N1华理模考测试题

考研数学（数学一）模拟试卷480(题后含答案及解析) 题型有：1. 选择题 2. 填空题 3. 解答题选择题下列每题给出的四个选项中，只有一个选项符合题目要求。

1．已知当χ→0时，f(χ)＝arcsinχ－arctanaχ与g(χ)＝bχ[χ－ln(1＋χ)]是等价无穷小，则( )A．a＝b＝1。

B．a＝1，b＝2。

C．a＝2，b＝1。

D．a＝b≠1。

正确答案：A解析：根据等价无穷小的定义，那么1－a＝0，，则有a＝1，b＝1。

故选A。

2．设函数f(χ)在[0，1]上连续，且＝1。

f(χ)＝bnsinπχ，χ∈R，其中bn＝2∫01f(χ)sinnπχdχ，n＝1，2，3…，测＝( )A．0B．1C．－1D．正确答案：C解析：因为＝1，所以可得f(χ)＝1，又因为函数连续，则题目中把f(χ)展开为正弦级数，可知f(χ)为奇函数，可将函数f(χ)奇延拓，得到T＝2，3．设f(χ)是连续且单调递增的奇函数，设F(χ)＝∫0χ(2u－χ)f(χ－u)du，则F(χ)是( )A．单调递增的奇函数B．单调递减的奇函数C．单调递增的偶函数D．单调递减的偶函数正确答案：B解析：令χ－u＝t，则F(χ)＝∫0χ(χ－2t)f(t)dt，F(－χ)＝∫0－χ(－χ－2t)f(t)dt，令t＝－u，F(－χ)＝∫0χ(－χ＋2u)f(－u)du＝∫0χ(χ－2u)f(－u)du。

因为f(χ)是奇函数，f(χ)＝－f(－χ)，F(－χ)＝∫0χ(χ－2u)f(u)du，则有F(χ)＝－F(－χ)为奇函数。

F′(χ)＝∫0χf(t)dt －χf(χ)，由积分中值定理可得∫0χf(t)dt＝f(ξ)χ，ξ介于0到χ之间，F′(χ)＝f(ξ)χ－χf(χ)＝[f(ξ)－f(χ)]χ，因为f(χ)单调递增，当χ＞0时，ξ∈[0，χ]，f(ξ)－f(χ)＜0，所以F′(χ)＜0，F(χ)单调递减；当χ＜0时，ξ∈[χ，0]，f(ξ)－f(χ)＞0，所以F′(χ)＜0，F(χ)单调递减。

江苏省2024届高考考前综合模拟卷（一）物理高频考点试题一、单选题 (共7题)第(1)题新能源汽车的发展是为了减少对传统燃料的依赖，减少环境污染和减少温室气体的排放。

如图所示为我国比亚迪一型号汽车某次测试行驶时的加速度和车速倒数的关系图像。

若汽车质量为，它由静止开始沿平直公路行驶，且行驶中阻力恒定，最大车速为，下列说法正确的是（ ）A．汽车匀加速所需时间为B．汽车牵引力的额定功率为C．汽车在车速为时，功率为D．汽车所受阻力为第(2)题如图所示，光滑水平面上的正方形导线框，以某一初速度进入竖直向下的匀强磁场并最终完全穿出。

线框的边长小于磁场宽度。

下列说法正确的是（）A．线框进磁场的过程中电流方向为顺时针方向B．线框出磁场的过程中做匀减速直线运动C．线框在进和出的两过程中产生的焦耳热相等D．线框在进和出的两过程中通过导线横截面的电荷量相等第(3)题如图所示，两个带等量正电的点电荷位于M、N两点上，E、F是MN连线中垂线上的两点，O为EF、MN的交点，EO=OF。

一不计重力带负电的点电荷在E点由静止释放后（）A．做匀加速直线运动B．在O点所受静电力最大C．由E到O的时间等于由O到F的时间D．由E到F的过程中电势能先增大后减小第(4)题下列说法错误的是（ ）A．利用电容传感器可制成麦克风B．物体受合外力越大，则动量变化越快C．利用红外传感器可制成商场的自动门D．牛顿运动定律不适用，则动量守恒定律也不适用第(5)题为观察光的传播现象，一同学用半圆柱形玻璃砖进行实验，其横截面如图所示，此时底面与右侧竖直光屏平行。

一束白光从玻璃砖左侧垂直于射到圆心上，在光屏上点出现白色亮斑，使玻璃砖底面绕逆时针缓慢旋转，观察到屏上的白色亮斑在偏离点的同时变成下紫、上红的彩色光斑。

随着角缓慢变大，下列说法正确的是（ ）A．折射光斑在竖直屏上向上移动B．红光在玻璃砖中传播速度最大C．彩色光斑沿光屏向上移动，紫光最先消失D．彩色光斑沿光屏向下移动，红光最先消失第(6)题2023年9月17日，我国在西昌卫星发射中心使用“长征二号”丁运载火箭，成功将“遥感三十九号”卫星发射升空。

