小及运动过程轨道摩擦力对其所做的功*W*~f~； - -(2)某游客从*AB*段某处滑下，恰好停在*B*点，又因受到微小扰动，继续沿圆弧轨道滑到*P*点后滑离轨道，求*P*点离水面的高度*h*.(提示：在圆周运动过程中任一点，质点所受的向心力与其速率的关系为*F*~向~＝*m*) - -【答案】(1)　－(*mgH*－2*mgR*)　(2)*R* - -【解析】(1)游客从*B*点做平抛运动，有 - -2*R*＝*v~B~t*① - -*R*＝*gt*^2^② - -由①②式得*v~B~*＝③ - -从*A*到*B*，根据动能定理，有 - -*mg*(*H*－*R*)＋*W*~f~＝*mv*－0④ - -由③④式得*W*~f~＝－(*mgH*－2*mgR*) - -(2)设*OP*与*OB*间夹角为*θ*，游客在*P*点时的速度为*v~P~*，受到的支持力为*N*，从*B*到*P*由机械能守恒定律，有 - -*mg*(*R*－*R*cos *θ*)＝*mv*－0⑤ - -过*P*点时，根据向心力公式，有 - -*mg*cos *θ*－*N*＝*m*⑥ - -*N*＝0⑦ - -cos *θ*＝⑧ - -由⑤⑥⑦⑧式解得*h*＝*R*. - -【知识点】圆周运动、动能定理、牛顿第二定律、平抛运动 - -【难度】难 - -【题型】计算题 - -如图甲所示，轻弹簧左端固定在竖直墙上，右端点在*O*位置．质量为*m*的物块*A*(可视为质点)以初速度*v*~0~从距*O*点右方*x*~0~处的*P*点向左运动，与弹簧接触后压缩弹簧，将弹簧右端压到*O*′点位置后，*A*又被弹簧弹回．*A*离开弹簧后，恰好回到*P*点．物块*A*与水平面间的动摩擦因数为*μ*.求： - -![\\\\张美英\\j\\张美英\\2017\\一轮\\物理\\2017 物理 人教 -通用\\X30.TIF](./Res/Images/media/image9.tiff){width="1.3666666666666667in" -height="1.4916666666666667in"} - -(1)物块*A*从*P*点出发又回到*P*点的过程，克服摩擦力所做的功． - -(2)*O*点和*O*′点间的距离*x*~1~. - -(3)如图乙所示，若将另一个与*A*完全相同的物块*B*(可视为质点)与弹簧右端拴接，将*A*放在*B*右边，向左推*A*、*B*，使弹簧右端压缩到*O*′点位置，然后从静止释放，*A*、*B*共同滑行一段距离后分离．分离后物块*A*向右滑行的最大距离*x*~2~是多少？ - -【答案】(1)*mv*　(2)－*x*~0~　(3)*x*~0~－ - -【解析】　(1)物块*A*从*P*点出发又回到*P*点的过程，根据动能定理得克服摩擦力所做的功为*W*~f~＝*mv*. - -(2)物块*A*从*P*点出发又回到*P*点的过程，根据动能定理得 - -2*μmg*(*x*~1~＋*x*~0~)＝*mv* - -解得*x*~1~＝－*x*~0~ - -(3)*A*、*B*在弹簧处于原长处分离，设此时它们的共同速度是*v*~1~，弹出过程弹力做功为*W~F~* - -只有*A*时，从*O*′到*P*有 - -*W~F~*－*μmg*(*x*~1~＋*x*~0~)＝0－0 - -*A*、*B*共同从*O*′到*O*有 - -*W~F~*－2*μmgx*~1~＝×2*mv* - -分离后对*A*有*mv*＝*μmgx*~2~ - -联立以上各式可得*x*~2~＝*x*~0~－. - -【知识点】动能定理 - -【难度】中 - -【题型】计算题 - -如图所示，半径*R*＝0.5 -m的光滑圆弧面*CDM*分别与光滑斜面体*ABC*和斜面*MN*相切于*C*、*M*点，斜面倾角分别如图所示．*O*为圆弧圆心，*D*为圆弧最低点，*C*、*M*在同一水平高度．斜面体*ABC*固定在地面上，顶端*B*安装一定滑轮，一轻质软细绳跨过定滑轮(不计滑轮摩擦)分别连接小物块*P*、*Q*(两边细绳分别与对应斜面平行)，并保持*P*、*Q*两物块静止．若*PC*间距为*L*~1~＝0.25 -m，斜面*MN*足够长，物块*P*的质量*m*~1~＝3 -kg，与*MN*间的动摩擦因数*μ*＝，重力加速度*g*＝10 m/s^2^，求：(sin -37°＝0.6，cos 37°＝0.8) - -![\\\\张美英\\j\\张美英\\2017\\一轮\\物理\\2017 物理 人教 -通用\\X31.tif](./Res/Images/media/image10.tiff){width="2.7in" -height="1.0583333333333333in"} - -(1)小物块*Q*的质量*m*~2~； - -(2)烧断细绳后，物块*P*第一次到达*D*点时对轨道的压力大小； - -(3)物块*P*在*MN*斜面上滑行的总路程． - -【答案】(1)4 kg　(2)78 N　(3)1.0 m - -【解析】(1)根据共点力平衡条件，两物块的重力沿斜面的分力相等，有： - -*m*~1~*g*sin 53°＝*m*~2~*g*sin 37° - -解得：*m*~2~＝4 kg - -即小物块*Q*的质量*m*~2~为4 kg. - -(2)小物块*P*第一次到达*D*点过程，由动能定理得*m*~1~*gh*＝*m*~1~*v* - -根据几何关系，有： - -*h*＝*L*~1~sin 53°＋*R*(1－cos 53°) - -在*D*点，支持力和重力的合力提供向心力：*F~D~*－*m*~1~*g*＝*m*~1~ - -解得：*F~D~*＝78 N - -由牛顿第三定律得，物块*P*对轨道的压力大小为78 N. - -(3)分析可知最终物块在*CDM*之间往复运动，*C*点和*M*点速度为零． - -由全过程动能定理得：*m*~1~*gL*~1~sin 53°－*μm*~1~*g*cos 53°*L*~总~＝0 - -解得*L*~总~＝1.0 m - -即物块*P*在*MN*斜面上滑行的总路程为1.0 m. - -【知识点】物体的平衡、动能定理、牛顿第二定律 - -【难度】难 diff --git a/dsRagAnything/Test/Ocr/T3_DocxToMd.py b/dsRagAnything/Test/Ocr/T3_DocxToMd.py index 86c195c1..703b473e 100644 --- a/dsRagAnything/Test/Ocr/T3_DocxToMd.py +++ b/dsRagAnything/Test/Ocr/T3_DocxToMd.py @@ -2,5 +2,7 @@ import subprocess docx_file='./Docx/《动能定理》巩固练习.docx' temp_markdown='./Res/《动能定理》巩固练习.md' +# 1、先用Pandoc转换，得到图片 subprocess.run(['pandoc', docx_file, '-f', 'docx', '-t', 'markdown', '-o', temp_markdown, - '--extract-media=./Res/Images/']) \ No newline at end of file + '--extract-media=./Res/Images/']) +# 2、把docx转为图片，然后OCR diff --git a/dsRagAnything/output/Math/ocr/Math.md b/dsRagAnything/output/Math/ocr/Math.md deleted file mode 100644 index d2e48c0a..00000000 --- a/dsRagAnything/output/Math/ocr/Math.md +++ /dev/null @@ -1,89 +0,0 @@ -# 024年普通高等学校招生全国统一考试 - -# 数学 - -本试卷共4页，22小题，满分150分。考试用时120分钟。 - -意事项：1．答题前，请务必将自已的姓名、准考证号用黑色字迹的签字笔或钢笔分别填写在试题卷和答题卡上。用2B铅笔将试卷类型（A）填涂在答题卡相应位置上。将条形码横贴在答题卡右上角“条形码粘贴处”。2.作答选择题时，选出每小题答案后，用2B铅笔把答题卡上对应题目选项的答案信息点涂黑：如需改动，用橡皮擦干净后，再选涂其他答案，答案不能答在试卷上。3.非选择题必须用黑色字迹钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内相应位置上；如需改动，先划掉原来的答案，然后再写上新的答案：不准使用铅笔和涂改液。不按以上要求作答的答案无效。4.考生必须保持答题卡的整洁。考试结束后，将试卷和答题卡一并交回。 - -# 一、选择题：本大题共8小题，每小题5分，共计40分.每小题给出的四个选项中，只有一个选项是正确的，请把正确的选项填涂在答题卡相应的位置上. - -1.已知集合A={x|−5f(x−1)+f(x−2)，且当x<3时，f(x)=x，则下列结论中一定正确的是A.f(10)>100 B.f(20)>1000 C.f(10)<1000D.f(20)<10000二、选择题：本大题共3小题，每小题6分，共计18分.每小题给出的四个选项中，有多项符合题目要求。全部选对得6分，选对但不全的得部分分，有选错的得0分。 - -9.为了解推动出口后的亩收入（单位：万元）情况，从该种植区抽取样本，得到推动出口后亩收入的样本均值2.1，样本方差=0.01，已知该种植区以往的亩收入X服从正态分布N(1.8,0.1²)，假设推动出口后的亩收入Y服从正态分布(x,)，则（若随机变量Z服从正态分布N(μσ)，则P(Z<+)≈0.8413） - -A.P(X>2)>0.2 B.P(X>2)<0.5 -C.P(Y>2)>0.5 D.P(Y>2)<0.8 - -10.设函数f(x)=(x−1)(x−4)，则 - -A.x=3是f(x)的极小值点 B.当0f(x) - -11.造型可以做成关丽的丝带，将其看作图中曲线C的一部分.已知C过坐标原点O，且C上的点满足横坐标大于-2，到点F(2,0)的距离与到定直线x=a(a<0)的距离之积为4，则 - -![](images/59086cc384346487ce511d49671d1292dc0c811a3ee51527fda22ad5320566cc.jpg) - -A.a=-2 -B.点(2√2,0)在C上 -C.C在第一象限的点的纵坐标的最大值为1 -D.当点(x，3)在C上时，≤x+2 - -# 三、填空题：本大题共3小题，每小题5分，共计15分 - -12.设双曲线C =>0,b>0)的左右焦点分别为F，F2，过作平行于y轴的直 }\$ 线交C于A、B两点，若|FA=13，|AB|=10，则C的离心率为_ 13.若曲线在点(0,1)处的切线也是曲线y=ln(x+1)+a的切线，则a=_ - -14.甲乙两人各有四张卡片，每张卡片上标有一个数字，假的卡片上分别标有数字1，3，5，7，乙的卡片上分别标有数字2，4，6，8.两人进行四轮比赛，在每轮比赛中，两人各自从自己持有的卡片中随机选一张，并比较所选卡片上的数字大小，数字大的人得1分，数字小的人得0分，然后各白弃置此轮所选的卡片（弃置的卡片在此后的轮次中不能使用），则四轮比赛后，甲的总得分不小于2的概率为 - -# 四、解答题：本题共6小题，共70分。解答应写出文字说明、证明过程或演算步骤。15.（13分） - -记△ABC的内角A，B，C的对边分别为a，b，c，已知sinC=√coB。 - -^{+b²-c{=√2ab. - -（1）求B； -（2）若△ABC的面积为3+√，求c. - -16.（15分） - -=1(a>b>0)上两点.\$b{r}\$ -（1）求C的离心率： -（2）若过P的直线I交C于另一点B，且△ABP的面积为9，求I的方程. - -17.（15分） - -如图，四棱锥P-ABCD中，PA⊥底面ABCD，PA=AC=2，BC=1，AB=√.（1）若AD⊥PB，证明：AD//平面PBC：(2)若AD⊥DC，且二面角A-CP-D的正弦值为√2\$7求AD. - -![](images/68816d467f0086c289a436af04fad25fde27512b22554b1094715129ecce776e.jpg) - -18.（17分） - -已知函数f(x)=ln−x +αx+b(x−1).2-x -（1）若b=0，且f(x)≥0，求a的最小值； -（2）证明：曲线y=f(x)是中心对称图形； -（3）若f(x)>2当且仅当1f(x−1)+f(x−2)，且当x<3时，f(x)=x，则下列结论中一定正确的是A.f(10)>100 B.f(20)>1000 C.f(10)<1000D.f(20)<10000二、选择题：本大题共3小题，每小题6分，共计18分.每小题给出的四个选项中，有多项符合题目要求。全部选对得6分，选对但不全的得部分分，有选错的得0分。", - "page_idx": 0 - }, - { - "type": "text", - "text": "", - "page_idx": 0 - }, - { - "type": "text", - "text": "9.为了解推动出口后的亩收入（单位：万元）情况，从该种植区抽取样本，得到推动出口后亩收入的样本均值2.1，样本方差=0.01，已知该种植区以往的亩收入X服从正态分布N(1.8,0.1²)，假设推动出口后的亩收入Y服从正态分布(x,)，则（若随机变量Z服从正态分布N(μσ)，则P(Z<+)≈0.8413）", - "page_idx": 0 - }, - { - "type": "text", - "text": "A.P(X>2)>0.2 B.P(X>2)<0.5 \nC.P(Y>2)>0.5 D.P(Y>2)<0.8", - "page_idx": 0 - }, - { - "type": "text", - "text": "10.设函数f(x)=(x−1)(x−4)，则", - "page_idx": 0 - }, - { - "type": "text", - "text": "A.x=3是f(x)的极小值点 B.当0f(x)", - "page_idx": 0 - }, - { - "type": "text", - "text": "11.造型可以做成关丽的丝带，将其看作图中曲线C的一部分.已知C过坐标原点O，且C上的点满足横坐标大于-2，到点F(2,0)的距离与到定直线x=a(a<0)的距离之积为4，则", - "page_idx": 0 - }, - { - "type": "image", - "img_path": "images/59086cc384346487ce511d49671d1292dc0c811a3ee51527fda22ad5320566cc.jpg", - "image_caption": [], - "image_footnote": [], - "page_idx": 0 - }, - { - "type": "text", - "text": "A.a=-2 \nB.点(2√2,0)在C上 \nC.C在第一象限的点的纵坐标的最大值为1 \nD.当点(x，3)在C上时，≤x+2", - "page_idx": 0 - }, - { - "type": "text", - "text": "三、填空题：本大题共3小题，每小题5分，共计15分", - "text_level": 1, - "page_idx": 0 - }, - { - "type": "text", - "text": "12.设双曲线C =>0,b>0)的左右焦点分别为F，F2，过作平行于y轴的直 }\\$ 线交C于A、B两点，若|FA=13，|AB|=10，则C的离心率为_ 13.若曲线在点(0,1)处的切线也是曲线y=ln(x+1)+a的切线，则a=_ ", - "page_idx": 0 - }, - { - "type": "text", - "text": "14.甲乙两人各有四张卡片，每张卡片上标有一个数字，假的卡片上分别标有数字1，3，5，7，乙的卡片上分别标有数字2，4，6，8.两人进行四轮比赛，在每轮比赛中，两人各自从自己持有的卡片中随机选一张，并比较所选卡片上的数字大小，数字大的人得1分，数字小的人得0分，然后各白弃置此轮所选的卡片（弃置的卡片在此后的轮次中不能使用），则四轮比赛后，甲的总得分不小于2的概率为", - "page_idx": 0 - }, - { - "type": "text", - "text": "四、解答题：本题共6小题，共70分。