考点6

考点规范练辽宋夏金元的经济、社会与文化一、选择题1.(2021湖南卷,5)宋孝宗时绍兴府赈灾,有人户状告“检放秋苗不尽不实”。

朱熹受命调查后发现确实存在不实,但是当时田土大多已经种麦,没有稻根可据以核查受灾面积。

这反映了()A.绍兴府行政效率低下B.理学强调实事求是的精神C.宋代赈灾方式不合理D.绍兴农业精耕细作的特点2.宋代土地买卖盛行,出现“千年田换八百主”“田宅无定主”的现象,政府出台了较为严格的法律,对土地买卖实行规范化管理,要求买卖双方在政府机构办理登记备案手续,作为土地产权转移的证明。

这一做法()A.促进了土地私有制发展B.反映了宋代商业立法的完备C.有效保护了自耕农经济D.说明政府立法抑制土地兼并3.下面是北宋熙宁十年(1077)的商税统计情况表。

据此可以得出的结论是当时南方()A.已成为全国经济重心B.商业环境较北方优越C.农业生产较北方发达D.人口增长率高于北方4.下面是元朝各地的粮食岁收情况表(单位:石)。

据此可知元朝()A.继续维持重农抑商政策B.政治经济核心优势明显C.苏湖地区成为农业中心D.边远地区经济快速发展5.(2022福建厦门四模)宋元时期,市舶司对进出港船舶所载货物实行抽分(收取商税),元朝时期颁布的至元《市舶则法》规定“番货双抽,土货单抽”,这()A.体现了厚往薄来的理念B.突破了闭关自守的桎梏C.维护了自然经济的稳定D.推动了出口贸易的发展6.宋朝政府对土地买卖、典当基本不加干预,经营者仅办理法律手续,缴纳交易税即可。

对于百姓迁移住所、更换职业以及日常生活标准,官府也不再严格限制。

这主要说明宋朝()A.土地兼并日益严重B.对社会的控制有所放松C.社会矛盾趋向缓和D.政府行政能力显著降低7.(2021全国乙卷,26)宋代,官府强调“民生性命在农,国家根本在农,天下事莫重于农”,“毋舍本逐末”。

