月考试卷

月考初一语文试卷一、基础知识（30分）1. 下列加点字的读音完全正确的一项是（）（3分）A. 确凿（záo）脑髓（suǐ）气氛（fèn）倜傥（tì tǎng）B. 殷红（yīn）骊歌（lí）讪笑（shàn）炽痛（zhì）C. 澎湃（pài）屏障（zhàng）诧异（chà）祈祷（qí）D. 崎岖（qū）污秽（suì）深邃（suì）荒谬（miù）2. 下列词语书写无误的一项是（）（3分）A. 锋芒必露妇孺皆知心会神凝。

B. 一反既往慷慨淋漓群蚁排衙。

C. 望闻问切杂乱无章大廷广众。

D. 独裁者奥悔字贴。

3. 下列句子中加点成语使用不恰当的一项是（）（3分）A. 他说话总给人一股咄咄逼人之感，令人很不舒服。

B. 我小心翼翼地伸出左脚去探那块岩石，而且踩到了它。

C. 元宵节到了，街头人声鼎沸，大家都急着看花灯呢！D. 他平时学习刻苦认真，这次期中考试取得好成绩是可歌可泣的。

4. 下列句子没有语病的一项是（）（3分）A. 通过这次活动，使我明白了团结的重要性。

B. 他那崇高的革命品质，经常浮现在我的脑海中。

C. 他的家乡是黑龙江省青冈县人。

D. 语言是否通顺是衡量一篇作文好坏的重要标准之一。

5. 默写填空。

（10分）6. 名著阅读。

（5分）二、阅读理解（30分）“吹面不寒杨柳风”，不错的，像母亲的手抚摸着你。

风里带来些新翻的泥土的气息，混着青草味儿，还有各种花的香，都在微微润湿的空气里酝酿。

鸟儿将窠巢安在繁花嫩叶当中，高兴起来了，呼朋引伴地卖弄清脆的喉咙，唱出宛转的曲子，与轻风流水应和着。

牛背上牧童的短笛，这时候也成天在嘹亮地响。

雨是最寻常的，一下就是三两天。

可别恼。

看，像牛毛，像花针，像细丝，密密地斜织着，人家屋顶上全笼着一层薄烟。

树叶子却绿得发亮，小草也青得逼你的眼。

傍晚时候，上灯了，一点点黄晕的光，烘托出一片安静而和平的夜。

六年级月考数学试卷一．选择题（共10小题，30分）1.汽车的雨刷在挡风玻璃上画出了一个扇面，这说明了（）A．点动成线B．线动成面C．面动成体D．以上都不正确2．如图，将图中的纸片折起来可以做成一个正方体，这个正方体“文”字所在面的对面是（）字． A．创B．明C．市D．城3．下列四个几何体中，是棱柱的是（）A．B． C．D．4．在数轴上，点A表示的数是1，若点B到A的距离是3，则点B表示的数是（）A．4 B．﹣2 C．4或﹣2 D．3或﹣36．下列各对数中，互为相反数的是（）A．﹣（+1）和+（﹣1）B．﹣（﹣1）和+（﹣1）C．﹣（+1）和﹣1 D．+（﹣1）和﹣17．中国是最早采用正负数表示相反意义的量的国家，如果将“收入60元”记作“+60元”，那么“支出40元”记作（）A．+40元B．﹣40元C．+20元D．20元8．在，0，1，﹣9四个数中，最大的数是（）A．B．0 C．1 D．﹣99．有理数|﹣3|的相反数是（）A．B．﹣C．3 D．﹣310．若|x﹣2|+|y+1|＝0，则x+y的值为（）A．1 B．3 C．﹣2 D．2二．填空题（共10小题，30分）11．比较大小：﹣﹣．（用“＞”“＝”或“＜”连接）12．若m是﹣6的相反数，则m的值是．13．若，则x＝．14．如图，将一刻度尺放在数轴上（数轴的单位长度是1cm），刻度尺上“0cm”和“8cm”分别对应数轴上的﹣3和x，那么x的值为．15．化简：+（﹣5）＝，﹣（﹣3）＝．16．若a、b互为相反数，则2024+a+1+b＝．17．如果一个数的相反数等于它本身，那么这个数是．18．温度由﹣4℃上升7℃，达到的温度是℃．19．已知|x|＝3，|y|＝5，x＞y，则x+y＝．20．已知|a|＝6，|b|＝10当a，b异号时，求a+b＝．三．解答题（共6小题）21 （16分）计算（1）（﹣5）+8+（﹣4）；（2）3.5+（﹣2.9）+（﹣3.5）+（+3.1）；（2）．（4）（﹣2）+0+1+|﹣4|．（5）1+（﹣）++（﹣）；（6）3+（﹣2）+5+（﹣8）（7）（+1.25）+（﹣）+（﹣）+（+1）．（8）22（8分）将﹣2.5，﹣（﹣1），0，2，﹣|﹣2|，+（﹣1.5），在数轴上表示出来，并用“＞”把它们连接起来．23（9分）．出租车司机小李某天下午运营全是在东西走向的人民大道上进行的，如果规定向东为正，向西为负，这天下午他的行车里程（单位：千米）如下：+15，﹣2，+5，﹣1，+10，﹣3，﹣2，+12，+4，﹣5，+6（1）将最后一名乘客送到目的地时，小李距下午出车时的出发点多远？（2）若汽车耗油量为6升/100千米，这天下午小李共耗油多少升？25．（9分）某果农把自家果园的柑橘包装后放到了网上销售．原计划每天卖10箱，但由于种种原因，实际每天的销售量与计划量相比有出入，下表是某个星期的销售情况（超额记为正，不足记为负，单位：箱）．星期一二三四五六日+4 ﹣3 ﹣5 +7 ﹣8 +21 ﹣6 与计划量的差值（1）根据记录的数据可知前五天共卖出箱；（2）本周实际销售总量达到了计划数量没有？（3）若每箱柑橘售价为90元，同时需要支出运费17元/箱，那么该果农本周总共收入多少元？27 （9分）小康在解一道计算题（﹣1.25）+2.3+（﹣3.75）+（﹣7.3）时，给出如下过程：（﹣1.25）+2.3+（﹣3.75）+（﹣7.3）＝[（﹣1.25）+（﹣3.75）]+[2.3+（﹣7.3）]…第一步＝（﹣5）+（﹣9.6）…第二步＝﹣14.6．…第三步①小康的解题过程有错误，最开始出现错误的步骤是第步．②请给出正确的解题过程．。

