SK1期中
2023-2024学年湖北省荆州市荆州中学高一(上)期中数学试卷【答案版】
2023-2024学年湖北省荆州市荆州中学高一（上）期中数学试卷一、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．设集合A ＝{﹣2，﹣1，0，1}，B ＝{x |﹣1＜x ＜1}，则A ∩（∁R B ）＝（ ） A ．{﹣2，﹣1}B ．{﹣1，1}C ．{﹣2，0，1}D ．{﹣2，﹣1，1}2．已知命题p ：∀x ∈R ，x 2﹣3x +a ≠0，则（ ） A ．￢p ：∀x ∈R ，x 2﹣3x +a ＝0B ．￢p ：∃x ∈R ，x 2﹣3x +a ＝0C ．￢p ：∃x ∈R ，x 2﹣3x +a ≠0D ．a ＝2时，p 为真命题3．3133)16√2+(0.001)−13+√√2=（ ）A ．2√3−1.9B ．12+√2−√3C ．12D ．2√3+84．函数y =|x|x 2−1的图象大致为（ ） A ． B ．C ．D ．5．若a =5√3，b ＝50.3，c ＝0.82，则（ ） A ．b ＞c ＞aB ．b ＞a ＞cC ．c ＞a ＞bD ．a ＞b ＞c6．已知函数F （x ）＝x 3+2x ﹣2﹣x +5，若F （a ）＝7，则F （﹣a ）的值为（ ） A ．2B ．﹣7C ．3D ．﹣37．“a ∈(12，23]”是“f(x)={(13−a)x +1，(x ＜1)a x，(x ≥1)满足对任意x 1≠x 2都有f(x 1)−f(x 2)x 1−x 2＜0成立”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8．已知f （x ）是定义在实数集R 上的函数，在（0，+∞）内单调递增，f （2）＝0，且函数f （x +1）关于点（﹣1，0）对称，则不等式x •f （1﹣x ）＜0的解集是（ ） A ．（﹣∞，﹣2）∪（﹣1，0）∪（2，+∞） B ．（﹣∞，﹣2）∪（2，+∞） C ．（﹣1，0）∪（1，3）D ．（﹣∞，﹣1）∪（0，1）∪（3，+∞）二、选择题：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．下列说法正确的是（ ） A ．若a ＞b ，c ＜0，则ac＞bcB ．若a ＞b ＞0，m ＞0，则b a＜b+m a+mC ．对任意实数a ，b ，都有a 2+b 2﹣2|ab |≥0D ．若二次函数f （x ）＝x 2+ax +b ，实数x 1≠x 2，则f(x 1+x 22)＜f(x 1)+f(x 2)210．已知函数f(x)=2x2−4x+3，则（ ）A ．f （x ）在[2，+∞）上单调递增B ．f （x ）的值域为（0，+∞）C ．不等式f （x ）＜256的解集为（﹣1，5）D ．若g （x ）＝2﹣ax•f （x ）在（﹣∞，1]上单调递减，则实数a 的取值范围为[﹣2，+∞）11．设函数f （x ）＝min {|x ﹣3|，3|x |﹣1，|x +3|}，则下列说法正确的是（ ） A ．f （f （3））＝1 B ．函数f （x ）为偶函数 C ．函数f （x ）的最小值为0D ．当x ∈[﹣3，3]时，f （x ）﹣1≤a ，则a 的取值范围为[2，+∞） 12．已知不等式x 2y−1+y 2x−1≥3m 2−1对x ＞1，y ＞1恒成立，则m 的值可以是（ ）A ．−√2B ．﹣1C ．√3D ．2三、填空题：本题共4小题，每小题5分，共20分. 13．已知x 12−x −12=2，则x 2+x﹣2的值为 ．14．已知幂函数f （x ）＝（m 2+4m +4）x m +2在（0，+∞）上单调递减，若（2a ﹣1）﹣m＜（a +3）﹣m，则a的取值范围为 ．15．已知函数f （x ）＝x 2﹣2kx +4在[1，3]上的最大值为﹣12，则实数k 的值为 ．16．已知图象连续不断的函数f （x ）是定义域为[﹣4，4]的偶函数，若对任意的x 1，x 2∈（0，4]，当x 1＜x 2时，总有f(x 1)x 2−f(x 2)x 1＞0，则满足不等式（a +2）f （a +2）＜（1﹣a ）f （1﹣a ）的a 的取值范围为 ．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. 17．（10分）已知集合A ＝{x |（x ﹣a ）（x ﹣3a ）＜0}，集合B ＝{x |{2x ≥41−13x ≥0}． （1）当a ＝1时，求A ∪B ；（2）设a ＞0，A ∩B ＝B ，求实数a 的取值范围．18．（12分）若关于x 的不等式2x 2+ax ﹣（a +2）＜0的解集是{x|−32＜x ＜1}． （1）求实数a 的值； （2）当x ＞a 时，求y =x 2−2x+5x−a的最小值． 19．（12分）已知函数f （x ）＝（2k ﹣1）×3x +（k 2﹣8）是增函数，且f （1）＝5． （1）若a ＞0，b ＞0，[f （a ）+4]•[f （b ）+4]＝27，求9a+1b 的最小值；（2）是否存在实数m ，n （m ＜n ），使得当x ∈[m ，n ]时，函数y ＝f （x ）的最小值恰为−13m ，而最大值恰 为−13n ？若存在，求出m ，n 的值；若不存在，请说明理由； 20．（12分）已知函数f(x)=a x −ba x (a ＞0，且a ≠1)的图象过点（0，0）和(1，32)． （1）求证：f （x ）是奇函数，并判断f （x ）的单调性（不需要证明）；（2）若∀t ∈[13，3]，使得不等式f （t 2﹣kt +10）+f （a ）＞0都成立，求实数k 的取值范围． 21．（12分）先看下面的阅读材料：已知三次函数f （x ）＝ax 3+bx 2+cx +d （a ≠0），称相应的二次函数f 1(x)=3ax 2+2bx +c 为f （x ）的“导函数”，研究发现，若导函数f 1（x ）＞0在区间D 上恒成立，则f （x ）在区间D 上单调递增；若导函数f 1（x ）＜0在区间D 上恒成立，则f （x ）在区间D 上单调递减．例如：函数f （x ）＝﹣2x 3+3x 2+12x +5，其导函数f 1(x)=−6x 2+6x +12=−6（x 2﹣x ﹣2） ＝﹣6（x ﹣2）（x +1），由f 1（x ）＞0，得﹣1＜x ＜2，由f 1（x ）＜0，得x ＜﹣1或x ＞2，所以三次函数f （x ）在区间（﹣1，2）上单调递增，在区间（﹣∞，﹣1）和（2，+∞）上单调递减． 结合阅读材料解答下面的问题：（1）求三次函数f(x)=−x 3+12x 2+4x 的单调区间；（2）某市政府欲在文旅区内如图所示的矩形ABCD 地块中规划出一个儿童乐园（如图中阴影部分），形状为直角梯形OPRE （线段EO 和RP 为两条底边，OP ⊥OE ），已知AB ＝2km ，BC ＝6km ，AE ＝BF ＝4km ，其中曲线AF 是以A 为顶点、AD 为对称轴的抛物线的一部分． ①设OP ＝xkm （0＜x ＜2），求出梯形OPRE 的面积S 与x 的解析式； ②求该公园的最大面积．22．（12分）已知函数f(x)={−x(x −2a)+a 2−4a(x ≤2a)x(x −2a)+a 2−4a(x ＞2a)，（a ∈R ）．（1）当a ＝2时，求f （x ）＝x |x ﹣2a |+a 2﹣4a （a ∈R ）的单调区间； （2）如果关于x 的方程f （x ）＝0有三个不相等的非零实数解x 1，x 2，x 3，求1x 1+1x 2+1x 3的取值范围．2023-2024学年湖北省荆州市荆州中学高一（上）期中数学试卷参考答案与试题解析一、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．设集合A ＝{﹣2，﹣1，0，1}，B ＝{x |﹣1＜x ＜1}，则A ∩（∁R B ）＝（ ） A ．{﹣2，﹣1}B ．{﹣1，1}C ．{﹣2，0，1}D ．{﹣2，﹣1，1}解：B ＝{x |﹣1＜x ＜1}，则∁R B ＝{x |x ≥1或x ≤﹣1}，集合A ＝{﹣2，﹣1，0，1}，则A ∩（∁R B ）＝{﹣2，﹣1，1}． 故选：D ．2．已知命题p ：∀x ∈R ，x 2﹣3x +a ≠0，则（ ） A ．￢p ：∀x ∈R ，x 2﹣3x +a ＝0B ．￢p ：∃x ∈R ，x 2﹣3x +a ＝0C ．￢p ：∃x ∈R ，x 2﹣3x +a ≠0D ．a ＝2时，p 为真命题解：命题p ：∀x ∈R ，x 2﹣3x +a ≠0，则￢p ：∃x ∈R ，x 2﹣3x +a ＝0， 当a ＝2时，x ＝1或2时，x 2﹣3x +2＝0，故p 为假命题． 故选：B ．3．3133)16√2+(0.001)−13+√√2=（ ）A ．2√3−1.9B ．12+√2−√3C ．12D ．2√3+8解：原式=313×316×212212+(110)3×(−13)+2−√3=312+10+2−√3=12． 故选：C ． 4．函数y =|x|x 2−1的图象大致为（ ） A ． B ．C ．D ．解：由函数 y =|x|x 2−1，可得x ≠±1，故函数的定义域为（﹣∞，﹣1）∪（﹣1，1）∪（1，+∞）， 又 f(−x)=|−x|(−x)2−1=x x 2−1=f(x)，所以y =|x|x 2−1是偶函数，其图象关于y 轴对称，因此 A ，D 错误； 当 0＜x ＜1时，x 2−1＜0，y =|x|x 2−1＜0，所以C 错误． 故选：B ．5．若a =5√3，b ＝50.3，c ＝0.82，则（ ） A ．b ＞c ＞aB ．b ＞a ＞cC ．c ＞a ＞bD ．a ＞b ＞c解：∵5√3＞50.3＞50=1，∴a ＞b ＞1， ∵0＜0.82＜0.80＝1，∴0＜c ＜1， ∴a ＞b ＞c ． 故选：D ．6．已知函数F （x ）＝x 3+2x ﹣2﹣x +5，若F （a ）＝7，则F （﹣a ）的值为（ ）A ．2B ．﹣7C ．3D ．﹣3解：函数F （x ）＝x 3+2x ﹣2﹣x +5，F （a ）＝7，F （a ）+F （﹣a ）＝a 3+2a ﹣2﹣a +5+（﹣a ）3+2﹣a ﹣2a +5＝10，所以F （﹣a ）＝10﹣F （a ）＝10﹣7＝3． 故选：C ．7．“a ∈(12，23]”是“f(x)={(13−a)x +1，(x ＜1)a x，(x ≥1)满足对任意x 1≠x 2都有f(x 1)−f(x 2)x 1−x 2＜0成立”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解：由题意得f （x ）在R 上单调递减，故{ 13−a ＜00＜a ＜113−a +1≥a ，解得：13＜a ≤23，故“a ∈(12，23]”是“f(x)={(13−a)x +1，(x ＜1)a x，(x ≥1)满足对任意x 1≠x 2都有f(x 1)−f(x 2)x 1−x 2＜0成立”的充分不必要条件． 故选：A ．8．已知f （x ）是定义在实数集R 上的函数，在（0，+∞）内单调递增，f （2）＝0，且函数f （x +1）关于点（﹣1，0）对称，则不等式x •f （1﹣x ）＜0的解集是（ ）A ．（﹣∞，﹣2）∪（﹣1，0）∪（2，+∞）B ．（﹣∞，﹣2）∪（2，+∞）C ．（﹣1，0）∪（1，3）D ．（﹣∞，﹣1）∪（0，1）∪（3，+∞） 解：因为函数f （x +1）关于点（﹣1，0）对称， 所以f （x ）的图象关于原点对称，即f （x ）为奇函数， 因为f （x ）在（0，+∞）内单调递增，f （2）＝0， 故f （x ）在（﹣∞，0）上单调递增，f （﹣2）＝0， 由x •f （1﹣x ）＜0可得xf （x ﹣1）＞0， 即{x ＞0f(x −1)＞0或{x ＜0f(x −1)＜0，即{x ＞0x −1＞2或−2＜x −1＜0或{x ＜00＜x −1＜2或x −1＜−2，解得x ＞3或0＜x ＜1或x ＜﹣1． 故选：D ．二、选择题：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．下列说法正确的是（ ） A ．若a ＞b ，c ＜0，则ac＞bcB ．若a ＞b ＞0，m ＞0，则b a＜b+m a+mC ．对任意实数a ，b ，都有a 2+b 2﹣2|ab |≥0D ．若二次函数f （x ）＝x 2+ax +b ，实数x 1≠x 2，则f(x 1+x 22)＜f(x 1)+f(x 2)2解：对于A ，由1c＜0，a ＞b ，可得a c＜b c，故A 错误； 对于B ，若a ＞b ＞0，m ＞0，则ba −b+m a+m=m(b−a)a(a+m)＜0，可得b a＜b+m a+m，B 正确；对于C ，a 2+b 2﹣2|ab |＝（|a |﹣|b |）2≥0，当且仅当|a |＝|b |时，等号成立，故a 2+b 2﹣2|ab |≥0，C 正确； 对于D ，二次函数f （x ）＝x 2+ax +b ，实数x 1≠x 2， 则f(x 1+x 22)=14(x 1+x 2)2+a 2(x 1+x 2)+b ，f(x 1)+f(x 2)2=12[(x 12+ax 1+b)+(x 22+ax 2+b)]， 可得f(x 1+x 22)−f(x 1)+f(x 2)2=14(x 12+x 22)−12(x 12+x 22)=−14(x 1−x 2)2≤0， 由x 1≠x 2可知等号不能成立，故f(x 1+x 22)＜f(x 1)+f(x 2)2，D 正确． 故选：BCD ．10．已知函数f(x)=2x2−4x+3，则（ ）A ．f （x ）在[2，+∞）上单调递增B ．f （x ）的值域为（0，+∞）C ．不等式f （x ）＜256的解集为（﹣1，5）D ．若g （x ）＝2﹣ax•f （x ）在（﹣∞，1]上单调递减，则实数a 的取值范围为[﹣2，+∞）解：根据题意，设t ＝x 2﹣4x +3，则y ＝2t ， 依次分析选项：对于A ，t ＝x 2﹣4x +3是对称轴为x ＝2的二次函数，开口向上，则t ＝x 2﹣4x +3在[2，+∞）上单调递增，y ＝2t 在R 上单调递增，故f （x ）在[2，+∞）上单调递增，A 正确；对于B ，t ＝x 2﹣4x +3≥﹣1，则y ＝2t ≥12，则f （x ）的值域为[12，+∞），B 错误；对于C ，不等式f （x ）＜256＝28，即x 2﹣4x +3＜8，解可得﹣1＜x ＜5，即不等式的解集为（﹣1，5），C 正确；对于D ，g （x ）＝2﹣ax•f （x ）=2x2−(4+a)x+3，设m ＝x 2﹣（4+a ）x +3，则y ＝2m ，若g （x ）＝2﹣ax•f （x ）在（﹣∞，1]上单调递减，则m ＝x 2﹣（4+a ）x +3在（﹣∞，1]上单调递减，必有12（4+a ）≥1，解可得a ≥﹣2，即实数a 的取值范围为[﹣2，+∞），D 正确． 故选：ACD ．11．设函数f （x ）＝min {|x ﹣3|，3|x |﹣1，|x +3|}，则下列说法正确的是（ ） A ．f （f （3））＝1 B ．函数f （x ）为偶函数 C ．函数f （x ）的最小值为0D ．当x ∈[﹣3，3]时，f （x ）﹣1≤a ，则a 的取值范围为[2，+∞）解：在同一坐标系作出 y ＝3|x |﹣1，y ＝|x ﹣3|和 y ＝|x +3|的图象，如图所示，则A （﹣1，2），B （1，2），所以f （x ）={|x +3|，x ≤−13|x|−1，−1≤x ≤1|x −3|，x ≥1，其图象是图中实线部分．则f （f （3））＝f （0）＝0，故A 错误；函数f （x ）为偶函数，函数f （x ）的最小值为0，无最大值，B ，C 正确； 当x ∈[﹣3，3]时，f （x ）max ＝2，所以a ≥2﹣1＝1，D 错误． 故选：BC ． 12．已知不等式x 2y−1+y 2x−1≥3m 2−1对x ＞1，y ＞1恒成立，则m 的值可以是（ ）A ．−√2B ．﹣1C ．√3D ．2解：由题意x 2y−1+y 2x−1=[(x−1)+1]2y−1+[(y−1)+1]2x−1=(x−1)2y−1+1y−1+(y−1)2x−1+1x−1+2(x−1)y−1+2(y−1)x−1≥2√(x−1)2y−1⋅1y−1+2√(y−1)2x−1⋅1x−1+2√2(x−1)y−1⋅2(y−1)x−1=2(y−1x−1+x−1y−1)+4≥2×2√y−1x−1⋅x−1y−1+4=8，第一个等号成立当且仅当x ＝y ＝2＞1，第二个等号成立当且仅当x ＝y ＞1， 综上，(x 2y−1+y 2x−1)min =8，当且仅当x ＝y ＝2＞1时成立； 又不等式x 2y−1+y 2x−1≥3m 2−1对x ＞1，y ＞1恒成立，等价于3m 2﹣1≤8，解得−√3≤m ≤√3， 对比选项可知，m 的值可以是−√2或﹣1或√3． 故选：ABC ．三、填空题：本题共4小题，每小题5分，共20分.13．已知x 12−x−12=2，则x 2+x﹣2的值为 34 ．解：∵x 12−x −12=2，∴(x 12−x−12)2=x +x ﹣1﹣2＝4，∴x +x ﹣1＝6，∴（x +x ﹣1）2＝x +x ﹣2+2＝36，∴x +x ﹣1＝34．故答案为：34．14．已知幂函数f （x ）＝（m 2+4m +4）x m +2在（0，+∞）上单调递减，若（2a ﹣1）﹣m＜（a +3）﹣m，则a的取值范围为 （﹣∞，4） ．解：由题意可知{m 2+4m +4=1m +2＜0，解得m ＝﹣3，∴不等式（2a ﹣1）﹣m＜（a +3）﹣m，可化为（2a ﹣1）3＜（a +3）3，又∵函数y ＝x 3在R 上单调递增， ∴2a ﹣1＜a +3，解得a ＜4． 故a 的取值范围为（﹣∞，4）． 故答案为：（﹣∞，4）．15．已知函数f （x ）＝x 2﹣2kx +4在[1，3]上的最大值为﹣12，则实数k 的值为 172．解：函数f （x ）＝x 2﹣2kx +4开口向上，对称轴x ＝k ， 区间[1，3]的中点x ＝2，当k ≤2时，|3﹣k |≥|1﹣k |，所以x ＝3离对称轴较远，所以f （x ）max ＝f （3）＝9﹣6k +4＝﹣12，解得k =256＞2，不符合k ≤2； 当k ＞2时，|3﹣k |＜|1﹣k |，所以x ＝1离对称轴较远， 所以f （x ）max ＝f （1）＝1﹣2k +4＝﹣12，解得k =172＞2，符合条件． 所以k 的值为172．故答案为：172．16．已知图象连续不断的函数f （x ）是定义域为[﹣4，4]的偶函数，若对任意的x 1，x 2∈（0，4]，当x 1＜x 2时， 总有f(x 1)x 2−f(x 2)x 1＞0，则满足不等式（a +2）f （a +2）＜（1﹣a ）f （1﹣a ）的a 的取值范围为 (−12，2] ．解：因为函数f （x ）是定义域为[﹣4，4]的偶函数， 若对任意的x 1，x 2∈（0，4]，当x 1＜x 2时，总有f(x 1)x 2−f(x 2)x 1＞0，即x 1f （x 1）＞x 2f （x 2），令g （x ）＝xf （x ），则g （x ）在（0，4]上单调递减， 因为f （x ）为偶函数，即f （﹣x ）＝f （x ）， 故g （﹣x ）＝﹣xf （﹣x ）＝﹣xf （x ）＝﹣g （x ）， 根据奇函数的对称性可知，g （x ）在R 上单调递减，由不等式（a +2）f （a +2）＜（1﹣a ）f （1﹣a ）可得g （a +2）＜g （1﹣a ）， 所以{−4≤a +2≤4−4≤1−a ≤4a +2＞1−a，解得−12＜a ≤2．故答案为：(−12，2]．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）已知集合A ＝{x |（x ﹣a ）（x ﹣3a ）＜0}，集合B ＝{x |{2x ≥41−13x ≥0}． （1）当a ＝1时，求A ∪B ；（2）设a ＞0，A ∩B ＝B ，求实数a 的取值范围．解：（1）B ={x|{2x ≥41−13x ≥0}={x|{x ≥2x ≤3}={x|2≤x ≤3}， 当a ＝1时，A ＝{x |（x ﹣1）（x ﹣3）＜0}＝{x |1＜x ＜3}， ∴A ∪B ＝{x |1＜x ≤3}；（2）∵a ＞0，∴A ＝{x |a ＜x ＜3a }， 又A ∩B ＝B ，∴B ⊆A ， ∴{a ＜23a ＞3，∴1＜a ＜2， ∴实数a 的取值范围为（1，2）．18．（12分）若关于x 的不等式2x 2+ax ﹣（a +2）＜0的解集是{x|−32＜x ＜1}． （1）求实数a 的值；（2）当x ＞a 时，求y =x 2−2x+5x−a的最小值．