苏辙说:“凡今农工商贾之家,未有不舍其旧而为士者也。

”郑至道说,士农工商“皆百姓之本业,自生民以来未有能易之者也”。

一、考点1：圆的根本概念，圆心、半径、直径。

二、考点2：圆心决定圆的位置，半径〔直径〕决定圆的大小三、考点3：半径与直径的关系。

五、考点5：常见的轴对称图形与它们的对称轴。

六、考点6：圆的周长、圆周率、直径〔半径〕的概念和关系七、考点7：圆的周长公式及其应用。

〔一〕、告诉直径，求周长。

〔二〕、告诉半径，求周长。

〔三〕、告诉周长，求直径。

〔四〕、告诉周长，求半径。

八、考点8：圆的面积公式及其应用。

〔一〕、告诉半径，求面积。

〔二〕、告诉直径，求面积。

〔三〕、告诉周长，求面积。

九、考点9：圆的周长、面积、直径和半径的混合计算。

十、考点10：半圆的性质、周长和面积。

十一、考点11：周长和面积容易混淆的知识点。

十二、考点12：周长和面积大小比拟。

十三、考点13：圆的扩大〔缩小〕问题。

十四、考点14：阴影局部的面积。

第一单元圆一、考点1：圆的根本概念，圆心、半径、直径。

判断：1、通过圆心的线段是半径。

〔×〕2、通过圆心的线段是直径。

〔×〕3、两端都在圆上的线段是直径。

〔×〕4、两端都在圆上并且经过圆心的线段是直径。

〔√〕5、所有的直径都相等，所有的半径都相等。

〔×〕6、旋转式水龙喷头的射程是8m，8m就是指圆的直径。

〔×〕二、考点2：圆心决定圆的位置，半径〔直径〕决定圆的大小。

填空：1、〔圆心〕确定圆的位置，〔半径〕确定圆的大小。

2、〔〕决定圆的大小，〔〕决定圆的位置。

3、圆内最长的线段是〔直径〕，圆规两脚之间的距离是〔〕。

4、圆有〔无数〕条半径，圆有〔无数〕条直径。

判断：1、圆心决定圆的位置，半径决定圆的大小。

〔√〕2、半径决定圆的位置，圆心决定圆的大小。

〔×〕3、圆心决定圆的大小，半径决定圆的位置。

〔×〕4、半径决定圆的大小，圆心决定圆的位置。

〔√〕5、直径3厘米的圆大于半径2厘米的圆。

〔〕6、半径3分米的圆大于直径5分米的圆。

〔〕三、考点3：半径与直径的关系。

高考数学总复习考点知识讲解与提升练习专题6 函数的概念及其表示考点知识1.了解函数的含义.2.在实际情境中，会根据不同的需要选择恰当的方法(如图象法、列表法、解析法)表示函数.3.了解简单的分段函数，并会简单的应用．知识梳理1．函数的概念一般地，设A，B是非空的实数集，如果对于集合A中的任意一个数x，按照某种确定的对应关系f，在集合B中都有唯一确定的数y和它对应，那么就称f：A→B为从集合A 到集合B的一个函数，记作y＝f(x)，x∈A.2．函数的三要素(1)函数的三要素：定义域、对应关系、值域．(2)如果两个函数的定义域相同，并且对应关系完全一致，则这两个函数为同一个函数．3．函数的表示法表示函数的常用方法有解析法、图象法和列表法．4．分段函数若函数在其定义域的不同子集上，因对应关系不同而分别用几个不同的式子来表示，这种函数称为分段函数．常用结论1．直线x ＝a 与函数y ＝f (x )的图象至多有1个交点．2．在函数的定义中，非空数集A ，B ，A 即为函数的定义域，值域为B 的子集．3．分段函数虽由几个部分组成，但它表示的是一个函数．分段函数的定义域等于各段函数的定义域的并集，值域等于各段函数的值域的并集． 思考辨析判断下列结论是否正确(请在括号中打“√”或“×”)(1)若两个函数的定义域和值域相同，则这两个函数是同一个函数．(×)(2)函数y ＝f (x )的图象可以是一条封闭曲线．(×)(3)y ＝x 0与y ＝1是同一个函数．(×)(4)函数f (x )＝⎩⎨⎧ x －1，x ≥0，x 2，x <0的定义域为R .(√) 教材改编题1．(多选)下列所给图象是函数图象的是()答案CD解析A 中，当x >0时，每一个x 的值对应两个不同的y 值，因此不是函数图象；B 中，当x ＝x 0时，y 的值有两个，因此不是函数图象；CD 中，每一个x 的值对应唯一的y 值，因此是函数图象．2．下列各组函数表示同一个函数的是()A ．y ＝x －1与y ＝x 2－1x ＋1B ．y ＝x －1与y ＝－1xC ．y ＝2x 2与y ＝2xD ．y ＝2x －1与v ＝2t －1答案D解析y ＝x －1的定义域为R ，y ＝x 2－1x ＋1的定义域为{x |x ≠－1}，定义域不同，不是同一个函数，故选项A 不正确；y ＝x －1＝1x 与y ＝－1x的对应关系不同，不是同一个函数，故选项B 不正确； y ＝2x 2＝2|x |与y ＝2x 的对应关系不同，不是同一个函数，故选项C 不正确；y ＝2x －1与v ＝2t －1的定义域都是(－∞，1)∪(1，＋∞)，对应关系也相同，所以是同一个函数，故选项D 正确．3．已知函数f (x )＝⎩⎨⎧ ln x ，x >0，e x ，x ≤0，则函数f ⎝ ⎛⎭⎪⎫f ⎝ ⎛⎭⎪⎫13等于() A ．3B ．－3C.13D ．－13答案C解析由题意可知，f ⎝ ⎛⎭⎪⎫13＝ln 13＝－ln3，所以f ⎝ ⎛⎭⎪⎫f ⎝ ⎛⎭⎪⎫13＝f (－ln3)＝e －ln3＝13.题型一函数的定义域例1(1)函数y ＝ln (x ＋1)－x 2－3x ＋4的定义域为()A ．(－4，－1)B ．(－4,1)C ．(－1,1)D ．(－1,1]答案C解析由题意得⎩⎨⎧ x ＋1>0，－x 2－3x ＋4>0，解得－1<x <1，故定义域为(－1,1)．(2)已知函数f (x )的定义域为(－4，－2)，则函数g (x )＝f (x －1)＋x ＋2的定义域为________．答案[－2，－1)解析∵f (x )的定义域为(－4，－2)，要使g (x )＝f (x －1)＋x ＋2有意义，则⎩⎨⎧ －4<x －1<－2，x ＋2≥0，解得－2≤x <－1，∴函数g (x )的定义域为[－2，－1)．思维升华(1)无论抽象函数的形式如何，已知定义域还是求定义域，均是指其中的x 的取值集合；(2)若已知函数f (x )的定义域为[a ，b ]，则复合函数f (g (x ))的定义域由不等式a ≤g (x )≤b 求出；(3)若复合函数f (g (x ))的定义域为[a ，b ]，则函数f (x )的定义域为g (x )在[a ，b ]上的值域．跟踪训练1(1)函数f (x )＝1ln (x －1)＋3－x 的定义域为() A ．(1,3] B ．(1,2)∪(2,3]C ．(1,3)∪(3，＋∞) D．(－∞，3)答案B解析由题意知⎩⎨⎧ x －1>0，x －1≠1，3－x ≥0，所以1<x <2或2<x ≤3， 所以函数的定义域为(1,2)∪(2,3]．(2)(2023·南阳检测)已知函数f (x )＝lg1－x 1＋x ，则函数g (x )＝f (x －1)＋2x －1的定义域是()A ．{x |x >2或x <0}B.⎩⎨⎧⎭⎬⎫x ⎪⎪⎪ 12≤x <2 C ．{x |x >2}D.⎩⎨⎧⎭⎬⎫x ⎪⎪⎪ x ≥12答案B解析要使f (x )＝lg1－x 1＋x 有意义， 则1－x 1＋x >0， 即(1－x )(1＋x )>0，解得－1<x <1，所以函数f (x )的定义域为(－1,1)．要使g (x )＝f (x －1)＋2x －1有意义，则⎩⎨⎧ －1<x －1<1，2x －1≥0，解得12≤x <2， 所以函数g (x )的定义域为⎩⎨⎧⎭⎬⎫x ⎪⎪⎪ 12≤x <2.题型二函数的解析式例2(1)已知f (1－sin x )＝cos 2x ，求f (x )的解析式；(2)已知f ⎝⎛⎭⎪⎫x ＋1x ＝x 2＋1x 2，求f (x )的解析式； (3)已知f (x )是一次函数且3f (x ＋1)－2f (x －1)＝2x ＋17，求f (x )的解析式．(4)已知f (x )满足2f (x )＋f (－x )＝3x ，求f (x )的解析式．解(1)(换元法)设1－sin x ＝t ，t ∈[0,2]，则sin x ＝1－t ，∵f (1－sin x )＝cos 2x ＝1－sin 2x ，∴f (t )＝1－(1－t )2＝2t －t 2，t ∈[0,2]．即f (x )＝2x －x 2，x ∈[0,2]．(2)(配凑法)∵f ⎝⎛⎭⎪⎫x ＋1x ＝x 2＋1x 2＝⎝ ⎛⎭⎪⎫x ＋1x 2－2， ∴f (x )＝x 2－2，x ∈(－∞，－2]∪[2，＋∞)．(3)(待定系数法)∵f (x )是一次函数，可设f (x )＝ax ＋b (a ≠0)，∴3[a (x ＋1)＋b ]－2[a (x －1)＋b ]＝2x ＋17.即ax ＋(5a ＋b )＝2x ＋17，∴⎩⎨⎧ a ＝2，5a ＋b ＝17，解得⎩⎨⎧ a ＝2，b ＝7.∴f (x )的解析式是f (x )＝2x ＋7.(4)(解方程组法)∵2f (x )＋f (－x )＝3x ，①∴将x 用－x 替换，得2f (－x )＋f (x )＝－3x ，②由①②解得f (x )＝3x .思维升华函数解析式的求法(1)配凑法；(2)待定系数法；(3)换元法；(4)解方程组法．跟踪训练2(1)已知f (x －1)＝x 2＋4x －5，则f (x )的解析式是()A ．f (x )＝x 2＋6xB ．f (x )＝x 2＋8x ＋7C ．f (x )＝x 2＋2x －3D ．f (x )＝x 2＋6x －10答案A解析f (x －1)＝x 2＋4x －5，设x －1＝t ，x ＝t ＋1，则f (t )＝(t ＋1)2＋4(t ＋1)－5＝t 2＋6t ，故f (x )＝x 2＋6x . (2)若f ⎝ ⎛⎭⎪⎫1x ＝x 1－x，则f (x )＝________. 答案1x －1(x ≠0且x ≠1) 解析f (x )＝1x 1－1x＝1x －1(x ≠0且x ≠1)． (3)已知函数f (x )满足f (x )＋2f ⎝ ⎛⎭⎪⎫－1x ＝3x ，则f (2)等于() A ．－3B ．3C ．－1D ．1答案A解析f (x )＋2f ⎝ ⎛⎭⎪⎫－1x ＝3x ，① 则f ⎝ ⎛⎭⎪⎫－1x ＋2f (x )＝－3x ，② 联立①②解得f (x )＝－2x －x ，则f (2)＝－22－2＝－3. 题型三分段函数例3(1)已知函数f (x )＝⎩⎨⎧ f (x －1)，x >0，－ln (x ＋e )＋2，x ≤0，则f (2024)的值为() A ．－1B ．0C ．1D ．2答案C解析因为f (x )＝⎩⎨⎧ f (x －1)，x >0，－ln (x ＋e )＋2，x ≤0，所以f (2024)＝f (2023)＝f (2022)＝…＝f (1)，又f (1)＝f (1－1)＝f (0)＝－ln(0＋e)＋2＝－1＋2＝1，所以f (2024)＝1.(2)已知函数f (x )＝⎩⎨⎧ －x 2－3x ＋2，x <－1，2x －3，x ≥－1，若f (a )＝4，则实数a 的值是________；若f (a )≥2，则实数a 的取值范围是________．答案－2或5[－3，－1)∪[4，＋∞)解析若f (a )＝4，则⎩⎨⎧a <－1，－a 2－3a ＋2＝4或⎩⎨⎧ a ≥－1，2a －3＝4， 解得a ＝－2或a ＝5. 若f (a )≥2，则⎩⎨⎧ a <－1，－a 2－3a ＋2≥2或⎩⎨⎧ a ≥－1，2a －3≥2，解得－3≤a <－1或a ≥4，∴a 的取值范围是[－3，－1)∪[4，＋∞)．思维升华分段函数求值问题的解题思路(1)求函数值：当出现f (f (a ))的形式时，应从内到外依次求值．(2)求自变量的值：先假设所求的值在分段函数定义区间的各段上，然后求出相应自变量的值，切记要代入检验．跟踪训练3(1)已知函数f (x )＝⎩⎨⎧ x ＋2，x ≤0，x ＋1x ，x >0，若f (f (a ))＝2，则a 等于() A ．0或1B ．－1或1C ．0或－2D ．－2或－1答案D解析令f (a )＝t ，则f (t )＝2，可得t ＝0或t ＝1，当t ＝0时，即f (a )＝0，显然a ≤0，因此a ＋2＝0⇒a ＝－2，当t ＝1时，即f (a )＝1，显然a ≤0，因此a ＋2＝1⇒a ＝－1，综上所述，a ＝－2或－1.(2)(2023·重庆质检)已知函数f (x )＝⎩⎨⎧log 2x ，x >1，x 2－1，x ≤1，则f (x )<f (x ＋1)的解集为________．答案⎝ ⎛⎭⎪⎫－12，＋∞解析当x ≤0时，x ＋1≤1，f (x )<f (x ＋1)等价于x 2－1<(x ＋1)2－1，解得－12<x ≤0；当0<x ≤1时，x ＋1>1，此时f (x )＝x 2－1≤0，f (x ＋1)＝log 2(x ＋1)>0，∴当0<x ≤1时，恒有f (x )<f (x ＋1)；当x >1时，x ＋1>2，f (x )<f (x ＋1)等价于log 2x <log 2(x ＋1)，此时也恒成立．综上，不等式f (x )<f (x ＋1)的解集为⎝ ⎛⎭⎪⎫－12，＋∞. 课时精练1．函数f (x )＝lg(x －2)＋1x －3的定义域是() A ．(2，＋∞) B．(2,3)C ．(3，＋∞) D．(2,3)∪(3，＋∞)答案D解析∵f (x )＝lg(x －2)＋1x －3， ∴⎩⎨⎧ x －2>0，x －3≠0，解得x >2，且x ≠3，∴函数f (x )的定义域为(2,3)∪(3，＋∞)．2．(2023·三明模拟)已知集合A ＝{x |－2<x ≤1}，B ＝{x |0<x ≤4}，则下列对应关系中是从集合A 到集合B 的函数是()A ．f ：x →y ＝x ＋1B ．f ：x →y ＝e xC ．f ：x →y ＝x 2D ．f ：x →y ＝|x |答案B解析对于A ，当x ＝－1时，由f ：x →y ＝x ＋1得y ＝0，但0∉B ，故A 错误；对于B，因为从A＝{x|－2<x≤1}中任取一个元素，通过f：x→y＝e x在B＝{x|0<x≤4}中都有唯一的元素与之对应，故B正确；对于C，当x＝0时，由f：x→y＝x2得y＝0，但0∉B，故C错误；对于D，当x＝0时，由f：x→y＝|x|得y＝0，但0∉B，故D错误．3．已知f(x3)＝lg x，则f(10)的值为()A．1B.310C.13D.1310答案C解析令x3＝10，则x＝13 10，∴f(10)＝lg1310＝13.4.图中的文物叫做“垂鳞纹圆壶”，是甘肃礼县出土的先秦时期的青铜器皿，其身流线自若、纹理分明，展现了古代中国精湛的制造技术．科研人员为了测量其容积，以恒定的流速向其内注水，恰好用时30秒注满，设注水过程中，壶中水面高度为h，注水时间为t，则下面选项中最符合h关于t的函数图象的是()答案A解析水壶的结构：底端与上端细、中间粗，所以在注水恒定的情况下，开始水的高度增加的快，中间增加的慢，最后又变快， 由图可知选项A 符合．5．函数y ＝1＋x －1－2x 的值域为()A.⎝ ⎛⎭⎪⎫－∞，32B.⎝ ⎛⎦⎥⎤－∞，32 C.⎝ ⎛⎭⎪⎫32，＋∞D.⎣⎢⎡⎭⎪⎫32，＋∞ 答案B 解析设1－2x ＝t ，则t ≥0，x ＝1－t 22，所以y ＝1＋1－t 22－t ＝12(－t 2－2t ＋3)＝－12(t ＋1)2＋2，因为t ≥0，所以y ≤32.所以函数y ＝1＋x －1－2x 的值域为⎝ ⎛⎦⎥⎤－∞，32. 6．已知函数f (x )＝⎩⎨⎧ －x 2＋2x ＋3，x ≤2，6＋log a x ，x >2(a >0且a ≠1)，若函数f (x )的值域是(－∞，4]，则实数a 的取值范围是()A.⎝ ⎛⎭⎪⎫22，1B.⎣⎢⎡⎭⎪⎫22，1 C ．(1，2] D ．(1，2)答案B解析当x ≤2时，f (x )＝－x 2＋2x ＋3＝－(x －1)2＋4，当x ＝1时，f (x )＝－x 2＋2x ＋3取得最大值4，所以当x ≤2时，函数f (x )的值域是(－∞，4]，所以当x >2时，函数f (x )＝6＋log a x 的值域为(－∞，4]的子集，当a >1时，f (x )＝6＋log a x 在(2，＋∞)上单调递增，此时f (x )>f (2)＝6＋log a 2>6，不符合题意，当0<a <1时，f (x )＝6＋log a x 在(2，＋∞)上单调递减，此时f (x )<f (2)＝6＋log a 2≤4，即log a 2≤－2，所以a 2≥12，可得22≤a <1，所以实数a 的取值范围是⎣⎢⎡⎭⎪⎫22，1.7．(多选)下列四个函数，定义域和值域相同的是() A ．y ＝－x ＋1B ．133,0,1,0x x y x x ⎧≤⎪=⎨⎪>⎩C ．y ＝ln|x |D ．y ＝2x －1x －2答案ABD解析对A ，函数的定义域和值域都是R ；对B ，根据分段函数和幂函数的性质，可知函数的定义域和值域都是R ；对C ，函数的定义域为(－∞，0)∪(0，＋∞)，值域为R ；对D ，因为函数y ＝2x －1x －2＝2＋3x －2，所以函数的定义域为(－∞，2)∪(2，＋∞)，值域为(－∞，2)∪(2，＋∞)．所以ABD 是定义域和值域相同的函数．8．(多选)函数概念最早是在17世纪由德国数学家莱布尼茨提出的，后又经历了贝努利、欧拉等人的改译.1821年法国数学家柯西给出了这样的定义：在某些变数存在着一定的关系，当一经给定其中某一变数的值，其他变数的值可随着确定时，则称最初的变数叫自变量，其他的变数叫做函数．德国数学家康托尔创立的集合论使得函数的概念更严谨．后人在此基础上构建了高中教材中的函数定义：“一般地，设A ，B 是两个非空的数集，如果按某种对应法则f ，对于集合A 中的每一个元素x ，在集合B 中都有唯一的元素y 和它对应，那么这样的对应叫做从A 到B 的一个函数”，则下列对应法则f 满足函数定义的有()A ．f (x 2)＝|x |B ．f (x 2)＝xC ．f (cos x )＝xD ．f (e x )＝x答案AD解析令t ＝x 2(t ≥0)，f (t )＝|±t |＝t ，故A 符合函数定义；令t ＝x 2(t ≥0)，f (t )＝±t ，设t ＝4，f (t )＝±2，一个自变量对应两个函数值，故B 不符合函数定义；设t ＝cos x ，当t ＝12时，x 可以取±π3等无数多个值，故C 不符合函数定义； 令t ＝e x (t >0)，f (t )＝ln t ，故D 符合函数定义．9．已知函数f (x )＝⎩⎨⎧ cos x ，x <0，f (x －π)，x >0，则f ⎝ ⎛⎭⎪⎫11π3＝________. 答案12解析由已知得f ⎝ ⎛⎭⎪⎫11π3＝f ⎝ ⎛⎭⎪⎫8π3＝f ⎝ ⎛⎭⎪⎫5π3＝f ⎝ ⎛⎭⎪⎫2π3＝f ⎝ ⎛⎭⎪⎫－π3＝cos ⎝ ⎛⎭⎪⎫－π3＝12.10．已知f (x )＝x －1，则f (x )＝________.答案x 2－1(x ≥0)解析令t ＝x ，则t ≥0，x ＝t 2，所以f (t )＝t 2－1(t ≥0)，即f (x )＝x 2－1(x ≥0)．11．已知函数f (x )的定义域为[－2,2]，则函数g (x )＝f (2x )＋1－2x 的定义域为__________．答案[－1,0]解析由条件可知，函数的定义域需满足⎩⎨⎧ －2≤2x ≤2，1－2x ≥0，解得－1≤x ≤0，所以函数g (x )的定义域是[－1,0]．12．已知f (x )＝⎩⎨⎧ 2x ＋3，x >0，x 2－4，x ≤0，若f (a )＝5，则实数a 的值是__________；若f (f (a ))≤5，则实数a 的取值范围是__________．答案1或－3[－5，－1]解析①当a >0时，2a ＋3＝5，解得a ＝1；当a ≤0时，a 2－4＝5，解得a ＝－3或a ＝3(舍)．综上，a ＝1或－3.②设t ＝f (a )，由f (t )≤5得－3≤t ≤1.由－3≤f (a )≤1，解得－5≤a ≤－1.13．(2022·广州模拟)已知定义在R 上的函数f (x )满足，f (1－x )＋2f (x )＝x 2＋1，则f (1)等于()A ．－1B ．1C ．－13D.13答案B解析∵定义在R 上的函数f (x )满足，f (1－x )＋2f (x )＝x 2＋1，∴当x ＝0时，f (1)＋2f (0)＝1，①当x ＝1时，f (0)＋2f (1)＝2，②②×2－①，得3f (1)＝3，解得f (1)＝1.14．(2023·南昌模拟)已知函数f (x )＝⎩⎨⎧x ＋3，x ≤0，x ，x >0，若f (a －3)＝f (a ＋2)，则f (a )等于()A ．2B.2C ．1D ．0答案B解析作出函数f (x )的图象，如图所示．因为f (a －3)＝f (a ＋2)，且a －3<a ＋2，所以⎩⎨⎧ a －3≤0，a ＋2>0，即－2<a ≤3，此时f (a －3)＝a －3＋3＝a ，f (a ＋2)＝a ＋2，所以a ＝a ＋2，即a 2＝a ＋2，解得a ＝2或a ＝－1(不满足a ＝a ＋2，舍去)，则f (a )＝ 2.15．∀x ∈R ，用M (x )表示f (x )，g (x )中最大者，M (x )＝{|x |－1,1－x 2}，若M (n )<1，则实数n 的取值范围是()A ．(－2,2)B ．(－2,0)∪(0,2)C ．[－2,2]D ．(－2，2)答案B解析当x ≥0时，若x －1≥1－x 2，则x ≥1，当x <0时，若－x －1≥1－x 2，则x ≤－1，所以M (x )＝⎩⎨⎧ |x |－1，x ≥1或x ≤－1，1－x 2，－1<x <1，若M (n )<1，则当－1<n <1时，1－n 2<1⇒－n 2<0⇒n ≠0，即－1<n <0或0<n <1， 当n ≥1或n ≤－1时，|n |－1<1，解得－2<n ≤－1或1≤n <2，综上，－2<n <0或0<n <2.16．(多选)德国数学家狄利克雷在数学领域成就显著，以其名字命名的函数F (x )＝⎩⎨⎧ 1，x 为有理数，0，x 为无理数被称为狄利克雷函数．关于狄利克雷函数，下列说法正确的是()A ．F (F (x ))＝0B ．对任意x ∈R ，恒有F (x )＝F (－x )成立C ．任取一个不为0的实数T ，F (x ＋T )＝F (x )对任意实数x 均成立D ．存在三个点A (x 1，F (x 1))，B (x 2，F (x 2))，C (x 3，F (x 3))，使得△ABC 为等边三角形答案BD解析∵当x为有理数时，F(x)＝1，当x为无理数时，F(x)＝0，当x为有理数时，F(F(x))＝F(1)＝1，当x为无理数时，F(F(x))＝F(0)＝1，所以F(F(x))＝1恒成立，故A错误；因为有理数的相反数是有理数，无理数的相反数是无理数，所以对任意x∈R，恒有F(x)＝F(－x)成立，故B正确；若x是有理数，T是有理数，则x＋T是有理数；若x是有理数，T是无理数，则x＋T是无理数；若x是无理数，则x＋T是无理数或有理数，所以任取一个不为0的实数T，F(x＋T)＝F(x)不恒成立，故C错误；取x1＝－33，x2＝0，x 3＝33，可得F(x1)＝0，F(x2)＝1，F(x3)＝0，所以A⎝⎛⎭⎪⎫－33，0，B(0,1)，C⎝⎛⎭⎪⎫33，0，恰好△ABC为等边三角形，故D正确．。

考点规范练6 正午太阳高度的变化及四季、五带一、选择题(2018·天津和平模拟)下图为我国某地春分日时正午太阳与头顶夹角示意图。

据此完成第1~3题。

1.该地此日正午太阳高度是( )A.28°B.62°C.90°D.0°2.该地所在地理纬度是( )A.18°NB.28°NC.32°ND.52°N3.次日该地正午太阳高度将( )A.变大B.变小C.不变D.不确定(2018·湖南长沙质检)图1为甲、乙、丙三地等高旗杆正午影长变化曲线和朝向示意图,图2为①②③④四地正午太阳高度的变化示意图。