解答应写出文字说明、证明过程或演算步骤。15.（13分）", - "text_level": 1, - "page_idx": 0 - }, - { - "type": "text", - "text": "记△ABC的内角A，B，C的对边分别为a，b，c，已知sinC=√coB。", - "page_idx": 0 - }, - { - "type": "text", - "text": "^{+b²-c{=√2ab. ", - "page_idx": 0 - }, - { - "type": "text", - "text": "（1）求B； \n（2）若△ABC的面积为3+√，求c.", - "page_idx": 0 - }, - { - "type": "text", - "text": "16.（15分）", - "page_idx": 0 - }, - { - "type": "text", - "text": "=1(a>b>0)上两点.\\$b{r}\\$ \n（1）求C的离心率： \n（2）若过P的直线I交C于另一点B，且△ABP的面积为9，求I的方程.", - "page_idx": 0 - }, - { - "type": "text", - "text": "17.（15分）", - "page_idx": 0 - }, - { - "type": "text", - "text": "如图，四棱锥P-ABCD中，PA⊥底面ABCD，PA=AC=2，BC=1，AB=√.（1）若AD⊥PB，证明：AD//平面PBC：(2)若AD⊥DC，且二面角A-CP-D的正弦值为√2\\$7求AD.", - "page_idx": 0 - }, - { - "type": "image", - "img_path": "images/68816d467f0086c289a436af04fad25fde27512b22554b1094715129ecce776e.jpg", - "image_caption": [], - "image_footnote": [], - "page_idx": 0 - }, - { - "type": "text", - "text": "18.（17分）", - "page_idx": 0 - }, - { - "type": "text", - "text": "已知函数f(x)=ln−x +αx+b(x−1).2-x \n（1）若b=0，且f(x)≥0，求a的最小值； \n（2）证明：曲线y=f(x)是中心对称图形； \n（3）若f(x)>2当且仅当1f(x−1)+f(x−2)，且当x<3时，f(x)=x，则下列", - "type": "text" - } - ], - "index": 30 - }, - { - "bbox": [ - 37, - 1091, - 180, - 1114 - ], - "spans": [ - { - "bbox": [ - 37, - 1091, - 180, - 1114 - ], - "score": 0.999, - "content": "结论中一定正确的是", - "type": "text" - } - ], - "index": 31 - }, - { - "bbox": [ - 34, - 1118, - 610, - 1146 - ], - "spans": [ - { - "bbox": [ - 34, - 1118, - 146, - 1146 - ], - "score": 0.967, - "content": "A.f(10)>100", - "type": "text" - }, - { - "bbox": [ - 183, - 1118, - 310, - 1146 - ], - "score": 0.929, - "content": "B.f(20)>1000", - "type": "text" - }, - { - "bbox": [ - 328, - 1118, - 610, - 1146 - ], - "score": 0.951, - "content": "C.f(10)<1000D.f(20)<10000", - "type": "text" - } - ], - "index": 32 - } - ], - "index": 31 - }, - { - "type": "text", - "bbox": [ - 10, - 1160, - 607, - 1221 - ], - "lines": [ - { - "bbox": [ - 11, - 1160, - 599, - 1183 - ], - "spans": [ - { - "bbox": [ - 11, - 1160, - 599, - 1183 - ], - "score": 0.979, - "content": "二、选择题：本大题共3小题，每小题6分，共计18分.每小题给出的四个选项中，有多", - "type": "text" - } - ], - "index": 33 - }, - { - "bbox": [ - 39, - 1198, - 554, - 1221 - ], - "spans": [ - { - "bbox": [ - 39, - 1198, - 554, - 1221 - ], - "score": 0.99, - "content": "项符合题目要求。全部选对得6分，选对但不全的得部分分，有选错的得0分。", - "type": "text" - } - ], - "index": 34 - } - ], - "index": 33.5 - }, - { - "type": "text", - "bbox": [ - 13, - 1236, - 613, - 1383 - ], - "lines": [ - { - "bbox": [ - 17, - 1239, - 614, - 1258 - ], - "spans": [ - { - "bbox": [ - 17, - 1239, - 614, - 1258 - ], - "score": 0.989, - "content": "9.为了解推动出口后的亩收入（单位：万元）情况，从该种植区抽取样本，得到推动出口后", - "type": "text" - } - ], - "index": 35 - }, - { - "bbox": [ - 42, - 1279, - 614, - 1298 - ], - "spans": [ - { - "bbox": [ - 42, - 1279, - 614, - 1298 - ], - "score": 0.981, - "content": "亩收入的样本均值2.1，样本方差=0.01，已知该种植区以往的亩收入X服从正态", - "type": "text" - } - ], - "index": 36 - }, - { - "bbox": [ - 39, - 1317, - 613, - 1340 - ], - "spans": [ - { - "bbox": [ - 39, - 1317, - 613, - 1340 - ], - "score": 0.928, - "content": "分布N(1.8,0.1²)，假设推动出口后的亩收入Y服从正态分布(x,)，则（若随机变量Z", - "type": "text" - } - ], - "index": 37 - }, - { - "bbox": [ - 39, - 1361, - 371, - 1384 - ], - "spans": [ - { - "bbox": [ - 39, - 1361, - 371, - 1384 - ], - "score": 0.899, - "content": "服从正态分布N(μσ)，则P(Z<+)≈0.8413）", - "type": "text" - } - ], - "index": 38 - } - ], - "index": 36.5 - }, - { - "type": "text", - "bbox": [ - 33, - 1400, - 457, - 1467 - ], - "lines": [ - { - "bbox": [ - 37, - 1398, - 460, - 1426 - ], - "spans": [ - { - "bbox": [ - 37, - 1401, - 164, - 1425 - ], - "score": 0.927, - "content": "A.P(X>2)>0.2", - "type": "text" - }, - { - "bbox": [ - 331, - 1398, - 460, - 1426 - ], - "score": 0.942, - "content": "B.P(X>2)<0.5", - "type": "text" - } - ], - "index": 39 - }, - { - "bbox": [ - 34, - 1441, - 459, - 1468 - ], - "spans": [ - { - "bbox": [ - 34, - 1441, - 162, - 1468 - ], - "score": 0.924, - "content": "C.P(Y>2)>0.5", - "type": "text" - }, - { - "bbox": [ - 331, - 1441, - 459, - 1468 - ], - "score": 0.953, - "content": "D.P(Y>2)<0.8", - "type": "text" - } - ], - "index": 40 - } - ], - "index": 39.5 - }, - { - "type": "text", - "bbox": [ - 8, - 1486, - 251, - 1509 - ], - "lines": [ - { - "bbox": [ - 8, - 1483, - 254, - 1510 - ], - "spans": [ - { - "bbox": [ - 8, - 1483, - 254, - 1510 - ], - "score": 0.838, - "content": "10.设函数f(x)=(x−1)(x−4)，则", - "type": "text" - } - ], - "index": 41 - } - ], - "index": 41 - }, - { - "type": "text", - "bbox": [ - 37, - 1526, - 569, - 1593 - ], - "lines": [ - { - "bbox": [ - 36, - 1526, - 547, - 1554 - ], - "spans": [ - { - "bbox": [ - 36, - 1526, - 229, - 1554 - ], - "score": 0.898, - "content": "A.x=3是f(x)的极小值点", - "type": "text" - }, - { - "bbox": [ - 331, - 1526, - 547, - 1554 - ], - "score": 0.912, - "content": "B.当0f(x)", - "type": "text" - } - ], - "index": 43 - } - ], - "index": 42.5 - }, - { - "type": "text", - "bbox": [ - 13, - 1612, - 451, - 1718 - ], - "lines": [ - { - "bbox": [ - 8, - 1609, - 453, - 1641 - ], - "spans": [ - { - "bbox": [ - 8, - 1609, - 453, - 1641 - ], - "score": 0.968, - "content": "11.造型可以做成关丽的丝带，将其看作图中曲线C的一部分.已", - "type": "text" - } - ], - "index": 44 - }, - { - "bbox": [ - 36, - 1650, - 450, - 1679 - ], - "spans": [ - { - "bbox": [ - 36, - 1650, - 450, - 1679 - ], - "score": 0.943, - "content": "知C过坐标原点O，且C上的点满足横坐标大于-2，到点F(2,0)", - "type": "text" - } - ], - "index": 45 - }, - { - "bbox": [ - 39, - 1693, - 371, - 1717 - ], - "spans": [ - { - "bbox": [ - 39, - 1693, - 371, - 1717 - ], - "score": 0.928, - "content": "的距离与到定直线x=a(a<0)的距离之积为4，则", - "type": "text" - } - ], - "index": 46 - } - ], - "index": 45 - }, - { - "type": "image", - "bbox": [ - 454, - 1629, - 602, - 1860 - ], - "blocks": [ - { - "type": "image_body", - "bbox": [ - 454, - 1629, - 602, - 1860 - ], - "group_id": 0, - "lines": [ - { - "bbox": [ - 454, - 1629, - 602, - 1860 - ], - "spans": [ - { - "bbox": [ - 454, - 1629, - 602, - 1860 - ], - "score": 0.897, - "type": "image", - "image_path": "59086cc384346487ce511d49671d1292dc0c811a3ee51527fda22ad5320566cc.jpg" - } - ] - } - ], - "index": 48, - "virtual_lines": [ - { - "bbox": [ - 454, - 1629, - 602, - 1860 - ], - "spans": [], - "index": 48 - } - ] - } - ], - "index": 48 - }, - { - "type": "text", - "bbox": [ - 36, - 1736, - 331, - 1898 - ], - "lines": [ - { - "bbox": [ - 36, - 1736, - 114, - 1760 - ], - "spans": [ - { - "bbox": [ - 36, - 1736, - 114, - 1760 - ], - "score": 0.842, - "content": "A.a=-2", - "type": "text" - } - ], - "index": 47 - }, - { - "bbox": [ - 36, - 1775, - 188, - 1802 - ], - "spans": [ - { - "bbox": [ - 36, - 1775, - 188, - 1802 - ], - "score": 0.885, - "content": "B.点(2√2,0)在C上", - "type": "text" - } - ], - "index": 49 - }, - { - "bbox": [ - 36, - 1818, - 332, - 1842 - ], - "spans": [ - { - "bbox": [ - 36, - 1818, - 332, - 1842 - ], - "score": 0.991, - "content": "C.C在第一象限的点的纵坐标的最大值为1", - "type": "text" - } - ], - "index": 50 - }, - { - "bbox": [ - 33, - 1858, - 299, - 1903 - ], - "spans": [ - { - "bbox": [ - 33, - 1858, - 299, - 1903 - ], - "score": 0.788, - "content": "D.