限时练习
高一基本不等式限时训练练习题

高一基本不等式限时训练练习题第I卷(选择题)一、单选题(本大题共6小题,共30.0分)1.下列不等式一定成立的是()A. x+1x ≥2 B. x2+2√x2+2≥√2 C. x2+3√x2+4≥2 D. 2−3x−4x≥22.已知x>2,函数y=4x−2+x的最小值是()A. 5B. 4C. 6D. 83.已知t>0,则y=t2−4t+1t的最小值为()A. −2B. 12C. 1D. 24.若a,b都为正实数,2a+b=1,则ab的最大值是()A. 29B. 18C. 14D. 125.已知不等式2x+m+2x−1>0对一切恒成立,则实数m的取值范围是()A. m>−6B. m<−6C. m>−8D. m<−86.已知实数a,b满足ab=1,则a2+b2的最小值为()A. 4B. 3C. 2D. 1二、多选题(本大题共1小题,共5.0分)7.下列说法中正确的有()A. 不等式a+b≥2√ab恒成立B. 存在a,使得不等式a+1a≤2成立C. 若a,b∈(0,+∞),则ab +ba≥2D. 若正实数x,y满足x+2y=1,则2x +1y≥8第II卷(非选择题)三、单空题(本大题共4小题,共20.0分)8.若正数a,b满足a+b=1,则9a +1b的最小值为.9.若正实数x,y满足y(x−y)=1,则2x+y的最小值为.10.已知正实数x,y满足xy+2x+y=3,那么xy的最大值为______.11.函数的最小值是__________.四、解答题(本大题共4小题,共48.0分)12.如图,某人计划用篱笆围成一个一边靠墙(墙的长度没有限制)的矩形菜园.设菜园的长为xm,宽为ym.(1)若菜园面积为,则x,y为何值时,可使所用篱笆总长最小;(2)若使用的篱笆总长度为30m,求1x +2y的最小值.13.已知ab−4a−b−5=0(a>1)(1)求ab的最小值;(2)求a+b的最小值.14. (1)已知正数a,b 满足1a +2b =1,求ab 的最小值;(2)已知x >1,求函数f(x)=x +1x−1的最小值.15. (1)已知x <54,求函数y =4x −1+14x−5的最大值.(2)已知0<x <12,求y =12x(1−2x)的最大值.答案和解析1.【答案】B【解析】【分析】本题主要考查不等式求解范围,属于基础题.根据不等式求最值和特殊值法求解即可.【解答】解:A项中当x<0时,x+1x<0<2,∴A错误;B项中,2√x2+2=√x2+2≥√2,∴B正确;而对于C,当x=0时,2√x2+4=32<2,显然选项C不正确;D项中,取x=1,则2−3x−4x=−5<2,∴D错误.故选B.2.【答案】C【解析】【分析】本题考查利用基本不等式求最值,属于基础题.由于y=4x−2+x=4x−2+(x−2)+2,且x−2>0,利用基本不等式即可求解.【解答】解:y=4x−2+x,因为x>2,故x−2>0,所以根据基本不等式可知:y=4x−2+(x−2)+2≥2√4x−2×(x−2)+2=6,当且仅当4x−2=x−2即x=4时取“=”.故选C.3.【答案】A【解析】【分析】本题主要考查利用基本不等式求最值,属于基础题.对原式进行化简,利用基本不等式求最值即可,注意等号取得的条件.【解答】解:t>0,则y=t2−4t+1t =t+1t−4≥2√t·1t−4=−2,当且仅当t=1t,即t=1时,等号成立,则y=t2−4t+1t的最小值为−2.故选A.4.【答案】B【解析】【分析】本题主要考查了利用基本不等式求解最值,属于基础题.由已知结合基本不等式可得ab=12(2a⋅b)≤12(2a+b2)2,可得结果.【解答】解:因为a,b都为正实数,2a+b=1,则ab=12(2a⋅b)≤12(2a+b2)2=12×14=18,当且仅当2a=b=12时取等号.故选:B.5.【答案】A【解析】 【分析】本题考查了基本不等式,不等式恒成立问题,考查了计算能力,属于中档题. 不等式2x +m +2x−1>0可化为2(x −1)+2x−1>−m −2,将不等式恒成立问题转化为最值问题,再利用基本不等式进行求解即可. 【解答】解:不等式2x +m +2x−1>0可化为2(x −1)+2x−1>−m −2, ∵x >1,∴x −1>0, ∴2(x −1)+2x−1≥2×√2(x −1)⋅2x−1=4,当且仅当x =2时取等号,∵不等式2x +m +2x−1>0对一切x ∈(1,+∞)恒成立, ∴−m −2<4, 解得m >−6, 故选A .6.【答案】C【解析】 【分析】本题主要考查了基本不等式的应用,属基础题. 由重要不等式a 2+b 2≥2ab 即可求解. 【解答】解:由重要不等式可得:a 2+b 2≥2ab =2,当且仅当{ab =1a =b 即{a =1b =1或{a =−1b =−1时等号成立,所以a 2+b 2的最小值为2, 故选:C .7.【答案】BCD【解析】【分析】本题考查基本不等式,属于中档题.结合基本不等式的一正,二定,三相等的条件检验各选项即可判断.【解答】解:选项A:不等式a+b⩾2√ab恒成立的条件是a≥0,b≥0,故A不正确;选项B:当a为负数时,不等式a+1a⩽2成立,故B正确;选项C:若a,b∈(0,+∞),由基本不等式可知ba +ab⩾2√ba·ab=2,当且仅当a=b时,等号成立,故C正确;选项D:对于2x +1y=(2x+1y)(x+2y)=4+4yx+xy≥4+2√4yx·xy=8,当且仅当x=12,y=14时取等号,故D正确.故选BCD.8.【答案】16【解析】【分析】本题主要考查基本不等式的应用,属于基础题.可对式子9a +1b乘以1,也即乘以a+b,再使用基本不等式即可求出答案.【解答】解:∵正数a,b满足a+b=1,∴9a +1b=(9a+1b)(a+b)=9+ab+9ba+1=10+ab+9ba≥10+2√ab⋅9ba=16,当且仅当{ab=9baa+b=1,也即当{a=34b=14时取“=”.故答案为:16.9.【答案】2√6【解析】【分析】本题考查利用基本不等式求最值,属中档题.先由y(x−y)=1化简得x=1y+y,再利用基本不等式求出答案.【解答】解:由正实数x,y满足y(x−y)=1得xy=1+y2,即x=1y+y,所以2x+y=2y+3y⩾2√6,当且仅当2y=3y,即y=√6时,等号成立,3则2x+y的最小值为2√6.故答案为2√6.10.【答案】7−2√10【解析】【分析】由题意和基本不等式可得3≥xy+2√2xy,解不等式即可求出.本题考查基本不等式,涉及一元二次不等式的解集,属基础题.【解答】解:∵xy+2x+y=3,∴3≥xy+2√2xy,整理可得(√xy+√2)2≤5,解得√xy≤√5−√2,∴xy≤7−2√10当且仅当2x=y即x=−2+√10且y=−2+√10时取等号,2∴xy的最大值为7−2√10,故答为:7−2√10.11.【答案】2√6【解析】【分析】本题考查基本不等式的应用,考查学生的计算能力,属于一般题. 由 x >1,所以 x −1>0,化简 f (x )=2x 2−4x+5x−1=2(x−1)2+3x−1=2(x −1)+3x−1,利用基本不等式求最小值. 【解答】解:因为x >1,所以x −1>0, f (x )=2x 2−4x+5x−1=2(x−1)2+3x−1=2(x −1)+3x−1,2(x −1)+3x−1≥2√2(x −1)⋅3x−1=2√6, 当且仅当 2(x −1)=3x−1,即 x =1+√62, f(x)有最小值 2√6,故答案为2√6.12.【答案】解:(1)由已知可得xy =72,篱笆总长为(x +2y)m .又因为x +2y ≥2√2xy =24,当且仅当x =2y ,即x =12,y =6时等号成立. 所以当x =12,y =6时,可使所用篱笆总长最小. (2)由已知得x +2y =30, 又因为(1x +2y )(x +2y)=5+2y x+2x y≥5+2√2y x ⋅2x y=9,所以1x +2y ≥310,当且仅当x =y ,即x =10,y =10时等号成立. 所以1x +2y 的最小值是310.【解析】本题考查基本不等式的实际应用和利用基本不等式求最值. (1)由已知可得xy =72,篱笆总长为(x +2y)m ,结合基本不等式即可得解; (2)由已知得x +2y =30,又因为(1x +2y )(x +2y)=5+2y x+2x y,利用基本不等式即可求解.13.【答案】解:(1)∵ab −4a −b −5=0(a >1)∴b =4a +5a −1(a >1) ∴a ⋅b =a ⋅4a+5a−1=4a 2+5a a−1(a >1),令a −1=t(t >0),则a =t +1∴a ⋅b =4(t +1)2+5(t +1)t (t >0)a ⋅b =4t 2+13t +9t(t >0)a ⋅b =4t +9t +13(t >0),∵t >0,∴4t +9t ≥2√4t ⋅9t =12,当且仅当4t =9t ,即t =32时取“=”,∴ab ≥25,当且仅当{a =52b =10时取“=”, 即当{a =52b =10时,ab 有最小值25;(2)∵a +b =a +4a+5a−1(a >1),令a −1=t(t >0),则a =t +1, ∴a +b =t +1+4(t+1)+5t(t >0),∴a +b =t +9t+5(t >0), ∵t >0,∴t +9t ≥2√t ⋅9t =6,当且仅当t =9t ,即t =3取“=”.∴a +b ≥11,当且仅当{a =4b =7时取“=”,即当{a =4b =7时,a +b 有最小值11.【解析】本题考查基本不等式的应用,考查利用基本不等式求最值,属于基础题.(1)由已知可得b=4a+5a−1(a>1),即可得到a⋅b=4a2+5aa−1(a>1),令a−1=t(t>0),可得a⋅b=4t+9t+13(t>0),利用基本不等式即可求解ab的最小值;(2)由已知可得a+b=a+4a+5a−1(a>1),令a−1=t(t>0),即可得到a+b=t+9t+5(t>0),利用基本不等式即可求解a+b的最小值.14.【答案】(1)解:a>0,b>0,1 a +2b⩾2√2ab,又1a +2b=1,∴2√2ab⩽1,则√2ab ⩽12,∴2ab ⩽14,则ab⩾8,当且仅当a=2,b=4时等号成立,∴ab的最小值为8.(2)由题意,f(x)=x+1x−1=x−1+1x−1+1∵x>1,∴x−1>0,∴(x−1)+1(x−1)⩾2√(x−1)(1x−1)=2,当且仅当x=2时等号成立,∴f(x)⩾3,∴f(x)的最小值为3.【解析】本题主要考查了利用基本不等式求最值,属于基础题.(1)由题意1a +2b⩾2√2ab,又1a+2b=1,则√2ab⩽12,则ab⩾8,可得结果.(2)由题意,f(x)=x+1x−1=x−1+1x−1+1,利用基本不等式即可求最小值.15.【答案】解:(1)∵x<54,∴4x−5<0,5−4x>0.∴y=4x−1+14x−5=4x−5+14x−5+4=−[(5−4x)+15−4x]+4,第11页,共12页第12页,共12页 ∵5−4x +15−4x ⩾2√(5−4x )·15−4x =2,∴y ≤−2+4=2,当且仅当5−4x =15−4x 即x =1时取等号.∴y max =2.(2)∵0<x <12,∴1−2x >0,∴y =14×2x(1−2x)≤14×(2x +1−2x 2)2=14×14=116,当且仅当2x =1−2x (0<x <12),即x =14时,上式等号成立,故当x =14时,y max =116.【解析】(1)由y =4x −5+14x−5+4=4−(5−4x +15−4x ),利用基本不等式可求;(2)由y =12x(1−2x)=14×2x(1−2x),利用基本不等式可求;本题主要考查了利用基本不等式求解最值,要注意和为定值时,积有最大值,积为定值时,和有最小值的应用,属于基础试题.。