读图,完成第4~5题。

图1图24.有关图1中甲、乙、丙三地地理现象的判断,正确的是( )A.甲、乙两地有阳光直射现象B.一年中昼夜长短变化幅度最大的是乙地C.自转线速度:甲地<丙地<乙地D.一年中正午太阳高度变化幅度最小的是甲地5.图2中四条曲线能够反映乙地正午太阳高度变化的是( )A.①B.②C.③D.④(2018·天津河西三模)下图为我国南岭附近某区域地形、河流示意图,某中学学习小组测得某日P 城的昼长是12小时24分钟,PM、PN为太阳出没方向,且日落时正值北京时间18时44分。

读下图,完成第6~7题。

6.P城所在的经度为( )A.106°EB.112°EC.120°ED.128°E7.图中河流的干流流向大致为( )A.东南流向西北B.西南流向东北C.西北流向东南D.东北流向西南(2018·广东汕头模拟)江苏省土地资源相对紧缺,但利用城市建筑物发展光伏发电产业的潜力较大。

下图为江苏省城市分布图和太阳能电池方阵图。

据此完成第8~9题。

8.为保证太阳能电池方阵全年正常发电,图中D值最大的城市是( )A.徐州B.无锡C.南京D.苏州9.如果太阳能电池方阵的支架能够自动调节,支架调节到最短的季节是( )A.春季B.夏季C.秋季D.冬季读正午太阳高度年变化幅度图(极夜期不考虑负值),完成第10~11题。

专题6 分式及其运算考点一、分式的概念和性质1．（2022·云南·昆明中考模拟）要使12022x +有意义，则x 的取值范围为（ ）A ．0x ≠B ．2022x >-C ．2022x ≠D ．2022x ≠-2．（2022·湖南怀化·中考真题）代数式25x ，1π，224x +，x 2﹣23，1x ，12x x ++中，属于分式的有（ ）A ．2个B ．3个C ．4个D ．5个3．（2022·广东·中考三模）若分式55m m --的值为零，则m =（ ） A ．5-B ．5C ．5±D ．04．（2022·云南·中考三模）下列函数中，自变量x 的取值范围错误的是（ ） A ．11212y x x ⎛⎫=≠ ⎪-⎝⎭B ．)1y x =≥C ．)1y x =≤D ．21y x =-（x 为任意实数）5．（2022·湖北黄石·中考真题）函数11y x =-的自变量x 的取值范围是（ ） A ．3x ≠-且1x ≠B ．3x >-且1x ≠C ．3x >-D ．3x ≥-且1x ≠6．（2022·广西·中考真题）当x =______时，分式22xx +的值为零． 7．（2022·湖南邵阳·x 的取值范围是_________． 8．（2022·湖南·长沙市中考二模）若分式11x x --的值为零，则x 的值为______． 考点二、分式化简9．（2022·四川绵阳·中考二模）下列分式属于最简分式的是（ ） A ．265xy xB ．x y y x--C ．22x y x y++D ．2293x y x y-+10．（2022·四川眉山·中考真题）化简422a a +-+的结果是（ ） A ．1 B ．22a a +C ．224a a - D ．2a a +11．（2022·辽宁沈阳·中考真题）化简：21111x x x -⎛⎫-⋅= ⎪+⎝⎭______．12．（2022·四川自贡·中考真题）化简：22a3a42a3a2a4a4--⋅+-+++＝____________．13．（2022·西藏·中考真题）计算：222242a a aa a a+⋅---．14．（2022·辽宁大连·中考真题）计算2224214424x x xx x x x-+÷--+-．15．（2022·湖北十堰·中考真题）计算：2222a b b abaa a⎛⎫--÷+⎪⎝⎭．16．（2022·四川泸州·中考真题）化简：22311 (1). m m mm m-+-+÷17．（2022·湖南常德·中考真题）化简：231 122a aaa a+-⎛⎫-+÷⎪++⎝⎭18．（2022·甘肃武威·中考真题）化简：()2233322x x xx x x++÷-++．考点三、分式化简求值19．（2022·山东济南·中考真题）若m－n＝2，则代数式222m n mm m n-⋅+的值是（）A．－2B．2C．－4D．420．（2022·山东菏泽·中考真题）若22150a a --=，则代数式2442a a a a a -⎛⎫-⋅⎪-⎝⎭的值是________． 21．（2022·四川成都·中考真题）已知2272a a -=，则代数式2211a a a a a --⎛⎫-÷⎪⎝⎭的值为_________． 22．（2022·四川广安·中考真题）先化简：2242(2)244x xx x x x -++÷--+，再从0、1、2、3中选择一个适合的数代人求值．23．（2022·内蒙古内蒙古·中考真题）先化简，再求值：2344111x x x x x -+⎛⎫--÷ ⎪--⎝⎭，其中3x =．24．（2022·山东聊城·中考真题）先化简，再求值：244422a a a a a a --⎛⎫÷-- ⎪-⎝⎭，其中112sin 452a -⎛⎫=︒+ ⎪⎝⎭．25．（2022·辽宁锦州·中考真题）先化简，再求值：2233111211x x x x x x --⎛⎫÷-+ ⎪-++-⎝⎭，其中|1x =+．26．（2022·辽宁营口·中考真题）先化简，再求值：25244111a a a a a a +++⎛⎫+-÷⎪++⎝⎭，其中11|2|2a -⎛⎫=-- ⎪⎝⎭．27．（2022·湖北荆州·中考真题）先化简，再求值：222212a b a b a b a ab b ⎛⎫-÷ ⎪-+-+⎝⎭，其中113a -⎛⎫= ⎪⎝⎭，()02022b =-．28．（2022·四川广元·中考真题）先化简，再求值：22x x +÷（1﹣211x x --），其中x 是不等式组()211532x x x x ⎧-<+⎨+≥⎩的整数解．29．（2022·新疆·中考真题）先化简，再求值：22931121112a a a a a a a ⎛⎫--÷-⋅⎪-+--+⎝⎭，其中2a =．30．（2022·山东滨州·中考真题）先化简，再求值：2344111a a a a a ++⎛⎫+-÷⎪--⎝⎭，其中10(1tan 45π2)a -=︒+-答案与解析考点一、分式的概念和性质1．（2022·云南·昆明中考模拟）要使12022x +有意义，则x 的取值范围为（ ）A ．0x ≠B ．2022x >-C ．2022x ≠D ．2022x ≠-【答案】D【分析】根据分式有意义的条件列不等式求解即可．【详解】解：根据分式有意义即分母不为0，得到20220x +≠，即2022x ≠-，故D 正确． 故选：D ．【点睛】本题主要考查了分式有意义的条件，理解分式有意义的条件(分母不能为零)是解题关键．2．（2022·湖南怀化·中考真题）代数式25x ，1π，224x +，x 2﹣23，1x ，12x x ++中，属于分式的有（ ）A ．2个B ．3个C ．4个D ．5个A ．5-B ．5C ．5±D ．0【答案】A【分析】根据分式的值为零的条件列式计算即可． 【详解】解：由题意得：|m |−5＝0且m −5≠0， 解得：m ＝−5， 故选：A ．【点睛】本题考查的是分式的值为零的条件，掌握分式值为零的条件是分子等于零且分母不等于零是解题的关键．4．（2022·云南·云大附中三模）下列函数中，自变量x 的取值范围错误的是（ ） A ．11212y x x ⎛⎫=≠ ⎪-⎝⎭B ．)1y x =≥C ．)1y x =≤D ．21y x =-（x 为任意实数）5．（2022·湖北黄石·中考真题）函数1y x =-的自变量x 的取值范围是（ ） A ．3x ≠-且1x ≠ B ．3x >-且1x ≠C ．3x >-D ．3x ≥-且1x ≠6．（2022·广西·中考真题）当x =______时，分式22xx +的值为零． 【答案】0【分析】根据分式值为零，分子等于零，分母不为零得2x =0，x +2≠0求解即可． 【详解】解：由题意，得2x =0，且x +2≠0，解得：x =0， 故答案为：0．【点睛】本题考查分式值为零的条件，熟练掌握分式值为零的条件“分子为零，分母不为零”是解题的关键．7．（2022·湖南邵阳·x 的取值范围是_________．【答案】x >2##2＜x【分析】根据二次根式有意义的条件：被开方数是非负数和分式有意义的条件：分母不为0即可求出结论．【详解】解：由题意可得x-2>0， 解得：x >2， 故答案为：x >2．【点睛】本题考查的是分式及二次根式有意义的条件，掌握二次根式的被开方数是非负数、分式分母不为0解题的关键．8．（2022·湖南·长沙市开福区青竹湖湘一外国语学校二模）若分式11x x --的值为零，则x 的值为______．考点二、分式化简9．（2022·四川绵阳·二模）下列分式属于最简分式的是（ ） A ．265xy xB ．x y y x--C ．22x y x y ++D ．2293x y x y-+10．（2022·四川眉山·中考真题）化简422a a +-+的结果是（ ） A ．1 B ．22a a +C ．224a a -D ．2aa +11．（2022·辽宁沈阳·中考真题）化简：1111x x x -⎛⎫-⋅= ⎪+⎝⎭______． 【答案】1x -##1x -+12．（2022·四川自贡·中考真题）化简：2a 3a 42a 3a 2a 4a 4--⋅+-+++ ＝____________．【点睛】本题考查了分式的混合运算，熟练掌握约分，通分，因式分解的技巧是解题的关键．13．（2022·西藏·中考真题）计算：222242a a a a a a +⋅---． 24a a a a --2)(2)(2)a a a a -+-22a - 【点睛】本题考查了分式的化简，理解并掌握分式的计算法则，注意在解题过程中需注意的事项，仔细计算是本题的解题关键．14．（2022·辽宁大连·中考真题）计算2224214424x x x x x x x-+÷--+-．22222122x x x x x xx 211.xxx【点睛】本题考查的是分式的混合运算，掌握15．（2022·湖北十堰·中考真题）计算：2222a b b ab a a a ⎛⎫--÷+ ⎪⎝⎭．16．（2022·四川泸州·中考真题）化简：22311 (1). m m mm m-+-+÷17．（2022·湖南常德·中考真题）化简：231 122a aaa a+-⎛⎫-+÷⎪++⎝⎭18．（2022·甘肃武威·中考真题）化简：()2233322x x xx x x++÷-++．考点三、分式化简求值19．（2022·山东济南·中考真题）若m－n＝2，则代数式222m n mm m n-⋅+的值是（）A．－2B．2C．－4D．420．（2022·山东菏泽·中考真题）若22150a a--=，则代数式2442a aaa a-⎛⎫-⋅⎪-⎝⎭的值是________．【答案】15【分析】先按分式混合运算法则化简分式，再把已知变形为a2-2a=15，整体代入即可．21．（2022·四川成都·中考真题）已知2272a a -=，则代数式2211a a a a a--⎛⎫-÷ ⎪⎝⎭的值为_________． 【答案】72##3.5##312 【分析】原式括号中两项通分并利用同分母分式的减法法则计算，同时利用除法法则变形，约分得到最简22．（2022·四川广安·中考真题）先化简：2242(2)244x xxx x x-++÷--+，再从0、1、2、3中选择一个适合的数代人求值．23．（2022·内蒙古内蒙古·中考真题）先化简，再求值：344111x xxx x-+⎛⎫--÷⎪--⎝⎭，其中3x=．24．（2022·山东聊城·中考真题）先化简，再求值：244422a a a a a a --⎛⎫÷-- ⎪-⎝⎭，其中112sin 452a -⎛⎫=︒+ ⎪⎝⎭．25．（2022·辽宁锦州·中考真题）先化简，再求值：2233111211x x x x x x --⎛⎫÷-+ ⎪-++-，其中|1x =+．x 26．（2022·辽宁营口·中考真题）先化简，再求值：25244111a a a a a a +++⎛⎫+-÷ ⎪++⎝⎭，其中11|2|2a -⎛⎫=-- ⎪⎝⎭．27．（2022·湖北荆州·中考真题）先化简，再求值：222212a b a b a b a ab b ⎛⎫-÷ ⎪-+-+⎝⎭，其中113a -⎛⎫= ⎪⎝⎭，()02022b =-．28．（2022·四川广元·中考真题）先化简，再求值：22x x +÷（1﹣211x x --），其中x 是不等式组()211532x x x x ⎧-<+⎨+≥⎩的整数解．29．（2022·新疆·中考真题）先化简，再求值：22931121112a a a a a a a ⎛⎫--÷-⋅ ⎪-+--+⎝⎭，其中2a =．30．（2022·山东滨州·中考真题）先化简，再求值：344111a a a a a ++⎛⎫+-÷ ⎪--⎝⎭，其中10(1tan 45π2)a -=︒+-。

中国古代史6大专题考点大汇总考点 １ 半坡居民 河姆渡居民１．半坡居民生活在陕西西安东部半坡村，房屋主要是半地穴式圆形房屋，种植粟，半坡遗址是我国黄河流域原始农业文化的代表。