机密★启用前（新教材卷）华大新高考联盟2024届高三11月教学质量测评数学本试题卷共4页，共22题.满分150，考试时间120分钟★祝考试顺利★注意事项：1.答题前，考生务必将自己的学校､班级､姓名､准考证号填写在答题卷指定位置，认真核对与准考证号条形码上的信息是否一致，并将准考证号条形码粘贴在答题卷上的指定位置.2.选择题的作答：选出答案后，用2B 铅笔把答题卷上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其他答案标号.答在试题卷上无效.3.非选择题的作答；用黑色墨水的签字笔直接答在答题卷上的每题所对应的答题区域内.答在试题卷上或答题卷指定区域外无效.4.考试结束，监考人员将答题卷收回，考生自己保管好试题卷，评讲时带来.一､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.1.2i212i -+=+（ ）2.计算机在进行数的计算处理时，使用的是二进制.一个十进制数()*n n ∈N可以表示成二进制数()0122,k a a a a k ∈N ，即1001222k k k n a a a -=⋅+⋅++⋅ ，其中01a =，当1k …时，{}0,1k a ∈.若记012,,,,k a a a a 中1的个数为()f n ，则满足8k =且()4f n =的n 的个数为（ ）A.35B.28C.70D.563.已知双曲线22:14x y C m-=的焦距为6，则双曲线C 的焦点到渐近线的距离为（ ）A.2D.4.已知向量()(),2,3,1a b λ== ，若a 与b λ的值为（ ）A.83 B.43C.35.若函数()2e 4e 5xx f x =-+在(),m ∞+上单调递增，则实数m 的取值范围为（ ）A.()ln2,∞+B.[)ln2,∞+C.()2e ,∞+D.)2e ,∞⎡+⎣6.已知曲线32:3C y x x =-的图象是中心对称图形，其在点A 处的切线l 与直线90x y +=相互垂直，则点A 到曲线C 的对称中心的距离为（ ）A.B.C.D.7.已知()1tan 1tan tan 6,sin cos 3cos sin 22tan 2αβαβαβαβαβαβ⎛⎫⎪--⎡⎤-+-==⎪⎢⎥-⎣⎦ ⎪⎝⎭，则sin cos αβ=（ ）A.12 B.16 C.13- D.238.已知函数()22,4,1632113,4,xx f x x x x ⎧⎪=⎨⎪-+>⎩…则对于任意正数λ，下列说法一定正确的是（ ）A.()()ln 1f f λλ-…B.()()ln 1f fλλ-…C.()()22f f λλ…D.()()22f f λλ…二､多选题：本题共4小题，每小题5分，共20分.在每小题给出的选项中，有多项符合题目要求.全部选对的得5分，部分选对的得2分，有选错的得0分.9.已知集合20,{15}3x M xN x x x -⎧⎫=<=-<<⎨⎬+⎩⎭∣∣，则下列说法正确的是（ ）A.{12}M N xx ⋂=-<<∣B.{3R M x x =<-∣ð或2}x >C.{35}M N xx ⋃=-<<∣D.(){}31R M N xx ⋂=-<<-∣ð10.已知在正方体1111ABCD A B C D -中，点E 是线段1A D 的中点，则下列说法错误的是（ ）A.直线EB 与直线1B C 所成的角为60B.直线EB 与直线11C D 异面C.点E ∉平面1ABCD.直线EB ∥平面11B D C11.已知圆C 过点()()()4,2,2,0,6,0，点M 在线段()04y x x =……上，过点M 作圆C 的两条切线，切点分别为,A B ，以AB 为直径作圆C '，则下列说法正确的是（ ）A.圆C 的方程为22(4)2x y -+=，B.四边形ACBM 面积的最小值为4C.圆C '的面积的最小值为πD.圆C '的面积的最大值为3π12.已知椭圆2222:1(0)x y C a b a b+=>>的右焦点为()()1111,,,,F M x y N x y --在椭圆C 上但不在坐标轴上，若2,2FM FA FN FB ==，且OA OB ⊥，则椭圆C 的离心率的值可以是（ ）A.12D.910三､填空题：本题共4小题，每小题5分，共20分.13.某公司定期对流水线上的产品进行质量检测，以此来判定产品是否合格可用，已知某批产品的质量指标X 服从正态分布()15,9N ，其中[]6,18X ∈的产品为“可用产品”，则在这批产品中任取1件，抽到“可用产品”的概率约为__________.参考数据：若()2,X Nμσ~，则()()()0.6827,220.9545,330.9973P X P X P X μσμσμσμσμσμσ-+≈-+≈-+≈……………….14.已知某圆台的上､下底面积分别为4,36ππ，母线长为5，则该圆台的体积为__________.15.已知函数()sin cos (0)f x x x ωωω=+>的图象在0,3π⎛⎫⎪⎝⎭上有且仅有3条对称轴，则实数ω的取值范围为__________.16.已知数列{}n a 满足：当n 为奇数时，n a =，其中()()57350λλ--<，且21243n i i i n n a ==+∑，则当n a 取得最小值时，n =__________.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.17.（10分）已知在ABC 中，角,,A B C 所对的边分别为,,a b c ，且,22cos 1cC a B π==+.（1）求B 的值；（2）已知点M 在线段AB 上，且3ABAM=，求cos2BCM ∠的值.18.（12分）近年来，中学生的体质健康情况成了网络上的一个热门话题，各地教育部门也采取了相关的措施，旨在提升中学生的体质健康，其中一项便是增加中学生一天中的体育活动时间，某地区中学生的日均体育活动时间均落在区间[40,90]内，为了了解该地区中学生的日均体育活动时间，研究人员随机抽取了若干名中学生进行调查，所得数据统计如下图所示.（1）求a （2）现按比例进行分层抽样，从日均体育活动时间在[70,80)和[80,90]的中学生中抽取12人，再从这12人中随机抽取3人，求至多有1人体育活动时间超过80min 的概率；（3）以频率估计概率，若在该地区所有中学生中随机抽取4人，记日均体育活动时间在[60,80]的人数为X ，求X 的分布列以及数学期望.19.（12分）如图所示，在四棱锥S ABCD -中，90,ADC BCD SA SD SB ∠∠==== ，点E 为线段AD 的中点，且22AD SE BC CD ===.（1）求证：SE AC ⊥；（2）已知点F 为线段SE 的中点，点G 在线段BC 上（不含端点位置），若直线FG 与平面SAB 所成的角求BG BC 的值.20.（12分）已知数列{}n a 的前n 项和为n S ，其中32,14n n S a S λ=+=.（1）求数列{}n a 的通项公式；（2）若()310n n b n a =-⋅，求数列{}n b 的前n 项和为n T .21.（12分）已知抛物线2:4C y x =的焦点为F ，直线1l 过点F 且与抛物线C 交于,M N 两点，直线2l 过点F 且与抛物线C 交于,P Q 两点.（1）若点()3,0A ，且AMN的面积为1l 的斜率；（2）若点,M Q 在第一象限，直线MP 过点(),0λ，比较14MPF NQF S S + 与λ的大小关系.并说明理由.22.（12分）已知函数()ln m f x x mx x=++.（1）讨论函数()f x 的单调性；（2）已知*k ∈N ，若(),0,a b ∞∀∈+，当a b >()()m mma f b f a mb a b+++<++恒成立，求k 的最大值.华大新高考联盟2024届高三11月教学质量测评数学参考答案和评分标准一､选择题1.【答案】B【命题意图】本题考查复数的四则运算､复数的概念，考查数学运算､逻辑推理的核心素养.【解析】依题意，()()()()2i 12i 2i 222i 12i 12i 12i ---+=+=-++-，故2i212i -+=+，故选B.2.【答案】D【命题意图】本题考查排列组合､数学情境问题，考查数学运算､逻辑推理､数学建模的核心素养.