解：（1）因为不等式2x 2+ax ﹣（a +2）＜0的解集是{x|−32＜x ＜1}， 所以−32和1是方程2x 2+ax ﹣（a +2）＝0的两个根， 由根与系数的关系知，{−32+1=−a2−32×1=−a+22，解得a ＝1． （2）由（1）知，a ＝1，当x ＞a 时，x ﹣1＞0时，所以y =x 2−2x+5x−a =x 2−2x+5x−1=(x−1)2+4x−1=(x −1)+4x−1≥2√(x −1)4x−1=4， 当且仅当x ﹣1=4x−1，即x ＝3时取等号，所以y min ＝4．19．（12分）已知函数f （x ）＝（2k ﹣1）×3x +（k 2﹣8）是增函数，且f （1）＝5． （1）若a ＞0，b ＞0，[f （a ）+4]•[f （b ）+4]＝27，求9a+1b 的最小值；（2）是否存在实数m ，n （m ＜n ），使得当x ∈[m ，n ]时，函数y ＝f （x ）的最小值恰为−13m ，而最大值恰 为−13n ？若存在，求出m ，n 的值；若不存在，请说明理由； 解：∵f （x ）＝（2k ﹣1）×3x +（k 2﹣8），且f （1）＝5，∴3（2k ﹣1）+k 2﹣8＝5，即k 2+6k ﹣16＝0，解得k ＝2或k ＝﹣8，又函数f （x ）＝（2k ﹣1）×3x +（k 2﹣8）是增函数，∴2k ﹣1＞0，即k ＞12， ∴k ＝2，则f （x ）＝3×3x ﹣4．（1）由[f （a ）+4]•[f （b ）+4]＝27，得3a +b ＝3，∴a +b ＝1， 又a ＞0，b ＞0，∴9a+1b=(9a+1b)(a +b)=10+9b a+a b≥10+2√9b a⋅a b=16，当且仅当a b=9b a，即a =34，b =14时取等号，故9a+1b的最小值为16；（2）∵f （x ）＝3×3x ﹣4为增函数，∴当x ∈[m ，n ]时，函数y ＝f （x ）的最小值为f （m ），最大值为f （n ）， 由{f(m)=−13m f(n)=−13n ，得{3×3m −4=−13m3×3n−4=−13n，即{3×(3m )2−4×3m +1=03×(3n )2−4×3n +1=0， 可得3m ，3n 是方程3x 2﹣4x +1＝0的两个根， ∵m ＜n ，∴3m =13，3n ＝1，解得m ＝﹣1，n ＝0， ∴存在m ＝﹣1，n ＝0 满足要求．20．（12分）已知函数f(x)=a x −ba x (a ＞0，且a ≠1)的图象过点（0，0）和(1，32)． （1）求证：f （x ）是奇函数，并判断f （x ）的单调性（不需要证明）；（2）若∀t ∈[13，3]，使得不等式f （t 2﹣kt +10）+f （a ）＞0都成立，求实数k 的取值范围． 解：（1）证明：函数f(x)=a x −ba x (a ＞0，a ≠1)的图象过点（0，0）和(1，32)， 则{f(0)=1−b =0f(1)=a −b a =32，解得{b =1a =2，所以f(x)=2x −12x ， 函数定义域为R ，f(−x)=2−x −12−x =12x −2x =−(2x−12x )=−f(x)， 所以函数f （x ）是奇函数． 由函数y ＝2x 和y =−12x 都是R 上的增函数，所以f(x)=2x−12x 在R 上单调递增． （2）f （x ）是奇函数，且在R 上单调递增，不等式f （t 2﹣kt +10）+f （a ）＞0等价f （t 2﹣kt +10）＞﹣f （2）＝f （﹣2）， 可得t 2﹣kt +10＞﹣2，若∀t ∈[13，3]，使得不等式f （t 2﹣kt +10）+f （a ）＞0都成立， 等价于∀t ∈[13，3]，t 2−kt +12＞0恒成立，即t 2+12＞kt ，k ＜t 2+12t =t +12t 在[13，3]上恒成立，设g(t)=t +12t (t ∈[13，3])，∀t 1，t 2∈[13，3]，且t 1＜t 2， 有g(t 1)−g(t 2)=(t 1+12t 1)−(t 2+12t 2)=(t 1−t 2)(t 1t 2−12t 1t 2)，由13≤t 1＜t 2≤3，可得t 1−t 2＜0，19＜t 1t 2＜9＜12，t 1t 2−12＜0，则g （t 1）﹣g （t 2）＞0，所以g （t 1）＞g （t 2）， 所以g （t ）在[13，3]上单调递减， 所以g （t ）min ＝g （3）＝7，所以k ＜7， 所以实数k 的取值范围为（﹣∞，7）． 21．（12分）先看下面的阅读材料：已知三次函数f （x ）＝ax 3+bx 2+cx +d （a ≠0），称相应的二次函数f 1(x)=3ax 2+2bx +c 为f （x ）的“导函数”，研究发现，若导函数f 1（x ）＞0在区间D 上恒成立，则f （x ）在区间D 上单调递增；若导函数f 1（x ）＜0在区间D 上恒成立，则f （x ）在区间D 上单调递减．例如：函数f （x ）＝﹣2x 3+3x 2+12x +5，其导函数f 1(x)=−6x 2+6x +12=−6（x 2﹣x ﹣2） ＝﹣6（x ﹣2）（x +1），由f 1（x ）＞0，得﹣1＜x ＜2，由f 1（x ）＜0，得x ＜﹣1或x ＞2，所以三次函数f （x ）在区间（﹣1，2）上单调递增，在区间（﹣∞，﹣1）和（2，+∞）上单调递减． 结合阅读材料解答下面的问题：（1）求三次函数f(x)=−x 3+12x 2+4x 的单调区间；（2）某市政府欲在文旅区内如图所示的矩形ABCD 地块中规划出一个儿童乐园（如图中阴影部分）， 形状为直角梯形OPRE （线段EO 和RP 为两条底边，OP ⊥OE ），已知AB ＝2km ，BC ＝6km ，AE ＝BF ＝4km ，其中曲线AF 是以A 为顶点、AD 为对称轴的抛物线的一部分． ①设OP ＝xkm （0＜x ＜2），求出梯形OPRE 的面积S 与x 的解析式； ②求该公园的最大面积．解：（1）f(x)=−x 3+12x 2+4x 的导函数为f 1(x)=−3x 2+x +4， 由f 1（x ）＞0，得−1＜x ＜43，由f 1（x ）＜0，得x ＜﹣1或x ＞43，所以三次函数f （x ）在区间(−1，43)上单调递增，在区间（﹣∞，﹣1）和(43，+∞)上单调递减． （2）①以A 为原点，AB 所在的直线为x 轴建立平面直角坐标系， 设曲线AF 所在抛物线的方程为y ＝ax 2（a ＞0）， ∵抛物线过F （2，4），∴4＝a ×22，得a ＝1，∴AF 所在抛物线的方程为y ＝x 2，P （x ，x 2）（0＜x ＜2）， ∴又E （0，4），C （2，6），则EC 所在直线为y ＝x +4， 则OE ＝4﹣x 2，PR ＝4+x ﹣x 2，∴公园的面积S =12(4−x 2+4+x −x 2)⋅x =−x 3+12x 2+4x （0＜x ＜2）， ②由（1）知，S （x ）在(0，43)上单调递增，在(43，2)上单调递减， 当x =43时，S 取得最大值10427．故该公园的最大面积为10427km 2．22．（12分）已知函数f(x)={−x(x −2a)+a 2−4a(x ≤2a)x(x −2a)+a 2−4a(x ＞2a)，（a ∈R ）．（1）当a ＝2时，求f （x ）＝x |x ﹣2a |+a 2﹣4a （a ∈R ）的单调区间； （2）如果关于x 的方程f （x ）＝0有三个不相等的非零实数解x 1，x 2，x 3，求1x 1+1x 2+1x 3的取值范围．解：（1）当a ＝2时，f （x ）＝x |x ﹣2a |+a 2﹣4a ＝x |x ﹣4|﹣4， 当x ＞4时，f （x ）＝x 2﹣4x ﹣4；当x ≤4时，f （x ）＝﹣x 2+4x ﹣4， 即有f(x)={−x 2+4x −4，x ≤4x 2−4x −4，x ＞4，据二次函数的性质可知，f （x ）的单调递增区间为（﹣∞，2]和[4，+∞），单调递减区间为[2，4]． （2）f(x)={−x(x −2a)+a 2−4a(x ≤2a)x(x −2a)+a 2−4a(x ＞2a)，当a ＝0时，f(x)={−x 2，x ≤0x 2，x ＞0，不符合题意；当a ＞0时，方程有3个不相等的实数根，且f （x ）在（2a ，+∞）上递增，所以x ≥2a 时，x 2﹣2ax +a 2﹣4a ＝0有1个根，且x ＜2a 时，﹣x 2+2ax +a 2﹣4a ＝0有2个根， 所以只需满足{Δ=4a 2+4(a 2−4a)＞0f(2a)=a 2−4a ＜0，解得2＜a ＜4；当a ＜0时，当x ＞2a 时，方程x 2﹣2ax +a 2﹣4a ＝0的判别式Δ＝4a 2﹣4（a 2﹣4a ）＝16a ＜0， 由二次方程的解的分布可得方程x 2﹣2ax +a 2﹣4a ＝0无解，所以此时不符合题意； 综上：a 的取值范围是（2，4）．不妨设x 1＜x 2＜x 3，则x 1+x 2=2a ，x 1x 2=−a 2+4a ，x 3=2a+√4a 2−4(a 2−4a)2=a +2√a ，所以1x 1+1x 2+1x 3=x 1+x 2x 1x 2+1x 3=2a −a 2+4a +a+2√a =2a a(4−a)+√a (a+2√a)(a−2√a)=2a a(4−a)−a−2√a a(4−a)=a+2√a (a+2√a)(a−2√a)=1a−2√a =−1(√a)2−2√a =−1(√a−1)2−1， 因为2＜a ＜4，则√2−1＜√a −1＜1，可得2−2√2＜(√a −1)2−1＜0， 所以1x 1+1x 2+1x 3=(√a−1)2−12√2−2=1+√22． 故1x 1+1x 2+1x 3的取值范围为(1+√22，+∞)．。
小学上册K卷英语第1单元期中试卷(有答案)
小学上册英语第1单元期中试卷(有答案)英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.The _______ changes with the seasons.2.The characteristics of a plant can reveal much about its ______ and adaptations. (植物的特征可以揭示其栖息地和适应性。
)3. A __________ (溶剂) is a substance that dissolves a solute.4.The Kepler Space Telescope was designed to find ______.5.I want to _____ (explore) the caves.6.What is the currency used in the USA?A. DollarB. EuroC. PoundD. Yen答案: A7.What is the name of the famous scientist known for his work on the structure of DNA?A. James WatsonB. Francis CrickC. Rosalind FranklinD. Gregor Mendel答案: A8. A __________ (反应物) is a substance that undergoes a chemical change.9.The kangaroo hops on its strong _________. (后腿)10. A compass uses the Earth’s magnetic ______.11.The sky is _____ (blue/grey) today.12.The ______ has thick fur for warmth.13.Certain plants are _____ (容易) to grow at home.14.The books are ________ (在架子上).15.What do you call the animal that has a shell and moves slowly?A. RabbitB. SnailC. CatD. Dog答案: B16.The ______ (空气湿度) affects plant health.17.My mother is a ______. She helps with homework.18.I see a _____ (bird/fish) flying.19.The __________ is the habitat for polar bears. (北极)20.One of my favorite memories is when I __________. It was a special day because __________. I will always remember that moment fondly.21.Metals are typically good conductors of _____.22.The __________ is a major geographical region in Asia. (中亚)23.The ________ was a major turning point in the fight for freedom.24.ts have thorns to protect themselves from ______. (一些植物有刺来保护自己免受动物的侵害。
冀教版数学二年级上册期中测试题检测卷(4套)
期中评估检测题（第一套）（Ａ卷）（总分：１００分㊀㊀㊀㊀时间：７０分钟）一㊁计算（１２分）㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀２４ː４＝３ˑ３＝１２ː３＝２４－５－７＝３６ː６＝３０ː５＝２ˑ４＝３２＋１１＋２２＝１８ː３＝５ˑ３＝２０ː５＝４１－（２２＋１０）＝二㊁在ʻ里填上 ＞ ＜ 或 ＝ （１２分）㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀４２－８－８ʻ３５３６ː６ʻ６６ˑ４ʻ２４６３－３＋２０ʻ５０２５＋９＋２０ʻ５５４４－（１０＋４）ʻ２０三㊁估算一下下面哪些算式的得数比８０大，在（㊀㊀）中画 ɿ （６分）９０－１１（㊀㊀）３１＋５２（㊀㊀）２３＋４１＋２９（㊀㊀）９８－１７（㊀㊀）３８＋３９（㊀㊀）１００－１０－１２（㊀㊀）四㊁下面的两个角，哪个角大？哪个角小？用三角板比一比㊂在大的下面画 ɿ （２分）五㊁在方格纸上画一个直角（４分）六㊁把下面的加法算式改写成乘法算式（６分）４＋４＋４＝ѲˑѲ＝Ѳ６＋６＋６＋６＝ѲˑѲ＝Ѳ２＋２＋２＋２＋２＝ѲˑѲ＝Ѳ七㊁括号里最大能填几（１２分）（㊀㊀）ˑ４＜２５３４＞５ˑ（㊀㊀）４ˑ（㊀㊀）＜１７（㊀㊀）ˑ５＜２７１４＞６ˑ（㊀㊀）（㊀㊀）ˑ６＜３８八㊁看图列算式并计算出结果（１０分）（㊀㊀）个（㊀㊀）乘法算式：㊀㊀㊀㊀㊀㊀㊀㊀和㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀除法算式：㊀㊀㊀㊀㊀㊀㊀㊀和㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀九、解决问题（３６分）１．下面是姐姐㊁妹妹和弟弟三人各有的邮票枚数㊂（１８分）种类１０分２０分３０分４０分５０分姐姐（枚）２４１１２２１９４妹妹（枚）２６１８１８２０８弟弟（枚）７６１１２２６合计（枚）㊀㊀（１）算一算姐姐㊁妹妹和弟弟三人共有各种邮票的枚数，填在表格内㊂（１０分）（２）如果要把５０分的邮票三个人平均分配，每人可分得多少枚？（４分）（３）根据表格内容再提出两个问题并列式解决㊂（４分）２．看图完成练习㊂（１０分）（１）小华买一架玩具飞机㊁一辆玩具汽车㊁一艘玩具轮船，一共要用多少元？（３分）（２）小林有５０元钱，可以买哪几样玩具？（４分）（３）小青想花最少的钱买两样玩具，他可以买哪两样玩具？（３分）３．小亮计划写２０个大字㊂（８分）（１）一天写５个，几天能写完？（２）他昨天写了４个，今天写了７个，明天还要写多少个就能写完？期中评估检测题（第一套）（Ｂ卷）（总分：１００分㊀时间：７０分钟）一㊁填空题（３４分）１．计算８ː４＝（㊀㊀），用到的口诀是（㊀㊀㊀㊀）㊂根据口诀 三五十五 可以解决哪些计算？（㊀㊀㊀㊀）（㊀㊀㊀㊀）（㊀㊀㊀㊀）（㊀㊀㊀㊀）２．有１２根香蕉平均分给６只小猴，每只小猴分（㊀㊀）根；如果平均分给４只小猴，每只小猴分（㊀㊀）根㊂３．二年级一班有２２名女同学，男同学比女同学多１３人，全班共有（㊀㊀）人㊂４．一个正方体，从正面看是（㊀㊀），从侧面看是（㊀㊀），从上面看是（㊀㊀）㊂５．在括号里填上 ＞ ＜ 或 ＝ ㊂６＋３（㊀㊀）６ˑ３㊀㊀６ˑ６（㊀㊀）４７－１５６．在括号里填入适当的数㊂９＋８＝３０－（㊀㊀）㊀㊀６ˑ６＝４２－（㊀㊀）７．计算１００－３４－５６时，我们可以按照从左往右的顺序，先算（㊀㊀），得（㊀㊀），再算（㊀㊀），得（㊀㊀），最后得（㊀㊀）；也可以先计算（㊀㊀）＋（㊀㊀），再用１００－（㊀㊀），结果还是（㊀㊀）㊂８．把口诀补充完整㊂二四（㊀㊀）㊀㊀三五（㊀㊀）㊀㊀四六（㊀㊀）㊀㊀二（㊀㊀）一十９．数一数下面的图形中分别有几个角㊂（㊀㊀）个角㊀㊀㊀（㊀㊀）个角㊀㊀㊀（㊀㊀）个角㊀㊀㊀（㊀㊀）个角１０．二年级同学们去电影院看电影，二（１）班去了３９人，二（２）班去了３２人，二（３）班去了２８人㊂三个班一共去了（㊀㊀）人㊂二㊁竖式计算（１２分）㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀３６＋４８＝８４－６７＝３８＋４７－６５＝三㊁用你喜欢的方式进行计算（９分）㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀９６－５＝８０－６＝７４－４６＝５６－２６＝３０＋１５＝５ˑ６＝３ˑ４＝４５＋１２－９＝四㊁看图写算式（１２分）１．看图写出两个算式并写出口诀㊂（６分）㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀或㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀口诀：㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀２．写出乘法算式，再读出来㊂（６分）（１）４个２相加（２）３乘５（３）６和４相乘五㊁观察物体，画一画，连一连（８分）１．请你在淘气看到的图下面画，在笑笑看到的图下面画㊂２．右面这些照片分别是谁拍的？请连线㊂小云㊀㊀㊀㊀小红㊀㊀㊀小芳㊀㊀㊀六㊁解决问题（２５分）１．学校买了５８本科技书和３６本故事书，科技书比故事书多多少本？２．小明家的鸡圈里原来有４５只小鸡，妈妈上个星期卖掉了１２只，这个星期又卖掉了１５只㊂现在鸡圈里还剩下几只小鸡？３．公共汽车上原有３８名乘客，到儿童活动中心有９名乘客下车，有１２名乘客了上车㊂汽车上现在有多少名乘客？４．二年级一班有５组同学，平均每组有５人，全班同学都参加了合唱比赛，二年级一班有多少人参加了合唱比赛？。
外研社通用英语1(本科版) 期中测试卷 A附答案