辽宁省名校联盟2024-2025学年高二上学期第一次月考数学试卷一、单选题1．已知直线(20a x y ++=的倾斜角为30o ，则a =（ ）A ．BCD ．02．若()1,2,1a =--r，()1,3,2b =-r ，则()()2a b a b +⋅-=r r r r （ ）A ．22B ．22-C ．29-D ．293．如果0AB >且0BC <，那么直线0Ax By C ++=不经过（ ） A ．第一象限B ．第二象限C ．第三象限D ．第四象限4．如图，在四棱锥P -ABCD 中，底面ABCD 是平行四边形，点E 在侧棱PC 上，且12PE EC =，若AB a u u u r r=，AD b =u u u r r ，AP c =u u u r r ，则AE =u u u r （ ）A ．112333a b c ---r r rB ．112333a b c ++r r rC ．221333a b c ++r r rD ．221333a b c ---r r r5．已知m 为实数，直线()()12:220,:5210l m x y l x m y ++-=+-+=，则“12l l //”是“3m =-”的（ ）A ．充分不必要条件B ．必要不充分条件C ．充要条件D ．既不充分也不必要条件6．已知空间中三点()0,0,0A ，()1,1,2B -，()1,2,1C --，则以AB ，AC 为邻边的平行四边形的面积为（ ）A ．32B C ．3 D ．7．点()2,4A -到直线()():131440l m x m y m -+-++=（m 为任意实数）的距离的取值范围是（ ）A ．[]0,5B ．⎡⎣C ．[]0,4D ．⎡⎣8．在正三棱锥P ABC -中，4PA AB ==，点,D E 分别是棱,PC AB 的中点，则AD PE ⋅=u u u r u u u r（ ） A ．2-B ．4-C ．6-D ．8-二、多选题9．下列说法正确的是（ ）A ．直线10x y -+=与直线10x y --=B ．直线240x y --=在两坐标轴上的截距之和为6C ．将直线y x =绕原点逆时针旋转75o ，所得到的直线为y =D ．若直线l 向左平移3个单位长度，再向上平移2个单位长度后，回到原来的位置，则直线l 的斜率为23-10．在正方体1111ABCD A B C D -中，能作为空间的一个基底的一组向量有（ ）A ．1AA u u u r ，AB u u u r，AC u u u r B ．BA u u u r ，BC u u ur ，BD u u u rC ．1AC uuu r ，1BD u u u u r，1CB u u u rD ．1AD uuu r ，1BA u u u r ，AC u u u r11．如图，在棱长均为1的平行六面体1111ABCD A B C D -中，1BB ⊥平面,60ABCD ABC ∠=o ，,P Q 分别是线段AC 和线段1A B 上的动点，且满足()1,1BQ BA CP CA λλ==-u u u r u u u r u u u r u u u r，则下列说法正确的是（ ）A ．当12λ=时，PQ //1A D B ．当12λ=时，若()1,,PQ xAB yAD z AA x y z =++∈R u u u r u u u r u u u r u u u r ，则0x y z ++=C ．当13λ=时，直线PQ 与直线1CC 所成角的大小为π6D ．当()0,1λ∈时，三棱锥Q BCP -三、填空题12．已知直线l 过点()1,2，且在y 轴上的截距为在x 轴上的截距的两倍，则直线l 的方程是. 13．在空间直角坐标系O xyz -中，已知()()()2,2,0,2,1,3,0,2,0A B C -，则三棱锥O ABC -的体积为．14．在棱长为4的正方体1111ABCD A B C D -中，点E ，F 分别为棱DA ，1BB 的中点，M ，N 分别为线段11D A ，11A B 上的动点（不包括端点），且EN FM ⊥，则线段MN 的长度的最小值为.四、解答题15．如图，正方体1111ABCD A B C D -的棱长为2.(1)用空间向量方法证明：11//AC 平面1ACD ；(2)求直线BD 与平面1ACD 所成角的正弦值.16．已知点()1,3P ，点()3,1N --，直线1l 过点()2,4-且与直线PN 垂直. (1)求直线1l 的方程；(2)求直线2:250+-=l x y 关于直线1l 的对称直线的方程. 17．平行六面体ABCD A B C D -''''，(1)若4AB =，3AD =，3AA '=，90BAD ∠=︒，60BAA '∠=︒，60DAA '∠=︒，求AC '长； (2)若以顶点A 为端点的三条棱长均为2，且它们彼此的夹角都是60°，则AC 与BD '所成角的余弦值．18．如图，四边形ABCD 是直角梯形，//,,22,AB CD AB BC AB BC CD E ⊥===为BC 的中点，P 是平面ABCD 外一点，1,,PA PB PE BD M ==⊥是线段PB 上一点，三棱锥M BDE -的体积是19.(1)求证：PA ⊥平面ABCD ； (2)求二面角M DE A --的余弦值.19．图，在三棱台111ABC A B C -中，ABC V 是等边三角形，11124,2AB A B CC ===，侧棱1CC ⊥平面ABC ，点D 是棱AB 的中点，点E 是棱1BB 上的动点（不含端点B ）.(1)证明:平面AA B B 平面11DCC；1(2)求平面ABE与平面ACE的夹角的余弦值的最小值.。