２．河姆渡居民生活在浙江余姚河姆渡村，房屋主要是干栏式建筑，种植水稻，河姆渡遗址是我国长江流域原始农业文化的代表。

考点 ２ 炎帝、黄帝的传说故事黄帝和炎帝被后人尊称为中华民族的人文初祖。

考点 １ 夏朝的建立 西周分封制１．禹建立中国历史上第一个王朝———夏朝，标志着中国王朝的产生。

禹死后，他的儿子启继承父位，从此，世袭制代替禅让制。

２．为稳定周初政治形势，巩固疆土，周王根据血缘关系远近和功劳大小分封宗亲和功臣等，从而确立了周王朝的社会等级制度分封制。

考点 ２ 商鞅变法公元前３５６年，秦孝公任用商鞅主持变法。

政治上确立县制；废除贵族世袭特权；改革户籍制度；严明法度，禁止私斗。

经济上废除井田制；鼓励耕织；统一度量衡；军事上奖励军功。

商鞅变法为以后秦国统一全国奠定了基础。

考点 ３ 秦统一中国 秦代的中央集权制度和统一措施１．公元前２２１年，秦王嬴政建立起我国历史上第一个统一的多民族的封建国家———秦朝。

２．秦始皇在政治上创立了大一统的中央集权制度。

国家的最高统治者称为皇帝，皇帝之下，设有中央政权机构，由丞相、太尉、御史大夫统领；地方上建立郡县制，开创了此后我国历代王朝地方行政的基本模式。

文化上统一文字，将小篆作为通用文字颁行全国；思想上实行“焚书坑儒”。

经济上统一货币，以秦国的圆形方孔半两钱作为标准货币；统一度量衡制度。

交通上统一车轨和道路的宽窄，修筑道路；开凿灵渠。

军事上修筑长城，北击匈奴。

考点 ４ 西汉的建立 “文景之治” 汉武帝巩固“大一统”王朝１．刘邦于公元前２０２年建立汉朝，定都长安，史称西汉。

刘邦即汉高祖。

２．汉文帝和汉景帝统治时期，历史上称为“文景之治”。

３．汉武帝在政治上采纳主父偃的“推恩”建议，思想文化上接受董仲舒“罢黜百家，独尊儒术”的建议，把儒家学说立为正统思想，兴办太学；经济上把铸币权收归中央，统一铸造五铢钱，实行盐铁官营、专卖。

六、房地产开发流程分为三个阶段，即投资决策、前期准备和开发建设。

（一）投资决策投资决策的工作内容主要是通过房地产市场调研，进行开发项目选择，基于房地产开发项目可行性分析，作出合理的投资决策。

房地产开发的成败在很大程度上取决于投资决策分析的科学与否。

房地产开发投资机会选择的思路一般是从宏观逐步聚焦到微观。

首先，要从宏观角度选定投资区域。

房地产市场是一个区域性市场，不同区域的投资环境和房地产市场供求关系不同，投资机会也有明显差异。

房地产开发企业应选择投资环境良好、有市场前景、企业具有竞争优势且符合企业发展战略的投资区域。

其次，要从中观角度确定投资地区及具体城市。

最后，在选定的投资城市中，根据所搜集的城市房地产信息，从微观层面选择投资开发的房地产类型和区位，并搜集可供开发的房地产项目和可利用的资源。

（二）前期准备主要包括：取得建设用地使用权、委托场地勘察和规划设计、申请规划设计方案审查和建设工程规划许可、工程建设准备、申请施工许可等。

1.取得建设用地使用权建设用地土地使用权供应方式有两种，即出让和划拨。

房地产开发企业应根据开发建设项目性质通过出让竞争或者申请划拨取得开发建设用地使用权。

建设用地土地使用权供应方式依法取得开发建设用地后，房地产开发企业委托勘察单位进行场地勘察。

3.委托规划设计规划设计是房地产开发建设的方向指引，需要综合各方面因素，确定合理的技术经济指标，统筹安排建设用地，提出科学的功能布局，做到经济效益、社会效益和环境效益的统一。

（1）规划设计的主要控制指标控制性详细规划或土地规划设计中确定的容积率、建筑高度、建筑密度、绿地率、建筑间距等控制性指标，是房地产开发项目编制修建性详细规划的重要依据。

（2）组织规划设计和建筑设计2组织规划设计和建筑设计内容工程项目批准、核准或备案后，随着项目规划设计工作推进，开发建设单位应依法办理环境保护、土地使用、资金利用、安全生产、城市规划等许可手续。

其中：地震安全性评价在工程设计前完成；环境影响评价、节能评价等评估评价和取水许可等事项在开工前完成；可将用地预审意见作为使用土地证明文件申请办理建设工程规划许可证；供水、供电、燃气、热力、排水、通信等市政公用基础设施报装可提前到开工前办理，在工程施工阶段完成相关设施建设，竣工验收后直接办理接入4.申请规划设计方案审查和建设工程规划许可事宜。

自考现代管理学核心考点解析六
1、管理学的研究对象：
是研究生产力方面的问题是研究生产关系方面的问题是研究上层建筑方面的问题
2、管理学的学科特征
管理学是一门理论性与应用性相统一的学科
管理学是一门定性和定量相统一的学科
管理学是一门软科学
管理学具有鲜明的时代特征5管理学是一门自然属性与社会属性相统一的学科
3、简述现代管理学及其特征。

现代管理学是在总结管理发展历史经验和借鉴传统管理理论的基础上综合运用现代社会科学，自然科学和技术科学所提供的理论和方法，研究现代条件下进行的各种管理活动的基本规律和一般方法的学问。