当点(x，3)在C上时，≤x+2", - "type": "text" - } - ], - "index": 51 - } - ], - "index": 49.5 - }, - { - "type": "title", - "bbox": [ - 11, - 1914, - 376, - 1937 - ], - "lines": [ - { - "bbox": [ - 8, - 1914, - 377, - 1937 - ], - "spans": [ - { - "bbox": [ - 8, - 1914, - 377, - 1937 - ], - "score": 0.989, - "content": "三、填空题：本大题共3小题，每小题5分，共计15分", - "type": "text" - } - ], - "index": 52 - } - ], - "index": 52 - }, - { - "type": "text", - "bbox": [ - 10, - 1949, - 604, - 2055 - ], - "lines": [ - { - "bbox": [ - 5, - 1948, - 604, - 1980 - ], - "spans": [ - { - "bbox": [ - 5, - 1948, - 142, - 1978 - ], - "score": 0.877, - "content": "12.设双曲线C", - "type": "text" - }, - { - "bbox": [ - 151, - 1948, - 604, - 1980 - ], - "score": 0.872, - "content": "=>0,b>0)的左右焦点分别为F，F2，过作平行于y轴的直", - "type": "text" - } - ], - "index": 53 - }, - { - "bbox": [ - 145, - 1967, - 174, - 1990 - ], - "spans": [ - { - "bbox": [ - 145, - 1967, - 174, - 1990 - ], - "score": 0.636, - "content": "}$", - "type": "text" - } - ], - "index": 54 - }, - { - "bbox": [ - 36, - 1997, - 466, - 2025 - ], - "spans": [ - { - "bbox": [ - 36, - 1997, - 466, - 2025 - ], - "score": 0.963, - "content": "线交C于A、B两点，若|FA=13，|AB|=10，则C的离心率为_", - "type": "text" - } - ], - "index": 55 - }, - { - "bbox": [ - 5, - 2029, - 469, - 2058 - ], - "spans": [ - { - "bbox": [ - 5, - 2029, - 469, - 2058 - ], - "score": 0.883, - "content": "13.若曲线在点(0,1)处的切线也是曲线y=ln(x+1)+a的切线，则a=_", - "type": "text" - } - ], - "index": 56 - } - ], - "index": 54.5 - }, - { - "type": "text", - "bbox": [ - 7, - 2065, - 608, - 2212 - ], - "lines": [ - { - "bbox": [ - 8, - 2065, - 589, - 2089 - ], - "spans": [ - { - "bbox": [ - 8, - 2065, - 589, - 2089 - ], - "score": 0.988, - "content": "14.甲乙两人各有四张卡片，每张卡片上标有一个数字，假的卡片上分别标有数字1，3，", - "type": "text" - } - ], - "index": 57 - }, - { - "bbox": [ - 37, - 2099, - 610, - 2118 - ], - "spans": [ - { - "bbox": [ - 37, - 2099, - 610, - 2118 - ], - "score": 0.988, - "content": "5，7，乙的卡片上分别标有数字2，4，6，8.两人进行四轮比赛，在每轮比赛中，两人", - "type": "text" - } - ], - "index": 58 - }, - { - "bbox": [ - 39, - 2129, - 604, - 2148 - ], - "spans": [ - { - "bbox": [ - 39, - 2129, - 604, - 2148 - ], - "score": 0.99, - "content": "各自从自己持有的卡片中随机选一张，并比较所选卡片上的数字大小，数字大的人得1", - "type": "text" - } - ], - "index": 59 - }, - { - "bbox": [ - 37, - 2158, - 607, - 2182 - ], - "spans": [ - { - "bbox": [ - 37, - 2158, - 607, - 2182 - ], - "score": 0.984, - "content": "分，数字小的人得0分，然后各白弃置此轮所选的卡片（弃置的卡片在此后的轮次中不", - "type": "text" - } - ], - "index": 60 - }, - { - "bbox": [ - 36, - 2187, - 408, - 2211 - ], - "spans": [ - { - "bbox": [ - 36, - 2187, - 408, - 2211 - ], - "score": 0.987, - "content": "能使用），则四轮比赛后，甲的总得分不小于2的概率为", - "type": "text" - } - ], - "index": 61 - } - ], - "index": 59 - }, - { - "type": "title", - "bbox": [ - 10, - 2235, - 562, - 2289 - ], - "lines": [ - { - "bbox": [ - 8, - 2235, - 560, - 2259 - ], - "spans": [ - { - "bbox": [ - 8, - 2235, - 560, - 2259 - ], - "score": 0.994, - "content": "四、解答题：本题共6小题，共70分。解答应写出文字说明、证明过程或演算步骤。", - "type": "text" - } - ], - "index": 62 - }, - { - "bbox": [ - 5, - 2267, - 95, - 2290 - ], - "spans": [ - { - "bbox": [ - 5, - 2267, - 95, - 2290 - ], - "score": 0.973, - "content": "15.（13分）", - "type": "text" - } - ], - "index": 63 - } - ], - "index": 62.5 - }, - { - "type": "text", - "bbox": [ - 13, - 2301, - 507, - 2324 - ], - "lines": [ - { - "bbox": [ - 33, - 2295, - 511, - 2328 - ], - "spans": [ - { - "bbox": [ - 33, - 2295, - 511, - 2328 - ], - "score": 0.897, - "content": "记△ABC的内角A，B，C的对边分别为a，b，c，已知sinC=√coB。", - "type": "text" - } - ], - "index": 64 - } - ], - "index": 64 - }, - { - "type": "text", - "bbox": [ - 8, - 2333, - 153, - 2356 - ], - "lines": [ - { - "bbox": [ - 5, - 2330, - 146, - 2362 - ], - "spans": [ - { - "bbox": [ - 5, - 2330, - 146, - 2362 - ], - "score": 0.553, - "content": "^{+b²-c{=√2ab.", - "type": "text" - } - ], - "index": 65 - } - ], - "index": 65 - }, - { - "type": "text", - "bbox": [ - 40, - 2363, - 287, - 2423 - ], - "lines": [ - { - "bbox": [ - 43, - 2366, - 116, - 2391 - ], - "spans": [ - { - "bbox": [ - 43, - 2366, - 116, - 2391 - ], - "score": 0.902, - "content": "（1）求B；", - "type": "text" - } - ], - "index": 66 - }, - { - "bbox": [ - 43, - 2398, - 293, - 2426 - ], - "spans": [ - { - "bbox": [ - 43, - 2398, - 293, - 2426 - ], - "score": 0.917, - "content": "（2）若△ABC的面积为3+√，求c.", - "type": "text" - } - ], - "index": 67 - } - ], - "index": 66.5 - }, - { - "type": "text", - "bbox": [ - 8, - 2566, - 94, - 2591 - ], - "lines": [ - { - "bbox": [ - 4, - 2565, - 94, - 2591 - ], - "spans": [ - { - "bbox": [ - 4, - 2565, - 94, - 2591 - ], - "score": 0.978, - "content": "16.（15分）", - "type": "text" - } - ], - "index": 68 - } - ], - "index": 68 - }, - { - "type": "text", - "bbox": [ - 24, - 2596, - 524, - 2704 - ], - "lines": [ - { - "bbox": [ - 264, - 2606, - 412, - 2632 - ], - "spans": [ - { - "bbox": [ - 264, - 2606, - 412, - 2632 - ], - "score": 0.87, - "content": "=1(a>b>0)上两点.", - "type": "text" - } - ], - "index": 70 - }, - { - "bbox": [ - 249, - 2620, - 276, - 2642 - ], - "spans": [ - { - "bbox": [ - 249, - 2620, - 276, - 2642 - ], - "score": 0.626, - "content": "$b{r}$", - "type": "text" - } - ], - "index": 69 - }, - { - "bbox": [ - 42, - 2649, - 178, - 2673 - ], - "spans": [ - { - "bbox": [ - 42, - 2649, - 178, - 2673 - ], - "score": 0.966, - "content": "（1）求C的离心率：", - "type": "text" - } - ], - "index": 71 - }, - { - "bbox": [ - 43, - 2681, - 524, - 2704 - ], - "spans": [ - { - "bbox": [ - 43, - 2681, - 524, - 2704 - ], - "score": 0.959, - "content": "（2）若过P的直线I交C于另一点B，且△ABP的面积为9，求I的方程.", - "type": "text" - } - ], - "index": 72 - } - ], - "index": 70.5 - }, - { - "type": "text", - "bbox": [ - 1, - 2853, - 85, - 2874 - ], - "lines": [ - { - "bbox": [ - -2, - 2850, - 88, - 2879 - ], - "spans": [ - { - "bbox": [ - -2, - 2850, - 88, - 2879 - ], - "score": 0.976, - "content": "17.（15分）", - "type": "text" - } - ], - "index": 73 - } - ], - "index": 73 - }, - { - "type": "text", - "bbox": [ - 1, - 2882, - 432, - 3058 - ], - "lines": [ - { - "bbox": [ - 29, - 2885, - 432, - 2908 - ], - "spans": [ - { - "bbox": [ - 29, - 2885, - 432, - 2908 - ], - "score": 0.963, - "content": "如图，四棱锥P-ABCD中，PA⊥底面ABCD，PA=AC=2，", - "type": "text" - } - ], - "index": 74 - }, - { - "bbox": [ - 1, - 2915, - 130, - 2943 - ], - "spans": [ - { - "bbox": [ - 1, - 2915, - 130, - 2943 - ], - "score": 0.889, - "content": "BC=1，AB=√.", - "type": "text" - } - ], - "index": 75 - }, - { - "bbox": [ - 36, - 2949, - 316, - 2972 - ], - "spans": [ - { - "bbox": [ - 36, - 2949, - 316, - 2972 - ], - "score": 0.93, - "content": "（1）若AD⊥PB，证明：AD//平面PBC：", - "type": "text" - } - ], - "index": 76 - }, - { - "bbox": [ - 34, - 2979, - 403, - 3015 - ], - "spans": [ - { - "bbox": [ - 34, - 2979, - 403, - 3015 - ], - "score": 0.876, - "content": "(2)若AD⊥DC，且二面角A-CP-D的正弦值为√2$", - "type": "text" - } - ], - "index": 77 - }, - { - "bbox": [ - 374, - 3004, - 399, - 3026 - ], - "spans": [ - { - "bbox": [ - 374, - 3004, - 