滨城高中联盟2024-2025学年度上学期高二10月份考试数学试题（时间：120分钟，满分：150分）第I 卷（选择题）一､单项选择题：本题共8小题，每小题5分，共40分.在每小题给出的四个选项中，只有一项是符合题目要求的.1.在四面体中，已知点是的中点，记，则等于（ ）A. B.C. D.2.若平面的法向量为，直线的方向向量为，直线与平面的夹角为，则下列关系式成立的是（ ）A. B.C. D.3.若直线的一个法向量是，则该直线的倾斜角为（ ）A. B. C. D.4.已知空间向量，则向量在向量上的投影向量是（ ）A. B. C. D.5.设是的二面角内一点，是垂足，，则的长度为（ ）A.B.56.对于空间一点和不共线三点，且有，则（ ）A.四点共面B.四点共面ABCD E CD ,,AB a AC b AD c === BE 1122a b c -++ 1122a b c -+ 1122a b c -+ 1122a b c -++ αμ l vl αθcos v v μθμ⋅= cos v v μθμ⋅=sin v v μθμ⋅= sin v vμθμ⋅= AB )1a =- 30 60 120 150()()1,1,2,1,2,1a b =-=- a b ()1,1,1-555,,663⎛⎫- ⎪⎝⎭555,,636⎛⎫- ⎪⎝⎭111,,424⎛⎫- ⎪⎝⎭P 120 l αβ--,,,PA PB A B αβ⊥⊥4,3PA PB ==AB O ,,A B C 2OP PA OB OC =-+ ,,,O A B C ,,,P A B CC.四点共面D.五点共面7.将正方形沿对角线折成直二面角，下列结论不正确的是（）A.B.，所成角为C.为等边三角形D.与平面所成角为8.正方形的边长为12，其内有两点，点到边的距离分别为3，2，点到边的距离也分别是3和2.如图，现将正方形卷成一个圆柱，使得和重合.则此时两点间的距离为（ ）二､多项选择题：体题共3小题，每小题6分，共18分.在每小题给出的四个选项中，有多项符合题目要求.全部选对的得6分，部分选对的按部分得分，有选错的得0分.9.下列说法中，正确的有（ ）A.直线必过定点B.方程是直线的一般式方程C.直线的斜率为D.点到直线的距离为110.已知空间单位向量两两垂直，则下列结论正确的是（ ）A.向量与共线B.问量C.可以构成空间的一个基底,,,O P B C ,,,,O P A B C ABCD BD AC BD⊥AB CD 60︒ADC V AB BCD 60︒11ABB A ,P Q P 111,AA A B Q 1,BB AB AB 11A B ,P Q ()32y ax a a =-+∈R ()3,20Ax By C ++=10x ++=()5,3-20y +=,,i j k i j + k j - i j k ++ {},,i j i j k +-D.向量和11.如图，已知正六棱柱的底面边长为2，所有顶点均在球的球面上，则下列说法错误的是（ ）A.直线与直线异面B.若是侧棱上的动点，则C.直线与平面D.球的表面积为第II 卷（非选择题）三､填空题：本题共3小题，每小题5分，共15分.12.已知点关于直线对称的点是，则直线在轴上的截距是__________.13.若三条直线相交于同一点，则点到原点的距离的最小值为__________.14.已知正三棱柱的底面边长为是其表面上的动点，该棱柱内切球的一条直径是，则的取值范围是__________.四､解答题：本题共5小题，共77分.解答应写出文字说明，证明过程或演算步骤.15.（本小题满分13分）已知直线与两坐标轴围成的三角形的面积为3，分别求满足下列条件的直线的方程：（1）过定点；（2）斜率为.16.（本小题满分15分）如图，在四面体中，面是的中点，是i j k ++ k ABCDEF A B C D E F ''''-''O DE 'AF 'M CC 'AM MD +'AF 'DFE 'O 18π()1,2A -y kx b =+()1,6B --y kx b =+x 2,3,100y x x y mx ny =+=++=(),m n ABC A B C '-''P MN PM PN ⋅ l l ()3,4A -16ABCD AD ⊥,2,BCD AD M =AD P的中点，点在棱上，且.请建立适当的空间直角坐标系，证明：面.17.（本小题满分15分）如图所示，平行六面体中.（1）用向量表示向量，并求；（2）求18.（本小题满分17分）如图，在五棱锥中，平面是等腰三角形.（1）求证：平面平面；（2）求直线与平面所成角的大小.19.（本小题满分17分）如图，在三棱柱中，棱的中点分别为在平面内的射影为是边长为2的等边三角形，且，点在棱上运动（包括端点）.请建立适当的空间直角坐标系，解答下列问题：BM Q AC3AQ QC=PQ∥BCD1111ABCD A B C D-111ππ1,2,,23AB AD AA BAD BAA DAA∠∠∠======1,,AB AD AA1BD1BD1cos,BD ACP ABCDE-PA⊥,ABCDE AB∥,CD AC∥,ED AE∥,45,24,BC ABC AB BC AE PAB∠====VPCD⊥PACPB PCD111ABC A B C-1,AC CC1,,D E CABC,D ABCV12AA=F11B C（1）若点为棱的中点，求点到平面的距离；（2）求锐二面角的余弦值的取值范围.F 11B C F BDE F BD E --滨城高中联盟2024-2025学年度上学期高二10月份考试数学试题参考答案一､单选题1.A2.D3.B4.C5.D6.B7.D8.【答案】B【详解】解法一：如图建系设圆柱底面半径为，则，所以，则所以.解法二：如图，设过点且平行底面的截面圆心为，过点且平行底面的截面圆心为，设圆柱底面半径为，则，所以，则，.r 2π12r =6πr =33,3,,9ππQ P ⎫⎛⎫--⎪ ⎪⎪ ⎪⎭⎝⎭PQ =P 1O Q 2O r 2π12r =6πr =121122222π,,63πO P O Q PQ PO O O O Q +===++222211221212||22PQ PO O O O Q r O O PO O Q∴=++=++⋅ 222266π36262cos 336,ππ3πPQ ⎛⎫⎛⎫=⋅++⋅⋅=⋅+∴= ⎪ ⎪⎝⎭⎝⎭9.AD 10.BCD.11.【答案】AC【详解】对于A ，如图①，连接，则，所以，所以直线与直线共面，故A 错误；对于B ，将平面沿着翻折到与平面共面的位置，得到矩形，如图②所示.因为底面边长为，所以则的最小值为，故B 正确；对于C ，以为坐标原点，所在直线分别为轴､轴､轴，建立如图①所示的空间直角坐标系，则，所以.设平面的法向量为，则，即，令，得，所以平面的一个法向量为.设直线与平面所成角为，则，故C 错误；对于D ，如图③，设球的半径为，根据对称性可知，正六棱柱的外接球的球心在上下底面的中心的连线的中点处.，则，所以球的表面积，故D 正确.,AD A D ''AD ∥,A D A D ''''∥E F ''AD ∥E F ''DE 'AF 'ACC A ''CC 'CDD C ''ADD A ''2π2,3ABC ∠=AC =AM MD +'AD =='F ,,FA FD FF 'x y z ()(()()(2,0,0,,0,0,0,0,,A F F D E '-'(()(,0,,AF FD FE =''=-=- DFE '(),,m x y z = 00FD m FE m ⎧⋅=⎪⎨⋅=⎪'⎩ 00y x =⎧⎪⎨-++=⎪⎩1z =x =DFE ')m = AF 'DFE 'θ1sin 3θO R 12O O 1122,O C O O ==22222211922R OC O C O O ==+=+=O 294π4π18π2S R ==⨯=12.13.【答案】【详解】由解得把代入可得，所以，所以点到原点的距离当时等号成立，此时.所以点到原点的距离的最小值为14.【答案】【详解】由题意知内切球的半径为1，设球心为，则.因为.四､解答题15.【答案】（1）或.（2）或.【详解】（1）由题意知直线的斜率存在，设为则直线的方程为，它在轴，轴上的截距分别是，由已知，得，解得或.故直线的方程为或.（2）设直线在轴上的截距为，则直线的方程是，它在轴上的截距是，8-2,3,y x x y =⎧⎨+=⎩1,2.x y =⎧⎨=⎩()1,240mx ny ++=2100m n ++=102m n =--(),m n d ==4n =-2m =-(),m n []0,4O ()()PM PN PO OM PO ON ⋅=+⋅+ ()2OP PO OM ON OM ON =+⋅++⋅ 2||1PO =- []0,4PM PN ⋅∈ 2360x y +-=83120x y ++=660x y -+=660x y --=l kl ()34y k x =++x y 43,34k k--+()43436k k ⎛⎫+⨯+=± ⎪⎝⎭123k =-283k =-l 2360x y +-=83120x y ++=l y b l 16y x b =+x 6b -由已知，得，所以.