与传统管理学相比，现代管理学具有变革性，开放性，严密性，实用性等特点。

4、简述现代管理学的研究内容。

关于管理、管理学和现代管理学的基本问题;
关于管理职能的基本问题;
关于管理方法与技术的基本问题。

考点巩固卷6 七选五2023年高考真题【2023▪新高考I卷】Personal ForgivenessTaking responsibility for mistakes is a positive step, but don’t beat yourself up about them. To err (犯错) is human. 16 You can use the following writing exercise to help you do this.In a journal or on a piece of paper, put the heading “Personal strengths.” 17 Are you caring? Creative? Generous? A good listener? Fun to be around? They don’t have to be world-changing, just aspects of your personality that you’re proud of.At the top of a second page, put the heading “Acts of kindness.” On this one, list all the positive things you’ve done for others. It might be the time when you helped a friend with their homework, when you did the ironing without being asked, or when you baked cookies after the family had had a tiring day. 18 You could ask a friend or family member to help add to your list. 19 That way, you could exchange thoughts on what makes each of you special and the aspects of your personality that shine through. In fact, don’t wait until you’ve made a mistake to try this—it’s a great way to boost self-confidence at any time.It’s something of a cliché (陈词滥调) that most people learn not from their successes but their mistakes. The thing is, it’s true. 20 We’ re all changing and learning all the time and mistakes are a positive way to develop and grow.A. A little self-forgiveness also goes a long way.B. Now list all the characteristics you like about yourself.C. They might even like to have a go at doing the exercise.D. It’s just as important to show yourself some forgiveness.E. It doesn’t mean you have to ignore what’s happened or forget it.F. Whatever it is, no matter how small it might seem, write it down.G. Whatever the mistake, remember it isn’t a fixed aspect of your personality.【2023▪新高考II卷】As an artist who shares her journey on social media, I’m often asked by curious followers how to begin an art journey. Unfortunately, there is no magic list I can offer. I do remember, though, what it was like to be a complete beginner. So I’ve put together some good tips for starting an art journey.▪Start small. I suggest using a sketchbook (素描本) for small studies. These small studies provide inspiration and may be a springboard for more complex works in the future. 16 You’ll want to look back on your journeyto see how far you’ve come.▪Paint often and paint from life. There’s no better way to improve than to put in those brush miles. Whether you paint still lifes, portraits, or landscapes, paint from life as much as possible. 17▪Continually challenge yourself to try something new. 18 Artistic growth can be a bit painful. Welcome to the club；we’ve all been there. I love taking on challenges. I once took up a challenge to create a painting every day for a month and post the works online.▪ 19 Seeking and accepting constructive feedback (反馈) is crucial to growth. I post my work on social media and, in turn, have met some of the kindest people. They make me feel valued and respected, no matter my level of artistic ability.The journey you’re on won’t follow a straight path. 20 Push through, give it time and put in the effort. You will harvest the rewards of an artistic life.A. Get out of your comfort zone.B. Make career plans and set goals.C. Don’t throw away your beginner art.D. Share your work if you feel comfortable doing so.E. You’ll hit roadblocks, and you’ll feel discouraged at times.F. Evaluate your performance and, if needed, redefine your role.G. You’ll develop that painting muscle memory that only comes with repetition.【2022▪新高考I卷】Fitness Magazine recently ran an article titled “Five Reasons to Thank Your Workout Partner.” One reason was: “You’ll actually show up if you know someone is waiting for you at the gym, ” while another read: “ 36 ” With a workout partner, you will increase your training effort as there is a subtle (微妙) competition.So, how do you find a workout partner?First of all, decide what you want from that person. 37 Or do you just want to be physically fit, able to move with strength and flexibility? Think about the exercises you would like to do with your workout partner.You might think about posting what you are looking for on social media, but it probably won’t result in a useful response. 38 If you plan on working out in a gym, that person must belong to the same gym.My partner posted her request on the notice board of a local park. Her notice included what kind of training she wanted to do, how many days a week and how many hours she wanted to spend on each session, and her age. It also listed her favorite sports and activities, and provided her phone number. 39You and your partner will probably have different skills. 40 Over time, both of you will benefit — your partner will be able to lift more weights and you will become more physically fit. The core (核心) of yourrelationship is that you will always be there to help each other.A. Your first meeting may be a little awkward.B. A workout partner usually needs to live close by.C. You’ll work harder if you train with someone else.D. Do you want to be a better athlete in your favorite sport?E. How can you write a good “seeking training partner” notice?F. Just accept your differences and learn to work with each other.G. Any notice for a training partner should include such information.【2022▪新高考II卷】Writing an essay is a difficult process for most people. However, the process can be made easier if you learn to practice three simple techniques.36 When you are first trying to think of ideas for an essay, put your pen to your paper and write nonstop for ten or fifteen minutes without letting your pen leave the paper. Stay loose and free. 37 Don’t worry about grammar or spelling. Even though this technique won’t work for everyone, it helps many people get a good store of ideas to draw on.The next technique is to write your draft rapidly without worrying about being perfect. 38 Yet, by learning to live with imperfection, you will save yourself headaches and a wastepaper basket full of crumpled (弄皱) paper. Think of your first draft as a path cut out of the jungle—as part of an exploration, not as a complete highway.The third technique is to try printing out a triple—spaced (三倍行距) copy to allow space for revision. 39 As a result, these writers never get in the habit of crossing out chunks (大块) of their draft and writing revisions in the blank space. After you have revised your draft until it is too messy to work from anymore, you can enter your changes into your word processor. 40 The resulting blank space invites you to revise.A. Make sure your handwriting is neat.B. Let your pen follow the waves of thought.C. The second draft of the essay should be better.D. First of all, learn the technique of nonstop writing.E. Too many writers try to get their drafts right the first time.F. Many beginning writers don’t leave enough space to revise.G. Then you can print out a fresh draft, again setting your text on triple-space.2023年高考模拟真题（2022·甘肃张掖·临泽县第一中学校考一模）Sleep problem may happen in many people. Good news isthat people can actually“Train”their brains to fall asleep.1. Make a schedule, and stick to itMelatonin(褪黑素)is a hormone produced by the body to regulate when you get sleepy and when you wake up. As night approaches, levels of melatonin rise, becoming a signal to the body that it’s time for bed. To work properly, the release of this hormone needs to occur at regular times. 1 .2. 2 .“The best sleep tip you can ever give somebody is get up - don’t lay in bed awake but not sleeping,” clinical psychologist and sleep expert Michael Grandner said. Why is that so important? 3 . Instead of being a restful spot where you peacefully fall asleep, your bed becomes an anxious place where you toss and turn and wake up tired. What you need to do is to go to bed extra early and the bed has the power to help overcome your racing mind and allow you to fall asleep.3. Change your attitude about sleepMany people view sleeping as the final thing they have to do in a busy day, worth delaying to finish the housework, schoolwork, office work or the latest television series. 4 . “Don’t see your sleep as the amount of time you have left in your day,” he advised. “See your sleep as the amount of time you need in order to set yourself up for a productive tomorrow.”It may sound like a small shift in thinking, but it’s important. Most adults need between seven and eight hours of sleep to be fully rested, according to the US Centers for Disease Control and Prevention. So if a person needs to rise at 7 am each day, he would require a bedtime of 11 pm. When you have to stop and get ready to go to bed, do it without hesitation. 5 .A．Go to bed early and get up early.B．Don’t lay in bed awake.C．Otherwise, it will makes the next day more stressful.D．Because lying in bed awake can form an association in your brain that can lead to long-time sleep problem.E．Because lying in bed awake may make you more tired when getting up.F．Therefore, it’s important to have a standard wake up time, even on weekends or vacations.G．That thinking needs to be changed.（2023·河北·校联考三模）Unlike other natural disasters such as hurricanes, earthquakes are very hard to see coming, even for scientists. 6 Thus, specific practices for earthquake preparedness are necessary. Here are four steps you can take to prepare yourself in advance.Drop, cover and holdIf you feel the ground start to shake, drop, take cover under as table piece of furniture, and hold on. You can hide under something like a desk or table, with one arm holding on to a leg of the table and your other arm protecting your neck and head. 7 In modern homes, it is no stronger than any other part of the house and will not protect you from injury.Make a family plan8 Create a meeting point—somewhere easy for everyone to remember, or you could also meet at home. Whatever plan you decide on, don’t rely on your phone as your main form of communication. Technology fails all the time in disasters. A major earthquake in California, for example, damaged cell towers and knocked out communication services for days.Secure your furnitureThose hanging shelves above your bed could be a danger during an earthquake. People often get injured from “flying or falling objects” like furniture or glass during earthquakes. So examine your home and ask yourself, “What could be a potential danger to my safety?” 9Make digital copies of important documentsImportant documents may get destroyed during earthquakes. Therefore, scan or take photos of your important documents, such as your license, financial records and insurance policy information. 10 This step can help ensure your documents will be available even if your computer is lost in a quake.A．Then send them to your e-mail.B．These are all important personal documents.C．Make sure your household has a plan of action.D．Whatever you do, do not stand in a doorframe.E．If you find the answer, you need to runaway immediately.F．Nowadays early detection systems can only give seconds of warming ahead.G．If possible, remove those heavy and big objects above your bed immediately.（2023·湖北武汉·校联考一模）If something that you’re doing doesn’t challenge you, then it doesn’t change you. We all need some normal stress in our lives, after all. 11 So challenge the following limits:1.Figure out what you’re scared of and do it continuously.If you’re a salesman, and you’re scared of talking to people personally or over the phone now, instead of being scared and thinking you’ll fail, spend at least five minutes a day to pick up the phone and make a call. 12 But don’t stop on the first try! Eventually, you can look at fear in the eye and say, “Go on. I’m not scared!”2. 13Make sure this hobby is not linked to your career; you have to relax and relieve your stress while performingthis. Some examples might be cooking, sewing, painting and so on. Apart from helping you challenge yourself, taking a class for your hobby may also give you extra income.3. Set aside at least nine minutes a day for physical exercise.14 A simple 9-minute run around your neighborhood can do wonders for yourself. Exercise can not only help you maintain your regular weight, but also make you feel better about yourself.4.Travel and allow yourself to be interested in new people.Don’t just limit yourself to your fellow travelers, try to connect with the service staff. You never know what kind of people they’re going to be. Get out of your house or go online to book your ticket right now. 15 A．Someone may hang up on you.B．You should do it continuously.C．You don’t need to go to the gym.D．Running in the gym may be a better choice.E．Start to travel now and learn to challenge yourself.F．Take a class for a hobby you’ve been wanting to develop.G．You can never see any improvement if you stick to your comfort zone.（2023·江苏盐城·盐城中学校考三模）The Upside to Being Outside Research shows that being in nature makes people feel good, whether they’re roughing it in the wilderness for days or just hanging out at a local park for a while. One study was conducted in the city of Birmingham, Alabama. Researchers found that most participants’ mood and well-being improved significantly when they spent time in urban parks, even though the average visit was only around half an hour.16 For example, scientists in the United Kingdom studied the impact of the “30 Days Wild” campaign. It challenged people to interact with nature for 30 days by enjoying earthy activities like feeding birds and planting flowers. Participants were measurably happier and healthier throughout the challenge…and for months afterwards, too. 17How does nature boost people’s happiness? Scientists say that spending time in natural settings reduces stress and anxiety, which benefits mental and physical health. Research shows our brains are more relaxed in natural settings.To most people, it’s not news that nature can be calming. But multiple studies have found that spending time in nature also has some more surprising benefits, like improving creativity and problem-solving. 18 Another found that exposure to nature helped people score better on tests. That’s more proof that going outside is a smart move!What accounts for the connection with cognition and creativity? It could be that a good dose of nature acts asa cure to information overload. Everyday life involves a lot of multitasking. Some scientists theorize that spending time in nature enables our brains to rest and recover from mental tiredness. 19Naturally, scientific studies don’t cover everything that’s great about the great outdoors. 20 From recreation and exercise to happiness and creativity, there are lots of upsides to getting outside.A．One study revealed that people were better at figuring out puzzles after a four-day camping trip.B．According to many scientific studies, there’s a good chance it’ll make you happier, healthier, and more creative.C．What’s more, the lift people get from nature is long lasting.D．Lots of people enjoy fun activities outside, like swimming, riding bikes, or climbing trees.E．When the only light you’ve seen all day is the glow of a screen, it might be a good idea to switch it off.F．This means that whether you’re studying or playing video games, heading outside to give your brain a break might help you get to the next level.G．So, kicking back in a park is a bit like treating your mind to a restful mini vacation.（2023·江西·江西师大附中校考三模）During job or school interviews, you’re likely to be asked what your strengths and weaknesses are, because the interviewers are interested in how your areas of strengths and weaknesses might affect your performance in this position. 21 For instance, you may be skilled in cooking, but if you’re applying for an office job, this strength may be irrelevant.However, knowing your personal areas of strengths and weaknesses is not a piece of cake. It takes self-awareness and self-reflection. 22 Or, ask some of your friends what they see as your best qualities or shortcomings.23 For example, let’s say my strength is creativity and yours is planning; we both want to have the same career. We might go about getting there in very different ways. If I did something creative to get my dream job and you planned carefully, we’d both likely be successful. But if I tried planning and you tried something creative, both of us might fail. 24Having a weakness doesn’t have to be a bad thing. It could be something you struggle with, but it could also be something you haven’t spent time developing yet. 25 For example, maybe your area of weakness is relevant to gratitude. You just haven’t spent a lot of time thinking about gratitude before. But now you engage in a bunch of activities that help you turn gratitude into an area of strength. Hey, now you’ve got one more skill!A．Is it proper to begin with a truthful answer?B．So ask yourself what you are good or weak at.C．Our areas of strengths can help us achieve our goals.D．Thus, it’s helpful to know your strengths related to the role.E．Many job applicants are unsure how to approach this question.F．By turning a weakness into a strength, you build other important skills.G．That’s why it is important to know and use our strengths to reach goals.（2023·江苏南京·金陵中学校考模拟预测）Do Weighted Blankets Work?Sleep is supposed to be a natural thing, but if you wrestle with insomnia (失眠症), you may be tempted to try pieces of equipment that promise better sleep. 26“They’ve become the sleep tool to have,” says Alanna McGinn, founder and lead sleep expert at Good Night Sleep Site. “I’m a huge supporter of them because they can work so well.”About 32 percent of Americans don’t get enough sleep, according to the Centers for Disease Control and Prevention. 27 Insomnia impacts as many as 35 percent of adults from time to time, while 10 percent have chronic trouble falling and staying asleep.Choose one that’s around 10 percent of your body weight. 28 Inside is a layer of plastic, glass or metal balls surrounded by filling. McGinn says the blanket’s heaviness acts as a touch therapy called deep pressure stimulation. Just as wrapping babies tightly can send them to sleep, these blankets help your heart and breathing rates slow and your body release feel-good hormones, including serotonin (血清素).Are they effective? A 2020 review study in the U.S. looked at eight previous studies and concluded that weighted blankets helped reduce anxiety — but not necessarily insomnia. 29 A randomized controlled study in Sweden looked at 120 people with insomnia and also depression or anxiety. 30 People with conditions such as diabetes or breathing issues, however, should check with their doctor before using one. “And if you’re someone who is a little afraid of an enclosed space, it’s probably not the best thing for you,” adds McGinn.A．It recommends at least seven hours a night for adults.B．Those who used a weighted blanket slept better and were less tired or anxious.C．The study found a significant rise in the related symptoms.D．But other 2020 research tells a slightly different story.E．One that might sound a little weird but that has been known to work is a weighted blanket.F．Dealing with such problems can be more or less tricky.G．Weighted blankets range between two and 14 kilograms.（2023·山东·山东省实验中学校考二模）I’ve been living in Spain for decades and I securely guarantee that I have a talent in figuring out the cool hidden local spots. As a foreigner, I couldn’t care less about doing the touristy things or enjoying fancy cuisine. 31 So I always attempt to find something that’s appealing and fun yet represents the local culture, and that offers an interaction with the locals.My reputation for doing this has grown. 32 Since I am somewhat fluent in Spanish, I could charge people for this and become somewhat of an official tour guide. I choose not to though, because to me, the most important thing is making sure the tourist, who already spent a lot of time and money getting to where I am, has the fun and cultural experience they could possibly have. 33 In that case, tourists can explore the local culture further at the lowest cost. They could otherwise spend a significant sum of money on a guided tour that keeps them comfortable but separated from the culture. I choose to give them an experience that’s deeper and opens their mind, all for free.34 When someone is visiting your area, don’t just take them to the touristy spots. Show them the places that mean something to you. Show them your heart through the places that you show them and the experience you give them. There’s something good in almost every town out there. If you don’t have any spots in your area that you like, learn to find the good in the place you live. If you find the good in where you live, you will also find the good in yourself. It’s a time that both you and the tourist will probably never obtain again.35A．Everyone can do the same.B．I could hardly have imagined it would happen.C．It could also help me create a lifelong connection with them.D．What’s most crucial is experiencing the genuine country and culture.E．I know better than tourists themselves what they are eager to experience.F．Don’t rush the experience, thoroughly enjoy every moment with that person.G．I’m being asked frequently to offer people tours, both to friends and strangers.（2023·广东·华南师大附中校考三模）There are countless articles online that will give you advice on how to deal with homesickness, but here are some of my favorite advice and tips on what has helped me. 36 .Make food from your home countryAnd if you don’t cook, try learning to cook with friends or find new places to eat. This may just be me loving food, but eating with friends really makes things so much better. 37 .Food can be connected to memories. You can talk about what this reminds you of, while also creating new memories to mix with the ones that make you miss home.Call home—but not every minute of every dayI was a little annoyed when I saw so many online sources phrase it this way: “Talk to your parents—but not too much. Call home—but not too often.” 38 . It’s good to keep in touch with your family and friends. However, it’s a problem when you’re talking to them so much that it’s stopping you from having real experience in this new place.39 . Call the people you love often, keep them updated with your life and ask them how life is going for them. You’re going to need that. Think of it this way—the more you’re living outside of your room, the more you can tell them later about everything you’re learning.40There is nothing wrong with finding someone to talk about how you’re feeling. It can be friends and family, mentors or professors that you feel can understand you. Or it may mean talking to a counselor or getting psychological help if that’s what you think you need. Talking about mental health is becoming a lot more open. So, if you’re feeling homesick, it can also be helpful to do some research on who your university recommends you reach out to.A．Talk to someoneB．Do some researchC．There is nothing wrong with being homesickD．So, of course, keep in touch with your familyE．Hopefully, they will be helpful to you as wellF．But, the thing is, they really have a point when they say thatG．It’s a way to bond, an excuse to get closer, and you even get rewarded from it（2023·四川泸州·校考一模）Find it hard to get started? Try these suggestions to help you rise and shine—and be effective from morning till night.●Get up earlierSleeping in can be a hard habit to break. Actually it involves two things—going to bed earlier and getting up earlier. Start off by going to bed 15 minutes before your usual turn-in time and setting your alarm the same number of minutes earlier the next day. 41●Have a good stretch in bedBefore you even open your eyes, stretch every extremity(四肢) for 15 seconds. Lift your arm and begin by stretching each finger, next your hand, and then your arm. 42 End with a neck and back stretch that gets you out of bed. By doing this,you will enhance the flow of blood through your system, providing your tissues with extra oxygen.43The fewer choices you have to make first thing, the better. Before going to bed, decide what you’re going to wear, work out which route you’ll take to work and pack your bag.●Consult your morning calendarHang a large whiteboard in your kitchen. On it, write down all you need to know for that particular day, fromdoctor appointments to what you’re doing with your friends. Check it carefully while you sip your first cup of coffee or tea. 44●Get moving45 And if you can get yourself into the habit, exercising in the morning can give you energy to jump-start your day.A．Move on to your toes, feet and legs.B．It will help you to structure your day.C．Set your clothes out the night before.D．Spend less time choosing things when packing.E．Morning exercise can get you refreshed quickly.F．Gradually reset your sleep cycle until you get to your desired wake-up time.G．If you’re a night owl, an early morning jog might sound like punishment.（2023·四川成都·成都七中校考模拟预测）You know you really want to do well in your study. Your parents have put the pressure on you, or you have promised yourself you will do better. 46 How can you solve the problem? The following tips may give you a hand.Find a place that makes you want to study. If the books and seriousness of the library put you in the mood for focusing on study, go for it. If the comfortable chairs and coffee at your local café are what you need to get through your reading for English, go there. 47Set a study schedule. When you have many subjects to study, it can seem hard to get through everything. Give yourself a schedule where you set specific times to study particular subjects. 48 Besides, change subjects every two hours. A little variety keeps you refreshed and focused.49 If you find yourself distracted from studying by thoughts about something else, spend 5 minutes thinking about them, but then tell yourself studying is your main task now. If you are tired of study, step away from it. A short break helps refresh you so that you can stay focused when you come back to studying.Turn off the electronic devices. Texting, social media, calls and other distractions that come from your electronic devices are some of the biggest barriers to staying focused when you are studying. 50 Turn off the distracting electronic devices!A．Give yourself a brief study break.B．Get yourself clear about the study task.C．But you keep getting distracted!D．Luckily, the fix is easy and totally within your control.E．There’s no doubt that a library is the best place for studying well.资料收集整理【淘宝店铺:向阳百分百】11F．This makes studying seem less difficult, helping you stay on task. G．The most important thing is that the location motivates you to study.试卷第12页，共12页。