【解析】因为01a =，故在128,,,a a a 中只需有3个1即可，故所求个数为38C 56=，故选D.3.【答案】B【命题意图】本题考查双曲线的方程与性质，考查数学运算､直观想象的核心素养.【解析】依题意，49m +=，则5m =，故C20y ±=，故所求距离为d ，故选B.4.【答案】A【命题意图】本题考查平面向量的坐标运算､平面向量的数量积，考查数学运算､逻辑推理的核心素养.【解析】依题意，cos ,||||a b a b a b ⋅===，解得83λ=，故选A.5.【答案】B【命题意图】本题考查复合函数､函数的单调性，考查数学运算､逻辑推理､直观想象的核心素养.【解析】令e 0x t =>，则原函数化为245y t t =-+，其在()2,∞+上单调递增，故()f x 在()ln2,∞+上单调递增，则ln2m …，故选B.6.【答案】D【命题意图】本题考查导数的几何意义､两直线的位置关系，考查数学运算､逻辑推理､直观想象的核心素养.【解析】易知直线l 的斜率为9，设切点()00,x y ，而236y x x =-'，故200369x x -=，解得01x =-或03x =，故切点A 坐标为()1,4--或()3,0，故点A 到曲线C的对称中心的距离为=，故选D.7.【答案】A【命题意图】本题考查三角恒等变换，考查数学运算､逻辑推理､数据分析的核心素养.【解析】依题意，()()()cos sin2cos 122tan,1tan tan 2sin 2tansin cos 222αβαβαβαβαβαβαβαβαβαβ------=-=+-----()()()()cos cossin sin122cos cos cos2αβαβαβαβαβαβαβ---+-==---，故()()()2cos 16sin cos αβαβαβ-⋅=--，则()sin αβ-=1sin cos cos sin 3αβαβ-=①，而sin cos 3cos sin αβαβ=②，联立①②，解得1sin cos 2αβ=，故选A .8.【答案】C【命题意图】本题考查分段函数的图象与性质，考查数学运算､逻辑推理､直观想象､数据分析的核心素养.【解析】依题意，()f x 在(],4∞-上单调递增，在()4,16上单调递减，在[)16,∞+上单调递增；易知ln 1λλ-…，取1λ=，可知()()ln 1f f λλ=-，取e λ=，可知()()ln 1f f λλ<-，取2e λ=，可知()()ln 1f f λλ>-，故A ､B 错误；当02λ<…时，242λλ……，故()()22f f λλ…，当24λ<<时，24216λλ<<<，故()()22f f λλ>，当4λ…时，2216λλ>…，故()()22f f λλ…；综上，()()22f f λλ…恒成立，故C 正确，D 错误，故选C.二､多选题9.【答案】AC【命题意图】本题考查不等式的解法､集合的表示､集合的运算，考查数学运算､逻辑推理的核心素养.【解析】依题意，()(){230}{32}M x x x xx =-+<=-<<∣∣，故{12},{3R M N x x M x x ⋂=-<<=-∣∣…ð或()2},{35},{31}R x M N x x M N x x ⋃=-<<⋂=-<-∣∣……ð，故选AC.10.【答案】ABC【命题意图】本题考查空间线面的位置关系，考查数学运算､逻辑推理､直观想象的核心素养.【解析】因为11,BA BD A E ED ==，故1EB A D ⊥，而1B C ∥1A D ，故1EB B C ⊥，故A 错误；直线EB 与直线11C D 均在平面11ABC D 上，故B 错误；平面1ABC 就是平面11ABC D ，故点E ∈平面1ABC ，故C 错误；因为平面11B D C ∥平面1A BD ，且直线EB ⊂平面1A BD ，故直线EB ∥平面11B D C ，故D 正确；故选ABC .11.【答案】BD【命题意图】本题考查圆的方程､直线与圆的位置关系，考查数学运算､逻辑推理､直观想象的核心素养.【解析】依题意，圆C 圆心在直线4x =上，设()4,C c ，则2222(42)(44)(2)c c -+=-+-，解得0c =，圆22:(4)4C x y -+=，故A 错误；四边形ACBM面积S MA AC =⋅=，而min ||MC =min 4S =，故B 正确；结合图象的对称性可知，当M 在线段()04y x x =……的中点时，圆C '的面积最小，为2π，故C 错误；当M 在线段()04y x x =……的两个端点时，圆C '的面积最大，为3π，故D 正确；故选BD.12.【答案】CD【命题意图】本题考查椭圆的方程､椭圆的性质，考查数学运算､逻辑推理､直观想象的核心素养.【解析1】设直线:MN y kx =，其中0k ≠，联立2222,1,y kx x y ab =⎧⎪⎨+=⎪⎩解得x =,M N ⎛⎝，则2c A ⎛+ ⎝，2c B ⎛- ⎝，而OA OB ⊥ ，故222222222222110444c a b k a b b a k b a k -⋅-⋅=++，整理得()22221021e k e -=>-1e <<，观察可知，故选CD.【解析2】依题意，可得11,,22c x y A B -⎛⎫- ⎪⎝⎭，又有OA OB ⊥ ，故0OA OB ⋅= ，即22211044c x y --=，22211x y c +=；又有2211221x y a b +=，即圆222x y c +=与椭圆C 有公共点且公共点不在坐标轴上，故a c b >>，即222c a c >-，故21,2e e ⎫>∈⎪⎪⎭，故选CD.【解析3】依题意，2,2FM FA FN FB ==，故,A B 分别是线段,FM FN 的中点，故OA ∥,FN OB ∥FM ；又有OA OB ⊥，故,0FN FM OM ON ⊥+= ，则OM ON OF c ===；因为(),OM b a ∈，故b c <，即222a c c -<，得21,2e e ⎫>∈⎪⎪⎭，故选CD.三､填空题13.【答案】0.84【命题意图】本题考查正态分布及其应用，考查数学运算､直观想象､数学建模的核心素养.【解析】依题意，()215,3X N ~，故()()0.68270.997361830.842P X P X μσμσ+=-+==………….14.【答案】52π【命题意图】本题考查空间几何体的表面积与体积，考查数学运算､直观想象､数学建模的核心素养.【解析】易知该圆台的上､下底面的半径分别为2，6，故圆台的高为3，则圆台的体积()1436123523V ππππ=⨯++⨯=.15.【答案】2739,44⎛⎫⎪⎝⎭【命题意图】本题考查三角函数的图象与性质，考查数学运算､逻辑推理､直观想象的核心素养.【解析】依题意，()4f x x πω⎛⎫=+ ⎪⎝⎭，令()42x k k ππωπ+=+∈Z ，解得()4k x k ππωω=+∈Z ，则23434πππππωωωω+<+…，解得273944ω<…，故实数ω的取值范围为2739,44⎛⎤⎥⎝⎦.16.【答案】5【命题意图】本题考查数列的性质，考查数学运算､逻辑推理､数据分析的核心素养.【解析】因为21243ni ii n n a ==+∑，故当1n =时，244a =，故21a =，当2n …时，121243(1)(1)n i i i n n a -==-+-∑，则11122244462nn i i i in i i n n a a a -==-==-∑∑，故222313n n a n =>-；而当n 为奇数时，n a =12121n n a n λ--=-，而()()57350λλ--<，故7553λ<<，则()()()()112121212121212121n n nn n n n n a a n n n n λλλλ--+---+-=-=+-+-.令()()()()()1121212210n n n f n n n n λλλλλ--⎡⎤=--+=--+>⎣⎦，得122n λλ+>-；而()752231511211,1,,2,3,5353212222221λλλλλλλλ+-+<<∴<-<∴<<∴==+∈∴----当2n …时，2121n n a a +-<，当3n …时，2121n n a a +->，即奇数项中5a 最小；而25252593n a a λ=<<<，所以数列{}n a 的最小项为255a λ=，故当n a 取得最小值时，5n =.