所以直线的方程为或.16.解法一：以为坐标原点，所在直线为z 轴，线段的延长线为y 轴，建立如图所示空间直角坐标系，设，由题意得，因为，所以即即所以，所以又因为面BCD 的一个法向量为所以所以又因为面所以面.解法二：66b b -⋅=1b =±l 660x y -+=660x y --=D DA BD 2BD a =()()()10,2,0,0,0,2,0,0,1,0,,2B a A M P a ⎛⎫-- ⎪⎝⎭3AQ QC =34AQ AC = ()()3,,2,,24Q Q Q x y z x y -=-331,,442Q Q Q x x y y z ===331,,442Q x y ⎛⎫ ⎪⎝⎭33,,044PQ x y a ⎛⎫=+ ⎪⎝⎭()0,0,1n =0PQ n ⋅= PQ n⊥ PQ ⊄BCDPQ ∥BCD取的中点，连接，因为为BM 的中点，所以，所以平面，过作，交BC 于以为坐标原点，的方向分别为x 轴､y 轴､z 轴正方向，建立如图所示的空间直角坐标系.因为为中点，设则设点的坐标为.因为，所以.因为为的中点，故，又为的中点，故，所以又平面BCD 的一个法向量为，故，所以又平面BCD ，所以平面BC D.17.【答案】（1）2【详解】（1），BD O OP P OP ∥MD OP ⊥BCD O OE BD ⊥,E O ,,OE OD OP2,AD M =AD 2BD a=()()0,,2,0,,0A a B a -C ()00,,0x y 3AQ QC = 003131,,4442Q x a y ⎛⎫+ ⎪⎝⎭M AD ()0,,1M a P BM 10,0,2P ⎛⎫ ⎪⎝⎭00313,,0444PQ x a y ⎛⎫=+ ⎪⎝⎭()0,0,1n =0PQ n ⋅= PQ n⊥ PQ ⊄PQ ∥111,BD AD AA AB BD =+-= 111BD AD AB AD AA AB =-=+-则，所以.（2）由空间向量的运算法则，可得，因为且，因为是正方形，所以，则.18.【答案】（1）见详解（2）【详解】（1）证明：在中，因为，所以，因此故，所以，即又平面，所以.又平面，且，所以平面.又平面，所以平面平面.（或者建系求法向量，证明法向量垂直，略）（2）由（1）知两两相互垂直，分别以的方向为轴､轴､轴正方向，建立()2222211111222BD AD AA AB AD AA AB AD AA AD AB AB AA =+-=+++⋅-⋅-⋅ 111412*********=+++⨯⨯⨯--⨯⨯⨯=1BD = AC AB AD =+ 11,2AB AD AA ===11ππ,23BAD BAA DAA ∠∠∠===ABCD AC = ()()221111BD AC AD AA AB AB AD AD AB AD AA AB AA AD AB AD AB ⋅=+-⋅+=⋅++⋅+⋅--⋅ 22ππππ11cos121cos 21cos 111cos 22332=⨯⨯++⨯⨯+⨯⨯--⨯⨯=111cos ,BD AC BD AC BD AC ⋅===⋅ π6ABC V 45,4,ABC BC AB ∠=== 2222cos458AC AB BC AB BC =+-⋅⋅= AC =222BC AC AB =+90BAC ∠= AB AC⊥PA ⊥,ABCDE AB ∥CD ,CD PA CD AC ⊥⊥,PA AC ⊂PAC PA AC A ⋂=CD ⊥PAC CDC PCD PCD ⊥PAC ,,AB AC AP ,,AB AC AP x y z如图所示的空间直角坐标系，由于是等腰三角形，所以.又，因此，.因为，所以四边形是直角梯形.因为，所以，因此，故，所以.因此.设是面的一个法向量，则，解得.取，得.又，设表示向量与平面的法向量所成的角，则，又因为，所以，因此直线与平面所成的角为.PAB V PA AB ==AC =()()0,0,0,A B ()(0,,0,0,C P AC ∥,ED CD AC ⊥ACDE 2,45,AE ABC AE ∠== ∥BC 135BAE ∠= 45CAE ∠= sin452CD AE =⋅== ()D (()0,,CP CD =-= (),,m x y z =PCD 0,0m CP m CD ⋅=⋅= 0,x y z ==1y =()0,1,1m =(BP =- θBP PCD m1cos 2m BP m BP θ⋅==⋅ π0,2θ⎡⎤∈⎢⎥⎣⎦π3θ=PB PCD π619.【答案】（1（2）解法一：连接，因为在平面内的射影为，所以平面，由于平面，所以，由于三角形是等边三角形，所以，以为原点，分别以的方向为轴､轴､轴正方向，建立如图所示空间直角坐标系，则，因为所以又因为为中点，所以所以设面的一个法向量为则令，则所以所以点到平面的距离为（2）因为在棱上（包括端点）设12⎡⎢⎣1DC 1C ABC D 1DC ⊥ABC ,AC BD ⊂ABC 11,DC AC DC BD ⊥⊥ABC BD AC ⊥BD ==1DC ==D 1,,DB DA DC x y z (())11,0,1,0,,0,2C C B E ⎛-- ⎝)11C B CB == 1B F 11B C 12F 12BF ⎛= ⎝ BDE ()111,,m x y z =1(0,,2BD ED ⎛== ⎝ 111000x BD m y ED m ⎧=⎧⋅=⎪⎪⇒⎨⎨=⋅=⎪⎪⎩⎩ 11z =1y =()m = F BDE BF m m ⋅== F 11B C ()111,01C F C B λλ= ……因为，所以设平面的法向量为，令所以，设锐二面角为，则令，所以，设则二次函数的开口向上，对称轴为，所以当时，该二次函数单调递增，所以当时，该二次函数有最小值，当时，该二次函数有最大值，，即.所以锐二面角的余弦值的取值范围.解法二：（1）连接，因为在平面内的射影为，所以平面，由于平面，所以，)11C B = )1,,0C F λ=BDF ()222,,n x y z = 11,,0),DF DC C F λλ=+=+= 22220000DF n x y x DB n λ⎧⋅=++=⎪⇒⎨=⋅=⎪⎪⎩⎩ 2y =2z λ=-()m λ=- F BD E --θ1cos 2θ=[]()32,3t t λ-=∈cos θ==111,,32s s t ⎛⎫⎡⎤=∈ ⎪⎢⎥⎣⎦⎝⎭cos θ=221112611244y s s s ⎛⎫=-+=-+ ⎪⎝⎭14s =11,32s ⎡⎤∈⎢⎥⎣⎦13s =21111261333⎛⎫⨯-⨯+= ⎪⎝⎭12s =2111261122⎛⎫⨯-⨯+= ⎪⎝⎭⎡⎣1cos 2θ⎡∈⎢⎣F BD E --12⎡⎢⎣1DC 1C ABC D 1DC ⊥ABC ,AC BD ⊂ABC 11,DC AC DC BD ⊥⊥由于三角形是等边三角形，所以，又以为原点，分别以的方向为轴､轴､轴正方向，建立如图所示空间直角坐标系，则，又，故，则设平面的法向量为，则，故可设，又，所以点到平面的距离为.（2）设，则，设平面的法向量为，则令，所以，所以，设锐二面角为，ABC ,BD AC BD ⊥==1DC ==D 1,,DCDB DCx yz (()()11,1,0,0,,2C C E B ⎛ ⎝()11C B CB ==-(11,2B F ⎛-- ⎝()1,,2DE DB ⎛== ⎝ BDE ()111,,m x y z =1111020m DE x z m DB ⎧⋅=+=⎪⎨⎪⋅==⎩ ()m = 1,2BF ⎛=- ⎝ F BDE BF m m ⋅== ()()1111101,C F C B C B λλ=≤≤=- (()(11111DF DC C F DC C B λλλ=+=+=+-=- BDF ()222,,n x y z =22220000DF n x y y DB n λ⎧⎧⋅=-++=⎪⎪⇒⎨⎨=⋅=⎪⎪⎩⎩ 2x =2z λ=)n λ=F BD E --θ则令，所以，设则二次函数的开口向上，对称轴为，所以当时，该二次函数单调递增，所以当时，该二次函数有最小值，当时，该二次函数有最大值，，即.所以锐二面角的余弦值的取值范围.1cos 2θ=[]()32,3t t λ-=∈cos θ==111,,32s s t ⎛⎫⎡⎤=∈ ⎪⎢⎥⎣⎦⎝⎭cos θ=221112611244y s s s ⎛⎫=-+=-+ ⎪⎝⎭14s =11,32s ⎡⎤∈⎢⎥⎣⎦13s =21111261333⎛⎫⨯-⨯+= ⎪⎝⎭12s =2111261122⎛⎫⨯-⨯+= ⎪⎝⎭⎡⎣1cos 2θ⎡∈⎢⎣F BD E --12⎡⎢⎣。