考点测试6 函数的单调性一、基础小题1．若函数f (x )＝(2a －1)x ＋b 是R 上的减函数，则实数a 的取值范围为( ) A ．12，＋∞ B．－∞，12 C ．12，＋∞ D．－∞，12 答案 D解析 当2a －1<0，即a <12时，该函数是R 上的减函数．故选D ．2．下列函数中，在(0，＋∞)上单调递减的是( ) A ．f (x )＝1xB ．f (x )＝(x －1)2C ．f (x )＝e xD ．f (x )＝ln (x ＋1) 答案 A解析 f (x )＝(x －1)2在(0，＋∞)上不单调，f (x )＝e x与f (x )＝ln (x ＋1)在(0，＋∞)上单调递增，故选A ．3．下列四个函数中，在定义域内不是单调函数的是( ) A ．y ＝－2x ＋1 B ．y ＝1xC ．y ＝lg xD ．y ＝x 3答案 B解析 y ＝－2x ＋1在定义域内为单调递减函数；y ＝lg x 在定义域内为单调递增函数；y ＝x 3在定义域内为单调递增函数；y ＝1x在(－∞，0)和(0，＋∞)上皆为单调递减函数，但在定义域内不是单调函数．故选B ．4．已知函数y ＝f (x )在R 上单调递增，且f (m 2＋1)>f (－m ＋1)，则实数m 的取值范围是( )A ．(－∞，－1)B ．(0，＋∞)C ．(－1，0)D ．(－∞，－1)∪(0，＋∞) 答案 D解析 由题得m 2＋1>－m ＋1，故m 2＋m >0，解得m <－1或m >0．故选D ． 5．函数y ＝log 12(2x 2－3x ＋1)的递减区间为( )A ．(1，＋∞) B．⎝⎛⎦⎥⎤－∞，34 C ．⎝ ⎛⎭⎪⎫12，＋∞ D ．⎣⎢⎡⎭⎪⎫34，＋∞答案 A解析 由2x 2－3x ＋1>0，得函数的定义域为⎝ ⎛⎭⎪⎫－∞，12∪(1，＋∞)．令t ＝2x 2－3x ＋1，则y ＝log 12t ．∵t ＝2x 2－3x ＋1＝2⎝ ⎛⎭⎪⎫x －342－18，∴t ＝2x 2－3x ＋1的单调递增区间为(1，＋∞)． 又y ＝log 12t 在(0，＋∞)上是减函数，∴函数y ＝log 12(2x 2－3x ＋1)的单调递减区间为(1，＋∞)．故选A ．6．定义在R 上的函数f (x )对任意两个不相等的实数a ，b ，总有f (a )－f (b )a －b>0成立，则必有( )A ．函数f (x )先增加后减少B ．函数f (x )先减少后增加C ．f (x )在R 上是增函数D ．f (x )在R 上是减函数 答案 C解析 因为f (a )－f (b )a －b>0，所以，当a >b 时，f (a )>f (b )，当a <b 时，f (a )<f (b )，由增函数定义知，f (x )在R 上是增函数．故选C ．7．函数f (x )＝是增函数，则实数c 的取值范围是( )A ．[－1，＋∞) B．(－1，＋∞)C ．(－∞，－1)D ．(－∞，－1] 答案 A解析 作出函数图象可得f (x )在R 上单调递增，则c ≥－1，即实数c 的取值范围是[－1，＋∞)．故选A ．8．若函数f (x )＝8x 2－2kx －7在[1，5]上为单调函数，则实数k 的取值范围是( ) A ．(－∞，8] B ．[40，＋∞)C ．(－∞，8]∪[40，＋∞) D．[8，40] 答案 C解析 由题意知函数f (x )＝8x 2－2kx －7图象的对称轴为x ＝k8，因为函数f (x )＝8x 2－2kx －7在[1，5]上为单调函数，所以k 8≤1或k8≥5，解得k ≤8或k ≥40，所以实数k 的取值范围是(－∞，8]∪[40，＋∞)．故选C ．9．函数f (x )在(a ，b )和(c ，d )上都是增函数，若x 1∈(a ，b )，x 2∈(c ，d )，且x 1<x 2，则( )A ．f (x 1)<f (x 2)B ．f (x 1)>f (x 2)C ．f (x 1)＝f (x 2)D ．无法确定 答案 D解析 因为f (x )＝－1x在(－2，－1)和(1，2)上都是增函数，f (－1．5)>f (1．5)；f (x )＝2x在R 上是增函数，f (－1．5)<f (1．5)，所以函数值无法确定．故选D ．10．若f (x )＝－x 2＋2ax 与g (x )＝ax ＋1在区间[1，2]上都是减函数，则a 的取值范围是( )A ．(－1，0)∪(0，1]B ．(－1，0)∪(0，1)C ．(0，1)D ．(0，1] 答案 D解析 f (x )＝－(x －a )2＋a 2，当a ≤1时，f (x )在[1，2]上是减函数；g (x )＝ax ＋1，当a >0时，g (x )在[1，2]上是减函数，则a 的取值范围是0<a ≤1．故选D ．11．函数y ＝－(x －3)|x |的递增区间为________． 答案 0，32解析 y ＝－(x －3)|x |＝作出其图象如图，观察图象知递增区间为0，32．12．已知f (x )＝ax ＋1x ＋2，若对任意x 1，x 2∈(－2，＋∞)，有(x 1－x 2)[f (x 1)－f (x 2)]>0，则a 的取值范围是________．答案 ⎝ ⎛⎭⎪⎫12，＋∞ 解析 由f (x )＝ax ＋1x ＋2＝a ＋1－2ax ＋2，且y ＝f (x )在(－2，＋∞)是增函数，得1－2a <0，即a >12．二、高考小题13．(2017·全国卷Ⅱ)函数f (x )＝ln (x 2－2x －8)的单调递增区间是( ) A ．(－∞，－2) B ．(－∞，1) C ．(1，＋∞) D．(4，＋∞) 答案 D解析 由x 2－2x －8>0可得x >4或x <－2， 所以x ∈(－∞，－2)∪(4，＋∞)， 令u ＝x 2－2x －8，则其在x ∈(－∞，－2)上单调递减， 在x ∈(4，＋∞)上单调递增．又因为y ＝ln u 在u ∈(0，＋∞)上单调递增，所以y ＝ln (x 2－2x －8)在x ∈(4，＋∞)上单调递增．故选D ．14．(2017·北京高考)已知函数f (x )＝3x－⎝ ⎛⎭⎪⎫13x ，则f (x )( )A ．是奇函数，且在R 上是增函数B ．是偶函数，且在R 上是增函数C ．是奇函数，且在R 上是减函数D ．是偶函数，且在R 上是减函数 答案 A解析 ∵函数f (x )的定义域为R ，f (－x )＝3－x －⎝ ⎛⎭⎪⎫13－x ＝⎝ ⎛⎭⎪⎫13x －3x ＝－f (x )，∴函数f (x )是奇函数．∵函数y ＝⎝ ⎛⎭⎪⎫13x在R 上是减函数，∴函数y ＝－⎝ ⎛⎭⎪⎫13x在R 上是增函数．又∵y ＝3x在R 上是增函数，∴函数f (x )＝3x－⎝ ⎛⎭⎪⎫13x 在R 上是增函数．故选A ．15．(2016·北京高考)下列函数中，在区间(－1，1)上为减函数的是( ) A ．y ＝11－xB ．y ＝cos xC ．y ＝ln (x ＋1)D ．y ＝2－x答案 D解析 选项A 中，y ＝11－x ＝1－(x －1)的图象是将y ＝－1x 的图象向右平移1个单位得到的，故y ＝11－x在(－1，1)上为增函数，不符合题意；选项B 中，y ＝cos x 在(－1，0)上为增函数，在(0，1)上为减函数，不符合题意；选项C 中，y ＝ln (x ＋1)的图象是将y ＝ln x 的图象向左平移1个单位得到的，故y ＝ln (x ＋1)在(－1，1)上为增函数，不符合题意；选项D 符合题意．16．(2015·湖南高考改编)设函数f (x )＝ln (1＋x )－ln (1－x )，则f (x )是( ) A ．在(－1，1)上是增函数 B ．在(－1，1)上是减函数C ．在(－1，0)上是减函数，在(0，1)上是增函数D ．在(－1，0)上是增函数，在(0，1)上是减函数 答案 A解析 由f (x )＝ln (1＋x )－ln (1－x )，得f (x )＝ln ⎝⎛⎭⎪⎫1＋x 1－x ＝ln ⎝ ⎛⎭⎪⎫21－x －1．∵t ＝21－x －1在(－1，1)上单调递增，y ＝ln t 在(0，＋∞)上单调递增，∴y ＝f (x )在(－1，1)上单调递增．17．(2015·湖北高考)已知符号函数sgn x ＝f (x )是R 上的增函数，g (x )＝f (x )－f (ax )(a >1)，则( )A ．sgn[g (x )]＝sgn xB ．sgn[g (x )]＝－sgn xC ．sgn[g (x )]＝sgn[f (x )]D ．sgn[g (x )]＝－sgn[f (x )] 答案 B解析 ∵f (x )是R 上的增函数，a >1，∴当x >0时，x <ax ，有f (x )<f (ax )，则g (x )<0； 当x ＝0时，g (x )＝0；当x <0时，x >ax ，有f (x )>f (ax )，则g (x )>0．∴sgn[g (x )]＝∴sgn[g (x )]＝－sgn x ．故选B ．18．(2016·天津高考)已知f (x )是定义在R 上的偶函数，且在区间(－∞，0)上单调递增．若实数a 满足f (2|a －1|)>f (－2)，则a 的取值范围是________．答案 ⎝ ⎛⎭⎪⎫12，32 解析 由题意知函数f (x )在(0，＋∞)上单调递减．因为f (2|a －1|)>f (－2)，且f (－2)＝f (2)，所以f (2|a －1|)>f (2)，所以2|a －1|<212，解之得12<a <32． 三、模拟小题19．(2018·山西晋城一模)已知函数f (x )＝log a (－x 2－2x ＋3)(a >0且a ≠1)，若f (0)<0，则此函数的单调递增区间是( )A ．(－∞，－1]B ．[－1，＋∞)C ．[－1，1)D ．(－3，－1]答案 C解析 令g (x )＝－x 2－2x ＋3，由题意知g (x )>0，可得－3<x <1，故函数的定义域为{x |－3<x <1}．根据f (0)＝log a 3<0，可得0<a <1，则本题即求函数g (x )在(－3，1)内的单调递减区间．利用二次函数的性质可求得函数g (x )在(－3，1)内的减区间为[－1，1)，故选C ．20．(2018·广东深圳一检)已知函数f (x )＝log 2(5－ax )在[0，2]上是减函数，则a 的取值范围是( )A ．(0，＋∞) B．⎝⎛⎭⎪⎫－∞，52C ．⎝ ⎛⎭⎪⎫0，52D ．⎝ ⎛⎭⎪⎫1，52答案 C解析 ∵y ＝log 2x 是增函数，∴u ＝5－ax 在[0，2]上是减函数，且5－2a >0，即∴0<a <52．故选C ．21．(2018·云南昆明5月检测)已知函数f (x )＝若f (a－1)≥f (－a )，则实数a 的取值范围是( )A ．－∞，12B ．12，＋∞C ．0，12D ．12，1答案 A解析 函数f (x )＝e －x ＝1e x 在(－∞，0]上为减函数，函数y ＝－x 2－2x ＋1的图象开口向下，对称轴为x ＝－1，所以函数f (x )＝－x 2－2x ＋1在区间(0，＋∞)上为减函数，且e－＝－02－2×0＋1，所以函数f (x )在(－∞，＋∞)上为减函数．由f (a －1)≥f (－a )得a －1≤－a ．解得a ≤12．故选A ．22．(2018·广东名校联考二)设函数f (x )在R 上为增函数，则下列结论一定正确的是( )A ．y ＝1f (x )在R 上为减函数 B ．y ＝|f (x )|在R 上为增函数C ．y ＝－1f (x )在R 上为增函数 D ．y ＝－f (x )在R 上为减函数 答案 D解析 A 错误，如y ＝x 3，y ＝1f (x )在R 上无单调性； B 错误，如y ＝x 3，y ＝|f (x )|在R 上无单调性； C 错误，如y ＝x 3，y ＝－1f (x )在R 上无单调性； 故选D ．23．(2019·四川“联测促改”活动试题)已知函数f (x )在区间[－2，2]上单调递增，若f (log 2m )<f [log 4(m ＋2)]成立，则实数m 的取值范围是( )A ．14，2B ．14，1 C ．(1，4] D ．[2，4] 答案 A解析 ∵函数f (x )在区间[－2，2]上单调递增，∴即解得14≤m <2．∴实数m 的取值范围是14，2．故选A ．24．(2018·河南新乡一检)已知f (x )＝是(－∞，＋∞)上的增函数，那么实数a 的取值范围是________．答案 ⎣⎢⎡⎭⎪⎫32，3 解析 由题意可知，解得a ∈⎣⎢⎡⎭⎪⎫32，3．一、高考大题本考点在近三年高考中未涉及此题型． 二、模拟大题1．(2018·山东菏泽质检)已知f (x )定义在[－1，1]上且f (－x )＝－f (x )，当a ，b ∈[－1，1]，a ＋b ≠0时，有f (a )＋f (b )a ＋b>0．试判断函数f (x )在[－1，1]上的单调性，并证明．解 函数f (x )在[－1，1]上是增函数．证明：任取x 1，x 2∈[－1，1]且x 1<x 2，则－x 2∈[－1，1]．又f (－x )＝－f (x )，于是f (x 1)－f (x 2)＝f (x 1)＋f (－x 2)＝f (x 1)＋f (－x 2)x 1＋(－x 2)·(x 1－x 2)．又f (x 1)＋f (－x 2)x 1＋(－x 2)>0，x 1－x 2<0，所以f (x 1)－f (x 2)<0，即f (x 1)<f (x 2)，所以f (x )在[－1，1]上是增函数． 2．(2019·安徽肥东高级中学调研)函数f (x )＝2x －ax的定义域为(0，1]． (1)当a ＝－1时，求函数y ＝f (x )的值域；(2)若函数y ＝f (x )在定义域上是减函数，求a 的取值范围．解 (1)因为函数y ＝f (x )＝2x ＋1x ≥22当且仅当x ＝22时，等号成立，所以函数y ＝f (x )的值域为[22，＋∞)．(2)若函数y ＝f (x )在定义域上是减函数，则任取x 1，x 2∈(0，1]且x 1<x 2都有f (x 1)>f (x 2)成立，即(x 1－x 2)a ＋2x 1x 2x 1x 2>0，只要a <－2x 1x 2即可， 由x 1，x 2∈(0，1]，故－2x 1x 2∈(－2，0)， 所以a ≤－2，故a 的取值范围是(－∞，－2]．3．(2019·陕西西安长安区大联考)已知定义在区间(0，＋∞)上的函数f (x )满足f (x 1·x 2)＝f (x 1)＋f (x 2)，且当x >1时，f (x )>0．(1)求f (1)的值；(2)证明：f (x )为单调增函数；(3)若f 15＝－1，求f (x )在125，125上的最值．解 (1)因为函数f (x )满足f (x 1·x 2)＝f (x 1)＋f (x 2)，令x 1＝x 2＝1，则f (1)＝f (1)＋f (1)，解得f (1)＝0．(2)证明：设x 1，x 2∈(0，＋∞)，且x 1>x 2， 则x 1x 2>1，∴f x 1x 2>0，∴f (x 1)－f (x 2)＝fx 2·x 1x 2－f (x 2) ＝f (x 2)＋f x 1x 2－f (x 2)＝f x 1x 2>0，即f (x 1)>f (x 2)，∴f (x )在(0，＋∞)上是增函数． (3)因为f (x )在(0，＋∞)上是增函数． 若f 15＝－1，则f 15＋f 15＝f 125＝－2，即f 15×5＝f (1)＝f 15＋f (5)＝0，即f (5)＝1，则f (5)＋f (5)＝f (25)＝2，f (5)＋f (25)＝f (125)＝3，即f (x )在125，125上的最小值为－2，最大值为3．4．(2018·山西康杰中学月考)已知f (x )＝xx －a(x ≠a )．(1)若a ＝－2，试证f (x )在(－∞，－2)内单调递增； (2)若a >0且f (x )在(1，＋∞)内单调递减，求a 的取值范围． 解 (1)证明：设x 1<x 2<－2， 则f (x 1)－f (x 2)＝x 1x 1＋2－x 2x 2＋2＝2(x 1－x 2)(x 1＋2)(x 2＋2)． 因为(x 1＋2)(x 2＋2)>0，x 1－x 2<0， 所以f (x 1)－f (x 2)<0，即f (x 1)<f (x 2)， 所以f (x )在(－∞，－2)内单调递增． (2)解法一：设1<x 1<x 2， 则f (x 1)－f (x 2)＝x 1x 1－a－x 2x 2－a ＝a (x 2－x 1)(x 1－a )(x 2－a )． 因为a >0，x 2－x 1>0，所以要使f (x 1)－f (x 2)>0，只需(x 1－a )(x 2－a )>0恒成立，所以a ≤1． 综上所述，0<a ≤1． 解法二：f ′(x )＝－a (x －a )2．∵f (x )在(1，＋∞)内单调递减，∴f′(x)≤0在(1，＋∞)内恒成立，∴－a(x－a)2≤0在(1，＋∞)内恒成立，∴(x－a)2>0在(1，＋∞)内恒成立．当a>1时，x＝a时，(x－a)2＝0不符合题意．∴a≤1．综上所述0<a≤1．。