Midterm Test APart I Listening comprehension (10 points)Section AIn this section, you will hear a news report. At the end of the news report, you will hear three questions. Both the news report and the questions will be spoken only once. After you hear a question, you must choose the best answer from the four choices marked A, B, C, and D.Questions 1 to 3 are based on the news report you have just heard.1. A. 75 percent of its population.B. 85 percent of its population.C. 75 percent of priority patients.D. 95 percent of priority patients.2. A. General practitioners.B. Newly graduated medical students.C. Doctors at hospitals.D. Doctors of traditional Chinese medicine.3. A. Medical insurance system. B. Government.C. Individuals.D. All of the above.Section BIn this section, you will hear a long conversation. At the end of the conversation, you will hear four questions. Both the conversation and the questions will be spoken only once. After you hear a question, you must choose the best answer from the four choices marked A, B, C, and D.Questions 4 to 7 are based on the conversation you have just heard.4. A. New Year’s Day. B. Thanksgiving Day.C. Valentine’s Day.D. Easter.5. A. Wash their hair. B. Take a bath.C. Decorate their houses.D. Cook a big meal.6. A. Have traditional food. B. Go to church.C. Visit relatives.D. Watch sports.7. A. Pleasure and happiness. B. Good luck and success.C. Health and wealth.D. Laughter and joy.Section CIn this section, you will hear a passage. At the end of the passage, you will hear three questions. Both the passage and the questions will be spoken only once. After you hear a question, you must choose the best answer from the four choices marked A, B, C, and D.Questions 8 to 10 are based on the passage you have just heard.8. A. The 1st century BC. B. The 16th century.C. The 18th century.D. The 19th century.9. A. The arrival of potatoes. B. The arrival of tomatoes.C. The arrival of peppers.D. The arrival of carrots.10. A. Before World War I. B. After World War I.C. Before World War II.D. After World War II.Part II Vocabulary & Structure (20 points)Section AChoose the best option for each sentence.1. I have a _______ to make—I lied about my age.A. confusionB. collisionC. confessionD. corruption2. It would have been nice to give him a _______ and a kiss but there wasn’t time.A. cuddleB. bubbleC. dribbleD. riddle3. They managed to _______ until help arrived.A. hold onB. hold forthC. hold awayD. hold with4. It was me _______ broke the vase.A. whomB. whichC. whoD. when5. The two teams are _______ for the championships.A. capturingB. battlingC. warningD. teasing6. _______ are usually the first things that attract tourists and they are icons of the cities.A. LandmarksB. HolidaysC. GiftsD. Changes7. When Johnson arrived home after the championships, a big _______ was held in his honor.A. dramaB. paradeC. exhibitionD. display8. Pop music is such an important part of society _______ it has even influenced our language.A. asB. thatC. whichD. where9. He won’t be able to pass the final exams _______ he works hard.A. ifB. unlessC. forD. since10. Volunteering can bring great benefits, so a lot of people _______ a paintbrush, a trash bag, or whatever they need to help their community in spare time.A. grabB. pushC. catchD. glance Section BFill in each blank with the proper form of the words or phrases in brackets.1. ____________ (If/If only) you heat ice, it turns to water.2. I won’t let you in _____________ (if/unless) you show me your pass.3. They resigned _____________ (rather than/other than) take part in such a dishonest transaction.4. He made _____________ (such/so) a good speech that he won warm applause.5. According to the report, residents of Hawaii have the longest life _____________ (span/scale): 77.2 years.Section CComplete the passage with the appropriate words or phrases in brackets.Chinese New Year starts with the new moon on the first day of the new year and ends on the full moon 15 days later. The 15th day of the new year is calledthe Lantern Festival, which is (1) _______________(consumed/celebrated/manifested) at night with lantern displays and children carrying lanterns in a parade.New Year's Eve and New Year's Day are celebrated as a family affair, a time of (2) _______________ (reunion/separation/isolation). The celebration was traditionally highlighted with a ceremony given (3) _______________ (instead of/in aid of/in honor of) Heaven and Earth (万物) and the family ancestors.The ceremony honoring the ancestors, the most (4) _______________ (irrelevant/trivial/vital) of all the rituals, united the living members with those who had (5) _______________ (passed out/passed away/passed by). Departed relatives are remembered with great respect because they were responsible for laying the foundations for the fortune and glory of the family.The presence of the ancestors is acknowledged on New Year's Eve with a dinner arranged for them at the family banquet table. The spirits of the ancestors, together with the living, celebrate the start of the New Year as one great community. The communal feast called "surrounding the stove" or weilu. It symbolizes family unity and honors the past and present generations.Part III Reading comprehension (40 points)Section AIn this section, there is a passage with 10 blanks. You are required to select one word for each blank from a list of choices given in a word bank following the passage. Read the passage carefully before making your choices. You may not use any of the words in the bank more than once.There is an interestingancient China, there was a king who was very to the people. The peoplewere so angry that some brave ones overthrowing the king. So they wrote notes about the meeting place and time and put them into cakes. On the 15th day of the eighth lunar month, every person was told to buy the cakes. When they atethem, they the notes. So they gathered together to make a sudden attackon the king. From then on, the Chinese peoplethat day and eat “mooncakes” in memory of that important event.When the Mid-autumn Festival is near, shop windows are beautifullyas, fruits and moon cakes to their friends andthey have a feast. After the feast, they go out to watch the moon.It is believed that the moon is round and brightest on that night. Manyhave been written about it, and poets are never tired of reading and writing suchpoems. In Chineseto a mirror, a jade rabbit and so on. It seems that Chinese literature takes far more interest in the moon than in the sun.Section BIn this section, you are going to read a passage with five statements attached to it. Each statement contains information given in one of the paragraphs. Identify the paragraph from which the information is derived. You may choose a paragraph more than once. Each paragraph is marked with a letter.A)China is a country with a long history, and so is its diet culture. Since ancienttimes, China has such a claim: people regard food as their prime want(民以食为天).B)China has eight regional styles of cooking. They are Shandong cuisine, Jiangsucuisine, Sichuan cuisine, Cantonese cuisine, Zhejiang cuisine, Anhui cuisine, Hunan cuisine and Fujian cuisine.C)This situation results from natural factors and social factors. Geography andclimate lead to crop varieties. Politics, economy and dietary habits are the social factors that cause the differences.D)Although there are eight regional styles of cooking, they have commoncharacteristics. First, flavor variety. Second, diet difference. Third, aesthetic feelings like color, taste, shape and so on. Fourth, health preservation (养生).E)I n China, foods are given different meanings so that on particular occasion onekind of food only can be eaten by some specific individuals.F) A snapper’s head or shells can be served to honor a guest or to show welcomein some districts.G)Long noodles is the symbol of longevity in China so that seniors may be offereda bowl of such noodles on their birthday.H)In central China, if a baby is born, red boiled eggs are presented to announcethe news. An even number, usually six or eight of red boiled eggs with a black point dotted on one end will be delivered for a boy, and an odd number, usually five or seven without black points for a girl.I)Fish is always served to symbolize prosperity and wealth accumulation on NewYear’s Eve.J)There are other foods and snacks symbolizing good wishes under special circumstances, such as duck, chicken and melon seeds.__________ 1. If a baby is born, red boiled eggs are presented to announce the news. __________ 2. All the regional styles of cooking have common characteristics.__________ 3. Long noodles symbolize long life.__________ 4. In China, there are eight regional styles of cooking.