四､解答题17.【命题意图】本题考查正弦定理､余弦定理､三角恒等变换，考查数学运算､逻辑推理､直观想象的核心素养.【解析】（1）依题意，222b c a =-，而2cos a B a c +=，由余弦定理，即2222,2a c b a a c ac+-⋅+=故()()20a c a c -+=，故2a c =，代入2cos 1c a B =+中，得1cos 2B =，而0B π<<，故3B π=；（2）不妨设3AB c ==，则31,2,cos 2AM BM BC AB B ====，在BCM 中，由余弦定理得，222132cos 4CM BC BM BC BM B =+-⋅⋅=，由正弦定理得，sin sin CM BM B BCM ∠=，故sin sin BM B BCM CM ∠⋅==，21211cos212sin 121313BCM BCM ∠∠=-=-⨯=-.18.【命题意图】本题考查频率分布直方图､样本的数字特征､离散型随机变量的分布列以及数学期望，考查数学运算､逻辑推理､数学建模的核心素养.【解析】（1）依题意，100.350.30.10.051a ++++=，解得0.02a =；所求平均数为450.2550.35650.3750.1850.0559.5⨯+⨯+⨯+⨯+⨯=；（2）从日均体育活动时间在[)70,80中抽取8人，日均体育活动时间在[]80,90中抽取4人，故所求概率321884312C C C 42C 55P +==；（3）依题意，24,5X B ⎛⎫~ ⎪⎝⎭，故()()4314381232160,1C 562555625P X P X ⎛⎫⎛⎫⎛⎫======⎪ ⎪⎪⎝⎭⎝⎭⎝⎭，()()22323442321623962C ,3C 5562555625P X P X ⎛⎫⎛⎫⎛⎫⎛⎫======⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭，()421645625P X ⎛⎫=== ⎪⎝⎭；X01234P 816252166252166259662516625故()28455E X =⨯=.19.【命题意图】本题考查空间线面的位置关系､向量法求空间角，考查数学运算､逻辑推理､直观想象的核心素养.【解析】（1）连接BE ，如图所示.因为90ADC BCD ∠∠== ，故BC ∥AD ，因为12BC AD DE==，故四边形BCDE 为矩形，不妨设2BE CD ==；SA SD =且点E 为线段AD 的中点，SE AD ∴⊥，所以SD ==，故SB SD ==；故222SE BE SB +=，即SE BE ⊥；又AD BE E ⋂=，故SE ⊥平面ABCD ；而AC ⊂平面ABCD ，故SE AC ⊥；（2）以E 为原点，EA 为x 轴，EB 为y 轴，ES 为z 轴建立如图所示的空间直角坐标系，则不妨设4AD =，则()()()()2,0,0,0,2,0,2,2,0,0,0,4A B C S -，所以()()2,2,0,0,2,4AB SB =-=- ，设平面SAB 的法向量为()111,,n x y z =，则0,0,n AB n SB ⎧⋅=⎪⎨⋅=⎪⎩ 即1111220,240,x y y z -+=⎧⎨-=⎩取()2,2,1;n = 设()0,2BG t =∈，则(),2,0G t -，而()0,0,2F ，所以(),2,2GF t =- ，设直线FG 与平面SAB所成的角为,tan θθ=，则sin cos ,GF θ= 化简得2112440t t -+=，解得(2211t t ==舍去）；故111BG BC =.20.【命题意图】本题考查数列的基本运算､错位相减法，考查数学运算､逻辑推理的核心素养.【解析】（1）当2n …时，112,2n n n n S a S a λλ--=+=+，两式相减可得12n n a a -=；而当1n =时，112S a λ=+，得1a λ=-；3247S λλλλ=---=-，故714λ-=，解得2λ=-，则12a =，故2nn a =；（2）依题意，()3102n n b n =-⋅，故()1237242123102nn T n =-⋅-⋅-⋅++-⋅ ，()()2341272421231323102n n n T n n +=-⋅-⋅-⋅++-⋅+-⋅ ，两式相减可得()12313232232310220n n n T n +-=⋅+⋅+⋅++⋅--⋅- ，即()()1212331022012n n n T n +--=⋅--⋅--，故()1313226n n T n +=-⋅+.21.【命题意图】本题考查抛物线的方程､直线与抛物线的综合性问题，考查数学运算､逻辑推理､直观想象的核心素养.【解析】设()()()()11223344,,,,,,,M x y N x y P x y Q x y ；（1）设直线1:1l x ny =+，联立21,4,x ny y x =+⎧⎨=⎩得2440y ny --=，2Δ16160n =+>；则12124,4y y n y y +==-；故12122AMN S y y =⋅⋅-== ，解得2n =±，故直线1l 的斜率为12±；（2）设直线MP 的方程为x my λ=+，联立直线MP 与抛物线的方程，2,4,x my y x λ=+⎧⎨=⎩消去x 得2440y my λ--=，故134y y λ=-；由（1）可知，214y y =-，同理可得434y y =-，故2213213241sin 2116sin 2MPF NQF MF PF MFP MF PF y y y y S S NF QFy y NF QF NFQ ∠λ∠===== ，显然1λ≠，故21144MPF NQF S S λλ+=+ …，当且仅当12λ=时等号成立.22.【命题立意】本题考查利用导数研究函数的性质，考查数学运算､逻辑推理的核心素养.【解析】（1）依题意，()()22210,,m mx x m x f x m x x x∞'+-∈+=+-=，若0m =，则()()10,f x f x x=>'在()0,∞+上单调递增；若0m ≠，则2Δ140m =+>，令()0f x '=，解得12x x ==，其中12121,1x x x x m +=-=-若0m >，则120x x <<，故当x ⎛∈ ⎝时，()0f x '<，当x ∞⎫∈+⎪⎪⎭时，()0f x '>，故()f x在⎛ ⎝上单调递减，在∞⎫+⎪⎪⎭上单调递增；若0m <，则210x x <<，故当x ⎛∈ ⎝时，()0f x '>，当x ∞⎫∈+⎪⎪⎭时，()0f x '<，故()f x在⎛ ⎝上单调递增，在∞⎫+⎪⎪⎭上单调递减；综上所述，当0m =时，()f x 在()0,∞+上单调递增；当0m >时，故()f x在⎛ ⎝上单调递减，在∞⎫+⎪⎪⎭上单调递增；当0m<时，()f x在⎛⎝上单调递增，在∞⎫+⎪⎪⎭上单调递减；（2ln lnm m m mma b mb a ma mbb b a a++-+<+-++，lnab<1lnakabb⎛⎫-<，即1112lnaabka bb-⎛⎫⋅<+⎪⎝⎭恒成立，令1)t t=>，有()221112ln2tk t tt-⋅<++恒成立，得()1112ln2tk tt-⋅<+恒成立，所以1ln01tk tt-⋅-<+恒成立令()1ln1tg t k tt-=⋅-+，有()()22222211212(1)(1)(1)(1)t k tkt tg t kt t t t t t'-+---+=⋅-==++⋅+⋅，（注：()10g=）（i）当()10g'>时，即2k>时，易知方程()22110t k t-+--=有一根1t大于1，一根2t小于1，所以()g t在[)11,t上单调递增，故有()()110g t g>=，不符；（ii）当02k<…时，有2222(1)4(1)(1)0kt t t t t-+-+=--……，所以()0g t'…，当且仅当1t=时等号成立，从而()g t在()1,∞+上单调递减，故当1t>时，恒有()()10g t g<=，符合.由i ii､可知，正实数k的取值范围为02k<…，因此，k的最大值为2.。