2023年中考数学基础满分挑战训练四十分钟限时练习卷七含答案解析

40分钟限时练习(7)一.选择题(共8小题,满分24分,每小题3分)1.(3分)下列变形正确的是( )A.(﹣3a3)2=﹣9a5B.2x2y﹣2xy2=0C.―3ba÷2ab=―32a2D.(2x+y)(x﹣2y)=2x2﹣2y2【分析】原式各项计算得到结果,即可作出判断.【解答】解:A、原式=9a6,错误;B、原式不能合并,错误;C、原式=―32a2,正确;D、原式=2x2﹣4xy+xy﹣2y2=2x2﹣3xy﹣2y2,错误.故选:C.【点评】此题考查了分式的乘除法,合并同类项,幂的乘方与积的乘方,以及平方差公式,熟练掌握公式及运算法则是解本题的关键.2.(3分)如图所示的几何体由一个圆柱体和一个长方体组成,从上面看该几何体得到的平面图形是( )A.B.C.D.【分析】根据圆柱体和长方体的俯视图解答.【解答】解:圆柱体的俯视图是圆,长方体的俯视图是长方形,所以,组合图形为长方形内有一个圆的图形.故选:C.【点评】本题考查了画几何体的三视图;用到的知识点为:主视图,左视图与俯视图分别是从物体的正面,左面,上面看得到的图形.3.(3分)如果点P(﹣2,b)在直线y=2x﹣l上,那么下列正确的是( )A.b的值为5B.点P关于y轴的对称点Q的坐标为(2,﹣5)C.点P到x轴的距离为2D.点P关于原点的对称点M的坐标为(5,2)【分析】根据点P(﹣2,b)在直线y=2x﹣l上,可得点P的坐标为(﹣2,﹣5),再根据关于x、y轴对称的点的坐标、关于原点对称的点的坐标特征即可判断.【解答】解:∵点P(﹣2,b)在直线y=2x﹣l上,∴当x=﹣2时,b=﹣5,所以A选项错误;∵点P坐标为(﹣2,﹣5),∴点P关于y轴的对称点Q的坐标为(2,﹣5),所以B选项正确;点P到x轴的距离为5,所以C选项错误;点P关于原点的对称点M的坐标为(2,5),所以D选项错误.故选:B.【点评】本题考查了一次函数图象上点的坐标特征、关于x、y轴对称的点的坐标、关于原点对称的点的坐标,解决本题的关键是掌握一次函数的性质.4.(3分)如图,直线l1∥l2,直线AD与l1,l2分别相交于点B,C,图中三个角∠α,∠β,∠γ之间的关系,下列式子中表述正确的是( )A.γ=2α+βB.γ=α+2βC.γ=α+βD.γ=α+β﹣180°【分析】根据平行线的性质得到∠ACE=α,根据平角的定义得到∠CED=180°﹣β,再根据三角形外角的性质即可求解.【解答】解:∵l1∥l2,∴∠ACE=α,∵∠CED=180°﹣β,∴α=180°﹣β+γ,即γ=α+β﹣180°.故选:D.【点评】本题考查了平行线的性质,三角形外角的性质,关键是得到∠ACE=α,∠CED =180°﹣β.5.(3分)如图所示的图形,长方形纸片沿AE折叠后,点D与D′重合,且已知∠CED′=50°.则∠AED是( )A.60°B.50°C.75°D.65°【分析】利用折叠的性质得到∠DEA与∠D′EA的关系,再利用角的和差关系及平角的定义求出∠DEA.【解答】解:∵△ED′A是△EDA折叠成的,∴∠DEA=∠D′EA.∵∠DEA+∠D′EA+CED′=180°.∴2∠DEA=180°﹣50°=130°.∴∠DEA=65°.故选:D.【点评】本题主要考查了折叠的性质,掌握折叠后的两个图形全等及平角的定义是解决本题的关键.6.(3分)一次函数y=x+1的图象如图所示,下列说法正确的是( )A.y的值随着x的增大而减小B.函数图象经过第二、三、四象限C.函数图象与y轴的交点坐标为(1,0)D.y=x+1的图象可由y=x的图象向上平移1个单位长度得到【分析】根据画出函数的图象性质、一次函数图象上点的坐标特征以及平移的规律进行判断即可.【解答】解:A、一次函数y=x+1中,k=1>0,所以y随x的增大而增大,故错误;B、由图象可知,函数图象经过一、二、三象限,故错误;C、令x=0,则y=1,所以直线与y轴的交点为(0,1),故错误;D、根据平移的规律,把直线y=x向上平移1个单位得到直线y=x+1,故正确.故选:D.【点评】本题主要考查了一次函数的图象和性质,要掌握它的性质和平移的规律才能灵活解题.7.(3分)如图,在矩形ABCD中,AB=3,AD=4,点P在AD上,PE⊥AC于E,PF⊥BD于F,则PE+PF等于( )A.75B.125C.135D.145【分析】连接OP,过D作DM⊥AC于M,求出AC长,根据三角形的面积公式求出CM 的值,根据S△AOD=S△APO+S△DPO代入求出PE+PF=DM即可.【解答】解:连接OP,过D作DM⊥AC于M,∵四边形ABCD是矩形,∴AO=OC=12AC,OD=OB=12BD,AC=BD,∠ADC=90°∴OA=OD,由勾股定理得:AC=32+42=5,∵S△ADC=12×3×4=12×5×DM,∴DM=12 5,∵S△AOD=S△APO+S△DPO,∴12(AO×DM)=12(AO×PE)+12(DO×PF),即PE+PF=DM=12 5,故选:B.【点评】本题考查了矩形的性质、三角形的面积公式、勾股定理的应用,关键是求出PE+PF =DM.8.(3分)如图,在⊙O中半径OC与弦AB垂直于点D,且AB=16,OC=10,则CD的长是( )A.2B.3C.4D.5【分析】根据垂径定理以及勾股定理即可求答案.【解答】解:连接OA,设CD=x,∵OA=OC=10,∴OD=10﹣x,∵OC⊥AB,∴由垂径定理可知:AB=16,由勾股定理可知:102=82+(10﹣x)2,∴x=4,∴CD=4,故选:C.【点评】本题考查垂径定理,解题的关键是熟练运用垂径定理以及勾股定理,本题属于基础题型.二.填空题(共8小题,满分32分,每小题4分)9.(4分)已知23的整数部分为a,小数部分为b,则a﹣b= 8―23 .【分析】由4<23<5,可求出a=4,b=23―4,再将a、b的值代入所求式子即可.【解答】解:∵16<23<25,∴4<23<5,∴a=4,b=23―4,∴a﹣b=4﹣(23―4)=8―23.故答案为:8―23.【点评】本题考查估计无理数的大小;熟练掌握无理数的整数部分与小数部分的求法是解题的关键.10.(4分)当x = ﹣4 时,分式x 2―162x ―8的值为0.【分析】根据分式的值为零的条件:分子等于0,且分母不等于0即可得出答案.【解答】解:根据题意得x 2﹣16=0,2x ﹣8≠0,∴x =±4,x ≠4,∴x =﹣4,故答案为:﹣4.【点评】本题考查了分式的值为零的条件,掌握分式的值为零的条件:分子等于0,且分母不等于0是解题的关键.11.(4分)将4个数a 、b 、c 、d 排成2行、2列,两边各加一条竖直线记成|a b c d |,这个记号叫做2阶行列式.定义|a b c d |=ad ―bc ,若|x +1x ―11―x x +1|=6,则x = ±2 .【分析】理解题意,按新定义|a b c d |=ad ―bc ,将问题转化为方程.若|x +1x ―11―x x +1|=6,即(x +1)(x +1)﹣(x ﹣1)(1﹣x )=6,再解方程即可.【解答】解:由题意,得:(x +1)(x +1)﹣(x ﹣1)(1﹣x )=6,∴x 2+2x +1+x 2﹣2x +1=6,∴2x 2+2=6,∴x =±2.【点评】本题是考查接受新定义能力的题目,解答的关键是理解题意,将问题转化为解一元二次方程.12.(4分)M 是△ABC 的边BC 的中点,AN 平分∠BAC ,BN ⊥AN 于点N ,且AB =10,BC =15,MN =3,则△ABC 的周长等于 41 .【分析】延长线段BN 交AC 于E ,易证△ABN ≌△AEN ,可得N 为BE 的中点;由已知M 是BC 的中点,可得MN 是△BCE 的中位线,由中位线定理可得CE 的长,根据AC =AE +CE 可得AC 的长,进而得出△ABC 的周长.【解答】解:延长线段BN 交AC 于E .∵AN 平分∠BAC ,∴∠BAN =∠EAN ,又∵AN=AN,∠ANB=∠ANE=90°,∴△ABN≌△AEN,∴AE=AB=10,BN=NE,又∵M是△ABC的边BC的中点,∴CE=2MN=2×3=6,∴△ABC的周长是AB+BC+AC=10+15+10+6=41.故答案为41.【点评】本题主要考查了中位线定理和全等三角形的判定及性质.解决本题的关键是作出辅助线,利用全等三角形得出线段相等,进而应用中位线定理解决问题.13.(4分)反比例函数y=k1x与正比例函数y=k2x图象的一个交点为第三象限内一点(﹣2,m).则不等式k1x>k2x的解集为 x<﹣2或0<x<2 .【分析】根据函数的对称性可得另一个交点在第一象限,其坐标为(2,﹣m),再根据两个函数的交点坐标以及图象的性质得出答案.【解答】解:由两个函数的对称性可得,反比例函数y=k1x与正比例函数y=k2x图象的另一个交点在第三象限,坐标为(2,﹣m),当反比例函数大于正比例函数值时,自变量x的取值范围为x<﹣2或0<x<2,故答案为:x<﹣2或0<x<2.【点评】本题考查一次函数与反比例函数的交点,理解正比例函数与反比例函数的性质是正确判断的前提.14.