399, - 3026 - ], - "score": 0.998, - "content": "7", - "type": "text" - } - ], - "index": 78 - }, - { - "bbox": [ - -4, - 3030, - 53, - 3059 - ], - "spans": [ - { - "bbox": [ - -4, - 3030, - 53, - 3059 - ], - "score": 0.976, - "content": "求AD.", - "type": "text" - } - ], - "index": 79 - } - ], - "index": 76.5 - }, - { - "type": "image", - "bbox": [ - 451, - 2873, - 601, - 3052 - ], - "blocks": [ - { - "type": "image_body", - "bbox": [ - 451, - 2873, - 601, - 3052 - ], - "group_id": 1, - "lines": [ - { - "bbox": [ - 451, - 2873, - 601, - 3052 - ], - "spans": [ - { - "bbox": [ - 451, - 2873, - 601, - 3052 - ], - "score": 0.904, - "type": "image", - "image_path": "68816d467f0086c289a436af04fad25fde27512b22554b1094715129ecce776e.jpg" - } - ] - } - ], - "index": 80.5, - "virtual_lines": [ - { - "bbox": [ - 451, - 2873, - 601, - 2962.5 - ], - "spans": [], - "index": 80 - }, - { - "bbox": [ - 451, - 2962.5, - 601, - 3052.0 - ], - "spans": [], - "index": 81 - } - ] - } - ], - "index": 80.5 - }, - { - "type": "text", - "bbox": [ - 1, - 3143, - 85, - 3166 - ], - "lines": [ - { - "bbox": [ - -2, - 3142, - 88, - 3169 - ], - "spans": [ - { - "bbox": [ - -2, - 3142, - 88, - 3169 - ], - "score": 0.959, - "content": "18.（17分）", - "type": "text" - } - ], - "index": 82 - } - ], - "index": 82 - }, - { - "type": "text", - "bbox": [ - 21, - 3178, - 387, - 3316 - ], - "lines": [ - { - "bbox": [ - 29, - 3182, - 283, - 3210 - ], - "spans": [ - { - "bbox": [ - 29, - 3182, - 172, - 3210 - ], - "score": 0.799, - "content": "已知函数f(x)=ln−x", - "type": "text" - }, - { - "bbox": [ - 175, - 3182, - 283, - 3209 - ], - "score": 0.826, - "content": "+αx+b(x−1).", - "type": "text" - } - ], - "index": 83 - }, - { - "bbox": [ - 148, - 3197, - 184, - 3217 - ], - "spans": [ - { - "bbox": [ - 148, - 3197, - 184, - 3217 - ], - "score": 0.905, - "content": "2-x", - "type": "text" - } - ], - "index": 84 - }, - { - "bbox": [ - 36, - 3226, - 323, - 3249 - ], - "spans": [ - { - "bbox": [ - 36, - 3226, - 323, - 3249 - ], - "score": 0.883, - "content": "（1）若b=0，且f(x)≥0，求a的最小值；", - "type": "text" - } - ], - "index": 85 - }, - { - "bbox": [ - 36, - 3259, - 315, - 3283 - ], - "spans": [ - { - "bbox": [ - 36, - 3259, - 315, - 3283 - ], - "score": 0.923, - "content": "（2）证明：曲线y=f(x)是中心对称图形；", - "type": "text" - } - ], - "index": 86 - }, - { - "bbox": [ - 34, - 3290, - 384, - 3313 - ], - "spans": [ - { - "bbox": [ - 34, - 3290, - 384, - 3313 - ], - "score": 0.908, - "content": "（3）若f(x)>2当且仅当1f(x−1)+f(x−2)，且当x<3时，f(x)=x，则下列", - "type": "text" - } - ], - "index": 30 - }, - { - "bbox": [ - 37, - 1091, - 180, - 1114 - ], - "spans": [ - { - "bbox": [ - 37, - 1091, - 180, - 1114 - ], - "score": 0.999, - "content": "结论中一定正确的是", - "type": "text" - } - ], - "index": 31 - }, - { - "bbox": [ - 34, - 1118, - 610, - 1146 - ], - "spans": [ - { - "bbox": [ - 34, - 1118, - 146, - 1146 - ], - "score": 0.967, - "content": "A.f(10)>100", - "type": "text" - }, - { - "bbox": [ - 183, - 1118, - 310, - 1146 - ], - "score": 0.929, - "content": "B.f(20)>1000", - "type": "text" - }, - { - "bbox": [ - 328, - 1118, - 610, - 1146 - ], - "score": 0.951, - "content": "C.f(10)<1000D.f(20)<10000", - "type": "text" - } - ], - "index": 32 - }, - { - "bbox": [ - 11, - 1160, - 599, - 1183 - ], - "spans": [ - { - "bbox": [ - 11, - 1160, - 599, - 1183 - ], - "score": 0.979, - "content": "二、选择题：本大题共3小题，每小题6分，共计18分.每小题给出的四个选项中，有多", - "type": "text" - } - ], - "index": 33 - }, - { - "bbox": [ - 39, - 1198, - 554, - 1221 - ], - "spans": [ - { - "bbox": [ - 39, - 1198, - 554, - 1221 - ], - "score": 0.99, - "content": "项符合题目要求。全部选对得6分，选对但不全的得部分分，有选错的得0分。", - "type": "text" - } - ], - "index": 34 - } - ], - "index": 31, - "bbox_fs": [ - 13, - 1057, - 617, - 1146 - ] - }, - { - "type": "text", - "bbox": [ - 10, - 1160, - 607, - 1221 - ], - "lines": [], - "index": 33.5, - "bbox_fs": [ - 11, - 1160, - 599, - 1221 - ], - "lines_deleted": true - }, - { - "type": "text", - "bbox": [ - 13, - 1236, - 613, - 1383 - ], - "lines": [ - { - "bbox": [ - 17, - 1239, - 614, - 1258 - ], - "spans": [ - { - "bbox": [ - 17, - 1239, - 614, - 1258 - ], - "score": 0.989, - "content": "9.为了解推动出口后的亩收入（单位：万元）情况，从该种植区抽取样本，得到推动出口后", - "type": "text" - } - ], - "index": 35 - }, - { - "bbox": [ - 42, - 1279, - 614, - 1298 - ], - "spans": [ - { - "bbox": [ - 42, - 1279, - 614, - 1298 - ], - "score": 0.981, - "content": "亩收入的样本均值2.1，样本方差=0.01，已知该种植区以往的亩收入X服从正态", - "type": "text" - } - ], - "index": 36 - }, - { - "bbox": [ - 39, - 1317, - 613, - 1340 - ], - "spans": [ - { - "bbox": [ - 39, - 1317, - 613, - 1340 - ], - "score": 0.928, - "content": "分布N(1.8,0.1²)，假设推动出口后的亩收入Y服从正态分布(x,)，则（若随机变量Z", - "type": "text" - } - ], - "index": 37 - }, - { - "bbox": [ - 39, - 1361, - 371, - 1384 - ], - "spans": [ - { - "bbox": [ - 39, - 1361, - 371, - 1384 - ], - "score": 0.899, - "content": "服从正态分布N(μσ)，则P(Z<+)≈0.8413）", - "type": "text" - } - ], - "index": 38 - } - ], - "index": 36.5, - "bbox_fs": [ - 17, - 1239, - 614, - 1384 - ] - }, - { - "type": "index", - "bbox": [ - 33, - 1400, - 457, - 1467 - ], - "lines": [ - { - "bbox": [ - 37, - 1398, - 460, - 1426 - ], - "spans": [ - { - "bbox": [ - 37, - 1401, - 164, - 1425 - ], - "score": 0.927, - "content": "A.P(X>2)>0.2", - "type": "text" - }, - { - "bbox": [ - 331, - 1398, - 460, - 1426 - ], - "score": 0.942, - "content": "B.P(X>2)<0.5", - "type": "text" - } - ], - "index": 39, - "is_list_start_line": true - }, - { - "bbox": [ - 34, - 1441, - 459, - 1468 - ], - "spans": [ - { - "bbox": [ - 34, - 1441, - 162, - 1468 - ], - "score": 0.924, - "content": "C.P(Y>2)>0.5", - "type": "text" - }, - { - "bbox": [ - 331, - 1441, - 459, - 1468 - ], - "score": 0.953, - "content": "D.P(Y>2)<0.8", - "type": "text" - } - ], - "index": 40, - "is_list_start_line": true - } - ], - "index": 39.5, - "bbox_fs": [ - 34, - 1398, - 460, - 1468 - ] - }, - { - "type": "text", - "bbox": [ - 8, - 1486, - 251, - 1509 - ], - "lines": [ - { - "bbox": [ - 8, - 1483, - 254, - 1510 - ], - "spans": [ - { - "bbox": [ - 8, - 1483, - 254, - 1510 - ], - "score": 0.838, - "content": "10.设函数f(x)=(x−1)(x−4)，则", - "type": "text" - } - ], - "index": 41 - } - ], - "index": 41, - "bbox_fs": [ - 8, - 1483, - 254, - 1510 - ] - }, - { - "type": "text", - "bbox": [ - 37, - 1526, - 569, - 1593 - ], - "lines": [ - { - "bbox": [ - 36, - 1526, - 547, - 1554 - ], - "spans": [ - { - "bbox": [ - 36, - 1526, - 229, - 1554 - ], - "score": 0.898, - "content": "A.x=3是f(x)的极小值点", - "type": "text" - }, - { - "bbox": [ - 331, - 1526, - 547, - 1554 - ], - "score": 0.912, - "content": "B.当0f(x)", - "type": "text" - } - ], - "index": 43 - } - ], - "index": 42.5, - "bbox_fs": [ - 36, - 1526, - 572, - 1598 - ] - }, - { - "type": "text", - "bbox": [ - 13, - 1612, - 451, - 1718 - ], - "lines": [ - { - "bbox": [ - 8, - 1609, - 453, - 1641 - ], - "spans": [ - { - "bbox": [ - 8, - 1609, - 453, - 1641 - ], - "score": 0.968, - "content": "11.造型可以做成关丽的丝带，将其看作图中曲线C的一部分.