__________ 5. Fish is usually served on New Year’s Eve to symbolize prosperity. Section CThere are two passages in this section. Each passage is followed by some questions. For each of them, you must choose the best answer from the four choices marked A, B, C, and D.Passage OneAs the world navigates the current pandemic, there has been a dramatic increase in how much time families are spending together, leading many parents in the US to feel pressured into being everything–parent, friend, teacher–for their child. Child developmental psychologist Junlei Li, who worked with the China Welfare Institute, says it doesn’t have to be that way, and families can look to China’s families for examples of how to find balance and support through the pandemic.Find ways to connect and share within and beyond your familyThe China Welfare Institute asked for videos and photos submissions of things parents and children are doing together, and shared stories of lots of families, providing a glimpse of what support can look like. Li suggests that all families should find similar ways to enjoy being with each other that relieve pressure for all members of the family.Emphasize playPlay provides a way for children to process their emotions, says Li. Families should plan time to play every day. Children should take the lead in thinking about how they want to play, what they want to play, and whom they want to play with. Although many children have limited opportunity right now, Li says families can create the environment where children can match their needs through play.Find ways to create new modes of learningLi witnessed many families in China taking advantage of learning through observation and doing. He suggests finding simple ways to let your child pitch in. Consider when childr en demand what they want or don’t want to eat and take advantage of this time to let children take part in cooking. For example, have children come up with something they want to cook with their parents and then eat it. Along the way, Li says it helps restore some sense of control in children too.Ultimately, these small adjustments can help the whole family as everyone gets used to differences in their daily life, says Li.1. Why do parents feel pressured according to the passage?A. Because they have more duties than before.B. Because they are afraid of the pandemic.C. Because their children don’t listen to them.D. Because they have lots of housework to do.2. Why did the China Welfare Institute share stories of families?A. To improve the image of the organization.B. To show other families how to support each other during the pandemic.C. To honor the families who did well in supporting each other.D. To attract more people working with the organization.3. How should play be carried out to truly help children?A. Let parents make the rules about what to do.B. Let the China Welfare Institute supervise the play.C. Let more people join the play, such as the families’ neighbors.D. Let children take the lead in play.4. Which is not the benefit of creating new modes of learning?A. To help children learn more things through observation and doing.B. To help children become a better cook.C. To help children restore sense of control.D. To help families find balance and support through the pandemic.5. Which is the best title of this passage?A. Pressured Chinese during the pandemic.B. How to spend your time with children.C. Three small adjustments that can take the pressure off families during the pandemic.D. How to learn skills in a new way during the pandemic.Passage TwoChina has various traditional festivals which have been deep-rooted in Chinese culture with a thousand years of history. Here we listed the top four Chinese festivalswith dates and celebrations.Chinese New YearThe Chinese New Year, also known as the Spring Festival, falls on the first day of the first lunar month.Chinese New Year is the most important festival in China.It is a grand family reunion time for Chinese people around the world.The theme of the Spring Festival is to see the old year off and get ready for the new. There are lots of traditions and celebrations associated with the festival, such as putting up spring couplets, setting off fireworks, having a reunion dinner,and giving red packets.Lantern FestivalThe Lantern Festival, also known as Yuan Xiao Jie or Shang Yuan Festival, falls on the 15th day of the first lunar month. It symbolizes the end of the Chinese New Year celebration.Yuanxiao is a must-eat food for the Lantern Festival.Shaped like a round ball, yuanxiao symbolizes people’s desires for happiness and family reunion.Besides eating yuanxiao, Chinese people would also light colorful lanterns and guess lantern riddles to celebrate this festival.Dragon Boat FestivalThe Dragon Boat Festival, also known as Duan Wu Jie in Chinese,falls on the fifth day of the fifth lunar month. Chinese people celebrate this festival by racing dragon boats, eating zongzi, drinking realgar wine,and hanging Chinese mugwort to honor Qu Yuan, an ancient historic figure, who sacrificed himself for the love of his country.Qingming FestivalThe Qingming Festival, also called Tomb Sweeping Day,is not only a traditional Chinese festival but also the fifth of the traditional Chinese 24 Solar Terms. It usually falls on April 4 or April 5 every year.Qingming, literally meaning “clear and bright”, heralds a season of rising temperature and increasing rainfall, which is a high time for plowing and sowing. It is also a day for people to go out for tomb sweeping, spring outings, and kite flying.6. Why do the dates of traditional Chinese festivals usually change every year?A. Because they are based on the Chinese lunar calendar.B. Because they are according to the solar calendar.C. Because they are on special days.D. Because the government changes the dates.7. Which is NOT the tradition of the Spring Festival?A. Putting up spring couplets.B. Setting off fireworks.C. Giving red packets.D. Eating yuanxiao.8. What does yuanxiao symbolize according to the passage?A. Family union.B. People's desires for happiness.C. Success.D. Good wishes.9. When would people drink realgar wine?A. On Spring Festival.B. On Lantern Festival.C. On Dragon Boat Festival.D. On Qingming Festival.10. Which is NOT the feature of Tomb Sweeping Day?A. Tomb sweeping.B. Spring outings.C. Kite flying.D. Tree planting.Part IV Translation (15 points)Section ATranslate the following sentences into English.1.让我接受不了的是他说话的方式。
北京市海淀区2023~2024学年高三上期中数学参考答案
第 1 页（共 7 页）海淀区2023—2024学年第一学期期中练习高三数学参考答案一、选择题（共10小题，每小题4分，共40分） （1）B （2）A （3）D （4）C （5）C （6）D（7）C（8）C（9）B （10）A二、填空题（共5小题，每小题5分，共25分） （ 11 ）(1,0)(0,)-+∞（12）43（13）1- 1（答案不唯一）（14）3π2 π8（15）①③三、解答题（共6小题，共85分） （16）（共14分）解：（Ⅰ）设等比数列{}n a 的公比为q .因为23a =，1310a a +=， 所以13a q ⋅=，21110a a q +⋅=． 所以13,1,q a =⎧⎨=⎩或11,39.q a ⎧=⎪⎨⎪=⎩因为n a 均为整数， 所以13,1.q a =⎧⎨=⎩所以13n n a -= (1,2,3,)n =．（Ⅱ）由（Ⅰ）知，312n n S -=(1,2,3,)n =．所以1113131132323222k k k k k S S +++--+-=⋅-⋅=， 2112131311322222k k k k k S S +++++--+-=-⋅=．第 2 页（共 7 页）所以1121132322k k k k k S S S S +++++-=-=.所以3k S ，12k S +，2k S +是以1132k ++为公差的等差数列．（17）（共14分）解：选择条件①：π()13f =.（Ⅰ）因为()2cos cos()f x x x ϕ=⋅+，所以ππ2cos cos()133ϕ⋅+=，即πcos()13ϕ+=.所以π2π()3k k ϕ=-∈Z .因为||2ϕπ<，所以π3ϕ=-． （Ⅱ）由（Ⅰ）可得：π()2cos cos()3f x x x =⋅-12cos (cos )2x x x =212cos 22x x =⋅11cos2222x x =+ π1cos(2)32x =-+.因为π[,0]2x ∈-，所以4πππ2333x ---≤≤．所以当π2π3x -=-，即π3x =-时，πcos(2)3x -取得最小值1-. 所以()f x 在区间π[,0]2-上的最小值是12-；当ππ233x -=-，即0x =时，πcos(2)3x -取得最大值12． 所以()f x 在区间π[,0]2-上的最大值是1．第 3 页（共 7 页）选择条件③：x ∀∈R ，2π()()3f x f ≥. （Ⅰ）由题意得：()2cos cos()f x x x ϕ=⋅+2cos (cos cos sin sin )x x x ϕϕ=⋅-⋅ 22cos cos sin 2sin x x ϕϕ=⋅-⋅cos2cos sin 2sin cos x x ϕϕϕ=⋅-⋅+ cos(2)cos x ϕϕ=++.因为x ∀∈R ，2π()()3f x f ≥， 所以()f x 的最小值为2π()3f ，即4πcos()13ϕ+=-.所以4ππ(21)π2π()33k k k ϕ=+-=-∈Z . 因为||2ϕπ<，所以π3ϕ=-． （Ⅱ）同选择条件①的（Ⅱ）.（18）（共12分）解：（Ⅰ）由题意令240x -=得2x =±．所以(2,0)A -，(2,0)B .因为点(,0)P t 在线段AB 上（不与端点重合）， 所以22t -<<.因为APQ △为等腰直角三角形， 所以||||PQ AP =.由题意可知点Q 在x 轴上方， 所以(,2)Q t t +． 因为点Q 在曲线C 上， 所以224t t +=-.所以12t =-（舍），21t =，即(1,3)Q .所以APQ △的面积为119||||33222AP PQ =⨯⨯=．第 4 页（共 7 页）（Ⅱ）由题意可知2(,4)Q t t -，22t -<<.所以23211()(2)(4)(248)22S t t t t t t =+-=--++．所以21'()(344)2S t t t =--+.令23440t t --+=，得12t =-，223t =． ()S t 与'()S t 在区间(2,2)-上的情况如下：因为2()327S =，所以当23t =时，()S t 取得最大值12827．（19）（共13分）解：（Ⅰ）连接AB .因为135ADB ∠=︒，120BDC ∠=︒，所以105ADC ∠=︒． 因为45ACD ∠=︒， 所以30CAD ∠=︒. 在ACD △中，sin sin CD ADCAD ACD=∠∠． 所以AD =． 因为30BCD ∠=︒， 所以30DBC ∠=︒． 所以BD CD =.在ABD △中，2222cos135AB AD BD AD BD =+-⋅︒25CD =.因为50CD =，第 5 页（共 7 页）所以AB ==，即A ，B两点之间的距离为m . （Ⅱ）CD 与AB 不垂直．理由如下：延长CD 交AB 于点E . 在ABD △中，sin sin AB ADADB ABD=∠∠.所以1sin 2ABD ∠<. 因为090ABD ︒<∠<︒， 所以30ABD ∠<︒.所以18090BEC CBE BCD ∠=︒-∠-∠>︒. 所以直线CD 与直线AB 不垂直．（20）（共14分）解：（Ⅰ）因为1(1)4f =，2(4)19f =，所以11,1422,1619a b a b +⎧=⎪⎪+⎨+⎪=⎪+⎩解得0,3.a b =⎧⎨=⎩（Ⅱ）由（Ⅰ）得()f x =．所以'()f x =2=.令'()0f x =，得1x =．当(0,1)x ∈时，'()0f x >；当(1,)x ∈+∞时，'()0f x <. 所以()f x 的单调递增区间是(0,1)；单调递减区间是(1,)+∞. （Ⅲ）由（Ⅱ）可知当1x =时，()f x 取得最大值14. ①当14m =时，存在直线14y =是曲线()y f x =在点1(1,)4处的切线，且1()4f x ≤EDCBA第 6 页（共 7 页）对[0,)x ∈+∞恒成立，符合题意． ②当14m >时，设直线y kx m =+为曲线()y f x =的切线，切点为00(,)x y ，则000,1.4x y >⎧⎪⎨≤⎪⎩ 所以000y mk x -=<． 取1mx k=-，则10x >.因为11()03f x x =>+，10kx m +=，所以11()kx m f x +<，即存在1(0,)x ∈+∞，11()kx m f x +<，不符合题意. 综上可知，m 的最大值是14．（21）（共15分）解：（Ⅰ）19A =,235A =． （Ⅱ）由题意知221()332n n S =-⨯-. ①若j 为奇数，则111()02j j j j S S a ++-==-<.所以 j ∉Ω．②若j 为偶数，则当1,2,k j j =++时，211211[()()][()()]0322322j k j k k j S S -=⨯---≥⨯->. 所以 j ∈Ω．所以 {|2,1,2,}x x m m Ω===.（Ⅲ）（1）若Ω为有限集，设其最大元素为m （若Ω为空集，取0m =），则当1,2,j m m =++时，存在k j >满足0k j S S -<.令11i m =+，1min{*|,0}n n n k i i k k i S S +=∈>-<N （1,2,n =），则第 7 页（共 7 页）10n n n i i A S S +=-<. 所以 sgn()1n A =-（1,2,n =）；（2）若Ω为无限集，设12{,,}j j Ω=，其中12j j <<，记1n n n j j B S S +=-，则0n B ≥（1,2,n =）.①若数列{}n B 中只有有限项为正数，记max{*|0}n m n B =∈>N （若{}n B 中没有正数项，取0m =），则0m n B +=（1,2,n =）．令n m n i j +=（1,2,n =），则10n n n i i m n A S S B ++=-==（1,2,n =）.所以 sgn()0n A =（1,2,n =）；②若数列{}n B 中有无穷项为正数，将这些项依次记为12,,t t B B ，其中12t t <<，则10n t t nnt j j B S S +=->（1,2,n =）.令n n t i j =（1,2,n =），则+1+1+11+++=0tt n n n n n nn j j t t t t A S S B B B B -=-=>.所以 sgn()1n A =（1,2,n =）.综上所述，对任意的无穷数列{}n a 都存在数列{}n i ，使得{sgn()}n A 为常数列.。