炎德·英才大联考雅礼中学2025届高三月考试卷（一）语文本试卷共四道大题，23道小题，满分150分。

时量150分钟。

一、现代文阅读（35分）（一）现代文阅读Ⅰ（本题共5小题，19分）阅读下面的文字，完成1~5题。

材料一：积极情绪（Positive Emotion）可以定义为正面的情绪或者具有正面向上价值的情绪。

情绪的认知理论认为，“积极情绪就是在目标实现过程中取得进步或得到他人积极评价时所产生的感受。

”由此可见，积极情绪就是经历了内在、外在的刺激，正确地解决了问题，达到某种成功与满意度，满足了个体的需求，感觉到个体的存在价值伴有随之而来的愉悦的心情与感受。

积极情绪并不是消极接受、坦然享受、乐不思蜀的感觉。

这些只是浅薄的感受，即时地享乐。

积极情绪拓展到更深的层面——从欣赏到热爱。

它并不是简单的迷恋，而是一种真心喜欢、经过努力而获得的欢愉、欣喜。

“积极情绪”这个词，指向了重要的人性瞬间。

那些轻微而短暂的愉悦状态，其实要比你想象的强大得多。

作为人类，生来就能够体验到微弱短促却愉悦舒畅的积极情绪。

它有着不同的形态和滋味。

回想一下，当感到与他人或与所爱的人心灵相通时；当感到有趣、有创意或忍俊不禁时；当感到自己的灵魂被蕴含在生命中的纯粹的美所打动时；或者当因一个新颖的主意或爱好而感到活力无限、兴致勃勃时，你都会不由自主地产生爱、喜悦、感激、宁静、兴趣和激励这样的积极情绪，它们会打开你的心扉。