已", - "type": "text" - } - ], - "index": 44 - }, - { - "bbox": [ - 36, - 1650, - 450, - 1679 - ], - "spans": [ - { - "bbox": [ - 36, - 1650, - 450, - 1679 - ], - "score": 0.943, - "content": "知C过坐标原点O，且C上的点满足横坐标大于-2，到点F(2,0)", - "type": "text" - } - ], - "index": 45 - }, - { - "bbox": [ - 39, - 1693, - 371, - 1717 - ], - "spans": [ - { - "bbox": [ - 39, - 1693, - 371, - 1717 - ], - "score": 0.928, - "content": "的距离与到定直线x=a(a<0)的距离之积为4，则", - "type": "text" - } - ], - "index": 46 - } - ], - "index": 45, - "bbox_fs": [ - 8, - 1609, - 453, - 1717 - ] - }, - { - "type": "image", - "bbox": [ - 454, - 1629, - 602, - 1860 - ], - "blocks": [ - { - "type": "image_body", - "bbox": [ - 454, - 1629, - 602, - 1860 - ], - "group_id": 0, - "lines": [ - { - "bbox": [ - 454, - 1629, - 602, - 1860 - ], - "spans": [ - { - "bbox": [ - 454, - 1629, - 602, - 1860 - ], - "score": 0.897, - "type": "image", - "image_path": "59086cc384346487ce511d49671d1292dc0c811a3ee51527fda22ad5320566cc.jpg" - } - ] - } - ], - "index": 48, - "virtual_lines": [ - { - "bbox": [ - 454, - 1629, - 602, - 1860 - ], - "spans": [], - "index": 48 - } - ] - } - ], - "index": 48 - }, - { - "type": "list", - "bbox": [ - 36, - 1736, - 331, - 1898 - ], - "lines": [ - { - "bbox": [ - 36, - 1736, - 114, - 1760 - ], - "spans": [ - { - "bbox": [ - 36, - 1736, - 114, - 1760 - ], - "score": 0.842, - "content": "A.a=-2", - "type": "text" - } - ], - "index": 47, - "is_list_start_line": true - }, - { - "bbox": [ - 36, - 1775, - 188, - 1802 - ], - "spans": [ - { - "bbox": [ - 36, - 1775, - 188, - 1802 - ], - "score": 0.885, - "content": "B.点(2√2,0)在C上", - "type": "text" - } - ], - "index": 49, - "is_list_start_line": true - }, - { - "bbox": [ - 36, - 1818, - 332, - 1842 - ], - "spans": [ - { - "bbox": [ - 36, - 1818, - 332, - 1842 - ], - "score": 0.991, - "content": "C.C在第一象限的点的纵坐标的最大值为1", - "type": "text" - } - ], - "index": 50, - "is_list_start_line": true - }, - { - "bbox": [ - 33, - 1858, - 299, - 1903 - ], - "spans": [ - { - "bbox": [ - 33, - 1858, - 299, - 1903 - ], - "score": 0.788, - "content": "D.当点(x，3)在C上时，≤x+2", - "type": "text" - } - ], - "index": 51, - "is_list_start_line": true - } - ], - "index": 49.5, - "bbox_fs": [ - 33, - 1736, - 332, - 1903 - ] - }, - { - "type": "title", - "bbox": [ - 11, - 1914, - 376, - 1937 - ], - "lines": [ - { - "bbox": [ - 8, - 1914, - 377, - 1937 - ], - "spans": [ - { - "bbox": [ - 8, - 1914, - 377, - 1937 - ], - "score": 0.989, - "content": "三、填空题：本大题共3小题，每小题5分，共计15分", - "type": "text" - } - ], - "index": 52 - } - ], - "index": 52 - }, - { - "type": "text", - "bbox": [ - 10, - 1949, - 604, - 2055 - ], - "lines": [ - { - "bbox": [ - 5, - 1948, - 604, - 1980 - ], - "spans": [ - { - "bbox": [ - 5, - 1948, - 142, - 1978 - ], - "score": 0.877, - "content": "12.设双曲线C", - "type": "text" - }, - { - "bbox": [ - 151, - 1948, - 604, - 1980 - ], - "score": 0.872, - "content": "=>0,b>0)的左右焦点分别为F，F2，过作平行于y轴的直", - "type": "text" - } - ], - "index": 53 - }, - { - "bbox": [ - 145, - 1967, - 174, - 1990 - ], - "spans": [ - { - "bbox": [ - 145, - 1967, - 174, - 1990 - ], - "score": 0.636, - "content": "}$", - "type": "text" - } - ], - "index": 54 - }, - { - "bbox": [ - 36, - 1997, - 466, - 2025 - ], - "spans": [ - { - "bbox": [ - 36, - 1997, - 466, - 2025 - ], - "score": 0.963, - "content": "线交C于A、B两点，若|FA=13，|AB|=10，则C的离心率为_", - "type": "text" - } - ], - "index": 55 - }, - { - "bbox": [ - 5, - 2029, - 469, - 2058 - ], - "spans": [ - { - "bbox": [ - 5, - 2029, - 469, - 2058 - ], - "score": 0.883, - "content": "13.若曲线在点(0,1)处的切线也是曲线y=ln(x+1)+a的切线，则a=_", - "type": "text" - } - ], - "index": 56 - } - ], - "index": 54.5, - "bbox_fs": [ - 5, - 1948, - 604, - 2058 - ] - }, - { - "type": "text", - "bbox": [ - 7, - 2065, - 608, - 2212 - ], - "lines": [ - { - "bbox": [ - 8, - 2065, - 589, - 2089 - ], - "spans": [ - { - "bbox": [ - 8, - 2065, - 589, - 2089 - ], - "score": 0.988, - "content": "14.甲乙两人各有四张卡片，每张卡片上标有一个数字，假的卡片上分别标有数字1，3，", - "type": "text" - } - ], - "index": 57 - }, - { - "bbox": [ - 37, - 2099, - 610, - 2118 - ], - "spans": [ - { - "bbox": [ - 37, - 2099, - 610, - 2118 - ], - "score": 0.988, - "content": "5，7，乙的卡片上分别标有数字2，4，6，8.两人进行四轮比赛，在每轮比赛中，两人", - "type": "text" - } - ], - "index": 58 - }, - { - "bbox": [ - 39, - 2129, - 604, - 2148 - ], - "spans": [ - { - "bbox": [ - 39, - 2129, - 604, - 2148 - ], - "score": 0.99, - "content": "各自从自己持有的卡片中随机选一张，并比较所选卡片上的数字大小，数字大的人得1", - "type": "text" - } - ], - "index": 59 - }, - { - "bbox": [ - 37, - 2158, - 607, - 2182 - ], - "spans": [ - { - "bbox": [ - 37, - 2158, - 607, - 2182 - ], - "score": 0.984, - "content": "分，数字小的人得0分，然后各白弃置此轮所选的卡片（弃置的卡片在此后的轮次中不", - "type": "text" - } - ], - "index": 60 - }, - { - "bbox": [ - 36, - 2187, - 408, - 2211 - ], - "spans": [ - { - "bbox": [ - 36, - 2187, - 408, - 2211 - ], - "score": 0.987, - "content": "能使用），则四轮比赛后，甲的总得分不小于2的概率为", - "type": "text" - } - ], - "index": 61 - } - ], - "index": 59, - "bbox_fs": [ - 8, - 2065, - 610, - 2211 - ] - }, - { - "type": "title", - "bbox": [ - 10, - 2235, - 562, - 2289 - ], - "lines": [ - { - "bbox": [ - 8, - 2235, - 560, - 2259 - ], - "spans": [ - { - "bbox": [ - 8, - 2235, - 560, - 2259 - ], - "score": 0.994, - "content": "四、解答题：本题共6小题，共70分。解答应写出文字说明、证明过程或演算步骤。", - "type": "text" - } - ], - "index": 62 - }, - { - "bbox": [ - 5, - 2267, - 95, - 2290 - ], - "spans": [ - { - "bbox": [ - 5, - 2267, - 95, - 2290 - ], - "score": 0.973, - "content": "15.（13分）", - "type": "text" - } - ], - "index": 63 - } - ], - "index": 62.5 - }, - { - "type": "text", - "bbox": [ - 13, - 2301, - 507, - 2324 - ], - "lines": [ - { - "bbox": [ - 33, - 2295, - 511, - 2328 - ], - "spans": [ - { - "bbox": [ - 33, - 2295, - 511, - 2328 - ], - "score": 0.897, - "content": "记△ABC的内角A，B，C的对边分别为a，b，c，已知sinC=√coB。", - "type": "text" - } - ], - "index": 64 - } - ], - "index": 64, - "bbox_fs": [ - 33, - 2295, - 511, - 2328 - ] - }, - { - "type": "text", - "bbox": [ - 8, - 2333, - 153, - 2356 - ], - "lines": [ - { - "bbox": [ - 5, - 2330, - 146, - 2362 - ], - "spans": [ - { - "bbox": [ - 5, - 2330, - 146, - 2362 - ], - "score": 0.553, - "content": "^{+b²-c{=√2ab.", - "type": "text" - } - ], - "index": 65 - } - ], - "index": 65, - "bbox_fs": [ - 5, - 2330, - 146, - 2362 - ] - }, - { - "type": "list", - "bbox": [ - 40, - 2363, - 287, - 2423 - ], - "lines": [ - { - "bbox": [ - 43, - 2366, - 116, - 2391 - ], - "spans": [ - { - "bbox": [ - 43, - 2366, - 116, - 2391 - ], - "score": 0.902, - "content": "（1）求B；", - "type": "text" - } - ], - "index": 66, - "is_list_end_line": true - }, - { - "bbox": [ - 43, - 2398, - 293, - 2426 - ], - "spans": [ - { - "bbox": [ - 43, - 2398, - 293, - 2426 - ], - "score": 0.917, - "content": "（2）若△ABC的面积为3+√，求c.", - "type": "text" - } - ], - "index": 67, - "is_list_start_line": true, - "is_list_end_line": true - } - ], - "index": 66.5, - "bbox_fs": [ - 43, - 2366, - 293, - 2426 - ] - }, - { - "type": "text", - "bbox": [ - 8, - 2566, - 94, - 2591 - ], - "lines": [ - { - "bbox": [ - 4, - 2565, - 94, - 2591 - ], - "spans": [ - { - "bbox": [ - 4, - 2565, - 94, - 2591 - ], - "score": 0.978, - "content": "16.