(4分)如图所示,正比例函数y=k1x与反比例函数y=k2x的图象有一个交点(2,﹣1),则这两个函数图象的另一个交点坐标是 (﹣2,1) .【分析】反比例函数的图象是中心对称图形,则与经过原点的直线的两个交点一定关于原点对称.【解答】解:由图象可知:直线y=k1x经过原点与双曲线y=k2x相交于两点,又由于双曲线y=k2x与直线y=mx均关于原点对称.则两点关于原点对称,一个交点的坐标为(2,﹣1),则另一个交点的坐标为(﹣2,1).故答案为:(﹣2,1).【点评】本题考查反比例函数图象的中心对称性,即两点关于原点对称.15.(4分)如图,点O为正八边形ABCDEFGH的中心,则∠ADB= 22.5 度.【分析】求出∠AOB=45°,根据同弧所对的圆心角和圆周角的关系即可得到结论.【解答】解:如图,连接OA,OB,∵∠AOB=3608=45°,∴∠ADB=12∠AOB=22.5°,故答案为:22.5.【点评】本题考查正多边形与圆,同弧所对的圆心角和圆周角的关系,解题的关键是掌握圆周角定理,学会添加常用辅助线.16.(4分)如图,正方形ABCD的边长为2,点E是AB边上一个动点,点F是CD边上一个动点,且AE=CF,过点B作BG⊥EF于点G,连接AG,则AG长的最小值是 10 2―22 .【分析】设正方形的中心为O ,可证EF 经过O 点.连接OB ,取OB 中点M ,连接MA ,MG ,则MA ,MG 为定长,利用两点之间线段最短解决问题即可.【解答】解:设正方形的中心为O ,可证EF 经过O 点.连接OB ,取OB 中点M ,连接 MA ,MG ,则MA ,MG 为定长,过点M 作MH ⊥AB于H .则MH =BH =12,AH =32,由勾股定理可得MA =102,MG =12OB =22,∵AG ≥AM ﹣MG =102―22,当A ,M ,G 三点共线时,AG 最小=102―22,故答案为:102―22.【点评】本题主要考查了正方形的性质,解直角三角形,直角三角形斜边中线的性质等知识,解题的关键是求出AM ,MG 的值.三.解答题(共4小题,满分44分)17.(10分)(1)―83×254÷765;(2)(3―1×27+24―623)×12―(32―6)2.【分析】(1)先根据二次根式的乘法和除法法则运算,然后化简即可;(2)先根据负整数指数幂的意义计算,再把二次根式化为最简二次根式,然后根据二次根式的乘法法则和完全平方公式计算.【解答】解:(1)原式=―13×2×17×8×54×56=―221×2×3×2×5=―410 7;(2)原式=(13×33+26―26)×23―(18﹣123+6)=3×23―24+123=6﹣24+123=123―18.【点评】本题考查了二次根式的混合运算,熟练掌握二次根式的性质、二次根式的乘法和除法法则和负整数指数幂是解决问题的关键.18.(10分)解方程:(1)10x=3x+7;(2)1x+3―23―x=12x2―9.【分析】(1)通过去分母、去括号、移项、x的系数化为1解分式方程.(2)先对分式方程的分母进行因式分解,确定最简公分母,再通过去分母、去括号、移项、合并同类项、x的系数化为1解这个分式方程.【解答】解:(1)10x=3x+7,两边同乘x(x+7),得10(x+7)=3x.去括号,得10x+70=3x.移项,得7x=﹣70.x的系数化为1,得x=﹣10.当x=﹣10时,x(x+7)≠0.∴这个分式方程的解为x=﹣10.(2)∵1x+3―23―x=12x2―9,∴1x+3―23―x=12(x+3)(x―3).方程两边同乘(x+3)(x﹣3),得x﹣3+2(x+3)=12.去括号,得x﹣3+2x+6=12.移项,得x+2x=12﹣6+3.合并同类项,得3x=9.x的系数化为1,得x=3.当x=3时,(x+3)(x﹣3)=0.∴x=3是这个分式方程的增根.∴这个分式方程无解.【点评】本题主要考查解分式方程,熟练掌握解分式方程的方法是解决本题的关键.19.(12分)疫情期间,学生居家学习,考虑学生们的健康成长,A市教育局依据国家“五项管理”和“双减政策”,提出了“每天锻炼一小时,健康生活一辈子”活动口号.为了解A市九年级学生参加体育锻炼的情况,随机抽查了A市部分九年级学生半个月参加体育锻炼(每天锻炼时间超过1小时)的天数,并用得到的数据绘制了两幅不完整的统计图(如图),请根据图中提供的信息,回答下列问题:(1)a= 10 .并写出该扇形所对圆心角的度数为 36 °.请补全条形图.(2)在这次抽样调查中,众数和中位数分别是多少?(3)如果A市共有九年级学生4000人,请你估计半个月来A市九年级学生“活动时间不少于6天”的学生人数大约有多少人?【分析】(1)根据各部分所占的百分比的和等于1列式计算即可求出a,用360°乘a即可得出其扇形的圆心角度数;然后用被抽查的学生人数乘以8天所占百分比求出8天的人数,补全条形统计图即可;(2)用众数和中位数的定义解答;(3)用总人数乘以“活动时间不少于6天”的百分比,计算即可得解.【解答】解:(1)a%=1﹣(40%+20%+25%+5%)=1﹣90%=10%,故a=10,该扇形所对圆心角的度数为:360°×10%=36°;被抽查的学生人数:240÷40%=600人,8天的人数:600×10%=60人,补全统计图如图所示:故答案为:10;36;(2)参加社会实践活动5天的人数最多,所以,众数是5天,600人中,按照参加社会实践活动的天数从少到多排列,第300人和301人都是6天,所以,中位数是6天;(3)4000×(20%+25%+10%+5%)=2400(人).故“活动时间不少于6天”的学生人数大约有2400人.【点评】本题考查的是条形统计图和扇形统计图的综合运用,读懂统计图,从不同的统计图中得到必要的信息是解决问题的关键.条形统计图能清楚地表示出每个项目的数据;扇形统计图直接反映部分占总体的百分比大小.20.(12分)如图所示,已知AC=AE,AB=AD,∠1=∠2,(I)试证明:∠B=∠D;(2)若∠1=90°时,直线BC、DE的位置怎样?【分析】(1)先证∠EAD=∠CAB,再利用SAS证明△EAD≌△CAB,根据全等三角形对应角相等即可;(2)由(1)结论△EAD≌△CAB得∠B=∠D,再由∠B+∠BGA=90°,根据等量代换得∠D+∠DGH=90°,故可判断DE⊥BC.【解答】(1)证明:∵∠1=∠2,∴∠EAD=∠CAB,在△EAD和△CAB中,AC=AE,∠EAD=∠CAB,AB=AD∴△EAD≌△CAB(SAS),∴∠B=∠D.(2)解:直线BC、DE相互垂直.理由如下:由(1)可知△EAD≌△CAB,∴∠B=∠D,∵∠1=∠2=90°,∴∠B+∠BGA=90°,∴∠CGB+∠D=90°,∴∠BHD=90°,∴BC与DE相互垂直.【点评】本题主要考查三角形全等的判定和性质.利用SAS找对应的相等边和角是关键.。
浅谈高效课堂策略之限时训练

过短时间的讲解或是训练能让学生获得 相应的知识,成绩得到一定的提高。因此, 在众多高效课堂策略里面,“限时训练”应 该是最为有效的策略之一,它既能兼顾学 生的知识层面的训练,也能在短时间内提 高学生的应试能力。
一、限时训练的有效性 1.及时巩固教学内容,检查教学效果, 查漏补缺。 高考备考时间很短,往往一节复习课 所安排的知识量都是非常大的,因为这些 知识学生原来都学过,所以老师没必要也 不可能再详细重讲每一个知识点,大多数 老师都采取讲练结合的方式。一轮复习的 时候,大部分教师采取的模式是:主干知 识快速串讲,然后再通过一两个例题将重 难点突破,最后重点是进行限时训练。通 过有针对性的练习可以全面准确地把握 学生的掌握程度与学习效果,充分暴露问 题,及时补救矫正,使知识得到落实。 2.训练答题心态,提高答题的速度、 准确性及规范性。 很多学生考试考不好其实是有原因 的,比如:有些学生在答题时紧张度不够, 经常精神不集中,做着做着就想别的事情 去了;有些学生又过于紧张,一遇到不会 做的题目就觉得自己这里没学好,那里没 记好,总是患得患失;还有一些学生是因 为答题不够规范而被扣分的。在心理学上 有这样一个理论:当人解决简单问题的时 候,最佳的状态往往是需要高点焦虑水平 的,而解决复杂问题的时候却反而需要低 点焦虑水平。所以,对于这些问题其实都 可以通过限时训练来解决,通过不断模拟 应试环境的限时训练,逐步提高学生对应 试环境的心态适应性和熟练度,答题心态 放平和了,紧张度合适了,限时答题熟练
人教版高中语文选修《中国古代诗歌散文欣赏》第一单元《书愤》限时训练题+Word版缺答案

《书愤》限时练习题时间:50分钟班级:_____ _____组_____号姓名:____________ 分数:__________第Ⅰ部分写出《书愤》中的相关文学常识及本文的重点字词。
(1分)第Ⅱ部分一、名句默写。
(24分,每空3分)(1)早岁那知世事艰,。
(陆游《书愤》)纸上得来终觉浅,。
(陆游《冬夜读书示子聿》)(2) ,铁马秋风大散关。
(陆游《书愤》),家祭无忘告乃翁。
(陆游《示儿》)(3)塞上长城空自许,。
(陆游《书愤》)小楼一夜听春雨,。
(陆游《临安春雨初霁》)(4) ,千载谁堪伯仲间!(陆游《书愤》),柳暗花明又一村。
(陆游《游山西村》)二、选择题(选择题每题5分)1.下列加线字注音有误的一项是()A.庇护(pì)塞子(sāi)堵塞(sè)B.鬓角(bìn)鬃毛(zōng)修葺(qì)C.伯父(bó)喋血(dié)间谍(dié)D.混沌(dùn)啼叫(tí)锲而不舍(qiè)2.下列词语中,有两个错别字的一项是()A.国事国是世道惹是生非B.渡河斑竹记载欢渡春节C.禅让震撼针砭惩前毖后D.名世瓜州痉孪仁至义尽3.对下列句中加线词的解释错误的一项是()A.中原北望气如山气:气概,气势B.塞上长城空自许许:答应C.出师一表真名世名:闻名D.千载谁堪伯仲间堪:能够4.下列和“楼船夜雪瓜洲渡,铁马秋风大散关”在艺术手法上不同的一项是()A.细草微风岸,危樯独夜舟。
B.枯藤老树昏鸦,小桥流水人家,古道西风瘦马。
C.夕阳古道无人语,禾黍秋风听马嘶。
D.鸡声茅店月,人迹板桥霜。
5.下列各项中,对所给诗句中“空”字的赏析不正确的一项是()A.“映阶碧草自春色,隔叶黄鹂空好音”中的“空”字让景物具有了浓厚的情感,在景语之中蕴含了令人寻味的“情语”:尽管鸟鸣草绿,却无人欣赏。
B.“山围故国周遭在,潮打空城寂寞回”中的“空”字写尽了古之繁荣与今之萧条的对比,在写景的同时写出了“城”之变迁,也就写出了对物是人非的感慨。
(部编版)中考字音字形限时练习(字表二1000字、含答案解析)