小学上册K卷英语第1单元期中试卷
小学上册英语第1单元期中试卷考试时间：90分钟（总分:100）B卷一、综合题(共计100题共100分)1. 选择题：What do you call a person who studies the environment?A. EcologistB. Environmental scientistC. ConservationistD. All of the above答案:D2. 选择题：What do you call the person who teaches you in school?A. DoctorB. TeacherC. ChefD. Engineer答案：B3. 听力题：A chemical reaction can release energy in the form of _____.4. 填空题：The _____ (水果) from berry bushes is nutritious.5. 填空题：A snail leaves a slimy ______ (痕迹).6. 填空题：She has a big _____ (洋娃娃) collection.7. 填空题：I wish I could have a _________ (玩具飞船) to explore outer space.8. 选择题：What do you call a person who studies ancient cultures?A. HistorianB. ArchaeologistC. AnthropologistD. Sociologist9. 听力题：The Earth is about ______ billion years old.10. 听力题：The capital of Libya is __________.11. 听力题：The ice cream is ________ cold.12. 选择题：What is the largest land animal?A. ElephantB. LionC. GiraffeD. Rhino答案:A13. 听力题：The process of rusting is an example of a __________ reaction.14. 填空题：My brother is always __________. (忙碌)15. 填空题：The __________ (历史的情感纽带) connect communities.16. 填空题：The ancient Egyptians believed in many _____ gods.17. 听力题：My sister is a ______. She loves to make crafts.18. 填空题：The owl hoots softly in the ______ (夜晚).19. 听力填空题：Celebrating holidays is special for me. During __________, my family and I __________. We decorate our home with __________ and cook delicious meals together.20. 听力题：My turtle is very ______ and slow.He is a _____ (厨师) who makes delicious food.22. 听力题：Plants release oxygen during ______.23. 听力题：The chemical formula for magnesium chloride is ______.24. 填空题：Napoleon Bonaparte was a leader in _____.25. 听力题：We have a _____ (展览) at the museum.26. 听力题：We will _____ (travel/stay) at home.27. 听力题：The chemical formula for potassium chloride is __________.28. 选择题：What is the value of 5 × 5 15?A. 10B. 15C. 20D. 25答案:A29. 听力题：I like to _____ (探索) different cuisines.30. 选择题：What do we call the study of the classification of organisms?A. TaxonomyB. EcologyC. BiologyD. Genetics31. 选择题：Which sport uses a net and a ball?A. SoccerB. TennisC. BaseballD. Golf答案: BWhich animal is known for being very slow?A. RabbitB. TurtleC. CheetahD. Elephant答案:B33. 选择题：What do we call the time when the leaves change color?A. SpringB. WinterC. FallD. Summer34. 填空题：The ________ (土地利用) is important for agriculture.35. 选择题：What do you call the study of living things?a. Biologyb. Chemistryc. Physicsd. Astronomy答案:a36. 听力题：The _____ (bird/fish) is chirping.37. 听力题：In a chemical reaction, substances change into __________ substances.38. 听力题：The sun is shining ________ today.39. 听力题：My friend is a ______. He wants to be an astronaut.40. 填空题：Certain plants have ______ that allow them to survive in cold climates. (某些植物有耐寒的特性，使它们能够在寒冷的气候中生存。
2023—2024学年北京市海淀区高三上学期期中练习数学试题(含答案)
a
2
2 cos
2
2 sin 2 可看作是点 Q
2 cos, 2 sin 到点 R a, 2 的距离，即可
求解. 【详解】以 M 为圆心，以 MA, MC 为 x, y 轴，建立如图所示的空间直角坐标系，
由于 AB AC 2, 所以 BC 2 2, BM CM 2 ，
(1)求 A, B 两点之间的距离；
(2)判断直线 CD 与直线 AB 是否垂直，并说明理由．
20．已知函数
f x
x a ，且 f 1 1 , f 4 2 ．
x2 b
4
19
(1)求 a,b 的值；
(2)求 f x 的单调区间；
(3)设实数 m 满足：存在 k R ，使直线 y kx m 是曲线 y f x 的切线，且 kx m f x 对
A． 9 4
B．3
6．设
a
log4 6,b
log23, c
3 2
，则（
）
A． a b c
B． c b a
C．9 C． b a c
D．36 D． b c a
7．“ sin tan 0”是“ 为第一或第三象限角”的（ ）
A．充分而不必要条件
B．必要而不充分条件
C．充分必要条件
D．既不充分也不必要条件
x 0, 恒成立，求 m 的最大值．
21．设无穷数列an 的前 n 项和为 Sn ,in 为单调递增的无穷正整数数列，记 An Sin1 Sin ，
n 1, 2, ，定义 Ω j N* Sk S j 0, k j 1, j 2, ．
(1)若 an n, in n2 n 1, 2, ，写出 A1, A2 的值；
因为 y log2 x 是增函数， 6 8 9 ，
山东省诸城市树一中学2023年化学九上期中考试试题含解析
山东省诸城市树一中学2023年化学九上期中考试试题注意事项：1．答卷前，考生务必将自己的姓名、准考证号、考场号和座位号填写在试题卷和答题卡上。
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一、单选题（本题包括12个小题，每小题3分，共36分．每小题只有一个选项符合题意）1．下列变化中，属于化学变化的是（）A．干冰升华B．纸张燃烧C．铜丝折弯D．酒精挥发2．下列实验操作正确的是A．取用液体B．倾倒液体C．读取液体体积D．点燃酒精灯3．水是地球上最普通，最常见的物质之一，下列有关水的说法正确的是（）A．淡水资源取之不尽，无需节约B．长期饮用蒸馏水不利于健康C．大量使用农药、化肥对水体无污染D．矿泉水中只含有水分子，不含其他粒子4．元素在自然界里分布并不均匀，如澳大利亚多铁矿，山东的黄金储量居我国首位，但从整个的地壳含量的多少分析，最丰富的金属元素是A．Al B．Fe C．O D．Si5．区分下列物质，括号中所用方法或试剂正确的是A．食盐水与蒸馏水(蒸发)B．二氧化锰和木炭粉(看颜色)C．氧气和二氧化碳(闻气味)D．食盐与蔗糖(水)6．下列成语中，涉及化学变化的是（）A．滴水成冰B．死灰复燃C．刻舟求剑D．大海捞针7．鉴别空气、氧气和二氧化碳三瓶气体，最常用的方法是（）A．将带火星的木条分别伸入集气瓶中B．观察颜色并闻它们的气味C．将燃着的木条分别伸入集气瓶中D．将气体分别通入紫色石蕊溶液中8．在反应4Zn+10HNO3═4Zn（NO3）2+X+3H2O中，X的化学式为（）A．NH3B．NH4NO3C．NO D．NO29．粗盐提纯实验中，搭建蒸发装置时，下述操作中应首先进行的是 ( )A．将蒸发皿放置在铁圈上B．固定铁圈位置C．点燃酒精灯D．放置酒精灯10．美国科学家在真空环境下对镁铝粉末进行高压挤压，将空气挤出，得到全透明的铝合金，常称为全透明铝．它比玻璃要强韧得多，能经受沙尘和雨水的侵蚀，可应用于汽车玻璃等．有关全透明铝叙述正确的是( )A．全透明铝应该属于纯净物B．全透明铝也可能应用于手机屏幕C．全透明铝中原子不运动D．全透明铝与普通铝粉的化学性质相同11．2019年1月3日，嫦娥四号探测器成功软着陆月球背面。
小学上册K卷英语第一单元期中试卷
小学上册英语第一单元期中试卷英语试题一、综合题(本题有50小题，每小题1分，共100分.每小题不选、错误，均不给分)1 We play ________ (games) after school.2 What is the smallest continent?A. AsiaB. AfricaC. AustraliaD. Europe3 What is 20 + 30?a. 40b. 50c. 60d. 70答案:b4 What is the name of the musical instrument with keys?A. GuitarB. FluteC. PianoD. Drums答案: C5 The chemical formula for caffeine is ________.6 It is _____ to play outside. (fun)7 I saw a ladybug on the ________.8 What is the name of the planet known for its rings?A. SaturnB. JupiterC. NeptuneD. Uranus答案:A9 The __________ was a major conflict fought in Europe. (第一次世界大战)10 The __________ is a significant natural resource found in forests. (木材)11 The _______ of a substance affects its reactivity. (温度)12 What is the opposite of morning?A. NightB. NoonC. AfternoonD. Evening13 What do you wear to keep warm in winter?A. ShortsB. T-shirtC. CoatD. Sandals答案: C. Coat14 War was a period of tension between the USA and the ______ (苏联). The Cold15 The _____ (小羊) bleats when it is hungry.16 Did you see the _____ (小狗) wagging its tail?17 What do you call a place where books are kept?A. LibraryB. MuseumC. ClassroomD. Theater答案: A18 My mom makes the best _____ (soup/salad).19 I saw a ________ jumping in the river.20 Please pass me the ________.21 What is the smallest unit of life?A. OrganB. TissueC. CellD. System答案: C22 The clock shows _____ (ten/twelve).23 What do we call a person who studies the behavior of people?A. PsychologistB. SociologistC. AnthropologistD. All of the above24 The beauty of floral displays can enhance any ______ or event. (花卉展示的美丽可以提升任何场合或活动的氛围。
小学下册K卷英语第1单元期中试卷
小学下册英语第1单元期中试卷考试时间：100分钟（总分:110）A卷一、综合题(共计100题共100分)1. 填空题：__________ (外部条件) can alter the outcome of a chemical experiment.2. 听力题：Star maps help astronomers locate _______ in the night sky.3. 选择题：What is the name of the small, red fruit that is often mistaken for a vegetable?A. TomatoB. PeachC. CherryD. Strawberry答案: A4. 听力题：The ______ runs the local store.5. 听力题：A ______ has bright feathers.6. 听力题：My aunt is a ______. She loves gardening.7. 选择题：Which planet is known as the Red Planet?A. EarthB. MarsC. JupiterD. Saturn答案:B8. 选择题：What is the opposite of hot?B. WarmC. CoolD. Spicy9. 选择题：What is the opposite of hot?A. WarmB. ColdC. CoolD. Freezing答案: B10. 选择题：What is the name of the famous cartoon character known for his love of carrots?A. Daffy DuckB. Bugs BunnyC. Tweety BirdD. Porky Pig11. 填空题：The _____ (diary) helps track plant growth.12. 听力题：Light pollution makes it hard to see the _______ at night.13. 选择题：What is the capital city of Japan?A. BeijingB. SeoulC. TokyoD. Bangkok答案:C14. 填空题：The _____ (植物挑战) encourages sustainable practices.15. 听力题：The chemical formula for carbon dioxide is __________.16. 选择题：What is the main ingredient in chocolate?A. CocoaB. SugarC. Milk答案：A17. 听力题：She is wearing a _____ (dress/shirt) today.18. 填空题：A ________ (植物数据分析) informs research.19. 听力题：The process of ______ can lead to new land formations.20. 选择题：What do we call the act of creating something new?A. InventionB. InnovationC. CreationD. All of the above答案: D21. 填空题：A ______ (海豚) can perform tricks for people.22. 听力题：The ____ is a fierce predator found in the wild.23. 选择题：What do we call the person who makes bread?A. BakerB. ButcherC. FarmerD. Chef24. 听力题：My ______ likes to cook delicious food.25. 选择题：What is the largest mammal in the ocean?A. SharkB. WhaleC. DolphinD. Octopus答案:B26. 听力题：I have a pet ______ (hamster).I have a ________ that makes me laugh.28. 听力题：The process of adding more solute to a saturated solution does not increase the _______.29. 听力题：The chemical name for water is ______ oxide.30. 填空题：The __________ (历史的启示作用) motivates individuals.31. oasis) is a fertile area in a desert. 填空题：The ____32. 选择题：What do you call a story that is told using pictures?A. ComicB. NovelC. BiographyD. Journal答案:A33. 填空题：My ________ (玩具名称) brings happiness to my life.34. 填空题：I saw a ________ in the flower bed.35. 选择题：Which of these is a season?A. JanuaryB. SummerC. TuesdayD. Breakfast答案: B36. local governance) empowers residents in decision-making. 填空题：The ____37. 填空题：The __________ (多元文化) enrich our society.38. 填空题：I enjoy making _______ (手工艺品). It lets me be _______ (形容词) and creative.The _____ (lake/ocean) is blue.40. 