（15分）", - "type": "text" - } - ], - "index": 68 - } - ], - "index": 68, - "bbox_fs": [ - 4, - 2565, - 94, - 2591 - ] - }, - { - "type": "list", - "bbox": [ - 24, - 2596, - 524, - 2704 - ], - "lines": [ - { - "bbox": [ - 264, - 2606, - 412, - 2632 - ], - "spans": [ - { - "bbox": [ - 264, - 2606, - 412, - 2632 - ], - "score": 0.87, - "content": "=1(a>b>0)上两点.", - "type": "text" - } - ], - "index": 70, - "is_list_end_line": true - }, - { - "bbox": [ - 249, - 2620, - 276, - 2642 - ], - "spans": [ - { - "bbox": [ - 249, - 2620, - 276, - 2642 - ], - "score": 0.626, - "content": "$b{r}$", - "type": "text" - } - ], - "index": 69, - "is_list_end_line": true - }, - { - "bbox": [ - 42, - 2649, - 178, - 2673 - ], - "spans": [ - { - "bbox": [ - 42, - 2649, - 178, - 2673 - ], - "score": 0.966, - "content": "（1）求C的离心率：", - "type": "text" - } - ], - "index": 71, - "is_list_start_line": true, - "is_list_end_line": true - }, - { - "bbox": [ - 43, - 2681, - 524, - 2704 - ], - "spans": [ - { - "bbox": [ - 43, - 2681, - 524, - 2704 - ], - "score": 0.959, - "content": "（2）若过P的直线I交C于另一点B，且△ABP的面积为9，求I的方程.", - "type": "text" - } - ], - "index": 72, - "is_list_start_line": true - } - ], - "index": 70.5, - "bbox_fs": [ - 42, - 2606, - 524, - 2704 - ] - }, - { - "type": "text", - "bbox": [ - 1, - 2853, - 85, - 2874 - ], - "lines": [ - { - "bbox": [ - -2, - 2850, - 88, - 2879 - ], - "spans": [ - { - "bbox": [ - -2, - 2850, - 88, - 2879 - ], - "score": 0.976, - "content": "17.（15分）", - "type": "text" - } - ], - "index": 73 - } - ], - "index": 73, - "bbox_fs": [ - -2, - 2850, - 88, - 2879 - ] - }, - { - "type": "text", - "bbox": [ - 1, - 2882, - 432, - 3058 - ], - "lines": [ - { - "bbox": [ - 29, - 2885, - 432, - 2908 - ], - "spans": [ - { - "bbox": [ - 29, - 2885, - 432, - 2908 - ], - "score": 0.963, - "content": "如图，四棱锥P-ABCD中，PA⊥底面ABCD，PA=AC=2，", - "type": "text" - } - ], - "index": 74 - }, - { - "bbox": [ - 1, - 2915, - 130, - 2943 - ], - "spans": [ - { - "bbox": [ - 1, - 2915, - 130, - 2943 - ], - "score": 0.889, - "content": "BC=1，AB=√.", - "type": "text" - } - ], - "index": 75 - }, - { - "bbox": [ - 36, - 2949, - 316, - 2972 - ], - "spans": [ - { - "bbox": [ - 36, - 2949, - 316, - 2972 - ], - "score": 0.93, - "content": "（1）若AD⊥PB，证明：AD//平面PBC：", - "type": "text" - } - ], - "index": 76 - }, - { - "bbox": [ - 34, - 2979, - 403, - 3015 - ], - "spans": [ - { - "bbox": [ - 34, - 2979, - 403, - 3015 - ], - "score": 0.876, - "content": "(2)若AD⊥DC，且二面角A-CP-D的正弦值为√2$", - "type": "text" - } - ], - "index": 77 - }, - { - "bbox": [ - 374, - 3004, - 399, - 3026 - ], - "spans": [ - { - "bbox": [ - 374, - 3004, - 399, - 3026 - ], - "score": 0.998, - "content": "7", - "type": "text" - } - ], - "index": 78 - }, - { - "bbox": [ - -4, - 3030, - 53, - 3059 - ], - "spans": [ - { - "bbox": [ - -4, - 3030, - 53, - 3059 - ], - "score": 0.976, - "content": "求AD.", - "type": "text" - } - ], - "index": 79 - } - ], - "index": 76.5, - "bbox_fs": [ - -4, - 2885, - 432, - 3059 - ] - }, - { - "type": "image", - "bbox": [ - 451, - 2873, - 601, - 3052 - ], - "blocks": [ - { - "type": "image_body", - "bbox": [ - 451, - 2873, - 601, - 3052 - ], - "group_id": 1, - "lines": [ - { - "bbox": [ - 451, - 2873, - 601, - 3052 - ], - "spans": [ - { - "bbox": [ - 451, - 2873, - 601, - 3052 - ], - "score": 0.904, - "type": "image", - "image_path": "68816d467f0086c289a436af04fad25fde27512b22554b1094715129ecce776e.jpg" - } - ] - } - ], - "index": 80.5, - "virtual_lines": [ - { - "bbox": [ - 451, - 2873, - 601, - 2962.5 - ], - "spans": [], - "index": 80 - }, - { - "bbox": [ - 451, - 2962.5, - 601, - 3052.0 - ], - "spans": [], - "index": 81 - } - ] - } - ], - "index": 80.5 - }, - { - "type": "text", - "bbox": [ - 1, - 3143, - 85, - 3166 - ], - "lines": [ - { - "bbox": [ - -2, - 3142, - 88, - 3169 - ], - "spans": [ - { - "bbox": [ - -2, - 3142, - 88, - 3169 - ], - "score": 0.959, - "content": "18.（17分）", - "type": "text" - } - ], - "index": 82 - } - ], - "index": 82, - "bbox_fs": [ - -2, - 3142, - 88, - 3169 - ] - }, - { - "type": "list", - "bbox": [ - 21, - 3178, - 387, - 3316 - ], - "lines": [ - { - "bbox": [ - 29, - 3182, - 283, - 3210 - ], - "spans": [ - { - "bbox": [ - 29, - 3182, - 172, - 3210 - ], - "score": 0.799, - "content": "已知函数f(x)=ln−x", - "type": "text" - }, - { - "bbox": [ - 175, - 3182, - 283, - 3209 - ], - "score": 0.826, - "content": "+αx+b(x−1).", - "type": "text" - } - ], - "index": 83, - "is_list_start_line": true, - "is_list_end_line": true - }, - { - "bbox": [ - 148, - 3197, - 184, - 3217 - ], - "spans": [ - { - "bbox": [ - 148, - 3197, - 184, - 3217 - ], - "score": 0.905, - "content": "2-x", - "type": "text" - } - ], - "index": 84, - "is_list_end_line": true - }, - { - "bbox": [ - 36, - 3226, - 323, - 3249 - ], - "spans": [ - { - "bbox": [ - 36, - 3226, - 323, - 3249 - ], - "score": 0.883, - "content": "（1）若b=0，且f(x)≥0，求a的最小值；", - "type": "text" - } - ], - "index": 85, - "is_list_start_line": true, - "is_list_end_line": true - }, - { - "bbox": [ - 36, - 3259, - 315, - 3283 - ], - "spans": [ - { - "bbox": [ - 36, - 3259, - 315, - 3283 - ], - "score": 0.923, - "content": "（2）证明：曲线y=f(x)是中心对称图形；", - "type": "text" - } - ], - "index": 86, - "is_list_start_line": true, - "is_list_end_line": true - }, - { - "bbox": [ - 34, - 3290, - 384, - 3313 - ], - "spans": [ - { - "bbox": [ - 34, - 3290, - 384, - 3313 - ], - "score": 0.908, - "content": "（3）若f(x)>2当且仅当1f(x−1)+f(x−2)，且当x<3时，f(x)=x，则下列" - }, - { - "category_id": 15, - "poly": [ - 26.0, - 751.0, - 124.0, - 751.0, - 124.0, - 767.0, - 26.0, - 767.0 - ], - "score": 0.999, - "text": "结论中一定正确的是" - }, - { - "category_id": 15, - "poly": [ - 24.0, - 770.0, - 101.0, - 770.0, - 101.0, - 789.0, - 24.0, - 789.0 - ], - "score": 0.967, - "text": "A.f(10)>100" - }, - { - "category_id": 15, - "poly": [ - 126.0, - 770.0, - 214.0, - 770.0, - 214.0, - 789.0, - 126.0, - 789.0 - ], - "score": 0.929, - "text": "B.f(20)>1000" - }, - { - "category_id": 15, - "poly": [ - 226.0, - 770.0, - 420.0, - 770.0, - 420.0, - 789.0, - 226.0, - 789.0 - ], - "score": 0.951, - "text": "C.f(10)<1000D.f(20)<10000" - }, - { - "category_id": 15, - "poly": [ - 6.0, - 1318.0, - 260.0, - 1318.0, - 260.0, - 1334.0, - 6.0, - 1334.0 - ], - "score": 0.989, - "text": "三、填空题：本大题共3小题，每小题5分，共计15分" - }, - { - "category_id": 15, - "poly": [ - 98.0, - 8.0, - 339.0, - 8.0, - 339.0, - 27.0, - 98.0, - 27.0 - ], - "score": 0.953, - "text": "024年普通等学校招生全国统一考试" - }, - { - "category_id": 15, - "poly": [ - 98.0, - 8.0, - 339.0, - 8.0, - 339.0, - 27.0, - 98.0, - 27.0 - ], - "score": 0.972, - "text": "024年普通高等学校招生全国统一考试" - }, - { - "category_id": 15, - "poly": [ - 6.0, - 1539.0, - 386.0, - 1539.0, - 386.0, - 1555.0, - 6.0, - 1555.0 - ], - "score": 0.994, - "text": "四、解答题：本题共6小题，共70分。解答应写出文字说明、证明过程或演算步骤。" - }, - { - "category_id": 15, - "poly": [ - 18.0, - 528.0, - 66.0, - 528.0, - 66.0, - 548.0, - 18.0, - 548.0 - ], - "score": 0.943, - "text": "A.-3m" - }, - { - "category_id": 15, - "poly": [ - 118.0, - 519.0, - 174.0, - 519.0, - 174.0, - 561.0, - 118.0, - 561.0 - ], - "score": 0.816, - "text": "B.