北京理工大学数学专业数学分析Ⅰ试题(MTH17001H0171001)2022级数学专业数学分析Ⅰ第一次阶段测验1.（10分）设某0。

试写出十个与某等价且尽可能不同的无穷小量。

2.（15分）设某n2inn112,n1,2,（1）求证：对任意自然数n，某n（2）用N语言证明lim某nn11；2n1，并研究数列某n中是否有最大数和最小数。

23.（15分）用语言叙述某0时函数f收敛和发散的严格含义，并用两种方法证明某0时函数f某co1发散。

某某a某b0，求常数a,b的值；并给出a,b的几何意4.（10分）已知lim某某1某义。

1某co某5.（10分）研究函数f某在某0点极限的存在性。

某6.（15分）证明定理：设yfu,u某构成复合函数yf某u1某某某的极若lim某,limfuA，其中A是实常数，则当某时，函数f限存在，且limf某limfu某u7.（15分）（1）叙述limf某的严格含义；某（2）叙述f在,内取得最大值的严格含义；（3）设f在,内连续，且limf某求证：f在,内必取得最大值。

某8.（10分）设n,bn0，且成立极限limnnbn1p0。

bn1求证：数列bn收敛，且limbn0。

n2022级数学专业数学分析Ⅰ第一次阶段测验1.（10分）设某0。

试写出十个与某等价且尽可能不同的无穷小量。

2.（15分）设某n2inn211,n1,2,，用N语言证明lim某nn1，并研究2数列某n中是否有最大数和最小数。

3.（15分）设f某11co。

按定义证明：f在某0点的任意邻域内无界，但某0时某某f不是无穷大量。

4.（10分）已知lim某义。

某a某b0，求常数a,b的值；并给出a,b的几何意某1某5.（15分）某0是函数f某1某co某的哪种类型的间断点？说明理由。

某1某6.（10分）证明定理：设yfu,u某构成复合函数yf若lim某,limfuA，其中A是实常数，则函数f某00u某某在某0点的左极限存在，且limf某limfu某00u7.（15分）（1）叙述limf某的严格含义；某（2）叙述f在,内取得最大值的严格含义；（3）设f在,内连续，且limf某求证：f在,内必取得最大值。

（精品）高中英语会考真题+模拟训练试题（含答案）2019年高中英语会考真题+模拟训练试题（共两套含答案）高中英语会考真题注意事项：1．本试卷分选择题和非选择题两部分，共36小题，考试时间150分钟，满分150分。

2．答卷前，考生务必用黑色字迹的钢笔或签字笔将自己的姓名、准考证号填写在答题卡上。

将条形码横贴在答题卡“考生条形码区”。

3．每小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑，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。

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。

第Ⅰ卷第一部分、阅读理解（共两节，满分60分）第一节、（共10小题；每小题4分，满分40分）阅读下列短文，然后从各题所给的四个选项（A、B、C和D）中，选出最佳选项并在答题卡上将该选项涂黑。

AThere was a man .He had four sons. He wanted his sons to learn how to judge things,so he let them go andlook at a pear tree that was far away.The first son went in winter, the second in the spring, the third in the summer , the youngest son in the fall.When they had all gone and come back, he called them together to describe what they had seen.The first son said the tree was ugly,bent and weak. The second son said no--it was covered with green buds(新芽) and full of hope. The third son said it was filled with blossoms and they smelt so sweet and looked sobeautiful. The last son disagreed with all of them, he said it was ripe and full of fruit, life and fulfillment(成就).The man then said to his sons that they were all right, because they each had seen but only one season in the tree’s life. He told them that you cannot judge a tree or a person by only one season, and that essence of who they are — the pleasure,the joy and love from that — can only be measured at the end, when all the seasons are up.winter, you’ll miss the hope of your spring, the beauty of y our summer, the If you give up when it’sfulfillment of your fall. Don’t let the pain of one season destr oy the joy of all the rest.1.When did the youngest son go to observe the pear tree?A.In springB.In autumnC.In summerD.In winter2.What does the u nderlined word “blossoms”in the third paragraph mean?A.Colorful flowersB.Weak treesC.Green budsD.Ripe fruit3.What’s mainly discussed in the text?A.Don’t judge somethingB.Autumn is the harvest season in a year.C.Never give up until you get successD.Spring is the best time to do the year’s workBAmerican teenagers are driving less than ever before.Surveys of American teenagers show that American young people prefer chatting with their fiends online or playing games on the Internet to driving around in theircars.For teenagers in the 50s and 60s of the 20thcentury,they had to have a car at an early age to show they werecool.Today, many teenagers have to choose between a car and the latest smart phones.With gas prices going up ,car driving is becoming more expensive.For almost half of the people between 18 and 26,surfing the Internet is more important than owning a car. Young adults today meet their friends just through Facebook and chat , swap photos and play games together.The golden age of the 50s and 60s of the 20th century when teenagers drove around just for fun is gone . Inthose days a shiny new car was something to boast about . It shower who you were . In those days a shiny new car was something to boast about . It showed who you were . In 1978 about half of all 16-year-olds got their driver’s licenses(驾驶执照)as soon as they had reached that age . In 2010 the figure dropped to only30%.Today driving is not as much fun as it was in the 50s and 60s of the 20th century. In the golden age car meanteverything for young people . Another reason why teenagers drive less may be stricter driving tests and the factthat 16-year-olds must drive with experienced drivers over21 .A study also shows that Americans of all ages have reduced car use , mostly becausehigh gas prices.4.Why did teenagers in the 50s and 60s have to buy a car?A.To go traveling with their families .B.To play games with their friend .C.To have more talks with their friendsD.To become cool and enjoy themselves.5.What make t oday’s American car sales fall down according to the last paragraph?A.High gas pricesB.Strict driving testsC.Heavy traffic/doc/61f5b599a01614791711cc7931b 765ce04087a07.html ck of fashion styles6.The text is organized by comparing the different needs between American teenagers in the 50s and60s of the 20th century and .A.American teenagers in 1978B.16-year-olds in AsiaC.today’s teenagers in AmericaD.middle-aged AsianCMarco Polo was born in Italy in 1254. When he was 17 years old, he traveled across Europe and Asia withhis father , who wanted to do trade with the Chinese . Eventually , they arrived in Beijing .At that time, China was ruled by the Yuan Dynasty Emperor, Kublai Khan.Kublai Khan welcomed Marco and his father. He was very happy to meet two foreignersPalace.and wanted to learn all about Europe. Marco and his father were guests at the Emperor’ｓAlthough Marco was young, he was very clever and could already speak four languages. The Emperor was impressed by him and they became friends.He asked Marco to serve in his courtand sent him to do many important tasks across the country.In 1291, after 17 years of service to the Emperor, Marco returned to Italy. He was now avery wealthy man. Not long after his return , a local war broke out near his town.During the war, Marco was the captain of a warship but was caught by the enemy and put into prison.However, Marco was lucky enough to meet another prisoner who enjoyed listening tohis stories about China. The prisoner was an author and he took dictation while Marco told all his stories to him.The prisoner then wrote the stories in a book called The Description of theworld, which became one of the best-selling books in Europe.Although people enjoyed reading his book, many of them thought that Marco’s storiesabout China were too fantastic to be true. But Marco always stood by his tales. Just beforewhen Marco was asked the question, “Was it all true?”，to which h e replied, “Ｉhave only told ahalf of what I saw!”7.How long did Marco polo serve the Emperor?A.34 yearsB.17 yearsC.27 yearsD.37 years8.Who wrote the stories in a book named The Description of the World?A.Marco poloB.Kublai KhanC.A prisonerD.A captain9.What did people think of Marco’s stories at first?A.Old and outdatedB.Enjoyable but horribleC.Long and boringD.Interesting but unbelievable10.The genre(体裁) of the text belongs to a(n)A.storyB.advertisementC.dramaD.news report第二节、七选五（共5小题；每小题4分，满分20分）根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。