听力题：I see a _______ (fox) in the forest.41. 听力题：I want to visit the ________.42. 选择题：What is the main function of leaves on a plant?A. Absorb waterB. Make foodC. Provide shelterD. Store nutrients答案:B43. 填空题：The __________ (历史的教训) is invaluable.44. 选择题：What do we call a person who studies stars?A. BiologistB. AstronomerC. GeologistD. Chemist45. 听力题：My cousin loves to paint ____ (murals).46. 填空题：Having a variety of ________ (玩具名) allows me to be more ________ (形容词) in play.47. 选择题：What is the name of the famous cartoon character known for his love of carrots?A. Bugs BunnyB. Mickey MouseC. Donald DuckD. Goofy答案: A48. 填空题：I find joy in small ______ (事物) like a sunny day or a nice cup of hot chocolate. Life is full of little pleasures.What is the process of making bread rise?A. BakingB. FermentationC. CookingD. Mixing答案:B50. 选择题：What is the main organ in the human body that pumps blood?A. BrainB. LungsC. HeartD. Liver答案: C51. 选择题：What do we call the study of the forces that cause motion?A. PhysicsB. ChemistryC. BiologyD. Geology答案:A52. 听力题：The Amazon Rainforest is located in _______.53. 听力题：My mom enjoys organizing ____ (family events).54. 听力题：She is drawing a ___. (sun)55. 填空题：The vulture eats _______ (腐肉).56. 选择题：What is the time of day when the sun rises?A. DawnB. DuskC. MidnightD. Noon57. 听力题：The _______ of a sound can change based on the distance from the source.A ladybug is often considered ______ (幸运的).59. 选择题：Which planet is known as the Red Planet?A. EarthB. VenusC. MarsD. Jupiter60. 填空题：My best friend is __________ (勇敢的).61. 听力题：My grandmother is a ______. She tells me stories from the past.62. 填空题：My brother's favorite animal is the ______ (狮子). It is strong and known as the ______ (森林之王).63. 选择题：What do we call a person who studies physics?A. PhysicistB. ChemistC. BiologistD. Mathematician64. 填空题：My mom and I bake __________ together. (饼干)65. 选择题：What do we call a piece of land surrounded by water on all sides?A. PeninsulaB. IslandC. CoastD. Bay答案: B. Island66. 选择题：What is the main source of energy for plants?A. WaterB. SoilC. SunlightD. Air答案: CWhat do we call a place where animals are kept?A. ZooB. FarmC. ParkD. Forest答案: A68. 填空题：My favorite character is __________ (超级英雄) because he is very brave.69. 填空题：The ________ was a landmark event in the history of civil liberties.70. 听力题：Plants need _______ to grow.71. 听力题：I have ___ (two/three) pets at home.72. 听力题：We eat dinner _____ the dining room. (in)73. 选择题：What is the main ingredient in a Caesar salad?A. LettuceB. SpinachC. KaleD. Arugula74. 填空题：The _______ (The Bolshevik Revolution) led to the establishment of a communist government in Russia.75. 听力题：They are _____ (jumping) on the trampoline.76. 选择题：What do you call a young male sheep?A. LambB. KidC. RamD. Ewe77. 填空题：The first electric light bulb was invented by ________.The __________ (科学技术发展) shapes the future.79. 选择题：What do you call a large group of animals living together?A. PackB. HerdC. FlockD. All of the above80. 填空题：Many gardeners share their __________ (经验) with others.81. 填空题：The _____ (金鲨) glides through the ocean with grace. 金鲨优雅地穿梭于海洋中。
小学上册K卷英语第1单元期中试卷
小学上册英语第1单元期中试卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.The ________ (灌木) can be trimmed into shapes.2.The teacher, ______ (老师), explains difficult concepts clearly.3.The ancient Greeks developed ________ to promote intellectual discourse.4.What is the capital of Singapore?A. Singapore CityB. Marina BayC. Orchard RoadD. SentosaA Singapore City5.What is the first month of the year?A. FebruaryB. MarchC. JanuaryD. DecemberC6.My favorite thing to do during the week is ______.7.What is the currency used in the UK?A. DollarB. EuroC. PoundD. Yen8. A _____ (植物实验室) can conduct important research.9.She is _______ (baking) cookies for the party.10.The weather is very ________ today.11.Her favorite animal is a ________.12.We breathe in _____ and breathe out carbon dioxide.13.My _____ (邻居) is very helpful.14.What do we call a person who repairs cars?A. DoctorB. MechanicC. PilotD. Chef15.I saw a _______ (小猫) chasing its tail.16.She has a ________ for her birthday.17.What instrument is used to measure temperature?A. BarometerB. ThermometerC. HygrometerD. AnemometerB18.The ______ (植物的生长需求) vary by species.19.The _____ (自然景观) features a variety of plant habitats.20.What is the name of the country known for kangaroos?A. CanadaB. AustraliaC. BrazilD. India21.The ______ has a striking appearance.22.My _____ (外甥) loves to play video games.23. A flamingo has long ______ (腿) and stands on one foot.24.What do we call the act of searching for something?A. ExplorationB. InvestigationC. ExaminationD. InquiryA25.The ancient Romans built _______ for public gatherings. (广场)26.The _______ (The Boston Massacre) fueled colonial resistance to British rule.27. A _______ is a reaction that releases heat.28.What do you call a story that is made up?A. FictionB. Non-fictionC. BiographyD. True story29.My favorite color is _______ (紫色).30.I love to eat ______ ice cream.31.The giraffe has a very long _________ (脖子).32.The bunny's nose twitches with _____ curiosity.33.Herbs can be used in both ______ (烹饪) and medicine.34.What is the name of the dinosaur with a long neck?A. Tyrannosaurus RexB. StegosaurusC. BrachiosaurusD. VelociraptorC35.The ________ loves to jump and run.36. A cow's moo can signify different ________________ (情绪).37.I enjoy ___ (baking) cookies.38.Which instrument is played with a bow?A. FluteB. ClarinetC. ViolinD. TrumpetC39. A ____ is a playful animal that loves to swim in the water.40.What is the capital of Egypt?A. CairoB. AlexandriaC. LuxorD. AswanA41.What is the capital city of Argentina?A. Buenos AiresB. SantiagoC. MontevideoD. Lima42.What do we call the study of numbers?A. AlgebraB. GeometryC. MathematicsD. CalculusC43.What do we call the person who makes bread?A. BakerB. ButcherC. FarmerD. Chef44.The __________ (地域文化) enriches our experiences.45.What do we call a young tiger?A. CubB. CalfC. PupD. KittenA46.The ______ works at the library.47. A candle burning is an example of a _______ reaction.48.He wants to be a _____ (doctor/teacher).49.The __________ (历史教育) is important for understanding society.50.The _____ (night) is quiet.51.What is the primary diet of a panda?A. FishB. BambooC. FruitsD. MeatB52.The movement of tectonic plates can create ______ such as mountains and valleys.53.What is 9 + 10?A. 18B. 19C. 20D. 21B54. A _______ is used to measure the amount of liquid in a container.55.How many continents are there?A. FiveB. SixC. SevenD. Eight56.What do you call a baby armadillo?A. PupB. KitC. CalfD. Cub57.What do you call the act of making a choice?A. DecidingB. ChoosingC. SelectingD. PickingA58.My grandma loves to read ____ (novels).59.Which animal says "meow"?A. DogB. CatC. CowD. PigB60. A _____ (植物探索小组) can lead to exciting discoveries.61.I can ______ (认真) consider different perspectives.62.The _______ (Industrial Age) brought significant technological advancements.63. A light year is the distance light travels in one ______.64. (Natives) were the original inhabitants of the Americas. The ____65.I see a big _____ (房子).66.What color do you get when you mix blue and yellow?A. GreenB. PurpleC. OrangeD. BrownA Green67.The __________ was a key moment in the history of the United States. (独立战争)68.The ________ were nomadic tribes that lived in Mongolia.69.The __________ (法老) were the rulers of ancient Egypt.70. A metal that reacts vigorously with water is called a ______ metal.71.My favorite pet is a _______ (狗).72. A shooting star is actually a ______ entering the Earth's atmosphere.73.What is the name of the famous clock tower in London?A. Big BenB. The ShardC. The Eiffel TowerD. The ColosseumA74.________ (植物资源保护) is vital for sustainability.75.The ancient Greeks made significant advances in ________ (建筑).76.The _____ of a star can change over time.77.My favorite character from a series is _______ (名字). 他/她的性格很 _______ (形容词).78.I have a ______ (new) bike.79.What is the smallest continent?A. AfricaB. AustraliaC. AsiaD. Europe80.I have a toy _______ that can dig in the sand.81.The ancient civilizations of ________ are known for their achievements in math.82.看图,判断句子内容与图片信息是(T)否(F)相符。
小学上册K卷英语第一单元期中试卷
小学上册英语第一单元期中试卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.How many sides does a rectangle have?A. ThreeB. FourC. FiveD. Six答案:B2.Certain flowers are favored for their ______ in arrangements and bouquets. (某些花因其在花束和花篮中的美观而受到青睐。