【时间:2分钟每小题:20分满分:100分】班级:姓名:成绩:1.下列加点字的读音有误的一项是()A.撰.文(zhuàn)和蔼.(ǎi)被褥.(rǔ)咄.咄逼人(duō)B.框.(kuàng)架遏制(è)铭.记(míng)长途跋.(bá)涉C.存恤.(xù)狰狞.(níng)倔.强(jué)煞.有介事(shà)D.挑剔.(tī)贿赂.(lù)绰.号(chuò)彬.彬有礼(bīn)2.下列词语书写有误的一项是()A.家眷战战兢兢眼花缭乱B.珐琅模棱两可踱来踱去C.搓捻销声匿迹前仆后继D.狼籍今非夕比辨伪去妄3.下列词语中加点字音有错误...的一项是()A.姊.妹(zǐ)池沼.(zhǎo)莽.莽榛榛(mǎng)B.灼.热(zhuó)淤.滩(yū)酣.然入梦(hān)C.轩敞.(chǎng)粗犷.(guǎng)不折不挠.(náo)D.烙.印(lào)徘徊.(huái)棱.角分明(líng)4.下列词语中加点字注音有误的一项是()A.殷.红(yān)佳肴.(yáo)菜畦.(qí)相得益彰.( zhāng)B.冗.杂(rǒng)德馨.(xīn)阔绰.(chuò)仙露琼浆(qióng)C.蹊跷.(qiāo)酝.酿(yùn)峰峦.(luán)千里迢迢.(tiáo)D.肖.像(xiào)藩篱.(lí)滑稽.(jī)矫.揉造作(jiāo)5.下列词语书写全都正确的一项是()A.题拔迁徙恍然大悟沧海一粟B.亢奋蔓延心不在焉心旷神怡C.范畴宽怒冥思苦想所向披靡D.闲暇前仆后继绿草如阴震耳欲聋答案解析1.下列加点字的读音有误的一项是(A)A.撰.文(zhuàn)和蔼.(ǎi)被褥.(rù)咄.咄逼人(duō)B.框.(kuàng)架遏制(è)铭.记(míng)长途跋.(bá)涉C.存恤.(xù)狰狞.(níng)倔.强(jué)煞.有介事(shà)D.挑剔.(tī)贿赂.(lù)绰.号(chuò)彬.彬有礼(bīn)2.下列词语书写有误的一项是( D )A.家眷战战兢兢眼花缭乱B.珐琅模棱两可踱来踱去C.搓捻销声匿迹前仆后继D.狼籍(藉)今非夕(昔)比辨伪去妄3.下列词语中加点字音有错误...的一项是(D)A.姊.妹(zǐ)池沼.(zhǎo)莽.莽榛榛(mǎng)B.灼.热(zhuó)淤.滩(yū)酣.然入梦(hān)C.轩敞.(chǎng)粗犷.(guǎng)不折不挠.(náo)D.烙.印(lào)徘徊.(huái)棱.角分明(léng)4.下列词语中加点字注音有误的一项是(D)A.殷.红(yān)佳肴.(yáo)菜畦.(qí)相得益彰.( zhāng)B.冗.杂(rǒng)德馨.(xīn)阔绰.(chuò)仙露琼浆(qióng)C.蹊跷.(qiāo)酝.酿(yùn)峰峦.(luán)千里迢迢.(tiáo)D.肖.像(xiào)藩篱.(lí)滑稽.(jī)矫.揉造作(jiǎo)5.下列词语书写全都正确的一项是(B)A.题拔(跋)迁徙恍然大悟沧海一粟B.亢奋蔓延心不在焉心旷神怡C.范畴宽怒(恕)冥思苦想所向披靡D.闲暇前仆后继绿草如阴(茵)震耳欲聋【时间:2分钟每小题:20分满分:100分】班级:姓名:成绩:1.下列句子中加点字注音有误的一项是()A.宁静的山村,炊烟是房屋升起的云朵,轻盈飘缈(miǎo)。
《细胞呼吸》40道选择题限时50分钟专项练习

《细胞呼吸》40道选择题限时50分钟专项练习姓名:__________班级:__________考号:__________1. 在人体细胞利用葡萄糖进行细胞呼吸过程中,关于[H]的来源和用途的叙述,最准确的是( )A. 答案AB. 答案BC. 答案CD. 答案D2. 玉米根部细胞中含有两种脱氢酶,在氧气不足的情况下,可以催化不同类型的无氧呼吸,如图所示(A~C表示物质,①~③表示生理过程)。
下列说法错误的是( )A. A为丙酮酸,C为酒精B. B只能在细胞质基质中生成C. ①~③过程中均有A TP的合成D. 长时间淹水的情况下,玉米根部细胞内可发生①②③过程3. 下图为探究酵母菌呼吸作用类型的装置图,实验中微生物均有活性。
假设环境因素对本实验无影响,下列表述正确的是( )A. 装置1中液滴左移、装置2中液滴不移动,说明酵母菌只进行了无氧呼吸B. 装置1中液滴左移、装置2中液滴右移,说明酵母菌只进行了有氧呼吸C. 将酵母菌替换成乳酸菌,装置1、装置2中液滴均不移动D. 将酵母菌替换为乳酸菌,装置1中液滴左移,装置2中液滴右移4. 雨水过多时,农作物会发生烂根现象,其原因主要是( )A. 土壤中缺乏氧气,根进行无氧呼吸产生酒精,对根细胞有毒害作用B. 土壤中水分充足,微生物繁殖而引起烂根C. 土壤中有毒物质溶解到水中,使根遭到毒害D. 土壤因水涝温度低,使根受到低温损害5. 某同学为了探究酵母菌的细胞呼吸方式,将少量的酵母菌混入适量的面粉揉成光滑面团后均等分装在2个洁净的塑料袋中,一组充满空气(甲组),一组则排净空气(乙组),扎紧袋口后放在相同且适宜的环境中观察20~30 min。
下列叙述不正确的是( )A. 一段时间后甲组的塑料袋内壁有水珠出现,面团变湿润B. 该实验中甲组为实验组,乙组为对照组C. 若放置的时间足够长,甲组也会产生酒精D. 该实验应选择大小合适、气密性良好的塑料袋6. 某一动物组织,有氧呼吸与无氧呼吸消耗的葡萄糖量的比为1∶3,则该组织消耗的O2量与产生的CO2量之比是( )A. 1∶1B. 2∶1C. 3∶1D. 1∶27. 有氧呼吸全过程中的物质变化可分为三个阶段:①C6H12O6→丙酮酸+[H];②丙酮酸+H2O→CO2+[H];③[H]+O2→H2O。
限时练三四
高一铭志班英语限时练六语篇型语法填空专项练习( A )It happened at Hillside Middle School, part of the Parma city school District. Two teachers in this school are dismissed (1)_____________ they performed acupuncture(针灸) on students without their parents’permission.Parma superintendent Jeff graham said that the two teachers performed acupuncture on students as part of the social studying class. The lesson (2)_____________(focus) on Chinese culture.In that class, (3)__________ teacher took a needle and stuck it in his own arm. Then ha put needles into the arms of students and allowed the students(4)___________(perform)acupuncture on each other.Graham said (5)_________ all of the needles used were sealed and sterile(消过毒的), the problem was that the teachers did not get permission from the parents.“I would be highly upset(6)_________ they came home and said that one of their teachers performed acupuncture on them without my(7)_____________”, said one parent. “They send permission slips home for field trips, spirit days, for so many things, but they thought (8)__________ wouldn’t be important to send one home for this?”Graham said the students were willing participants, but those 13-year-olds should not be making these types of (9)___________(decide). School officials said they (10)___________(inform) about the incident when a parent complained.( B )Each time Elizabeth Moore returns from a supermarket, she experts that her sons can help her unload groceries from the car. Her oldest son, 13-year-old Jake,is always the first one (1)__________(help), while her (2)____________(young)son, 8-year-old Sam, complains the whole time. Meanwhile, her middle son, 10-year-old Ben, by any means, tries to avoid (3)__________(leave)his room.