Lifestyles 单元检测(A卷——全员必做)Ⅰ.单项填空1．(2021·合肥一中模拟)—I'm sorry I took your bike by mistake.—Oh, really？________.A．It's OK with me B．It doesn't matterC．Don't be sorry D．I don't care2．(2021·江南十校联考)If someone is always ________ life, he won't experience the real happiness of life. A．complaining about B．complainingC．complained D．complained about3．(2021·安徽合肥模拟)—The cars give off a great deal of waste gas in the streets.—Yes. But I'm sure something will be done to ________ air pollution.A．reduce B．removeC．collect D．warn4．(2021·安徽江南十校模拟)Our teachers often encourage us that every minute we spend on studying will finally ________ in the near future.A．run out B．go offC．come out D．pay off5．(2021·衡阳市八中模拟)—What did he think of the trip to Beijing last month?—He had such a good time ________ he visited the Great Wall.A．until B．thatC．where D．when6．(2021·荆州模拟)Jimmy, you look very pale. I think it is ________ that you have a thorough medical check­up.A．concerned B．subtleC．ridiculous D．urgent7．(2021·唐山高三第一次模拟)—You know I dropped medicine and ________ physics.—You made a right decision.A．took up B．took inC．took apart D．took off8．(2021·吉林实验中学模拟)As you know, at a ________ of six miles we can't see much, still less on a foggy day.A．track B．distanceC．speed D．space9．(2021·福州质检)Life is hard. It is ________ to be. If we didn't suffer, we'd never learn anything.A．reported B．supposedC．devoted D．adopted10．(2021·四川省宜宾五校调查考试)A recent study has ________ an unexpected conclusion that the African elephant should be divided into two different species. A．kept up with B．made up withC．caught up with D．come up with11．(2021·长春质检)The man is so do you ________ him being here all the time?A．find B．feelC．stand D．see12．(2021·泉州质检)—Do you think it wise for parents to do everything for their children?—'s ________ they are mistaken.A．where B．whenC．what D．how13．(2021·江西七校联考)Each of us is likely to develop a personal ________ for certain types of entertainment.A．comparison B．possessionC．preference D．advantage14．(2021·太原市模拟)The new suspension bridge ________ by the famous architect is ________ now.A．designing; under constructionB．designed; under constructionC．designing; under the constructionD．designed; under the construction15．(2021·南京四校高三调研)Student loans are supposed to provide financial support for the students who would ________ not be able to go to college.A．otherwise B．meanwhileC．therefore D．neverthelessⅡ.阅读明白得A(2021·成都实验外国语学校模拟)There is a problem each of us faces in following advice on emotional healing: apologizing is difficult. We are trapped in what we think of ourselves by holding onto our pride. We can be selfish and not willing to admit our most obvious mistakes. Pride eats away at us as we argue or ignore the mistake.It's happened to me. I have had too much pride and selfishness to apologize to a loved one I hurt. When I did want to apologize, I couldn't bring myself to face the other person. This is the pride I'm talking about. Maybe apologies come difficult for men because they're expected to be dominant (占优势的). It's like the joke that a man never asks for directions when lost. Ladies are more emotionally open than guys and are willing to express it. Still, both genders wonder how to correctly apologize.In shifting the focus on apologizing away from you, what does not apologizing do to other people? They feel hurt that you are not willing to communicate your mistake. They lose trust in you as you hide behind your mistake avoiding reality. They become angry with you, wondering why you do not tell them the truth. They may begin to counter your lack of apologies by not apologizing themselves and from this the relationship goes downhill as the two of you get caught in a power struggle. You need to communicate your mistakes. A mistake you made is like a scratch and by not apologizing you are making the scratch a deeper wound and rubbing saltinto it. You need to stop hurting the other person and yourself by learning to apologize. There is real power in apologizing and emotional healing.1．People find it hard to apologize for their mistakes because of their ________. A．emotional feelingB．sticking to their prideC．making argumentD．being trapped in lies2．Why are men more unwilling to make apologies?A．They don't intend to hurt other people.B．They expect others to forgive them.C．They don't want to be considered weak.D．They aren't good at expressing themselves.3．What bad effect will there be if you refuse to apologize for your mistakes? A．Other people won't pay attention to you.B．You will lose confidence in yourself.C．You won't be forgiven even if you tell the truth.D．The friendship will get hurt and go worse.4．From the last paragraph, it can be inferred that ________. A．communication can stop you making mistakesB．mistakes would turn into deeper scratchesC．apologizing is good for you and other peopleD．apologizing is the most powerful in emotional healingB(2021·宁德模拟)Let's face it. No one drinks diet soda for the drink diet soda in the hope that it will help them lose weight or at least keep them from gaining it. Yet it seems to have exactly the opposite effect, according to a new study. Researchers from the University of Texas said those who drank two or more diet sodas a day had waist size increases that were six times greaterthan those who didn't drink diet soda.What we saw was that the more diet sodas a person drank, themore weight they were likely to gain，”said Sharon Fowler.The study was based on data from 474 participants in a large, ongoing research project, where the participants were followed for nearly 10 years.While the findings are surprising, they also offer some explanations.Nutrition expert, Melanie Rogers, who works with overweight patients in New York, has found that when patients are switched from regular to diet soda, they don't lose weight at all.“We weren't seeing weight loss necessarily, and that was confusing to us，” said Rogers.So why would diet soda cause weight gain? No one knows for sure yet, but it could be that people think they can eat more if they drink diet soda, and so over­compe nsate for the missing calories.A related study found some sweeteners (甜味剂) raised blood sugar levels in some mice.“Data from this and other potential studies suggest that the promotion ofdiet sodas and artificial sweeteners may be risky，” said Helen P．Hazuda, professor at the University of Texas's school of medicine. “They may be free of calories, but not of consequences.”5．People drink diet soda to ________.A．enjoy its tasteB．stay in fashionC．achieve weight lossD．gain more energy6．The new study suggests that drinking diet soda ________.A．causes people to become heavierB．helps people to be healthierC．makes people much thinnerD．offers people more calories7．We can learn from the passage that ________.A．regular soda makes people lose more weightB．diet soda drinkers tend to eat more foodC．diet soda does help reduce caloriesD．most blood diseases come from diet soda8．