新高考数学复习考点知识讲解 离散型随机变量的数字特征1、一般地，若离散型随机变量X 的分布列，如图所示则称∑==+++=ni i i n n p x p x p x p x X E 12211 )(为随机变量X 的均值或数学期望，简称期望。

均值是随机变量可能取值关于取值概率的加权平均数，它综合了随机变量的取值和取值的概率，反映了随机变量取值的平均水平2、用偏差平方关于取值概率的加权平均，来度量随机变量X 取值与其均值)(X E 的偏差程度，则称∑=-=-++-+-=ni i i n n p X E x p X E x p X E x p X E x X D 122222121))(())(())(())(()( 为随机变量X 的方差，称)(X D 为随机变量X 的标准差，记为)(X σ3、随机变量的方差和标准差都可以度量随机变量取值与其均值的偏离程度，反映了随机变量取值的离散程度。

方差或标准差越小，随机变量的取值越集中；方差或标准差越大，随机变量的取值越分散4、重要结论：b X aE b aX E +=+)()(；)()(X D a b aX D 2=+题型一 数学期望中的参数问题例 1 某射击运动员在一次射击比赛中所得环数ξ的分布列如下：ξ 3 4 5 6 Px0.10.3y已知ξ的均值E (ξ)＝4.3，则y 的值为( ) A ．0.6 B ．0.4 C ．0.2D ．0.1C [解析] 由题意知，x ＋0.1＋0.3＋y ＝1，又E (ξ)＝3x ＋4×0.1＋5×0.3＋6y ＝4.3，两式联立解得y ＝0.2.设随机变量X 的概率分布列如下表所示：X 0 1 2 Pa1316若F (x )＝P (X ≤x )，则当x 的取值范围是[1，2)时，F (x )等于( ) A.13 B ．16 C.12D ．56巩固练习知识典例D [解析] 由分布列的性质，得a ＋13＋16＝1，所以a ＝12.而x ∈[1，2)，所以F (x )＝P (X ≤x )＝12＋13＝56.题型二 期望、方差例 2 （多选）一组数据12321,21,21,,21n x x x x +++⋯+的平均值为7，方差为4，记12332,32,32,,32n x x x x +++⋯+的平均值为a ，方差为b ，则（ ） A ．a =7 B ．a =11C ．b =12D ．b =9【答案】BD（多选）设离散型随机变量X 的分布列为X 0 1 2 3 4 Pq0.40.10.20.2若离散型随机变量Y 满足21Y X =+，则下列结果正确的有（） A ．0.1q =B ．2EX =， 1.4DX =C ．2EX =， 1.8DX =D ．5EY =，7.2DY =【答案】ACD巩固练习题型三最值问题例3在一次随机试验中，事件A发生的概率为p，事件A发生的次数为ξ，则期望()Eξ=____，方差()Dξ的最大值为____．【答案】p 1 4已知随机变量ξ的分布列为P(ξ=m)=13，P(ξ=n)=a，若Eξ=2，则Dξ的最小值是_____.【答案】0题型四期望、方差中的计算例4袋中有20个大小相同的球，其中记上0号的有10个，记上n号的有n个(n＝1，2，3，4)，现从袋中任取一球，X表示所取球的标号．(1)求X的分布列、期望和方差；(2)若Y＝aX＋b，E(Y)＝1，D(Y)＝11，试求a，b的值．[解] (1)X的取值为0，1，2，3，4，其分布列为X 0123 4P 1212011032015所以E(X)＝0×12＋1×120＋2×110＋3×320＋4×15＝1.5，D(X)＝(0－1.5)2×12＋(1－1.5)2×120＋(2－1.5)2×110＋(3－1.5)2×320＋(4－1.5)2×15＝2.75.巩固练习(2)由D (Y )＝a 2D (X )得2.75a 2＝11，得a ＝±2， 又E (Y )＝aE (X )＋b ，所以当a ＝2时，由1＝2×1.5＋b ，得b ＝－2； 当a ＝－2时，由1＝－2×1.5＋b ，得b ＝4， 所以⎩⎨⎧a ＝2，b ＝－2或⎩⎨⎧a ＝－2，b ＝4.已知随机变量X 的分布列为X 01xP1213p若()23E X =. （1）求()D X 的值；（2）若32Y X =-，求()D Y 的值.【答案】（1）59；（2）5.题型五 实际应用例 5 一个袋中装有7个除颜色外完全相同的球，其中红球4个，编号分别为1，2，3，4；蓝球3个，编号分别为2，4，6，现从袋中任取3个球(假设取到任一球的可能性相巩固练习同)．(1)求取出的3个球中含有编号为2的球的概率；(2)记ξ为取到的球中红球的个数，求ξ的分布列和数学期望．[解] (1)设A＝“取出的3个球中含有编号为2的球”，则P(A)＝C12C25＋C22C15C37＝20＋535＝2535＝57.(2)由题意得，ξ可能取的值为0，1，2，3，则P(ξ＝0)＝C33C37＝135，P(ξ＝1)＝C14·C23C37＝1235，P(ξ＝2)＝C24·C13C37＝1835，P(ξ＝3)＝C34C37＝435.所以ξ的分布列为ξ012 3P 13512351835435所以E(ξ)＝0×135＋1×1235＋2×1835＋3×435＝127.若n是一个三位正整数，且n的个位数字大于十位数字，十位数字大于百位数字，则称n为“三位递增数”(如137，359，567等)．在某次数学趣味活动中，每位参加者需从所有的“三位递增数”中随机抽取1个数，且只能抽取一次．得分规则如下：若抽取的“三位递增数”的三个数字之积不能被5整除，参加者得0分；若能被5整除，但巩固练习不能被10整除，得－1分；若能被10整除，得1分．(1)写出所有个位数字是5的“三位递增数”；(2)若甲参加活动，求甲得分X的分布列和数学期望E(X)．[解] (1)个位数字是5的“三位递增数”有125，135，145，235，245，345.(2)由题意知，全部“三位递增数”的个数为C39＝84，随机变量X的取值为：0，－1，1，因此P(X＝0)＝C38C39＝23，P(X＝－1)＝C24C39＝114，P(X＝1)＝1－114－23＝1142.所以X的分布列为X 0－1 1P 231141142则E(X)＝0×23＋(－1)×114＋1×1142＝421.1、已知离散型随机变量X的概率分布列为（）X 1 3 5 P 0.5 m 0.2 巩固提升则其方差D (X )＝（ ） A ．1 B ．0.6C ．2.44D ．2.4【答案】C2、设01p <<，随机变量ξ的分布列如图，则当p 在()0,1内增大时，（ ）A ．()D ξ减小B ．()D ξ增大C ．()D ξ先减小后增大 D ．()D ξ先增大后减小【答案】D3、已知离散型随机变量X 的分布列如下：由此可以得到期望()E X 与方差()D X 分别为（ ） A ．() 1.4E X =，()0.2D X = B ．()0.44E X =，() 1.4D X = C ．() 1.4E X =，()0.44D X = D ．()0.44E X =，()0.2D X =【答案】C4、随机变量X 的分布列如下表，则E (5X ＋4)等于 ( )P 0.3 0.2 0.5A．16 B．11C．2.2 D．2.3【答案】A5、已知甲口袋中有3个红球和2个白球，乙口袋中有2个红球和3个白球，现从甲，乙口袋中各随机取出一个球并相互交换，记交换后甲口袋中红球的个数为ξ，则Eξ=（）A．145B．135C．73D．83【答案】A6、由以往的统计资料表明,甲、乙两运动员在比赛中得分情况为:现有一场比赛,派哪位运动员参加较好?()A．甲B．乙C．甲、乙均可D．无法确定【答案】A7、（多选）已知X的分布列为X －1 0 1P 12a16则下列说法正确的有（）A．P(X＝0)＝13B．E(X)＝－13C．D(X)＝2327D．P(X＞－1)＝12【答案】ABD8、下列说法正确的有________(填序号)．①离散型随机变量ξ的期望E(ξ)反映了ξ取值的概率的平均值；②离散型随机变量ξ的方差D(ξ)反映了ξ取值的平均水平；③离散型随机变量ξ的期望E(ξ)反映了ξ取值的波动水平；④离散型随机变量ξ的方差D(ξ)反映了ξ取值的波动水平．【答案】49、已知随机变量X的分布列如下表；且()2E X=，则p=________，(23)D X-=_____________.【答案】12410、已知某一随机变量X的分布列如下表：且E(X)＝6，则a＝________，b＝________. 【答案】0.3 611、随机变量X的分布列如下：其中a ，b ，c 成等差数列，则P (|X |＝1)＝________，公差d 的取值范围是________．[解析] 因为a ，b ，c 成等差数列，所以2b ＝a ＋c .又a ＋b ＋c ＝1，所以b ＝13，所以P (|X |＝1)＝a ＋c ＝23.又a ＝13－d ，c ＝13＋d ，根据分布列的性质，得0≤13－d ≤23，0≤13＋d ≤23，所以－13≤d ≤13.[答案] 23 ⎣⎢⎡⎦⎥⎤－13，13 12、随机变量ξ的取值为0，1，2，若P (ξ＝0)＝15，E (ξ)＝1, 则D (ξ)＝________.[解析] 设ξ＝1时的概率为p ，则E (ξ)＝0×15＋1×p ＋2×⎝ ⎛⎭⎪⎫1－p －15＝1，解得p ＝35，故D (ξ)＝(0－1)2×15＋(1－1)2×35＋(2－1)2×15＝25.[答案] 2513、甲乙两人进行围棋比赛，约定先连胜两局者直接赢得比赛，若赛完5局仍未出现连胜，则判定获胜局数多者赢得比赛，假设每局甲获胜的概率为23，乙获胜的概率为13，各局比赛结果相互独立.（1）求甲在4局以内（含4局）赢得比赛的概率；（2）记X 为比赛决出胜负时的总局数，求X 的分布列和均值（数学期望）.【答案】（1）5681；（2）22481.14、根据某电子商务平台的调查统计显示，参与调查的1 000位上网购物者的年龄情况如图所示．(1)已知[30，40)、[40，50)、[50，60)三个年龄段的上网购物者人数成等差数列，求a ，b 的值；(2)该电子商务平台将年龄在[30，50)之间的人群定义为高消费人群，其他年龄段的人群定义为潜在消费人群，为了鼓励潜在消费人群的消费，该平台决定发放代金券，高消费人群每人发放50元的代金券，潜在消费人群每人发放100元的代金券，现采用分层抽样的方式从参与调查的1 000位上网购物者中抽取10人，并在这10人中随机抽取3人进行回访，求此3人获得代金券总和X 的分布列与数学期望．[解] (1)由题意可知⎩⎨⎧2b ＝a ＋0.015，（0.01＋0.015×2＋b ＋a ）×10＝1，解得a ＝0.035，b ＝0.025.(2)利用分层抽样从样本中抽取10人，其中属于高消费人群的有6人，属于潜在消费人群的有4人．从中抽取3人，并计算3人所获得代金券的总和X ，则X 的所有可能取值为：150，200，250，300，P (X ＝150)＝C 36C 310＝16， P (X ＝200)＝C 26C 14C 310＝12， P (X ＝250)＝C 16C 24C 310＝310， P (X ＝300)＝C 34C 310＝130. 故X 的分布列为16＋200×12＋250×310＋300×130＝210.E(X)＝150×。

2022-2023年高级软考《系统分析师》历年真题高频考点汇总（附带答案）（图片大小可自由调整）一.全考点综合测验(共35题)1.【判断题】类是指具有相同或相似性质对象的抽象，对象是抽象的类，类的具体化就是对象。

正确答案：正确2.【单选题】数据字典是数据流图中所有元素的定义的集合，一般由以下四类条目组成( )。

A. 数据说明条目、控制流条目、加工条目、数据存储条目B.数据流条目、数据项条目、文件条目、加工条目C. 数据源条目、数据流条目、数据处理条目、数据文件条目D.数据流条目、数据文件条目、数据池条目、加工条目正确答案：C3.【多选题】软件工程三要素是( ) 。

A.技术、方法和工具B.方法、工具和过程C.方法、对象和类D.过程、模型、方法正确答案：CD4.【单选题】在E-R 模型中，包含以下基本成分( )。

A.数据、对象、实体B. 控制、联系、对象C. 实体、联系、属性D.实体、属性、联系正确答案：C5.【多选题】UML 语言支持的建模方式有( )。

A. 静态建模B.动态建模C.模块化建模D.功能建模正确答案：ABD6.【多选题】软件设计的主要任务是( )。

A. 将分析阶段获得的需求说明转换为计算机中可实现的系统B.完成系统的数据结构和程序结构设计C.完成模块的编码和测试D.对模块内部的过程进行设计正确答案：ABD7.【判断题】面向对象的的方法是以类作为最基本的元素，它是分析问题解决问题的核心。