“He gets held up looking for his shoes. By the time he turns up, we (4)____________(do) it,” says Elizabeth. “It amazes me (5)___________ different my children are from one another.”Why do three kids with the same parents, living in the same house, develop such distinct personalities? A key reason seems to be birth order. Many experts believe that(6)______ child’s place in the family (7)_________- affect the hobbies he chooses, the grades he’ll earn in school, and how much money he’ll make as an adult. An expert says, “For siblings(兄弟姐妹),the (8)___________(differ) in many aspects ofpersonality are about as great as they could be between a brother and a sister.” Birth order isn’t the only factor (9)___________ contributes to how a kid turns out, but giving it consideration can help you understand your kids’ personalities – so you can help them succeed in (10)________ own unique ways.( C )Life in the new century is different. In the 21 st century, technology is developing (1)________(fast)than before. New technological wonders surprise us. (2)___________, they make us want more of the comfort that they create. One of these wonders is television.(3)________ has become so popular all over the world that there is almost no country, region or village (4)___________ people don’t know what a TV set is. Also , it is universally considered that television plays (5)__________important role in people’s life.Television is the man source of information for many people. It (6)___________ provide us with the necessary information and keep us (7)__________(inform)during the day.Also, television is a way for may people to entertain. It offers a great many possibilities to have (8)___________. You can enjoy yourself (9)__________(sit) on your couch and relaxing. Another way people’s minds are influenced by TV is through advertisements. Commercials have become an important part of broadcasting and live coverage. Even movies(10)_________(interrupt) by short ads. Nowadays, commercials are not only a way to promote products in supermarkets. But also a way to bring in money to television channels.( D )As we all know, Americans eat turkey on Thanksgiving Day. However, what most of us don’t know is that (1)_________ eat turkey and many foods made with turkey meat all year round.Most of the turkeys(2)___________(eat) in the United State are raised on farms. Americans buy these birds at supermarkets. Some of them are fresh (3)________most have been frozen. All of these birds need (4)_________(cook)in an oven for several hours. More than ninety percent of Americans eat turkey on Thanksgiving Day in November, and forty-five million birds are sold for that holiday.Seventy percent of (5)________ average turkey is white meat while thirty percent is dark meat.In general, Americans like the white meat (6)_________ than the dark meat. Most American markets sell turkey white meat which is cooked and thinly sliced for making sandwiches. Sometimes turkey meat is used instead of beef to make the (7)__________(tradition) American hot dog. Turkey meat (8)_________also be cut into small (9)___________ and added to vegetables and liquid to make soups and stews. Turkeys have become so popular that the turkey production in the United States (10)_________ (grow)by three hundred percent since 1970.高一铭志班英语限时练七语篇型语法填空专项练习( E )Customs for saying goodbye in different countries vary. Before you come to France,you should know how to express (1)_________ here as it is very important.According头哦proper French etiquette(礼节), it is a custom to shake hands when greeting someone as well as when saying goodbye. (2)__________. On formal occasions, when (3)__________(leave), one should shake hands once again and say “Goodbye, sir/madam”. In some places, people even wish each other farewell(再会) by shaking hands every day when departing by shaking hands.Saying goodbye in(4)________ formal manner is also common in restaurants or stores. Actually, in an informal situation, the goodbye (5)_____________(accompany)with hugging or kissing.To behave well in front of the French, you’d better remember the fact that the French are very (6)__________ (pride) of their language. (7)__________(use)simple words like hello, thank you and goodbye in French can help you make a positive (8)___________ on them. Moreover, in order to have the right effect, you (9)__________ use the correct pronunciation of these words. Therefore,(10)__________ you want to be popular with French people in the near future, you’d better learn some simple French words first.