)3.What is the name of the famous bird known for its colorful feathers?A. ParrotB. PenguinC. SparrowD. Crow答案:A4.What is the opposite of "up"?A. DownB. LeftC. RightD. Around5.How many sides does a hexagon have?A. FourB. FiveC. SixD. Seven6. A substance that forms ions in solution is called an ______.7.My favorite ice cream flavor is ______ (巧克力).8.What do you call the sweet food made from nuts and sugar?A. NougatB. CandyC. PralineD. Fudge答案:B9.The _____ (crocodile) is in the river.10.My uncle is great at _______ (名词). 他能 _______ (动词)很多事情.11.The otter plays with _______ (石头) in the water.12.I made a cool _________ (玩具车) out of recycled materials.13.The _______ is the center of our solar system.14.She is wearing a ________ dress.15. A snake can be very ______.16.What is the name of the plant that grows in water and has broad leaves?A. CactusB. LilyC. FernD. Rose答案:B17.The teacher is very _______ (nice).18.The sun is ______ brightly during the day. (shining)19. A _____ (植物) may have medicinal properties.20.My sister loves __________ (动物园).21.What do you call a young eagle?A. EagletB. ChickC. NestlingD. Hatchling答案:A22.Many _____ (insect) live on the leaves.23.What is the name of the famous American president known for the Emancipation Proclamation?A. George WashingtonB. Abraham LincolnC. FranklinD. Roosevelt D. Thomas Jefferson答案:B24.She is _____ (drawing) with chalk.25.An example of a noble gas is _______. (氦)26.Which animal is known for its ability to fly at high altitudes?A. EagleB. SparrowC. PenguinD. Ostrich答案:A27.What is a common animal found on a farm?A. TigerB. PigC. ElephantD. Lion答案:B28.What do we call the force that keeps planets in orbit around the sun?A. MagnetismB. GravityC. FrictionD. Energy29.Which animal is known for having a pouch?A. ElephantB. KangarooC. DogD. Cat答案:B30.The __________ is the layer of the earth that is partially molten.31.The ______ (生态平衡) depends on plants.32.小猫) loves to explore. The ___33.I want to eat _______ (比萨饼) for dinner.34.The life cycle of a butterfly includes metamorphosis, which means ______.35.I like to ___ new things. (learn)36.The process of ______ can alter the landscape significantly.37.The owl can turn its head almost ______ (完全).38. A flamingo gets its pink color from its ______.39.We need to ______ (clean) our room.40. A solution can become saturated when it holds the maximum amount of ______.41.My brother is a ______. He enjoys mentoring younger students.42.The __________ (晨曦) over the mountains is stunning.43. A solution that contains a weak base is called a ______ solution.44.What is the capital of Vietnam?A. HanoiB. Ho Chi Minh CityC. Da NangD. Hue45.I enjoy participating in school ________ (活动) and meeting new friends.46.I have a ________ that tells stories.47.What do you call the area of land that drains into a river?A. WatershedB. BasinC. DeltaD. Floodplain答案:A48.My uncle teaches me about __________ (科技).49.Plants can enhance our ______ (生活质量).50.My favorite _____ is a playful puppy.51.My favorite drink is ________ (牛奶) before bed.52.The library is _____ (quiet/loud) and peaceful.53.The _______ (蛇) is often feared.54.The ________ (生态恢复行动) is ongoing.55.What is the capital of Japan?A. KyotoB. TokyoC. OsakaD. Hiroshima56.What is the smallest prime number?A. 0B. 1C. 2D. 357.What do you call a baby cat?A. PuppyB. KittenC. FoalD. Cub58.The hurricane blew down a ______.59.What is the capital of Liberia?A. MonroviaB. GbarngaC. BuchananD. Robertsport答案:A60. A ____ hops around and has big ears.61.The ______ has a striking appearance.62.The _____ (紫罗兰) blooms in spring.63.I like to _______ (与朋友一起)玩。
小学上册K卷英语第一单元期中试卷
小学上册英语第一单元期中试卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.What tool do you use to write?A. BrushB. HammerC. PencilD. Scissors答案:C Pencil2.The chemical structure of DNA contains ______.3.My brother is __________ years old.4.The _______ grows best in sunny locations.5.The pilot, ______ (飞行员), flies to many countries.6.My grandma gave me a _________ (手工制作的玩具) that is very special.7.The capital of Norway is _______.8.I enjoy playing ________ (桌游) on rainy days.9.My favorite food is _____ (pizza/salad).10.We are going to watch ________ (表演).11.Many _______ are used in traditional medicine.12.My dad is a ______ (doctor).13. A _______ is a factor that can affect the rate of a chemical reaction.14.What do we use to write?A. PaperB. PencilC. TableD. Chair答案:B15.An ionic compound is formed when electrons are _______ between atoms.16.The bison is a strong ____.17.The baby is _____ (crying/laughing).18.The first electric vehicle was built in the _______ century. (19)19.My dog loves to . (我的狗喜欢_。
2022-2023学年河南省商开高一数学上学期期中考试卷及答案解析
商开大联考2022-2023学年上学期期中考试高一数学考生注意：1．本试卷分选择题和非选择题两部分.满分150分，考试时间120分钟.2．答题前，考生务必用直径0.5毫米黑色墨水签字笔将密封线内项目填写清楚.3．考生作答时，请将答案答在答题卡上.选择题每小题选出答案后，用2B 铅笔把答题卡上对应题目的答案标号涂黑；非选择题请用直径0.5毫米黑色墨水签字笔在答题卡上各题的答题区域内作答，超出答题区域书写的答案无效，在试题卷、草稿纸上作答无效.4．本卷命题范围：人教A 版必修第一册第一章～第三章.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. 已知(){}(){},3,,1A x y x y B x y x y =+==-=∣∣，则A B = （ ）A. 2,1x y ==B. ()2,1 C.(){}2,1 D. {}2,1【答案】C 【解析】【分析】利用交集定义即可求得A B⋂【详解】由31x y x y +=⎧⎨-=⎩，可得21x y =⎧⎨=⎩则A B =(){}(){},3,1x y x y x y x y +=⋂-=∣∣()(){}3=,=2,11x y x y x y ⎧⎫+=⎧⎨⎨⎬-=⎩⎩⎭∣故选：C2. 已知a ，b ，c ，d 均为实数，则下列说法正确的是（ ）A. 若a b >，c d >，则a c b d +>+ B. 若a b >，c d >，则a c b d ->-C. 若a b >，c d >，则ac bd > D. 若ac bc >，则a b>【答案】A 【解析】【分析】根据不等式的性质，结合举反例的方法，可得答案.【详解】对于A ，根据同向不等式具有可加性可知A 正确；对于B ，21a b =>=，24c d =->=-，但45a c b d -=<-=，故B 错误；对于C ，21a b =>=，24c d =->=-，但44ac bd =-==-，故C 错误；对于D ，当0c <时，由ac bc >，得a b <，故D 错误．故选：A ．3. 下列函数中，与函数2y x =+是同一函数的是（ ）A. 22y =+B. 2y =+C. 22x y x=+ D.y =【答案】B 【解析】【分析】通过两个函数三要素的对比可得答案.【详解】2y x =+的定义域为R ．对于A ，22y =+的定义域为[)0,+∞，与2y x =+的定义域不同，不是同一函数；对于B ，22y x =+=+定义域为R ，与2y x =+的定义域相同，对应关系相同，是同一函数；对于C ，22x y x=+的定义域为{}0x x ≠，与2y x =+的定义域不同，不是同一函数；对于D，2,2,22,2x x y x x x +≥-⎧==+=⎨--<-⎩与2y x =+对应关系不同，不是同一函数．故选：B ．4. 已知p ：0a b >> q ：2211a b<，则p 是q 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【答案】A 【解析】【分析】根据0a b >>与2211a b <的互相推出情况判断出属于何种条件.【详解】当0a b >>时，220a b >>，所以2211a b<，所以充分性满足，当2211a b<时，取2,1a b =-=，此时0a b >>不满足，所以必要性不满足，所以p 是q 的充分不必要条件，的故选：A.5. 已知函数()f x 为R 上的奇函数，当0x <时，()2f x x =+，则()()03f f +等于（ ）A. 3- B. 1- C. 1D. 3【答案】C 【解析】【分析】根据(3)f (3)f =--以及(0)0f =可求出结果.【详解】因为函数()f x 为R 上的奇函数，当0x <时，()2f x x =+，所以()()()33321f f =--=--+=．而()00f =，∴()()031f f +=．故选：C ．6. 若0x <，则1x x+（ ）A 有最小值―2B. 有最大值―2C. 有最小值2D. 有最大值2【答案】B 【解析】【分析】运用基本不等式求解即可.【详解】因为0x <，则0x ->，所以1()()2x x -+≥=-，当且仅当1x x -=-即：=1x -时取等号.所以12x x+≤-，当且仅当=1x -时取等号.故选：B.7. 已知函数()f x 的图象由如图所示的两条曲线组成，则（ ）A. ()()35ff -= B. ()f x 是单调增函数.C. ()f x 的定义域是(][],02,3∞-⋃D. ()f x 的值域是[]1,5【答案】D 【解析】【分析】根据函数的图象，结合函数求值、函数单调性、定义域与值域，可得答案.【详解】对于选项A ，由图象可得()32f -=，所以()()()321ff f -==，A 错误；对于选项B ，()04f =，()21f =，()()02f f >，故()f x 不是单调增函数，B 错误；对于选项C ，由图象可得()f x 的定义域为[][]3,02,3-⋃，C 错误；对于选项D ，由图象可得()f x 的值域为[]1,5，D 正确．故选：D ．8. 若定义域为R 的奇函数()f x 在(),0-∞上单调递减，且()20f =，则满足20)(x f x x≥的x 的取值范围是（ ）A. [][)2,02,-⋃+∞ B. ][3,10,1⎡⎤--⋃⎣⎦C. [)[)2,02,-⋃+∞ D. [)(]2,00,2-U 【答案】D 【解析】【分析】首先根据函数奇偶性与单调性，得到函数()f x 在相应区间上的符号，再根据两个数的乘积大于等于零，分类转化为对应自变量不等式，最后求并集得结果.【详解】因为定义在R 上的奇函数()f x 在(,0)-∞上单调递减，且(2)0f =，所以()f x 在(0,)+∞上也是单调递减，且(2)0f -=，(0)0f =，所以当(,2)(0,2)x ∈-∞-⋃时，()0f x >，当(2,0)(2,)x ∈-+∞ 时，()0f x <，由20)(x f x x≥可得()0xf x ≥且0x ≠可得020x x <⎧⎨-≤<⎩或002x x >⎧⎨<≤⎩解得20x -≤<或02x <≤，所以满足20)(x f x x≥的x 的取值范围是[)(]2,00,2-U ，故选：D .二、选择题：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. 下列函数既是偶函数，又在()0,∞+上单调递增的是（ ）A. y =B. 2y x =C. yD. 1y x=【答案】BC 【解析】【分析】根据函数的单调性和奇偶性逐项分析判断.【详解】对A ：=y =在定义域内为奇函数，又∵y =在R 上单调递增，5u x =在R 上单调递增，则y =在R 上单调递增，A 错误；对B ：∵()22x x -=，则2y x =在定义域内为偶函数，且在()0,∞+内单调递增，B 正确；对C ：y又∵当()0,x ∈+∞，y 在()0,∞+内单调递增，C 正确；对A ：∵11=--x x ，则1y x =在定义域内为奇函数，且1y x=在()0,∞+内单调递减，D 错误；故选：BC.10. 下列关于幂函数y x α=的说法正确的是（ ）A. 幂函数的图象都过点()0,0，()1,1B. 当1,3,1α=-时，幂函数的图象都经过第一、三象限C. 当1,3,1α=-时，幂函数是增函数D. 若0α<，则幂函数的图象不过点()0,0【答案】BD 【解析】【分析】由幂函数的性质逐个判断即可.【详解】对于A ，当0α<时，幂函数的图象不通过点()0,0，A 错误；对于B ，幂指数1,3,1α=-时，幂函数分别为y x =，3y x =，1y x -=，三者皆为奇函数，图象都经过第一、三象限，故B 正确；对于C ，当1α=-时，幂函数1y x -=在(),0∞-，(0,+∞)上皆单调递减，C 错误；对于D ，若0α<，则函数图象不通过点()0,0，D 正确．故选：BD ．11. 下列结论正确的是（ ）A. 函数21x y x+=的最小值是2B. 若0ab >，则2b a a b+≥C. 若x ∈R ，则22122x x +++的最小值为2D. 若0,0a b >>22a b ++≥【答案】BD 【解析】【分析】根据题意，结合基本不等式，逐项判定，即可求解.【详解】对于A 中，当0x <时，可得0y <，所以A 错误；对于B 中，因0ab >，则2b a a b +≥=，当且仅当b a a b =时，即a b =时，等号成立，所以B 正确；对于C中，由221222x x ++≥=+，当且仅当22122x x +=+时，此时方程无解，即等号不成立，所以C 错误；对于D 中，因为0,0a b >>22a b ++≥≥，当且仅当a b =时，等号成立，所以D 正确.故选BD ．12. 已知函数()f x 的定义域为A ，若对任意x A ∈，存在正数M ，使得()f x M ≤成立，则称函数为()f x 是定义在A 上的“有界函数”.则下列函数是“有界函数”的是（ ）A. 3()4x f x x+=- B. ()f x =C. 25()22f x x x =-+ D. ()f x 【答案】BCD 【解析】【分析】“有界函数”值域需要有界，化简各函数，并求出函数的值域，然后进行判断.【详解】对于A ，3(4)77()1444x x f x x x x+--+===-+---，由于704x ≠-，所以()1f x ≠-，所以()[)0,f x ∈+∞，故不存在正数M ，使得()f x M ≤成立.对于B ，令21u x =-，则[]0,1u ∈，()f x =，所以()[]0,1f x ∈，故存在正数1，使得()1f x ≤成立.对于C ，令2222(1)1u x x x =-+=-+，则()5f x u=，易得1u ≥.所以()5051f x <≤=，即()(]0,5∈f x ，故存在正数5，使得()5f x ≤成立.对于D ，令t =[]0,2t ∈，24x t =-，则[]()22117()40,224f x t t t t ⎛⎫=-++=--+∈ ⎪⎝⎭，易得()1724f x ≤≤，所以()172,4f x ⎡⎤∈⎢⎥⎣⎦，故存在正数174，使得()174f x ≤成立.故选：BCD.三、填空题：本题共4小题，每小题5分，共20分.13. 已知命题p ：x ∀∈Q ，x N ∈，则p ⌝为______．【答案】x ∃∈Q ，x ∉N 【解析】【分析】由全称命题的否定为特称命题即可求解.【详解】因为p ：x ∀∈Q ，x ∈N ，所以p ⌝为x ∃∈Q ，x ∉N ．故答案为：x ∃∈Q ，x ∉N .14. 函数()1f x x=+的定义域为_____________.【答案】()(],00,1-∞⋃【解析】【分析】由题意列不等式组即可求得.【详解】要使函数()1f x x=有意义，只需10,0,x x -≥⎧⎨≠⎩解得：1x ≤且0x ≠，从而()f x 的定义域为()(],00,1-∞⋃.