The underlined word “They” in the last paragraph probably refers to ________. A．sweetenersB．diet sodas and artificial sweetenersC．sodasD．diet soda drinkers and sweetener takersLifestyles 单元检测(B卷——自主选做)Ⅰ.完形填空(2021·蚌埠质检)I had a bad habit of skipping to the last pages of a just wanted to see how it ended __1__ I was still in the middle of habit __2__ first my mom, then my friends, and __3__ even my own my __4__ wouldn't be limited just to the books I read but also to what others were __5__ as one day my daughter told me in anger, “Dad, please just read a book one __6__ a t a time like everyone else！”At times I didn't __7__ this bad habit to just books also tried to skip ahead in my own life and __8__ out what to do months or even years from now __9__ enjoying each day at I knew that the __10__ of my life wasn't done yet and that I had many pages __11__ to go, I still couldn't control my burning desire to write the __12__ of it halfway and again, I would __13__jump ahead and try to solve every potential problem before it , __14__，doesn't work like loves to __15__ us, and you never know what new problems, changes or opportunities each new day will __16__. Recently when I found myself living in the __17__ again, I felt a voice that gently told me I needed to “live one day at a time”．When I heard those words, I __18__，turned the book of my life back to the __19__ page, and thanked God for today. Each of us has to __20__ the book of life line by line, moment by moment and trust that our story will be brought to its perfect end.1．B．forC．while D．because 2．B．annoyedC．delighted D．embarrassed 3．B．obviouslyC．accidentally D．finally 4．B．misunderstandingC．disappointment D．disagreement 5．B．readingC．doing D．watching6．B．copyC．chapter D．edition 7．B．devoteC．apply D．limit8．B．figureC．let D．turn9．the part of B．other thanC．instead of D．on the basis of 10．B．riverC．picture D．play11．B．leftC．kept D．regretted12．B．beginningC．ending D．comments13．B．strangelyC．foolishly D．critically14．B．moreoverC．therefore D．however15．B．cheatC．satisfy D．frighten16．B．bringC．take D．award17．B．futureC．memory D．dream18．B．criedC．lost D．smiled19．B．hopefulC．favorite D．right20．B．reviewC．explain D．translateⅡ.阅读明白得(2021·漳州名校联考)Modern living is resulting in more people becoming disconnected from the natural world, at the expense of our health and well­being. Most concern is centred around children, who are missingout on opportunities afforded to previous generations, ones as simple as climbing trees or getting their knees dirty.In the modern world, the adults of the future are displaying the symptoms of “nature­deficit (缺少) disorder”. The term was made up by Richard Louv, author of Last Child in the Woods.In the introduction to his book, he said that over the past few decades the way children understood and experienced natur e had “changed greatly”. “Today, kids are aware of the global threats to the environment — but their physical contact, their intimacy (亲热) with nature, is fading. That's exactly the opposite of how it was when I was a child，” said Mr. Louv. He admitted that nature­deficit disorder was “by no means a medical diagnosis”．Tim Gill, author of the report Sowing the Seeds: Reconnecting London's Children with Nature, agreed that the term does not have any meaningful clinical basis. “My idea is that regular contact with nature is part of a balanced diet of childhood experiences. If children do not have those experiences then they are not going to thrive to the same degree as if they did，” Tim Gill added. “They are also likely to grow up not caring about the world around them.”“Forest schools” are a type of outdoor education in which children visit forests, learning social and living skills. They are intended to offer children regular opportunities to develop confidence and independenc e through hands­on learning in a woodland environment. They have appeared to have a beneficial effect on children with emotional or behavioural problems.Play England is an organization that focuses on giving children access to free play areas. “We believ e that kids should be outside playing for a good proportion of the day because it is how they can stay happy, less stressed and healthy，” said Play England director Cath Prisk.However, she added: “Research showed that parents think taking their kids to th e park is something you do as a rare treat instead of something you do routinely.”1．As a child, Richard Louv ________.A．was fond of writing medical booksB．spent a lot of time playing in the open airC．read a lot of books about natureD．was curious about wildlife2．When children with nature­deficit disorder grow up, they will probably ________. A．suffer from a mental diseaseB．be confident and independentC．ignore the surrounding worldD．have bad social skills3．What is a child not likely to learn in “forest schools” ?A．Cooking. B．Putting up a tent.C．Making friends. D．Writing.4．The underlined word “routinely” in the last paragraph can be replaced by “________”．A．regularly B．properlyC．hardly D．casuallyⅢ.任务型读写(2021·皖南八校联考)Do you love travelling? If the answer is yes, then have you ever thought about why? You may maintain that travelling can help you expand your scope of knowledge, especially geographical and historical learning. It will provide more chances for you to enjoy food and try on clothes that you otherwise cannot possibly have. A famous English author Francis Bacon (1561－1626) makes a point when he says that, “Travel, in the younger sort, is a part of education; in the elder, a part of experience.”Evidence of leisure travel can be traced (追溯) as far back as ancient Babylon. But this sort of travel only really took off after World War Ⅱ. This year, according to the World Travel & Tourism Council, the 1 billionth tourist will cross an international boundary before the end of this month. That means that one in seven people on the planet travelled this year, something that would not have been possible a few decades ago. Around 20 years ago only the rich could travel.While the US and France remain the two largest destinations for world travel, experts say much of the explosive growth in tourism has been to countries like Guatemala, the Dominican Republic, and the Ivory Coast, which weren't even on the world tourism map a decade ago. The top five destinations in the world, according to the United Nations World Tourism Organization, are Paris, London, New York, the Mediterranean and Turkey.Several factors have led to the boom in world travel. The prosperity of people inAsia is one factor. People in Asian developing countries have lifted their incomes above middle­class levels in the past few years. And a lot of them have used their new wealth to travel. In addition, travel costs have been reduced thanks to the rapid development of transportation and competition between airlines to give customers the best prices.答案Lifestyles 单元检测(A卷——全员必做)Ⅰ.1.选B It's OK with me.“我专门好。