( F )The Internet is an amazing information resource. Students, teachers, and researchers use it as (1)__________ investigative tool. Journalists use it to find information for stories. Doctors use it to learn more about unfamiliar diseases and the (2)___________ (late) medical development. Ordinary people use it for shopping, banking, bill-paying, and communicating with family and friends. People all over the world use it to connect with individuals from (3)___________ countries and cultures. However, (4)___________ there are many positive developments (5)____________ (associate) with the Internet, there are also certain fears and concerns. (6)___________ concern relates to a lack of control over (7)_____________ appears on the Internet. With television and radio there are editors to check the accuracy or appropriateness of the content ofprograms, and with television there are (8 )____________ (restrict) on what kinds of programs can (9)___________ (broadcast) and at what times of the day. With the Internet, parents cannot check a published guide to determine what is suitable (10)____________ their children to see.( G )Everyone knows that earthquakes can damage their property. But (1)__________ in some situations, more damage is done after an earthquake than when it (2)____________ (happen). However, you can do a great many things after an earthquake that may help to protect your home.Firstly, make sure there is no gas leak. The professional (3)__________ is to turn off the gas line if possible. If there is a gas leak and you can’t turn it off, (4)__________- is recommended that you get everyone out of the house (5)__________ go to a neighbor’s to call the fire department.Secondly, make sure none of the water pipes (6)____________ (break). Even if you don’t see any pipes leaking, you should call the water company to see if the water is safe to drink. You don’t want any one of your family members to get sick because he or she has drunk (7)_________ (safe) water, right?The last thing you should do is (8)__________ (make) sure the foundation of the house is not cracked or sinking. A cracked or sinking foundation can be a sign that the house (9)__________ collapse. In that case, leave the house and do not enter it until (10)_________ expert looks into the problem.(H )In my free time, I really like surfing the Internet. When I get home from work, I turn on my computer, wait _(1)_________it boots up completely, and then I go online. I usually check my email first and then write a few messages _(2)__________ family and friends. I sometimes scan the local news headlines at _(3)________ favorite news Website and read up on the latest local and international news. This Website often provides video news clips_(4)_________ you can view online. I sometimes order products or service online to save money and time instead of going to a store and_(5)_________(buy) what I'm looking for. For example, I _(6)_________ (order)a digital camera online the other day and saved about $50. Whatever I do, I realize that there are problems_(7)__________ using the Internet including scams, identify theft, and viruses, so I'm very careful not to give out my _(8)___________ (person) information. Furthermore, I don't download or open files I don't recognize. Using the Internet can be fun and_(9)_________ convenient way of shopping and finding out new information, _(10)___________ you just need to be careful.The answers(A)1.because 2.focused 3. a 4.to perform 5. although 6. if 7. permission8. it 9. decision 10. were informed(B ) 1. to help 2. youngest 3. leaving 4. have done 5. how 6. a 7. may8. differences 9. that 10. their(C ) 1.faster 2. Besides 3. it 4. where 5. an 6.can 7. informed8. fun 9. sitting 10. are interrupted( D ) 1. they 2. eaten 3. but 4. to be cooked 5. an 6. better 7. traditional8. can 9. pieces 10. has grown( E ) 1. it 2. therefore 3. leaving 4. a 5. is accompanied 6.proud7. Using 8. impression 9. must 10. if( F ) 1. an 2. latest 3.other/different 4. while 5.associated 6. One7. what 8. restrictions 9. be broadcast(ed) 10.for( G ) 1. actually 2. is happening 3. suggestion 4. it 5. and 6. are broken7. unsafe 8.to make 9. may 10. an(H)1. until / till 2. to 3. my 4. that / which 5. buying 6.ordered7. in 8. personal 9. a 10. but。
2023高三晚自习英语限时 基础练习卷(含答案)
2023高三晚自习限时(基础练习卷)一、基础巩固与翻译练习1. 在那一刻她似乎在嘲笑我,但随后我又从她的微笑中感受到悲伤。
(汉译英)2. 毕业在即,我既高兴又自豪,也认识到唯有不断学习、努力奋斗才会未来可期。
(approach)(汉译英)3. 纵观人类历史,如果一个民族无法适应时代变迁,它就很难在激烈的全球竞争中存活。
(survive) (汉译英)4. 春节期间的所见所闻让我们深刻地感受到:千千万万普通人最伟大,幸福都是奋斗出来的。
(happiness)5. 直到经历了令人精疲力竭的15天的征程,全体船员才意识到这个征程未结束。
(It was not until..) (汉译英)6. 通过志愿者服务与奉献,年轻人们在成长中能有所作为,也得到了机会去珍视生活中真正重要的东西。