正确答案：错误8.【单选题】在原型法中，原型是开发系统的( )。

A.反映用户最基本需求的可以运行的实验模型B.某一主要部分的详细设计方案（物理模型）C.反映用户需求的逻辑模型D.反映用户全部需求符合系统开发规范的应用软件程序正确答案：A9.【判断题】SD 法是一种面向数据结构的设计方法，强调程序结构与问题结构相对应正确答案：错误10.【判断题】程序设计语言的工程特性包括：可移植性、可重用性、可维护性、局部性和顺序性。

【背诵秘笈】2024年中考历史复习6册教材之七上核心考点及重难突破（全国通用）考点四：商鞅变法1.时间、统治者：公元前356年，秦孝公2.背景：战国时期，铁制农具和牛耕的使用进一步推广，社会生产力水平不断提高，新兴地主阶级的势力增强。

3.目的：富国强兵，在兼并战争中取胜，确立封建地主阶级的统治。

1.性质：一场比较彻底的封建性质的改革。

2.影响：使秦国的国力大为增强，提高了军队的战斗力，一跃成为最强盛的诸侯国，为以后秦国统一全国奠定了基础。

考点五：都江堰1.时间：战国后期，由秦国蜀郡郡守李冰主持，在成都附近的岷江上修筑。

2.功能：综合性的水利枢纽.发挥了防洪、灌溉、水运等多方面的作用。

3.意义：使成都平原成为“天府之国”；考点六：百家争鸣一、春秋时期的老子和孔子1.老子：道家学派创始人。

他的学说集中在《老子》（又称《道德经》）一书中。

2.思想主张：人们应顺应自然，世间的事物都有其对立面，对立的双方可以相互转化。

在政治上主张“无为而治”。

4.孔子，儒家学派创始人，他的思想由其弟子整理成《论语》一书。

5.思想贡献：（1）核心思想：“仁”，提出“仁者爱人”，己所不欲勿施于人等；（2）政治：推崇西周的制度，主张以德治国，反对苛政。

（3）教育：创办私学，主张“有教无类”，注重道德教育和文化知识教育。

二、战国时期的百家争鸣1.背景：战国时期，旧的社会制度进一步瓦解，新的社会制度逐步确立。

2.诸子百家中影响最大的学派墨家墨子主张“兼爱”“非攻”；选贤能的人治国；提倡节俭。

法家韩非反对空谈仁义，强调以法治国，树立君主的权威，建立中央集权专制统治【易混易错】夏朝是中国史书记载的第一个世袭制朝代，我国有文字可考的历史从商朝开始。

【难点突破】1.公元纪年与世纪年代的换算:世纪:百位数 +1千位数不动;年代:十位数数字不动。

例:公元前2070 年为公元前21 世纪70 年代。

2.商鞅变法的启示:顺应了历史发展的潮流,变法得到了秦孝公的支持,商鞅个人公正无私,敢于与旧势力坚决斗争,不畏艰难,不怕牺牲。

考点巩固06 非限制性定语从句2024年高考真题1.【2024年新高考全国Ⅱ卷】Chinese cultural elements commemorating (纪念) Tang Xianzu, ___56___ is known as “the Shakespeare of Asia,” add an international character to Stratford-upon-Avon, William Shakespeare’s hometown.2023年高考真题1.【2023年全国甲卷】“There was once a town in the heart of America, ___44___ all life seemed to enjoy peaceful existence with its surroundings,” her fable begins, borrowing some familiar words from many age-old fables.2.【2023年全国甲卷】Yet, the form of the fable still has values today, ___43___ Rachel Carson says in “A Fable for Tomorrow.”...2019-2022年高考真题1.（2022全国甲卷）On the 1,100. Kilometer journey, the man Cao Shengkang, ___________ lost his eyesight at the age of eight in a car accident, crossed 40 cities and counties in three province.2.（2020全国III卷）In ancient China lived an artist, ___________ paintings were almost lifelike. The artist’s reputation had made him proud.3.（2020天津卷）Dr. Rowan, ___________ secretary resigned two weeks ago, has had to do all his own typing.4.（2020江苏卷）Many lessons are now available online, from ___________students can choose for free.5.（2019全国II卷）Now Irene Astbury works from 9am to 5pm daily at the pet shop in Macclesfield, ___________ she opened with her late husband Les.2024年名校模拟题1．This evening, I’ll be talking to Dr Richard Fairhurst, new book The New Age of Invention has just been published.2．After several months, Ryan had raised the $2,000, with a well was built near a primary school in Uganda.3．I’m crazy about basketball, and pretty good at it too, is probably why I was so mad when we lost our last match.4．Following in the footsteps of his own teacher all those years ago, Mr. Wang has now passed on his skills to the new memebers, will take on many of the future repairs.5．Kobe, contribution to basketball is difficult to exaggerate (夸大), has inspired millions ofpeople.6．Taking targeted measures to help people lift themselves out of poverty, has been predicted, is fruitful. 7．The Amazon River, from the rainforest gets its name, is close to 6,400 kilometres in length -roughly 100 kilometres longer than the Yangtze River.8．Cultural heritage is a lot more than just relics. For example, our country has many nationalities,dances, crafts and other traditions are also very important.9．During my stay in America, I lived in university accommodation with other international students,allows me to meet people from diverse cultural backgrounds.10．The traditional clothing of the Han people is called Hanfu, beauty is being appreciated by younger generations.11．Dream Variation is a most celebrated poem, theme deals with the dream of a world free of racial discrimination.12．Tom was late for class again, made his teacher angry.13．Lucy was absent from Mr Smith's lecture yesterday, she made an apology to him.14．It is a family of 8 children, all have got PhD in chemistry.15．There are more than 4,000 students in our school, the majority of put their hearts into their studies. 16．The students, all of spent the whole day picking fruits, were extremely tired.17．There are various typical Chinese customs during the Spring Festival, two of are to make dumplings and set off fireworks.18．His opinion often conflicts with his parents, is often the case with teenagers.19．He is good at creating a lovely atmosphere his students learn actively.20．is seen from the picture, a student is overloaded with piles of homework and endlessafter­school training, making him breathless.21．Tom's love for the Chinese bamboo flute started in elementary school, clear sound guided him onto the road of flute learning.22．Hua Mulan, the story of has been told by generations in China, is a fighter from the Northern Wei Dynasty (386-534).23．Spring tea during Grain Rain is rich in vitamins and amino acids, can help to remove heat from the body and is good for the eyes.24．Besides, he proposed the establishment of a national school system, had a far­reaching influence on the Chinese educational system.25．Since the first ceremony in 1929, only thirteen awards were given out, the Oscars have grown in size and popularity.26．At present the masters use the full face, painted silk masks, can be worn in layers and be pulled off one by one in the blink of an eye.27．The brain interprets dieting and restriction as hunger, causes the storage of fat.28．The first thing coming to my mind is to get a driving license, is a must for most college students. 29．Judges will choose up to 50 honorable mention winners, will each receive a T-shirt in memory of Earhart's final flight.30．But some researchers find, the food system is not an equal one.31．Curtin is CEO of DC Central Kitchen in Washington, D．C．, recovers food and turns it into healthy meals.32．Chinese mainland, is indicated in the chart, has risen to 11th place on the 2022 Global Innovation Rating.33．Having enough fat and salt in your meals will reduce the urge to snack between meals and will improve the taste of your food. However, be careful not to go to extremes. Like anything, it is possible to have too much of both, is not good for the health.34．Beijing, the Summer Games were held in 2008, is the first city in the world to host both editions of the Olympic Games.35．Shaanxi’s biang biang noodles were a comforting and beloved food among locals, for the back story and written character were common knowledge.36．The government has also introduced a new proposal in order to limit the amount of after-school education kids can attend, especially during holidays and festivals, kids should be having fun.37．is known to us, body language can give away a lot about your mood.38．In addition, every student can be in harmony with foreign friends, makes it easy for you to get along with them.39．The lifestyle, however, was laid down by two historical men of letters. One was Bai Juyi, rebuilt the West Lake and made a new bank to benefit the locals.40．Famous for carrying his tennis rackets in a bamboo basket, Wang Fa, a 14-year-old dark horse, won the U14 boys’ singles title in the Guangzhou stop of the 2022 ASICS Tennis Junior Tour, has become an internet sensation.41．In particular, the Ling Si Hall, the rituals (典礼) are held, is a treasure of ancient architecture.42．The 19th China International Cultural Industries Fair kicked off in Shenzhen in South China’s Guangdong province on June 7, 2023, is expected to promote the development of the country’s cultural industry. 43．is known to all, Chinese learning calls for a large amount of patience. （用适当的词填空）44．Shu, is a native of Southwest China’s Guizhou Province, has a great affection for the traditional Chinese costume.45．The 150-metre-tall bridge crosses a deep, narrow valley, aim is to bring in thrill-seeking tourists. 46．The story centers around the deep friendship between poet Gao Shi and the romantic poet Li Bai offering a brief look into the glorious history of the Tang era, is known for its economic prosperity and cultural advancement.47．May 22 marks the annual International Day for Biological Diversity, theme for this year is “From Agreement to Action: Build Back Biodiversity”.48．Jim left home without telling anyone, made us very anxious.49．He gave me his advice, some of was very useful.50．Opposite the post office is a video shop, you can buy any kind of music CD you like. 51．Sometimes we had to work until the early hours of the morning, most people were still fast asleep. 52．Many young people, most of are well-educated, realize the importance of the biodiversity on the Earth. 53．The clever boy made a hole in the wall, which he could see what was happening inside the house. 54．This year, the 13th Spring Festival Joint Exhibition of Chinese Books, theme was “Reading China”, was held on January 24th in 85 bookstores worldwide.55．She received many gifts for her birthday, all of are thoughtful and well-chosen.56．When lost in work, he often is, he may forget all needed to be done.57．Covid-19, the most deadly virus in recent years, began to attack people in 2019, from effect people are still suffering.58．The fish in the deep ocean are among the strangest creatures in the Earth, many of have yet to be properly studied.59．“Nicolo,” real name cannot be exposed to the public because of Italy’ s privacy laws, finished working the whole night at a factory in Turin.60．I am looking for my glasses, without I can’t watch TV clearly.61．We shouldn’t spend our money testing so many people, most of are healthy.62．For this work, titled “Truckload of Plastic”, V on Wong and a group of volunteers collected more than 10,000 pieces of plastic, were then tied together to look like they’d been dumped (倾倒) from a truck all at once.63．A 90-year-old has been awarded “Woman of The Year” for being Britain’s oldest full-time employee—still working 40 hours a week. Now Irene Astbury works from 9am to 5pm daily at the pet shop in Maccles field, she opened with her late husband Les.64．We were impressed by the experience of the old man, was not willing to acknowledge defeat. 65．We are short of two people, without we will need three more days to finish the work. 66．Swimming is good for teenagers, some experts say will help them to stimulate their potential and promote their brain development.67．During their first day, is typical of Vancouver, it rained.68．There are many new central leaders in China now, of many once worked in the western provinces. 69．I gave some money to John, house was destroyed in the flood.70．The research team included Canadian doctor Allan Slomovic, has done ground-breaking work on eye care using stem cells.。

高考化学复习考点知识突破解析化学反应历程或机理1．科研人员利用Cu/ZnO作催化剂，在光照条件下实现了CO2和H2合成CH3OH，该反应历程示意图如下。

下列说法不正确的是( )A．过程I中ZnO表面上进行CO2的吸附与转化B．过程II中存在极性键的断裂与形成C．过程V中生成CH3OH时吸收能量D．总反应的化学方程式是CO2 + 3H2CH3OH + H2O【答案】C【详解】A项，过程I中在ZnO表面吸附CO2，且CO2和-OH转化为即HCO3-，故A正确；B项，过程II中涉及C-O的断裂与C-H和H-O键的形成，且C=O、C-H、H-O均为极性键，故B正确；C项，过程V中生成CH3OH 时，是CH3O-与-H形成CH3OH，存在H-O键形成的过程，则该过程放出能量，故C错误；D项，该反应总过程是CO2和H2在Cu/ZnO催化剂作用下，合成CH3OH，总反应方程式为CO2+ 3H2CH3OH + H2O，故D正确；故选C。

2．我国科研工作者研发的一种在较低温度下制备乙二醇的反应历程示意图如图所示。

下列说法正确的是( )A．Cu纳米笼簇能降低H2解离的活化能B．整个过程中只断裂碳氧双键C．中含有3种官能团D．等物质的量的甲醇和乙二醇完全燃烧消耗O2的质量相等【答案】A【详解】A项，根据示意图，Cu纳米笼簇作该反应的催化剂，能降低H2解离的活化能，故A正确；B项，由反应历程示意图可知，整个过程中除了断裂碳氧双键外，还有碳氧单键断裂，故B错误；C项，中含有酯基和羟基2种官能团，故C错误；D项，1mol甲醇完全燃烧消耗氧气的物质的量是1.5mol，1mol乙二醇完全燃烧消耗O2的物质的量是2.5mol，则等物质的量的甲醇和乙二醇完全燃烧消耗O2的质量不相等，故D错误；故选A。

3．已知活性氧可以把SO2快速氧化为SO3，根据计算机模拟结果，在炭黑表面上O2转化为活化氧的反应历程与能量变化关系如图所示。

下列说法正确的是( )A．O2转化为活化氧与碳氧键生成无关B．每活化1个O2分子最终吸收0.29 eV能量C．该过程的最大能垒(活化能)E正= 0.73 eVD．炭黑可加快SO2转化为SO3的反应速率【答案】D【详解】A 项，从图中可以看出从氧气到活性氧，需经过炭黑与氧气结合再分开的过程，此时有碳氧键生成和氧氧键的断裂，A 错误；B 项，开始状态时炭黑和氧气为0 eV ，结束后能量变为-0.29 eV ，故放出0.29 eV 的能量，B 错误；C 项，从图中可以看出，炭黑和氧气需要先吸收0.75 eV 的能量，再释放一些能量，然后吸收能量到0.73 eV ，故该过程中的最大能垒E 正=0.75 eV ，C 错误；D 项，反应体系中加入炭黑后，体系中的氧气变成活化氧，增加了体系中的活化分子百分数，增加了反应速率，D 正确；故选D 。