故答案为：()(],00,1-∞⋃15. 已知函数()f x 满足下列3个条件：①函数()f x 的图象关于y 轴对称；②函数()f x 在()0,∞+上单调递增；③函数()f x 无最值．请写出一个满足题意的函数()f x 的解析式：______．【答案】()21f x x=-（答案不唯一）【解析】【分析】结合函数的对称性、单调性及常见函数即可求解.【详解】由()f x 的图象关于y 轴对称知()f x 为偶函数，()f x 在(0,+∞)上单调递增，()f x 无最值，根据幂函数性质可知满足题意的一个函数为()21f x x=-.故答案为：()21f x x =-（答案不唯一）16. 已知函数()21x f x x=+，则不等式()211f x -<的解集是____________.【答案】()0,1【解析】【分析】由题可得()f x 为偶函数，且在()0,∞+上单调递增，后利用()()f x f x =可得答案.【详解】因为()f x 的定义域为R ，且()()f x f x -=，所以()f x 是偶函数.的又当0x >时，()21x f x x =+2222211x x x+-==-++单调递增.因为()f x 是偶函数，所以()f x 在(),1-∞单调递减，又因为()11f =，所以()211f x -<()()211f x f ⇔-<211121101x x x ⇔-<⇒-<-<⇒<<.故答案为：()0,1.四、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. 设全集U =R ，集合{}2680A x x x =-+=，31B x x ⎧⎫=<⎨⎬⎩⎭．（1）求()U A B ⋃ð；（2）设集合(){}233,C x x a a x a =+=+∈Z ，若A C 恰有2个子集，求a 的值．【答案】（1）(){03U A B x x ⋃=≤≤ð或}4x = （2）2或4．【解析】【分析】（1）解方程和不等式求出集合,A B ，再由补集、并集运算即可求解；（2）解方程求出集合C ,再通过a 的讨论即可求解.【小问1详解】2680x x -+=，解得2x =或4，则{}2,4A =；由31x<，解得0x <或3x >，则{0B x x =<或}3x >；所以{}03U B x x =≤≤ð，(){03U A B x x ⋃=≤≤ð或}4x =．【小问2详解】因为A C 恰有2个子集，所以A C 仅有一个元素．()()()23330x a a x x x a +=+⇒--=，当3a =时，{}3C =，A C ⋂=∅，不满足题意；当2a =时，{}2,3C =，{}2A C ⋂=，满足题意；当4a =时，{}4,3C =，{}4A C ⋂=，满足题意．综上，a 的值为2或4．18. 已知函数()1f x x x=+．（1）求证：()f x 在()0,1上单调递减，在()1,+∞上单调递增；（2）当1,22x ⎡⎤∈⎢⎥⎣⎦时，求函数()f x 值域．【答案】（1）证明见解析 （2）52,2⎡⎤⎢⎥⎣⎦．【解析】【分析】（1）根据函数单调性的定义，结合作差法，可得答案；（2）根据（1）的单调性，求得给定区间上的最值，可得答案.【小问1详解】证明：()12,0,1x x ∀∈，且12x x <，有()()()121221212121212121121211111x x x x f x f x x x x x x x x x x x x x x x x x ⎛⎫⎛⎫⎛⎫---=+-+=-+-=-+=-⋅ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭．由()12,0,1x x ∀∈，且12x x <，得210x x ->，1210x x -<，120x x >，所以()12211210x x x x x x --⋅<，即()()21f x f x <．所以()f x 在()0,1上单调递减．同理，当()12,1,x x ∈+∞，且12x x <，有()()()1221211210x x f x f x x x x x --=-⋅>．故()f x 在()1,+∞上单调递增．【小问2详解】由（1）得()f x 在1,12⎡⎤⎢⎥⎣⎦上单调递减；在[]1,2上单调递增．()12f =，()15222f f ⎛⎫== ⎪⎝⎭，所以()52,2f x ⎡⎤∈⎢⎥⎣⎦．故函数()f x 的值域为52,2⎡⎤⎢⎥⎣⎦．的19. 设函数()223y ax b x =+-+.（1）若关于x 的不等式0y >的解集为{}13x x -<<，求4y ≥的解集；（2）若1x =时，2,0,0y a b =>>，求14a b+的最小值.【答案】（1）{}1（2）9【解析】【分析】（1）根据不等式的解集得到方程的根，代入求出,a b ，从而解不等式求出解集；（2）先得到1a b +=，利用基本不等式“1”的妙用求出最小值.【小问1详解】由题知()2230ax b x +-+=的两个根分别是1-，3，则23093630a b a b +-+=⎧⎨+-+=⎩，解得1,4.a b =-⎧⎨=⎩故()2223234y ax b x x x =+-+=-++≥，2210x x -+≤，解得1x =.所求解集为{}1.【小问2详解】1x =时，2y =，即12++=a b ，所以有1a b +=，那么()1414a b a b a b ⎛⎫+=++ ⎪⎝⎭41459b a a b=+++≥+=，当且仅当41b a a b a b ⎧=⎪⎨⎪+=⎩，即1,323a b ⎧=⎪⎪⎨⎪=⎪⎩时，取等号.故14a b+的最小值为9.20. 已知集合(){}40A x x x =-≥，{}121B x a x a =+<<-．（1）若x A ∀∈，均有x B ∉，求实数a 的取值范围；（2）若2a >，设p ：x B ∃∈，x A ∉，求证：p 成立的充要条件为23a <<．【答案】（1）5,2⎛⎤-∞ ⎥⎝⎦（2）证明见解析【解析】【分析】（1）根据二次不等式，解得集合的元素，利用分类讨论思想，可得答案；（2）根据充要条件的定义，利用集合之间的包含关系，可得答案.【小问1详解】(){}(][)40,04,A x x x ∞∞=-≥=-⋃+．因为x A ∀∈，均有x B ∉，所以A B =∅ ．当2a ≤时，B =∅，满足题意；当2a >时，10214a a +≥⎧⎨-≤⎩，解得512a -≤≤，所以522a <≤．综上，52a ≤，即a 的取值范围是5,2⎛⎤-∞ ⎥⎝⎦．【小问2详解】证明：若p ：x B ∃∈，x A ∉为真命题，则p ⌝：x B ∀∈，x A ∈为假命题．先求p ⌝：x B ∀∈，x A ∈为真命题时a 的范围，因为2a >，所以B ≠∅，由p ⌝：x B ∀∈，x A ∈，得B A ⊆．则210a -≤或14a +≥，解得12a ≤或3a ≥，所以3a ≥．因为p ⌝：x B ∀∈，x A ∈为假命题，所以23a <<.综上，若2a >，则p 成立的充要条件为23a <<．21. 某市财政下拨专款100百万元，分别用于植绿护绿和处理污染两个生态维护项目，植绿护绿项目五年内带来的生态收益可表示为投放资金x （单位：百万元）的函数1y （单位：百万元）：12710x y x =+，处理污染项目五年内带来的生态收益可表示为投放资金x （单位：百万元）的函数2y （单位：百万元）：20.3y x =.设分配给植绿护绿项目的资金为x （单位：百万元），两个生态项目五年内带来的生态收益总和为y （单位：百万元）.（1）将y 表示成关于x 的函数；（2）为使生态收益总和y 最大，对两个生态项目的投资分别为多少？【答案】（1）27330(0100)1010x x y x x =-+≤≤+ （2）分配给植绿护绿项目20百万元，处理污染项目80百万元【解析】【分析】（1）由题意列式化简即可；（2）将原式变形构造成对勾函数，利用对勾函数的性质求最值即可.【小问1详解】若分配给植绿护绿项目的资金为x 百万元，则分配给处理污染项目的资金为()100x -百万元，∴272730.3(100)30(0100)101010x x x y x x x x =+-=-+≤≤++.【小问2详解】由（1）得27(10)2703(1010)2703(10)306010101010x x x y x x +-+-+⎡⎤=-+=-+⎢⎥++⎣⎦6042≤-=（当且仅当2703(10)1010x x +=+，即20x =时取等号），∴分配给植绿护绿项目20百万元，处理污染项目80百万元，生态收益总和y 最大.22. 设函数()()2*1488,,N f x mx m mn x m m n =+-++∈ .（1）若()f x 为偶函数，求n 的值；（2）若对*N n ∀∈，关于x 的不等式()0f x ≤有解，求m 的最大值.【答案】（1）2. （2）2.【解析】【分析】（1）根据函数为偶函数可得到14880m mn -+=，变形为714n m=+，结合*,1,N m n m ∈≥，即可确定答案.（2）根据对*N n ∀∈，关于x 的不等式()0f x ≤有解，可得22(1488)40m mn m ∆=-+-≥恒成立，结合二次不等式的解法，讨论n 取值，即可确定答案.【小问1详解】根据题意，函数()()2*1488,R,,N f x mx m mn x m x m n =+-++∈∈为偶函数，即满足()()f x f x -=，即()()22()1488()1488m x m mn x m mx m mn x m -+-+-+=+-++，R x ∈，则14880m mn -+=变形可得：714n m =+ ，又由*,1,N m n m ∈≥ ，则 101m<≤ ， 故77111711,44444n m <+≤<≤∴ ，又N n *∈ ，则2n = ；【小问2详解】根据题意，若对*N n ∀∈，关于x 的不等式()0f x ≤有解，由于*,N 0m m ∈>，则22(1488)416[(32)2][(42)2]0m mn m m n m n ∆=-+-=-+-+≥恒成立 ，当1n = 时，32(2)(1)0m m ∆=++≥ ，对*N m ∀∈都成立， 当2n =时，32(2)0m ∆=-+≥，解得2m ≤ ，又*N m ∈，则12m ≤≤ ，当3n ≥时，21232n n <-- ，则223m n ≤- 或 12m n ≥-,当 223m n ≤- 时，又由1m ≥，则n 只能取2，不符合题意，舍去，当 12m n ≥- 时，又由1m ≥，从3n =开始讨论:令1()2g n n =-,由于1()2g n n =-单调递减，故只需1(3)132m g ≥==-，此时m 的取值范围为[1,2] ；综上所述，m 的最大值为2.。
上海市七宝中学2024-2025学年高三上学期期中考试数学试题(含答案)
七宝中学2024-2025学年高三上学期期中考试数学试题一、填空题（第1-6题每题4分，第7-12题每题5分，满分54分）1．函数的定义域为______．2．计算______．3．已知是1与9的等比中项，则正实数______．4．在的展开式中，的系数为______（用数字作答）．5．在复平面内，复数对应的点位于第______象限。
6．已知，则______．7．已知集合，其中可以相同，用列举法表示集合中最小的4个元素所构成的集合为______．8．已知是函数的导函数，若函数的图象大致如图所示，则的极大值点为______（从中选择作答）．9．已知函数．在中，，且，则______．10．如图，线段相交于，且长度构成集合，则的取值个数为______．11．抛物线的焦点为，准线为是拋物线上的两个动点，且满足．设线段y =(4log =a a =4(x -2x 2ii-π1sin 42θ⎛⎫+= ⎪⎝⎭πcos 4θ⎛⎫-= ⎪⎝⎭{}22,,A a a x y x y ==+∈N ,x y A ()f x '()f x ()f x y e '=()f x ,,,a b c d ()22cos 2xf x x =+ABC △()()f A f B =a b ≠C ∠=,AD BC O ,,,AB AD BC CD {}1,3,5,,90x ABO DCO ∠=∠=︒x 24y x =F ,,l A B π3AFB ∠=AB的中点在准线上的投影为，则的最大值是______．12．平面上到两个定点距离之比为常数的动点的轨迹为圆，且圆心在两定点所确定的直线上，结合以上知识，请尝试解决如下问题：已知满足，则的取值范围为______．二、选择题（本大题共4题，满分20分）13．已知是非零实数，则下列不等式中恒成立的是（ ）A ．B ．C ．D14．已知直线，动直线，则下列结论正确的为（）A ．不存在，使得的倾斜角为B ．对任意的与都不垂直C ．存在，使得与重合D ．对任意的与都有公共点15．一组学生站成一排．若任意相邻的3人中都至少有2名男生，且任意相邻的5人中都至多有3名男生，则这组学生人数的最大值是（ ）A ．5B ．6C ．7D ．816．若，有限数列的前项和为，且对一切都成立．给出下列两个命题：①存在，使得是等差数列；②对于任意的，都不是等比数列．则（ ）A ．①是真命题，②是假命题B ．①是假命题，②是真命题C ．①②都是真命题D ．①②都是假命题三、解答题（本大题共有5题，满分76分）17．如图，为正方体，动点在对角线上（不包含端点），记．M l N MNAB(0,1)λλλ>≠,,a b c 1,2,1a c b a b ===⋅=1122c a c b ++-a 1a a>2211a a a a+≥+12a a+>-≥-1:10l x y --=()()2:10l k x ky k k +-+=∈R k 2l π21,k l 2l k 1l 2l 1,k l 2l 3n ≥12,,,n a a a k k S 1k k S S +>11k n ≤≤-3n ≥12,,,n a a a 3n ≥12,,,n a a a 1111ABCD A B C D -P 1BD 11D PD Bλ=（1）求证：；（2）若异面直线与所成角为，求的值．18．已知点是坐标原点．（1）若，求的值：（2）若实数满足，求的最大值．19．英语学习中学生喜爱用背单词"神器"提升自己的英文水平，为了解上海中学生和大学生对背单词“神器”的使用情况，随机抽取了200名中学生和80名大学生，统计他们最喜爱使用的一款背单词“神器”，结果如下：百词斩扇贝单词秒词邦沪江开心词场中学生80604020大学生30202010假设大学生和中学生对背单词“神器”的喜爱互不影响．（1）从该地区的中学生和大学生中各随机抽取1人，用频率估计概率，试估计这2人都最喜爱使用“百词斩”的概率；（2）采用分层抽样的方式先从样本中的大学生中随机抽取8人，再从这8人中随机抽取3人．记X 为这3人中最喜爱使用“扇贝单词”的人数，求X 的分布列和数学期望；（3）记样本中的中学生最喜爱使用这四款背单词“神器”的频率依次为，其方差为；样本中的大学生最喜爱使用这四款背单词“神器”的频率依次为，其方差为的方差为．写出的大小关系．（结论不要求证明）20．在平面直角坐标系中，分别是椭圆的左右焦点，设不经过的直线与椭圆交于两个不同的点，焦点到直线的距离为．（1）求该粗圆的离心率；（2）若直线经过坐标原点，求面积的最大值；（3）如果直线的斜率依次成等差数列，求的取值范围．21．若斜率为的两条平行直线，曲线满足以下两条性质：（Ⅰ）分别与曲线至少有两个切点；（Ⅱ）曲线上的所有点都在之间或两条直线上．则称直线为曲线的一对“双夹线”，把“双夹线”之间的距离称为曲线在“方向上的宽度”，记为．已知曲线1AP B C ⊥AP 11D B π3λ()())1,1,1,1,,A B CO θθ-BC BA -=sin2θ,m n π,0,2mOA nOB OC θ⎛⎫+=∈ ⎪⎝⎭22(3)m n ++1234,,,x x x x 21s 1234,,,y y y y 2212341234;,,,,,,,s x x x x y y y y 23s 222123,,s s s 12,F F 22143x y +=1F l ,A B 2F l d l 2F AB △11,,AF l BF d k 12,l l ():C y f x =12,l l C C 12,l l 12,l l C C k ()d k．（1）判断时，曲线是否存在“双夹线”，并说明理由；（2）若，试问：和是否是函数的一对“双夹线”？若是，求此时的值；若不是，请说明理由．（3）对于任意的正实数，函数是否都存在"双夹线"？若是，求的所有取值构成的集合；若不是，请说明理由．2025届七宝中学高三（上）期中考试参考答案一、填空题1、； 2、； 3、3； 4．18； 5、四；6．；7、； 8、a ； 9、；10、4；11、1； 12、10、【答案】412、【答案】二、选择题13～16、BDBC三、解答题17、（1）证明：如图，连接．由已知可得，平面平面，所以，又是正方形，所以，又平面平面，所以平面，又动点在对角线上，所以平面，所以平面，所以．():sin C f x mx n x =+0,1m n ==C 1,1m n ==-1:1l y x =+2:1l y x =-()y f x =()d k ,m n ()y f x =()d k ()1,+∞3412{}0,1,2,4π311,BC AD AB ⊥111,BCC B B C ⊂11BCC B 1AB B C ⊥11BCC B 11B C BC ⊥1BC ⊂11,ABC D AB ⊂111,ABC D AB BC B = 1B C ⊥11ABC D P 1BD P ∈11ABC D AP ⊂11ABC D 1AP B C ⊥（2）以点为坐标原点，分别以所在的直线为轴，如图建立空间直角坐标系，设，则，则．由已知，可得，设点，则，所以，所以，即，所以，．又异面直线与所成角为，所以，即，解得或0，因为，所以满足条件．18、【答案】（1）； （2）16．19、【答案】（1）； （2）； （3）20．【答案】（1）； （2 （3）．21、【答案】（1）存在；（2）是，3）是，C 1CD CB CC 、、x y z 、、1CD =()()()()()()()1110,0,0,1,0,0,0,1,0,0,0,1,1,0,1,0,1,1,1,1,0C D B C D B A ()11111,1,0,D B D B =-=11D PD Bλ=11D P D B λ= ()000,,P x y z ()10001,,1D P x y z =-- 00011x y z λλλ-=-⎧⎪=⎨⎪-=-⎩00011x y z λλλ=-+⎧⎪=⎨⎪=-+⎩()1,,1P λλλ-+-+(),1,1AP λλλ=---+AP ==AP 11D B π311π1cos ,cos 42AP D B 〈==〉 11cos ,2AP D 1λ=01λ<<45λ=12-320[]34E X =222231s s s <<12()d k =()0)d k n =>。
丹东2024年01版小学4年级K卷英语第1单元期中试卷
丹东2024年01版小学4年级英语第1单元期中试卷考试时间:90分钟（总分:100）考试人：_________题号一二三总分得分评级介绍：本试卷为丹东2024年小学四年级英语期中考，难度适中，重点考察词汇、句型及基础语法，旨在评估学生的语言应用能力和理解水平。
一、(选择题)总分:45分(2分/题)1、What is the name of the fairy tale character who wears a red cape?A, CinderellaB, Snow WhiteC, Little Red Riding HoodD, Rapunzel2、What is a synonym for "quick"?A, FastB, SlowC, LazyD, Tired3、What is the English translation of "角马"?A, AntelopeB, GnuC, GazelleD, Wildebeest4、What is the English translation of "植物创新"?A, Plant innovationB, Agricultural innovationC, Environmental innovationD, Ecological innovation5、为下列句子选择正确的译文。
6、What is the name of the story about the adventures of a hero? A, MythB, LegendC, FableD, Tale7、Which instrument has keys and is played by pressing them? A, GuitarB, DrumsC, PianoD, Flute8、She has a lovely smile. 她有一个迷人的微笑。