(difference) (汉译英)二、3篇阅读理解题A7. According to the text, which animal can help you relax?A.A snake. B.A dog.C.A honeyguide bird. D.A miniature horse.8. Miniature horses could serve .A.blind people who dislike dogs B.blind people who can live longer C.animal lovers who search for honey D.animal lovers who suffer from cancer 9. The text is about animals’ .A.special training B.great potentialsC.unique jobs D.high intelligenceBAfter being attacked by Hurricane Ida’s 150 mph winds and torrential rains, hundreds of thousands of Gulf Coast residents were left without power and fresh water this week as a 100-degree heat wave settled over the region. Ida smashed into Louisiana as a Category 4 hurricane, ripping off roofs, knocking out transmission lines, flooding roads, and reducing some brick buildings in downtown New Orleans to rubble. At least eight people died in the storm and the toll is expected to rise as emergency workers search wrecked homes and businesses.One of the most powerful hurricanes to ever hit the U.S. mainland, Ida brought a 5 to 12-foot storm surge that covered low-lying communities in southeastern Louisiana. Grand Isle is now “uninhabitable,” said Parish President Cynthia Lee Sheng, with 3 feet of sand covering the entire barrier island and 40 percent of the buildings completely destroyed.The storm caused a citywide blackout in New Orleans, but a Hurricane Katrina-level disaster was avoided there, thanks in part to the $ 14.5 billion spent on new levees, seawalls, and pumps after the 2005 storm. Experts are warning that Ida could worsen the Covid crisis in the Gulf Coast, as residents crowd together in homes and emergency shelters without immediate access to testing or medical care. ICUs in Louisiana, Mississippi, and Alabama hospitals were already near capacity be- fore the storm hit. Nearly 1 million people are still without power across Louisiana, and authorities waned it could be weeks before electricity is restored. “If you have already evacuated,” said Gov. John Bel Edwands, “do not return here.”;10. Which of the following best describes Hurricane Ida?A.Mild. B.Destructive. C.Uncontrollable. D.Impressive.;11. What does the underlined words “the toll” mean in Paragraph 1?A.The death number. B.The heat wave.C.The wind speed. D.The citywide blackout.;12. What is one of the reasons for Grand Isle to be uninhabitable?A.The entire island is covered with sand. B.It is one of the low-lying communities.C.The residents there can't wait to leave. D.Over half of its buildings were in ruins.;13. What can be inferred about the attitude of Gov. John Bel Edwards towards the prospect of Louisiana?A.Ambitious B.Undoubted. C.Indifferent. D.Unconfident.CPangolins (穿山甲) are the most trafficked (非法交易) mammals in the world and are facing extinction. To draw attention to these scaly (有鳞片的), anteater-like animals, a new wildlife documentary, Eye of the Pangolin, is attempting a u nique way to inspire action and conservation. Partnering with the non-profit organization Pangolin. Africa, the documentary was made available on YouTube in May 2019. The intention is to reach communities wherever the Internet is available, especiallyAfri can communities, who live near the animal’s habitats.Over two years, the documentary crew traveled to South Africa, Ghana, Central African Republic and Gabon in search of the four unique species of pangolin, which has never been achieved before. Filmmakers Bruce Young and Johan Vermeulen say that they went into the shoot knowing relatively little about pangolins, but grew to respect and appreciate the animals. Getting close to the creatures over two years was a crash course in these secretive creatures. Johan Vermeulen said, "One thing however that might seem unimportant is that they are actually quite fussy eaters. You would think they would eat any type of ant, but they all prefer a specific type ant."Pangolins are hunted illegally across Africa for their scales, which are used for traditional medicine, and their meat. In April 2019, Singaporean customs officials conducted two separate seizures of 24 tons of pangolin scales, which equals to the death of 69,000 pangolins.Though the documentary focuses less on the trafficking of pangolins, and more on the animals in their natural habitat, the aim of the documentary is to inspire viewers around the world to call for action to end trafficking and protecting these unique creatures.Filmed on location in South Africa, Ghana, Central African Republic, and Gabon, this powerful documentary is the story of two men on a mission to get all four species of African pangolin on camera for the very first time.14. What is the purpose of the documentary?A.To study the situation of pangolins.B.To collect fund to protect pangolins.C.To raise awareness of pangolin protection.D.To propose setting up pangolin reserves.15. What is the meaning of the underlined word “fussy” in paragraph 2?A.Picky. B.Messy.C.Showy. D.Heavy.16. What’s the documentary mainly about?A.The illegal trade of pangolins.B.The medical function of pangolin's scales.C.The life of pangolins in their natural habitats.D.The efforts of Pangolin, Africa to save pangolins.17. Where is the text most likely from?A.A brochure. B.A diary.C.A novel. D.A magazine.