\\a$" - }, - { - "category_id": 15, - "poly": [ - 229.0, - 526.0, - 266.0, - 526.0, - 266.0, - 554.0, - 229.0, - 554.0 - ], - "score": 0.74, - "text": "c. m" - }, - { - "category_id": 15, - "poly": [ - 334.0, - 528.0, - 378.0, - 528.0, - 378.0, - 549.0, - 334.0, - 549.0 - ], - "score": 0.977, - "text": "D.3m" - }, - { - "category_id": 15, - "poly": [ - 6.0, - 1541.0, - 385.0, - 1541.0, - 385.0, - 1554.0, - 6.0, - 1554.0 - ], - "score": 0.985, - "text": "四、解答题：本题共6小题，共70分。解答应写出文字说明、证明过程或演算步骤。" - }, - { - "category_id": 15, - "poly": [ - 5.0, - 1561.0, - 66.0, - 1561.0, - 66.0, - 1577.0, - 5.0, - 1577.0 - ], - "score": 0.97, - "text": "15.（13分）" - }, - { - "category_id": 15, - "poly": [ - 25.0, - 1051.0, - 158.0, - 1051.0, - 158.0, - 1070.0, - 25.0, - 1070.0 - ], - "score": 0.898, - "text": "A.x=3是f(x)的极小值点" - }, - { - "category_id": 15, - "poly": [ - 228.0, - 1051.0, - 377.0, - 1051.0, - 377.0, - 1070.0, - 228.0, - 1070.0 - ], - "score": 0.912, - "text": "B.当0f(x)" - }, - { - "category_id": 15, - "poly": [ - 2.0, - 613.0, - 99.0, - 613.0, - 99.0, - 632.0, - 2.0, - 632.0 - ], - "score": 0.917, - "text": "6.已知函数f(x)=" - }, - { - "category_id": 15, - "poly": [ - 96.0, - 622.0, - 189.0, - 622.0, - 189.0, - 641.0, - 96.0, - 641.0 - ], - "score": 0.82, - "text": "le+ln(x+1).x≥0" - }, - { - "category_id": 15, - "poly": [ - 95.0, - 606.0, - 364.0, - 606.0, - 364.0, - 634.0, - 95.0, - 634.0 - ], - "score": 0.791, - "text": "-x-2ax-a,x<0₂在R上单调递增，则a的取值范围是" - }, - { - "category_id": 15, - "poly": [ - 17.0, - 435.0, - 71.0, - 435.0, - 71.0, - 455.0, - 17.0, - 455.0 - ], - "score": 0.818, - "text": "A.-1-i" - }, - { - "category_id": 15, - "poly": [ - 123.0, - 435.0, - 177.0, - 435.0, - 177.0, - 455.0, - 123.0, - 455.0 - ], - "score": 0.799, - "text": "B.-1+i" - }, - { - "category_id": 15, - "poly": [ - 228.0, - 435.0, - 274.0, - 435.0, - 274.0, - 455.0, - 228.0, - 455.0 - ], - "score": 0.824, - "text": "C.1-i" - }, - { - "category_id": 15, - "poly": [ - 334.0, - 435.0, - 382.0, - 435.0, - 382.0, - 455.0, - 334.0, - 455.0 - ], - "score": 0.938, - "text": "D.1+i" - }, - { - "category_id": 15, - "poly": [ - 1.0, - 455.0, - 274.0, - 455.0, - 274.0, - 477.0, - 1.0, - 477.0 - ], - "score": 0.87, - "text": "3.已知向量a=(0,1)，b=(2,x)，若b⊥(b−4a)，则x=" - }, - { - "category_id": 15, - "poly": [ - 17.0, - 479.0, - 59.0, - 479.0, - 59.0, - 499.0, - 17.0, - 499.0 - ], - "score": 0.956, - "text": "A.-2" - }, - { - "category_id": 15, - "poly": [ - 122.0, - 479.0, - 164.0, - 479.0, - 164.0, - 499.0, - 122.0, - 499.0 - ], - "score": 0.93, - "text": "B.-1" - }, - { - "category_id": 15, - "poly": [ - 229.0, - 480.0, - 262.0, - 480.0, - 262.0, - 498.0, - 229.0, - 498.0 - ], - "score": 0.922, - "text": "C.1" - }, - { - "category_id": 15, - "poly": [ - 334.0, - 479.0, - 370.0, - 479.0, - 370.0, - 500.0, - 334.0, - 500.0 - ], - "score": 0.974, - "text": "D.2" - }, - { - "category_id": 15, - "poly": [ - 1.0, - 497.0, - 269.0, - 497.0, - 269.0, - 520.0, - 1.0, - 520.0 - ], - "score": 0.885, - "text": "4.已知cos(α+β)=m，tanαtanβ=2，则cos(α−β)=" - }, - { - "category_id": 15, - "poly": [ - 8.0, - 799.0, - 413.0, - 799.0, - 413.0, - 815.0, - 8.0, - 815.0 - ], - "score": 0.979, - "text": "二、选择题：本大题共3小题，每小题6分，共计18分.每小题给出的四个选项中，有多" - }, - { - "category_id": 15, - "poly": [ - 27.0, - 825.0, - 382.0, - 825.0, - 382.0, - 841.0, - 27.0, - 841.0 - ], - "score": 0.989, - "text": "项符合题目要求。全部选对得6分，选对但不全的得部分分，有选错的得0分。" - }, - { - "category_id": 15, - "poly": [ - 6.0, - 1541.0, - 386.0, - 1541.0, - 386.0, - 1554.0, - 6.0, - 1554.0 - ], - "score": 0.992, - "text": "四、解答题：本题共6小题，共70分。解答应写出文字说明、证明过程或演算步骤。" - }, - { - "category_id": 15, - "poly": [ - 4.0, - 1561.0, - 66.0, - 1561.0, - 66.0, - 1577.0, - 4.0, - 1577.0 - ], - "score": 0.973, - "text": "15.（13分）" - }, - { - "category_id": 15, - "poly": [ - 8.0, - 799.0, - 413.0, - 799.0, - 413.0, - 815.0, - 8.0, - 815.0 - ], - "score": 0.979, - "text": "二、选择题：本大题共3小题，每小题6分，共计18分.每小题给出的四个选项中，有多" - }, - { - "category_id": 15, - "poly": [ - 27.0, - 825.0, - 382.0, - 825.0, - 382.0, - 841.0, - 27.0, - 841.0 - ], - "score": 0.989, - "text": "项符合题目要求。全部选对得6分，选对但不全的得部分分，有选错的得0分。" - }, - { - "category_id": 15, - "poly": [ - 16.0, - 376.0, - 75.0, - 376.0, - 75.0, - 399.0, - 16.0, - 399.0 - ], - "score": 0.833, - "text": "A.(-1.0)" - }, - { - "category_id": 15, - "poly": [ - 121.0, - 376.0, - 175.0, - 376.0, - 175.0, - 399.0, - 121.0, - 399.0 - ], - "score": 0.81, - "text": "B.(2.3}" - }, - { - "category_id": 15, - "poly": [ - 228.0, - 374.0, - 300.0, - 374.0, - 300.0, - 399.0, - 228.0, - 399.0 - ], - "score": 0.789, - "text": "C.(-3,-1.0)" - }, - { - "category_id": 15, - "poly": [ - 333.0, - 376.0, - 401.0, - 376.0, - 401.0, - 399.0, - 333.0, - 399.0 - ], - "score": 0.778, - "text": "D.(-1,0,2" - }, - { - "category_id": 15, - "poly": [ - 54.0, - 406.0, - 124.0, - 406.0, - 124.0, - 426.0, - 54.0, - 426.0 - ], - "score": 0.842, - "text": "=1+i，则z=" - }, - { - "category_id": 15, - "poly": [ - 32.0, - 418.0, - 57.0, - 418.0, - 57.0, - 432.0, - 32.0, - 432.0 - ], - "score": 0.708, - "text": "=-1" - }, - { - "category_id": 15, - "poly": [ - -4.0, - 400.5, - 58.0, - 400.5, - 58.0, - 428.5, - -4.0, - 428.5 - ], - "score": 0.748, - "text": "2.三" - }, - { - "category_id": 15, - "poly": [ - 8.0, - 799.0, - 413.0, - 799.0, - 413.0, - 815.0, - 8.0, - 815.0 - ], - "score": 0.979, - "text": "二、选择题：本大题共3小题，每小题6分，共计18分.每小题给出的四个选项中，有多" - }, - { - "category_id": 15, - "poly": [ - 27.0, - 825.0, - 382.0, - 825.0, - 382.0, - 841.0, - 27.0, - 841.0 - ], - "score": 0.99, - "text": "项符合题目要求。全部选对得6分，选对但不全的得部分分，有选错的得0分。" - }, - { - "category_id": 15, - "poly": [ - -2.0, - 1962.0, - 61.0, - 1962.0, - 61.0, - 1982.0, - -2.0, - 1982.0 - ], - "score": 0.976, - "text": "17.（15分）" - }, - { - "category_id": 15, - "poly": [ - -2.0, - 2163.0, - 61.0, - 2163.0, - 61.0, - 2182.0, - -2.0, - 2182.0 - ], - "score": 0.959, - "text": "18.（17分）" - }, - { - "category_id": 15, - "poly": [ - -1.0, - 2343.0, - 61.0, - 2343.0, - 61.0, - 2363.0, - -1.0, - 2363.0 - ], - "score": 0.962, - "text": "19.（17分）" - }, - { - "category_id": 15, - "poly": [ - -2.0, - 1962.0, - 61.0, - 1962.0, - 61.0, - 1982.0, - -2.0, - 1982.0 - ], - "score": 0.976, - "text": "17.（15分）" - }, - { - "category_id": 15, - "poly": [ - 3.0, - 1766.0, - 65.0, - 1766.0, - 65.0, - 1784.0, - 3.0, - 1784.0 - ], - "score": 0.978, - "text": "16.（15分）" - }, - { - "category_id": 15, - "poly": [ - 12.0, - 853.0, - 423.0, - 853.0, - 423.0, - 866.0, - 12.0, - 866.0 - ], - "score": 0.989, - "text": "9.为了解推动出口后的亩收入（单位：万元）情况，从该种植区抽取样本，得到推动出口后" - }, - { - "category_id": 15, - "poly": [ - 29.0, - 881.0, - 423.0, - 881.0, - 423.0, - 894.0, - 29.0, - 894.0 - ], - "score": 0.981, - "text": "亩收入的样本均值2.1，样本方差=0.01，已知该种植区以往的亩收入X服从正态" - }, - { - "category_id": 15, - "poly": [ - 27.0, - 907.0, - 422.0, - 907.0, - 422.0, - 923.0, - 27.0, - 923.0 - ], - "score": 0.928, - "text": "分布N(1.8,0.1²)，假设推动出口后的亩收入Y服从正态分布(x,)，则（若随机变量Z" - }, - { - "category_id": 15, - "poly": [ - 27.0, - 937.0, - 256.0, - 937.0, - 256.0, - 953.0, - 27.0, - 953.0 - ], - "score": 0.899, - "text": "服从正态分布N(μσ)，则P(Z<+)≈0.8413）" - }, - { - "category_id": 15, - "poly": [ - 6.0, - 1422.0, - 406.0, - 1422.0, - 406.0, - 1438.0, - 6.0, - 1438.0 - ], - "score": 0.988, - "text": "14.