沪教牛津版小学五年级上模拟测试Module 1 Getting to know each other 英语试卷考试时间：60分钟；满分：100分学校：___________姓名：___________班级：___________注意事项：1．答题前填写好自己的学校. 姓名. 班级等信息2．请将答案正确填写在答题卡上Part 1 Listening (听力部分) 40%一．Listen and choose (选出你听到的句子中含有的单词并将序号填在前面的括号内。

) 5%( ) 1. A. want B. become C. teach( ) 2. A. bus driver B. taxi driver C. lifeguard( ) 3. A. bicycle B. bus C. underground( ) 4. A. when B. what C. whose( ) 5. A. ninth B. nine C. nineteenth二. Listen, read and choose (选出你听到的句子中含有的短语，将序号填在前面的括号内) 5%( ) 1. A. is afraid of B. is good at C. fall into( ) 2. A. help people B. driver a taxi C. cook nice food( ) 3. A. come to school B. go to school C. near my school( ) 4. A. by bike B. by bus C. on foot( ) 5. A. get on B. far from C. get off三. Listen, read and choose (选出你听到的句子，将序号填在前面的括号内) 5%( ) 1. A. I want to be a pilot.B. I want to cook food.C. I have a hat.( ) 2. A. He is afraid of flying.B. She is good at running.C.I like flying.( ) 3. A. He comes to school by car.B. I walk to school.C. What is it?( ) 4. A. My birthday is on 22nd April.B. It is Monday..C. It is 5th Judy.( ) 5. A. I have an orange hat.B. Here’s a card for you.C. Thank you.四Listen and choose (听录音，选出最佳答语) 5%( ) 1. A. It’s on 13th AugustB. Today is Sunday.C. Today is 1st May.( ) 2. A. Yes, they do.B. No, they don’t.C. Yes, they are.( ) 3. A. I go to work by car.B. She goes to work by car.C. Yes, I do.( ) 4. A. Yes, I am.B. Yes, I do.C. No, I am not.( ) 5. A. I want to be a nurse.B. She wants to teach Art.C. I like green.五. Listen and choose (根据录音内容选出适当的图片) 5% ( ) 1. A B.C.( ) 2. A. B.C.( ) 3. A. B.C.( ) 4. A. April 1 B. JAN1 C. December 2 ( ) 5. A. B.C.六．Listen and choose (根据录音所描述的内容选出适当的选项) 5% ( ) 1. A. It’s on 2nd March B. It’s on 1st March C. It’s on 3rd March ( ) 2. A. Happy Mother’s Day! B. Happy birthday,Mum! C. Thank you. ( ) 3. A. By plane B. I walk to Australia. C. By bike. ( ) 4. A. He is a fireman B. He is a teacher . C. He is a cook. ( ) 5. A. A teacher B. A singer C. A lifeguard.七. Listen and sort order (听录音，按录音顺序用1-5给下列图片排序) 5%( ) ( ) ( ) ( ) ( )八. Listen and complete the sentences with words. (根据听到的内容完成所缺单词) 5%This is my friend, Sally. There are four people in her family. Her father (1)_______a plane in the sky. He is a (2)_______. Her mother is a teacher. She (3)_______Chinese in a school. John is Sally’s brother. He wants to cook nice food, he wants to be a (4)________. Sally wants to help people. She wants to be a (5)________.Part 2 Writing (书写阅读部分) 60%一. Choose and write (选出合适的词并填空)5%1. I live________(to/on) Green Street.2. How do you come__________(to/of) school?3. I come to school_________(on/by) bus.4. It’s _________(near/far) our school.5. I go home on _______(foot/feet).二．Read and judge (读一读，判断下列单词划线部分的发音是否相同，相同用√表示，不同用×表示) 5%1. desk ask ( )2. post stop ( )3. wasp sport ( )4. pupil cute ( )5. sheep she ( )三. Look and choose (找出不同类的词，将答案写在括号内) 5% ( ) 1. A. cooker B. singer C. taxi driver( ) 2. A. want B. future C. teach( ) 3. A. bus B. car C. walk( ) 4. A. interesting B. favourite C. thing( ) 5. A. begin B. when C. bring四．Choose the best answer (选择填空) 10%( ) 1. Jason wants ______ a pilot.A.beB. to beC.being( ) 2. I’m ______ of flying. It’s too high.A.afraidB. happyC.interested( ) 3. Alice goes to school _______ bus.A.byB.onC.in( ) 4.John likes swimming. He _______ a lifeguard.A.wantsB.becomesC. teacher( ) 5. ---How_______your mother______to work?---She goes to work on foot.A.does;goesB.do;goC.does;go( ) 6. Kate lives ______ Winter Street.A.ofB. offC.on( ) 7. ---Do you live ________your school?---Yes. I get up early and take the underground to school.A.nearB.far fromC. behind( ) 8. ---When is Peter’s birthday?---It’s________ 26th September.A.inB.onC. at( ) 9. Here _____ some oranges ______ you.A.are;toB.is; forC. are; for( ) 10. ---Happy birthday,Tom!---________.A.GoodB.Thank youC.Sure五．Choose and write (选词填空，每词用一次，不得重复)：6%1. I live ________my school.2. Ms Chen________a car to work every day.3. ---_______do you go to bed?---I go to bed at 9:30p.m.4. ---_____ time does the party begin?---It begins at 7:00 p.m.5. The music ______ great! I like it.6. ---_______ you come to my birthday party, Jane?---Sure.六．Read and complete (读一读，情景选择) 12%( ) 1.你想知道对方是如何去上班的，你问：A. How do you go home?B. How do you go to work?C. How do you go to school?( ) 2.你说你家附近有一个地铁站，你说：A. There is a bus stop near my home.B. There is an underground station near my home.C. There is an airport near my home.( ) 3.你想知道对方是不是乘23路公交车上学，你问：A. Do you take Bus No.23 to school?B. Do you take Bus No.20 to school?C. Do you take Bus No.23 to work?( ) 4.你想知道对方是什么时候的生日，你问：A. When do you get up?B. When is your birthday?C. What is your birthday?( ) 5.你说那听起来很有趣，你说：A. That sounds exciting.B. That sounds boring.C. That sounds interesting.( ) 6.你想知道对方想成为什么，你问：A. What do you want to be ?B. What do you want ?C. What are you doing ?七．连词成句，注意大小写及标点符号(make sentences with words)12%1. not singing Froggy good is at (.)2.falls a chick lake into the (.)3.you what to do want be (?)4.do to you how school come (?)5.we school near live our (.)6. walks Tom to day school every (.)八．Read and judge (阅读短文，并判断，用“T”或“F”表示)5% I’m Peter. I want to become a pilot when I grow up. A pilot flies a plane. I love flying and I want to fly a plane in the sky.I’m Kitty. My mother is a teacher and she is a good teacher. She is nice to her students. All her students love her. I want to be a teacher too when I grow up.I’m Tim. My father is a painter. He is good at painting . But I don’t want to be a painter. I’m good at Maths and Science. When I grow up, I want to be a scientist(科学家). I like to make new things.( ) 1. Peter is afraid of flying.( ) 2. Kitty’s mother is a painter.( ) 3. Kitty wants to be a good teacher like her mother.( ) 4. Tim’s father is a scientist.( ) 5. Tim does not want to be a painter.参考答案一．Listen and choose (选出你听到的句子中含有的单词并将序号填在前面的括号内。

天津新华中学2024届物理高一下期末调研模拟试题注意事项：1．答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。

2．回答选择题时，选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其它答案标号。

回答非选择题时，将答案写在答题卡上，写在本试卷上无效。

3．考试结束后，将本试卷和答题卡一并交回。

一、选择题：本大题共10小题，每小题5分，共50分。

在每小题给出的四个选项中，有的只有一项符合题目要求，有的有多项符合题目要求。

全部选对的得5分，选对但不全的得3分，有选错的得0分。

1、一小船在静水中的速率是5m/s，要渡过宽120m的河流，水流的速度为3m/s，下列说法正确的是A．小船渡河的最短时间是30 s B．小船渡河的最短时间是40 sC．小船渡河的最短位移是120m D．小船渡河的最短位移是200m2、由于通讯和广播等方面的需要，许多国家发射了地球同步轨道卫星，这些卫星的A．质量可以不同B．轨道半径可以不同C．轨道平面可以不同D．速率可以不同3、如图，一个质量为m的刚性圆环套在粗糙的竖直固定细杆上，圆环的直径略大于细杆的直径，圆环的两边与两个完全相同的轻质弹簧的一端相连，轻质弹簧的另一端相连在和圆环同一高度的墙壁上的P、Q两点处，弹簧的劲度系数为k，开始时圆环处于O 点，弹簧处于原长状态且原长为l，细杆上的A、B两点到O点的距离都为l，将圆环拉至A点由静止释放，重力加速度为g，对于圆环从A点运动到B点的过程中，下列说法正确的是A．圆环通过O点的加速度小于gB．圆环与两弹簧组成的系统机械能不守恒C．圆环在O glD．圆环在B点的速度为gl4、(本题9分)做曲线运动的物体，在运动过程中一定变化的量是（）A．速率B．速度C．加速度D．合外力5、小球做匀速圆周运动的过程,以下各量不发生变化的是( )A．线速度B．向心力C．周期D．向心加速度6、质量为m的物体，在距地面h高处以的加速度由静止竖直下落到地面。