然而，无论是迷恋、欢笑还是爱，你由衷的积极情绪总是无法持续很长的时间。

良好的感觉来了又去，就如同好天气一样，这是人类的本性。

积极情绪会逐渐消退，如果它长盛不衰，人们会很难适应变化，无法觉察到好消息和坏消息之间的差异，或是邀请与冒犯之间的差异。

如果你想重塑生活，让它变得更美好，秘诀就是不要把积极情绪抓得太紧，也不要抗拒它稍纵即逝的本性，而是将它更多地植入生活——久而久之，你就会提高积极情绪的分量。

我们发现，在这一秘诀中最重要的是积极率，这是用来描述积极情绪与消极情绪的数量关系的一种方法。

2024-2025学年第一学期第16中学九上10月月考一、语法选择(共15小题，每小题1分，满分15分)When something goes wrong, what would you say? It can be very ____1____to say, “I know I am late, but it is not my fault. The car broke down.” It is probably not your fault, ___2_____ once you form the habit of blaming somebody or something else for a bad situation, you are a loser. You have no power and could do ____3____that helps change the situation. However, you can have great power over what happens to you if you stop ____4____ on whom to blame. Focus on how to make the situation____5____ than before. This is the winner’s key ____6____ success.Winners are great at solving problems. For example, if you were late because your car broke down, maybe your car should _____7___more often. Or you may start to take along with you the useful phone numbers, so you ____8____ call for help when you’re in need. For ___9_____ example, if your workmate is lack of responsibility or ability, find ways of dealing with his fault rather than _____10___blame the person. You should accept the fact and find creative ways ____11____successfully, paying no attention to ____12____ your workmate failed to do his job well.Being concentrated is a winner’s second key. For example, when I feel___13_____, it_____14___ a lot to repeat words such as “calm” “peace” or “focus”, either out loud or silently in my mind. It makes me feel more in control and increase my confidence. This habit can become second nature quite easily and is ____15____ powerful psychological tool.1. A. sastifying B. satisfied C. satisfy D. satisfaction2. A. and B. but C. so D. though3. A. everything B. something C. anything D. nothing4. A. focus B. focusing C. focused D. to focus5. A. good B. well C. better D. best6. A. to B. of C. by D. with7. A. check B. checked C. to check D. be checked8. A. should B. might C. can D. must9. A. other B. the other C. others D. another10. A. simple B. simply C. simplify D. sample11. A. to work B. working C. of work D. work12. A. how B. what C. which D. if13. A. nerve B. nervous C. nervously D. nervousness14. A. help B. will help C. helped D. would help15. A. / B. an C. the D. a二、完形填空(共10小题，每小题1分，满分10分)Late that night, we started our final part of the climb. Nervously we carried on after a short rest. Everyone looked ___16___. Outside of the tent it was totally black. It was just after __17____. Snow was falling. It was freezing.The group climbed silently through deep snow. I could not think. The height of the mountain was playing tricks on my __18____. I tried to keep concentrated(集中思想) by watching my feet and counting to ten ___19___.People around me were just standing still as they tried to get their breath. I tried to encourage them to keep walking. My friend looked at me ___20___. He was really tired. He kept trying to lie down and go to sleep. If he did, he would freeze to death. I told him to keep moving. He climbed on. When I checked my __21____, I saw, with surprise, that I'd been walking for three hours already. I felt as if I was fighting every step of the way. All I wanted to do was turn round and go down—but I must reach the top!I began to wonder if I was not strong enough. I was losing my mind. My breathing was very rapid. Each ___22_____ I took made me more and more dizzy(晕眩的). Someone told me we had another hour and a half to go.I forced myself to __23____. I had to concentrate really hard, because one careless step could make me ___24___.Then I saw Gilman's Peak up ahead of me. Someone at the top was telling me to make one last effort. The sun was beginning to __25____ above the clouds. I climbed up the last few meters and suddenly I realized I'd done it! I was there! I was at the top of Africa!16. A. bored B. surprised C. angry D. scared17. A. noon B. dinner C. midnight D. lunchtime18. A. legs B. ears C. mind D. nose19. A. all the time B. ever since C. so far D. day and night20. A. meaninglessly B. helplessly C. uselessly D. carelessly21. A. backpack B. shoes C. tent D. watch22. A. chance B. rest C. step D. trip23. A. walk on B. work on C. put on D. turn on24. A. succeed B. sleep C. die D. lose25. A. lose B. rise C. set D. hide三、阅读第一节阅读理解(共15小题，每小题2分，满分30分)AI took up baking when I was twelve. At that time I was working on my school bakery project with my classmates. I tried a few times, but I wasn’t very successful. My parents advised I learn from my grandmother, who later gave me her recipe and instruction as well. After two years’ practice, I was able to make delicious bread. I have come to realize making bread means a lot to me although it takes a long time.To make bread, others usually use quick-rise yeast (酵母), but I don’t. Every Saturday morning, after mixing proper amount of water with flour, sugar etc, I take time to wait for the dough to rise. This is my way to slow down and smell the roses.Baking does require great patience. In my hands, the dough is slowly growing. It’s becoming softer. I can feel the change, which connects me to something quite different from the modern way of living. To me, making bread is a push against our culture of convenience. It certainly takes more time than buying bread from a store, but I enjoy it.I’ve stuck with my grandmother’s recipe without making any change. Now this tradition has continued for years. Sometimes, in order to fit it in, I have to change my schedule. But I have never considered giving it up.By the time my children get home from school, the bread has been baked and cooled. They step into the house and the first thing they do is to take a deep breath of the warm, honeyed air. My bread-baking has also helped them to slow down and understand the value of taking their time and leading an unhurried life.26. How is the writer’s bread-making different from others’?A. She uses less water.B. She uses more sugar.C. She doesn’t bake it a long time.D. She doesn’t add quick-rise yeast.27.Which word best describes life in modern times according to the writer?A. Relaxing.B. Exciting.C. Fast.D. Happy.28.What does the underlined “it” in paragraph 4 refer to?A. The recipe.B. The plan.C. The change.D. The tradition.29. What does the writer want to teach her children to do?A. Do things in a slow way.B. Bake bread at an early age.C. Be thankful for parents’ work.D. Get home from school in time.B①Driving coaches might soon be joining the list of jobs that are replaced by robots in the near future. A company in China has developed an Al-powered driving coach called Robo Coach, andit's already been used in driving schools.②Robo Coach is not a human-like robot that sits next to you and talks about your driving skills. This robot, developed by Beijing Yi Jia Jia Technology, is actually a teaching and safety control system.③Another difference between Robo Coach and human ones is even more amusing. Robo Coach will call you "mommy" or "daddy” .④Besides voice, the system uses a dashboard（仪表板）screen and a smart rear-view mirror （后视镜）to communicate with the learner. Robo Coach uses sensors(传感器）to stop if the car runs into something or increase speed suddenly for no reason, similar to how self-driving cars work.⑤Robo Coach has more than 40 sensors on the car to notice people, other cars and roads. ___▲___ And to make faster decision making, the car is also provided with radar systems.⑥The system doesn't just keep new drivers from meeting accidents. It also collects information on the learner's driving behavior and even body position. It carefully studies their driving habits in real time to see if the learner is too traditional or easy to be angry during practice and then changes its teaching style. By recording all the problems a learner runs into during lessons, the system can help the new driver correct past mistakes and prevent new ones.⑦Robo Coach is now being used in five driver training centers owned by Yi Jia Jia’s parent company as well as other diving schools across China.30. Which sentence can be put in ▲in Paragraph 5?A. It can correct your mistakes any time.B. It studies learners’ driving habits and records them.C. It can stop immediately if learners meet any danger.D. It communicates with learners and helps make decision.31. What can we learn about Robo Coach according to the passage?A. It will sit next to you to correct your driving skills.B. It will replace human driving coaches very soon.C. It can help learners improve their driving skills safely.D. It is one of the self-driving cars with more than 40 sensors.32. What’s the purpose of the passage?A. To warn us that AI coaches will replace human’s place in the future.B. To show us that AI coaches are used in some driving schools in China.C. To tell us that many people are worried about the safety of AI coaches.D. To advise us that everyone can trust AI coaches to improve our driving skills.33. Which shows the best structure of the passage?A. ①/②③④/⑤⑥⑦B. ①/②③/④⑤⑥/⑦C. ①/②/③④⑤/⑥⑦D. ①/②③④/⑤⑥/⑦CNowadays many people go camping for fun. Camping can be enjoyed in thebackyard or deep in the wilderness. Whether camping for one night or severalweeks, being prepared is the key.Endless funOnce the tent, your base, is put up and the fire area is prepared, there is lots to do. Fishing and hiking are just some of the fun activities. At night, campers often sit by the fire, talking and telling stories. If the weather turns rainy, campers usually wait it out in their tents, reading, drawing or playing games.R equired equipmentShelter, bedclothes, food and water are necessary. Deciding what else you will need depends on the kind of camping trip you are planning and the length of your trip. Pack light if you are going to carry equipment any distance. Clothing should be prepared enough to protect against weather and insects. A hat, whistle, bug repellent(驱虫剂) and rope may come in handy. Don’t forget a flashlight, a compass, cookers and a first-aid box.V arious tentsThere are many types and styles of tents. You should choose your tent based on your needs. If you are camping alone in the backyard, a simple lean-to or small tent may do. If you are camping with your family, a larger cabin tent or camping trailer may be best.Proper locationsWhere you decide to set up your campsite is very important. Look for a high and dry location if it rains. The ground should be level because hills and rocks are uncomfortable to sleep on. A sunny exposure(接触) in the morning with shade in the afternoon is ideal.Green campingWherever you camp, it is important to respect the environment around you. If you are in a park, make sure to follow its rules. Put your garbage and waste in rubbish bins. If you are in the wilderness, keep noise to a minimum and do not disturb the plants or animals.34. Before campers take up some fun activities, they should .A. go fishing and hikingB. chat around the fireC. set up their baseD. wait for the rain35. According to the passage, which item is essential for camping?A. A skirt.B. A blanket.C. A hat.D. A rope.36. If the camper faces a strong wind, which kind of tent might be the best choice?A. Lean-to tents.B. Pup tents.C. Alpine tents.D. Dome tents.37. The underlined word “level” probably means “ ”.A. roughB. steepC. highD. flatDAlong the history of human society, it seems that there isn't a civilization without toys, but when and how they developed is unknown.They probably came about just to give children something to do.In ancient times, just like today, most boys played with some kinds of toys and most girls with another.In societies where social roles are strictly divided，boys copy the behavior of their fathers and girls copy the behavior of their mothers.This is true because boys and girls are preparing to step into the roles and responsibilities of the adult world even in the game.Surprisingly, from the history of toys, small changes have taken place over the centuries.The changes have been mostly about workmanship, mechanics and technology.It is amazing that toys are similar in the development of all parts of the world.What's more, toys used to be similar to what they are now.Among people in Egypt, the Americas, China, Japan and the Arctic, generally the same kinds of toys appeared.Changes depended on local customs and ways of life because toys show the real world around the people.Nearly every civilization had dolls，little weapons，toy soldiers，tiny animals and vehicles.Since toys can often be regarded as an art form, they have not been influenced by technological progress.The development from wheels to carriage to automobiles is a straight line.If we compare a rattle（拨浪鼓）used by a baby today to the one used in 3000 BC, we will find it does not appear to be more creative. Every rattle is a product of the artistic taste of the time and is limited by materials.38. Why are the toys for boys and girls different？A.Their fathers and mothers are different.B.Most of the boys are more active than girls.C.Their mothers are more powerful than their fathers.D. The future adult society requires men and women differently.39. Which of the following is TRUE according to the author's opinion？A.Not every civilization has toys in human history.B.Similar kinds of toys appears in almost all civilization.C.Toys have changed a lot during the long history.D. People from different countries have totally different kinds of toys.40. In the next part of the article, the writer may .A.talk about some popular toys in ChinaB.tell us what kinds of toys the boys likeC.show more about the history of the toys' developmentD. give another example to show toys are works of art第二节阅读填空（共5小题，每小题1分，共5分）When you’re dealing with a stressful situation or experiencing a hard time, people in your life can help you. When someone who cares knows what you’re going through, it helps you feel understood and not so alone.___41___.Problems seem smaller when you talk about them with the right person. You can do better and find out solutions more easily when you share your problems.There are lots of different ways to get and give help.___42___. Sometimes you just need advice on things. Help can be very easy, like a homework project, or it can go on for a while, like teaching to bring up a failing grade or advising to get through a difficult personal situation.It’s likely that you remember times someone helped you.___43___. Friends helped you get through sadness or deal with disappointment. Teachers might have guided you through the college application process.___44___. You might give a hand to your classmate who met difficulty.Friends, parents, teachers and other adults can be great resources when you need help. There are also times when you need the extra help that a professional can provide best. Doctors can offer specialized help for a health problem.___45___.A. Parents taught you to stop a bad habit.B. Sometimes you just want to hear an encouraging word.C. Turn to the professional people for help when you need.D. And you can also remember times when you helped othersE. Having a right person means a lot.笔试部分（满分30分）四、写作（满分30分）第一节语篇填词（共5小题，每小题1分，共5分）Around 500 years ago, there were many wise men around the world. They worked all their lives to find out the secrets of nature. At that time Galileo Galilei was one of the most f___46_____ astronomers and he discovered many things.In 1609, Galileo heard about a new invention called the telescope, and he decided to build one to look at the universe. When he looked at the Moon, he found mountains and craters（坑）. People at that time s____47____the Moon was a round ball, and they had no idea there are mountains on it.Galileo also discovered that everything falls at the same speed. This was another a____48____of his. He dropped two round metal balls off the Leaning Tower of Pisa in front of a large audience. One ball was very h__49______, and the other was light. Both balls hit the ground at e__50______the same time.第二节完成句子(共5小题，每小题2分，共10分)51. 他因为盗窃被送进了监狱。