甲乙两人各有四张卡片，每张卡片上标有一个数字，假的卡片上分别标有数字1，3，" - }, - { - "category_id": 15, - "poly": [ - 26.0, - 1445.0, - 420.0, - 1445.0, - 420.0, - 1458.0, - 26.0, - 1458.0 - ], - "score": 0.988, - "text": "5，7，乙的卡片上分别标有数字2，4，6，8.两人进行四轮比赛，在每轮比赛中，两人" - }, - { - "category_id": 15, - "poly": [ - 27.0, - 1466.0, - 416.0, - 1466.0, - 416.0, - 1479.0, - 27.0, - 1479.0 - ], - "score": 0.99, - "text": "各自从自己持有的卡片中随机选一张，并比较所选卡片上的数字大小，数字大的人得1" - }, - { - "category_id": 15, - "poly": [ - 26.0, - 1486.0, - 418.0, - 1486.0, - 418.0, - 1502.0, - 26.0, - 1502.0 - ], - "score": 0.984, - "text": "分，数字小的人得0分，然后各白弃置此轮所选的卡片（弃置的卡片在此后的轮次中不" - }, - { - "category_id": 15, - "poly": [ - 25.0, - 1506.0, - 281.0, - 1506.0, - 281.0, - 1522.0, - 25.0, - 1522.0 - ], - "score": 0.987, - "text": "能使用），则四轮比赛后，甲的总得分不小于2的概率为" - }, - { - "category_id": 15, - "poly": [ - 25.0, - 1195.0, - 79.0, - 1195.0, - 79.0, - 1212.0, - 25.0, - 1212.0 - ], - "score": 0.842, - "text": "A.a=-2" - }, - { - "category_id": 15, - "poly": [ - 25.0, - 1222.0, - 130.0, - 1222.0, - 130.0, - 1241.0, - 25.0, - 1241.0 - ], - "score": 0.885, - "text": "B.点(2√2,0)在C上" - }, - { - "category_id": 15, - "poly": [ - 25.0, - 1252.0, - 229.0, - 1252.0, - 229.0, - 1268.0, - 25.0, - 1268.0 - ], - "score": 0.991, - "text": "C.C在第一象限的点的纵坐标的最大值为1" - }, - { - "category_id": 15, - "poly": [ - 23.0, - 1279.0, - 206.0, - 1279.0, - 206.0, - 1310.0, - 23.0, - 1310.0 - ], - "score": 0.788, - "text": "D.当点(x，3)在C上时，≤x+2" - }, - { - "category_id": 15, - "poly": [ - 26.0, - 965.0, - 113.0, - 965.0, - 113.0, - 981.0, - 26.0, - 981.0 - ], - "score": 0.927, - "text": "A.P(X>2)>0.2" - }, - { - "category_id": 15, - "poly": [ - 228.0, - 963.0, - 317.0, - 963.0, - 317.0, - 982.0, - 228.0, - 982.0 - ], - "score": 0.942, - "text": "B.P(X>2)<0.5" - }, - { - "category_id": 15, - "poly": [ - 24.0, - 992.0, - 112.0, - 992.0, - 112.0, - 1011.0, - 24.0, - 1011.0 - ], - "score": 0.924, - "text": "C.P(Y>2)>0.5" - }, - { - "category_id": 15, - "poly": [ - 228.0, - 992.0, - 316.0, - 992.0, - 316.0, - 1011.0, - 228.0, - 1011.0 - ], - "score": 0.953, - "text": "D.P(Y>2)<0.8" - }, - { - "category_id": 15, - "poly": [ - 6.0, - 1108.0, - 312.0, - 1108.0, - 312.0, - 1130.0, - 6.0, - 1130.0 - ], - "score": 0.968, - "text": "11.造型可以做成关丽的丝带，将其看作图中曲线C的一部分.已" - }, - { - "category_id": 15, - "poly": [ - 25.0, - 1136.0, - 310.0, - 1136.0, - 310.0, - 1156.0, - 25.0, - 1156.0 - ], - "score": 0.943, - "text": "知C过坐标原点O，且C上的点满足横坐标大于-2，到点F(2,0)" - }, - { - "category_id": 15, - "poly": [ - 27.0, - 1166.0, - 256.0, - 1166.0, - 256.0, - 1182.0, - 27.0, - 1182.0 - ], - "score": 0.928, - "text": "的距离与到定直线x=a(a<0)的距离之积为4，则" - }, - { - "category_id": 15, - "poly": [ - 19.0, - 2364.0, - 407.0, - 2364.0, - 407.0, - 2386.0, - 19.0, - 2386.0 - ], - "score": 0.878, - "text": "设m为正整数，数列a，q2，\"，2是公差不为0的等差数列，若从中删去两项a" - }, - { - "category_id": 15, - "poly": [ - 1.0, - 2390.0, - 408.0, - 2390.0, - 408.0, - 2406.0, - 1.0, - 2406.0 - ], - "score": 0.95, - "text": "和a(i0,b>0)的左右焦点分别为F，F2，过作平行于y轴的直" - }, - { - "category_id": 16, - "poly": [ - 80.0, - 1354.0, - 106.0, - 1354.0, - 106.0, - 1372.0, - 80.0, - 1372.0 - ], - "score": 0.0, - "text": "" - }, - { - "category_id": 15, - "poly": [ - 100.0, - 1354.0, - 120.0, - 1354.0, - 120.0, - 1370.0, - 100.0, - 1370.0 - ], - "score": 0.636, - "text": "}$" - }, - { - "category_id": 15, - "poly": [ - 25.0, - 1375.0, - 321.0, - 1375.0, - 321.0, - 1394.0, - 25.0, - 1394.0 - ], - "score": 0.963, - "text": "线交C于A、B两点，若|FA=13，|AB|=10，则C的离心率为_" - }, - { - "category_id": 15, - "poly": [ - 4.0, - 1397.0, - 323.0, - 1397.0, - 323.0, - 1417.0, - 4.0, - 1417.0 - ], - "score": 0.883, - "text": "13.若曲线在点(0,1)处的切线也是曲线y=ln(x+1)+a的切线，则a=_" - }, - { - "category_id": 15, - "poly": [ - 6.0, - 1021.0, - 175.0, - 1021.0, - 175.0, - 1040.0, - 6.0, - 1040.0 - ], - "score": 0.838, - "text": "10.设函数f(x)=(x−1)(x−4)，则" - }, - { - "category_id": 15, - "poly": [ - 9.0, - 677.0, - 311.0, - 677.0, - 311.0, - 702.0, - 9.0, - 702.0 - ], - "score": 0.853, - "text": "7.当xe[0.2n]时，曲线y=sinx与y=2sin(3x-)的交点个数为" - }, - { - "category_id": 15, - "poly": [ - 3.0, - 355.0, - 301.0, - 355.0, - 301.0, - 374.0, - 3.0, - 374.0 - ], - "score": 0.849, - "text": "1.已知集合A={x|−52当且仅当1b>0)上两点." - }, - { - "category_id": 15, - "poly": [ - 172.0, - 1804.0, - 190.0, - 1804.0, - 190.0, - 1819.0, - 172.0, - 1819.0 - ], - "score": 0.626, - "text": "$b{r}$" - }, - { - "category_id": 16, - "poly": [ - 151.0, - 1805.0, - 169.0, - 1805.0, - 169.0, - 1821.0, - 151.0, - 1821.0 - ], - "score": 0.492, - "text": "$a$" - }, - { - "category_id": 15, - "poly": [ - 29.0, - 1824.0, - 123.0, - 1824.0, - 123.0, - 1840.0, - 29.0, - 1840.0 - ], - "score": 0.966, - "text": "（1）求C的离心率：" - }, - { - "category_id": 15, - "poly": [ - 30.0, - 1846.0, - 361.0, - 1846.0, - 361.0, - 1862.0, - 30.0, - 1862.0 - ], - "score": 0.959, - "text": "（2）若过P的直线I交C于另一点B，且△ABP的面积为9，求I的方程." - }, - { - "category_id": 16, - "poly": [ - 157.0, - 1790.5, - 195.0, - 1790.5, - 195.0, - 1808.5, - 157.0, - 1808.5 - ], - "score": 0.43, - "text": "422" - }, - { - "category_id": 15, - "poly": [ - 14.0, - 96.0, - 420.0, - 96.0, - 420.0, - 109.0, - 14.0, - 109.0 - ], - "score": 0.981, - "text": "意事项：1．答题前，请务必将自已的姓名、准考证号用黑色字迹的签字笔或钢笔分别填" - }, - { - "category_id": 15, - "poly": [ - 69.0, - 116.0, - 424.0, - 116.0, - 424.0, - 129.0, - 69.0, - 129.0 - ], - "score": 0.992, - "text": "写在试题卷和答题卡上。用2B铅笔将试卷类型（A）填涂在答题卡相应位置" - }, - { - "category_id": 15, - "poly": [ - 67.0, - 137.0, - 316.0, - 137.0, - 316.0, - 152.0, - 67.0, - 152.0 - ], - "score": 0.994, - "text": "上。将条形码横贴在答题卡右上角“条形码粘贴处”。" - }, - { - "category_id": 15, - "poly": [ - 51.0, - 158.0, - 426.0, - 158.0, - 426.0, - 174.0, - 51.0, - 174.0 - ], - "score": 0.967, - "text": "2.作答选择题时，选出每小题答案后，用2B铅笔把答题卡上对应题目选项的答" - }, - { - "category_id": 15, - "poly": [ - 69.0, - 180.0, - 421.0, - 180.0, - 421.0, - 193.0, - 69.0, - 193.0 - ], - "score": 0.976, - "text": "案信息点涂黑：如需改动，用橡皮擦干净后，再选涂其他答案，答案不能答" - }, - { - "category_id": 15, - "poly": [ - 67.0, - 198.0, - 122.0, - 198.0, - 122.0, - 215.0, - 67.0, - 215.0 - ], - "score": 0.997, - "text": "在试卷上。" - }, - { - "category_id": 15, - "poly": [ - 51.0, - 220.0, - 420.0, - 220.0, - 420.0, - 236.0, - 51.0, - 236.0 - ], - "score": 0.993, - "text": "3.非选择题必须用黑色字迹钢笔或签字笔作答，答案必须写在答题卡各题目指" - }, - { - "category_id": 15, - "poly": [ - 69.0, - 242.0, - 409.0, - 242.0, - 409.0, - 255.0, - 69.0, - 255.0 - ], - "score": 0.99, - "text": "定区域内相应位置上；如需改动，先划掉原来的答案，然后再写上新的答" - }, - { - "category_id": 15, - "poly": [ - 68.0, - 263.0, - 351.0, - 263.0, - 351.0, - 276.0, - 68.0, - 276.0 - ], - "score": 0.994, - "text": "案：不准使用铅笔和涂改液。不按以上要求作答的答案无效。" - }, - { - "category_id": 15, - "poly": [ - 52.0, - 283.0, - 393.0, - 283.0, - 393.0, - 296.0, - 52.0, - 296.0 - ], - "score": 0.984, - "text": "4.考生必须保持答题卡的整洁。考试结束后，将试卷和答题卡一并交回。" - }, - { - "category_id": 15, - "poly": [ - 4.0, - 1604.0, - 101.0, - 1604.0, - 101.0, - 1626.0, - 4.0, - 1626.0 - ], - "score": 0.553, - "text": "^{+b²-c{=√2ab." - }, - { - "category_id": 15, - "poly": [ - 24.0, - 2435.0, - 400.0, - 2435.0, - 400.0, - 2458.0, - 24.0, - 2458.0 - ], - "score": 0.824, - "text": "(1)写出所有的(i)，1≤i