五年级月考语文试卷一、基础知识（35分）1. 看拼音，写词语。

（10分）fēn fù（） lǎn duò（） qīn lüè（） dīng zhǔ（）huīhuáng（）líng lóng（） yǐn bì（）chóu xiè（） shāng yì（） jīn bì huīhuáng（）2. 给下列加点字选择正确的读音，打“√”。

（6分）间隔（jiàn jiān）强逼（qiáng qiǎng）划归（h uá huà）冠军（guàn guān）便宜（pián biàn）削弱（xuē xiāo）3. 把下列词语补充完整，并选择合适的词语填空。

（9分）（）（）忘形（）（）有味（）（）多端。

（）（）不迫（）（）归赵（）（）请罪。

他看书看得（），连妈妈叫他吃饭都没听见。

敌人（），我们要小心应对。

蔺相如见了廉颇就（），最终两人成为了好朋友。

4. 按要求写句子。

（10分）海力布对龙王说：“如果您真想给我点儿东西作纪念，请把您嘴里含着的那颗宝石送给我吧。

”（改为转述句）他想哥哥嫂子既然这样对待他，他又何必恋恋不舍呢？（改为陈述句）圆明园的毁灭是中国文化史上不可估量的损失。

（缩句）牛那么勤勤恳恳地干活，不好好照看它，怎么对得起它呢？（改为陈述句）用“一面……一面……”写一句话。

二、阅读理解（30分）（一）课内阅读。

（15分）过了几年，秦王约赵王在渑池会见。

赵王和大臣们商议说：“去吧，怕有危险；不去吧，又显得太胆怯。

”蔺相如认为对秦王不能示弱，还是去的好，赵王才决定动身，让蔺相如随行。

大将军廉颇带着军队送他们到边界上，做好了抵御秦兵的准备。

赵王到了渑池，会见了秦王。

秦王要赵王鼓瑟。

赵王不好推辞，鼓了了一段。

秦王就叫人记录下来，说在渑池会上，赵王为秦王鼓瑟。

一、选择题（每题2分，共20分）1. 下列词语中，字形、字音完全正确的是（）A. 质疑、耸人听闻、情不自禁B. 谨慎、驰骋、熏陶C. 奔跑、激动、喧哗D. 畅快、堵塞、恳求2. 下列句子中，成语使用不恰当的是（）A. 这篇文章语言生动，富有感染力。

B. 她的演技真是出神入化，让人叹为观止。

C. 他勤奋好学，成绩一直名列前茅。

D. 这场雨下得真是倾盆大雨。

3. 下列句子中，语病最多的是（）A. 他的成绩提高了，得益于老师的辛勤教导。

B. 通过这次比赛，我明白了团结就是力量。

C. 我非常喜欢阅读，尤其是科幻小说。

D. 为了实现中国梦，我们要努力学习，不断提高自己。

4. 下列词语中，不属于近义词的是（）A. 高兴、愉快、喜悦B. 美丽、漂亮、秀丽C. 快乐、欢快、欢乐D. 努力学习、勤奋、刻苦5. 下列句子中，句式转换错误的是（）A. 原句：这所学校的学生都很优秀。

改写后：这所学校的学生优秀。

B. 原句：他每天都很努力学习。

改写后：他每天都很勤奋。

C. 原句：我们要爱护环境，保护地球。

改写后：爱护环境，保护地球，我们要。

D. 原句：他认真学习，成绩不断提高。

改写后：他成绩不断提高，认真学习。

二、填空题（每题2分，共20分）6. 《庐山谣》中，“飞流直下三千尺，疑是银河落九天”一句，描绘了庐山的壮丽景色。

7. 《出塞》中，“秦时明月汉时关，万里长征人未还”一句，表达了诗人对边疆将士的敬意。

8. 《离骚》中，“路漫漫其修远兮，吾将上下而求索”一句，展现了诗人对理想的执着追求。

9. 《将进酒》中，“君不见黄河之水天上来，奔流到海不复回”一句，描绘了黄河的壮阔景象。

10. 《滕王阁序》中，“落霞与孤鹜齐飞，秋水共长天一色”一句，展现了滕王阁的壮丽景色。

三、阅读题（每题10分，共30分）11. 阅读下面这首诗，回答问题。

《江雪》千山鸟飞绝，万径人踪灭。

孤舟蓑笠翁，独钓寒江雪。

（1）这首诗描绘了一幅怎样的画面？（5分）（2）这首诗表达了诗人怎样的情感？（5分）12. 阅读下面这篇文章，回答问题。

山东省滕州市第一中学2024-2025学年高一上学期10月月考数学试卷一、单选题1．设集合{}0123,,,A =，{},,101,23,B =-，则R ()A B =I ð（ ） A ．∅B ． {}1,2C ．{}1-D ．{}1,2,32．设集合{}260M x x x =+-=，{}N 16N x x =∈<<，则M N =I （ ）A ．{}12x x <<B ．{}3C ．{}36x x -<<D ．{}23．“1a a<”是“1a <-”的（ ） A ．充分不必要条件 B ．必要不充分条件 C ．充要条件D ．既不充分也不必要条件4．若正数x ，y 满足44x y +=，则11x y+的最小值为（ ）A ．2B ．94C ．3D ．835．下列四组函数中，不是同一个函数的一组是（ ）A ．()f x x =与()g x =B ．()21f x x =+与()21g t t =+C ．()xf x x =与()1,01,0x g x x >⎧=⎨-<⎩D ．()2f x =与()g x =6．已知函数()f x 的定义域为[)0,+∞，则函数()25f x y x -=-的定义域为（ ）A ．()()2,55,-+∞UB ．[)()2,55,-+∞UC ．()()2,55,⋃+∞D ．[)()2,55,+∞U7．下列命题中真命题的个数是（ ）①函数()1f x =和()0g x x =是同一个函数；②“()2210a b +-=”是“()10a b -=”的必要条件；③集合{|A y y ==，{|B x y ==表示同一集合.A ．0B ．1C ．2D ．38．若a b >，且2ab =，则22(1)(1)a b a b-++-的最小值为（ ）A ．2B ．4C ．4D ．2二、多选题9．下列四个结论中正确的是（ ） A ．22,,4250x y x y x y ∃∈+-++=RB ．命题“2,3210x x x ∀∈--<R ”的否定是“2000,3210x x x ∃∈-->R ” C ．21,4x x x ∀∈+>R D ．“a b >”是“1a b >+”的必要不充分条件10．已知非零实数,a b >，下列结论中错误的结论有（ ）A ．11a b< B ．22a b > C ．22ab a b > D ．2211ab a b> 11．已知关于x 一元二次不等式220ax ax b -+>的解集为{}A x m x n =<<（其中m n <），关于x 一元二次不等式222ax ax b -+>-的解集为{}B x p x q =<<，则（ ）A ．AB B =I B ．()A B B ⋃⊆C ．m n p q +=+D ．当2b <-时，2q p q+的最小值为3三、填空题12．已知集合{}221,,0A a a =-，{}1,5,9B a a =--，若满足{}9A B ⋂=，则实数a 的值为．13．已知关于x 的不等式210mx mx -+≤，若此不等式的解集为∅，则实数m 的取值范围是 14．已知关于x 的不等式组()224502525x x x x x k ⎧-++<⎪⎨+<-+⎪⎩的解集中存在整数解且只有一个整数解，则k 的取值范围为.四、解答题15．设集合{}{}|121,|25A x a x a B x x =+<<-=-<<. (1)若3a =，求()R A B ⋃ð；(2)是否存在实数a ，使得A B A =U ，若存在，求实数a 的取值范围，否则说明理由. 16．设m ∈R ，已知集合3211x A xx +⎧⎫=<⎨⎬-⎩⎭，(){}2220B x x m x m =+--<. (1)当1m =时，求A B U ；(2)若“x B ∈”是“x A ∈”的必要不充分条件，求m 的取值范围.17．中国建设新的芯片工厂的速度处于世界前列，这是朝着提高半导体自给率目标迈出的重要一步.根据国际半导体产业协会(SEMI)的数据，在截至2024年的4年里，中国计划建设31家大型半导体工厂.某公司打算在2023年度建设某型芯片的生产线，建设该生产线的成本为300万元，若该型芯片生产线在2024年产出x 万枚芯片，还需要投入物料及人工等成本()V x （单位：万元），已知当05x <≤时，()125V x =；当520x <≤时，()240100V x x x =+-；当20x >时，()160081600V x x x=+-，已知生产的该型芯片都能以每枚80元的价格售出. (1)已知2024年该型芯片生产线的利润为()P x （单位：万元），试求出()P x 的函数解析式. (2)请你为该型芯片的生产线的产量做一个计划，使得2024年该型芯片的生产线所获利润最大，并预测最大利润.18．已知函数()f x 对任意x 满足：()()324f x f x x --=，二次函数()g x 满足：()()24g x g x x +-=且()14g =-.(1)求()f x ，()g x 的解析式；(2)若R a ∈，解关于x 的不等式()()()()2143a x a x g x f x +-+->-.19．对于函数()f x ，若()f x x =，则称实数x 为()f x 的“不动点”，若()()f f x x =，则称实数x 为()f x 的“稳定点”，函数()f x 的“不动点”和“稳定点”组成的集合分别记为A 和B ，即(){}A x f x x ==，()(){}B x f f x x ==.(1)对于函数()21f x x =-，分别求出集合A 和B ； (2)对于所有的函数()f x ，证明：A B ⊆；(3)设()2f x x ax b =++，若{}1,3A =-，求集合B .。

雅礼中学2025届高三月考试卷（三）思想政治本试题卷分为选择题和非选择题两部分，共8页。

时量75分钟，满分100分。

第Ⅰ卷选择题（共48分）一、选择题（本大题共16小题，每小题3分，共48分。

每小题只有一项符合题目要求）1．研读经典，致敬伟人。

对下列两则原文相同点的解读，科学的是（）1847年，马克思在《哲学的贫困》中指出：“当文明一开始的时候，生产就开始建立在级别、等级和阶级的对抗上，最后建立在积累的劳动和直接的劳动的对抗上。

没有对抗就没有进步。

这是文明直到今天所遵循的规律。

”1848年，马克思、恩格斯在《共产党宣言》中指出：“资产阶级赖以形成的生产资料和交换手段，是在封建社会里造成的。

在这些生产资料和交换手段发展的一定阶段上……封建的所有制关系，就不再适应已经发展的生产力了……起而代之的是自由竞争以及与自由竞争相适应的社会制度和政治制度、资产阶级的经济统治和政治统治。

”①两者都依据社会基本矛盾运动规律阐释社会形态的更替问题②前者揭示社会形态更替的条件性，后者揭示其更替的必然性③依据两者都能推断资本主义终将被社会主义取代的必然趋势④两者都揭示了人类社会的发展历史就是一部阶级斗争的历史A．①③B．①④C．②③D．②④2．习近平总书记提出：“我们的教育要善于从五千年中华传统文化中汲取优秀的东西，同时也不摒弃西方文明成果，真正把青少年培养成为拥有‘四个自信’的孩子。

”关于“四个自信”，下列说法正确的是（）①中国特色社会主义道路是实现社会主义现代化、创造美好生活的必由之路②中国特色社会主义理论体系科学回答了建设社会主义的一系列的基本问题③中国特色社会主义制度是党和人民在长期实践探索中形成的科学制度体系④中国特色社会主义文化是激励全党全国各族人民奋勇前进的强大物质力量A．①②B．①③C．②④D．③④3．中国特色社会主义开创于改革开放时期，但了解其形成和发展的脉络，认识其历史必然性和科学真理性，应该拉长时间尺度，了解社会主义演进的历程。