三、七选五阅读Ways to Boost Your Emotional Health by Improving Your Confidence Taking care of your emotional health is as important as taking care of your physical body. 18 When you feel good about yourself, it's much easier to cope with life's little ups and downs as well as bigger events. Here are ways you can practice better stress management and boost your self-esteem.▲ 19Alcohol can be a good stress reducer, but you must be careful. The same advice applies to food intake. You can eat what you want and enjoy it as long as you eat smaller portions and get regular exercise. Maintaining a proper weight is important for your physical and your emotional health.▲Lear n More to Lessen the Fear of the Unknown20 If you have a problem, learn whatever you can about the issue or the health condition you're facing. The more you know, the less you will fear what might happen.▲Get Moving to Improve Mood and Lessen Anx ietyAny form of exercise that you enjoy will do. Regular exercise works as a good partner for people who are on medication. Exercise also works well for people who have mild or moderate depression and don't need to be on medication. 21 .▲Develop a Passion by Investing Time in a New HobbyEveryone should have at least one hobby, whether it's taking care of plants, collecting antiques, or listening to music. 22 Having a hobby and taking pride in it is a great way to boost self-esteem.A.If you are unsure of how to get started, take a class and learn how to practice on your own for 30 minutes, three times a week.B.Knowledge is power.C.Think of it as a great tool for stress management.D.Manage Your Time by Setting Weekly Goals.E.If your emotional health is out of balance, you may experience high blood pressure.F.You should do something that brings you some real joy that no one can take from you.G.Eat and Drink Healthfully and Appropriately.四、语法填空阅读下面短文, 在空白处填入1个适当的单词或括号内单词的正确形式。
五种方法法求二面角及限时练习
五种方法求二面角及练习题一、 定义法:从一条直线出发的两个半平面所组成的图形叫做二面角, 这条直线叫做二面角的棱, 这两个半平面叫做二面角的面,在棱上取点,分别在两面内引两条射线与棱垂直,这两条垂线所成的角的大小就是二面角的平面角。
本定义为解题提供了添辅助线的一种规律。
如例1中从二面角S —AM —B 中半平面ABM 上的一已知点(B )向棱AM 作垂线,得垂足(F );在另一半平面ASM 内过该垂足(F )作棱AM 的垂线(如GF ),这两条垂线(BF 、GF )便形成该二面角的一个平面角,再在该平面角内建立一个可解三角形,然后借助直角三角函数、正弦定理与余弦定理解题。
例1(2009全国卷Ⅰ理)如图,四棱锥S ABCD -中,底面ABCD 为矩形,SD ⊥底面ABCD,AD =2DC SD ==,点M 在侧棱SC 上,ABM ∠=60°(I )证明:M 在侧棱SC 的中点 (II )求二面角S AM B --的大小。
证(I )略解(II ):利用二面角的定义。
在等边三角形ABM 中过点B作BF AM ⊥交AM 于点F ,则点F 为AM 的中点,过F 点在平面ASM 内作GF AM ⊥,GF 交AS 于G ,连结AC ,∵△ADC ≌△ADS ,∴AS-AC ,且M 是SC 的中点, ∴AM ⊥SC , GF ⊥AM ,∴GF ∥AS ,又∵F 为AM 的中点,∴GF 是△AMS 的中位线,点G 是AS 的中点。
则GFB ∠即为所求二面角. ∵2=SM ,则22=GF ,又∵6==AC SA ,∴2=AM ∵2==AB AM,060=∠ABM ∴△ABM 是等边三角形,∴3=BF在△GAB 中,26=AG ,2=AB ,090=∠GAB ,∴211423=+=BG 366232222113212cos 222-=-=⨯⨯-+=⋅-+=∠FB GF BG FB GF BFG ∴二面角S AMB --的大小为)36arccos(-FGFG练习1(2008山东)如图,已知四棱锥P -ABCD ,底面ABCD 为菱形,PA ⊥平面ABCD ,60ABC ∠=︒,E ,F 分别是BC , PC 的中点. (Ⅰ)证明:AE ⊥PD ;(Ⅱ)若H 为PD 上的动点,EH 与平面PAD 所成最大角的正切值E —AF —C 的余弦值. 分析:第1题容易发现,可通过证AE ⊥AD 后推出AE ⊥平面APD ,使命题获证,而第2题,则首先必须在找到最大角正切值有关的线段计算出各线段的长度之后,考虑到运用在二面角的棱AF 上找到可计算二面角的平面角的顶点S ,和两边SE 与SC ,进而计算二面角的余弦值。
2023年中考数学基础满分挑战训练四十分钟限时练习卷八含答案解析
40分钟限时练习(8)一.选择题(共8小题,满分24分,每小题3分)1.(3分)以下是回收、绿色包装、节水、低碳四个标志,其中为中心对称图形的是( )A.B.C.D.【分析】根据中心对称图形的概念判断.把一个图形绕某一点旋转180°,如果旋转后的图形能够与原来的图形重合,那么这个图形就叫做中心对称图形.【解答】解:选项A、B、D中的图形都不能找到这样的一个点,使图形绕某一点旋转180°后与原来的图形重合,所以不是中心对称图形.选项C中的图形能找到这样的一个点,使图形绕某一点旋转180°后与原来的图形重合,所以是中心对称图形.故选:C.【点评】本题考查的是中心对称图形,中心对称图形是要寻找对称中心,旋转180度后与自身重合.2.(3分)已知∠α=40°,∠β的两边与∠α的两边互相平行,则∠β的度数为( )A.40°B.50°C.140°D.40°或140°【分析】根据两边互相平行的两个角相等或互补解答.【解答】解:∵a∥b,∴∠1=∠α,∠2+∠α=180°,∵c∥d,∴∠1=∠3,∠2=∠4,∴∠3=∠α,∠4+∠α=180°,即若两角的两边互相平行,则这两个角相等或互补.∴∠β与∠α相等或互补,∵∠α=40°,∴∠β=40°或140°.故选:D.【点评】本题从两直线平行,同位角和同旁内角两种情况考虑比较简单.3.(3分)下面关于表示互为相反数的m与﹣m的点到原点的距离,表述正确的是( )A.表示数m的点距离原点较远B.表示数﹣m的点距离原点较远C.一样远D.无法比较【分析】根据数轴表示数的方法与相反数的定义得到m与﹣m的点到原点的距离相等.【解答】解:互为相反数的m与﹣m的点到原点的距离相等.故选:C.【点评】本题考查了相反数:a的相反数为﹣a.也考查了数轴.4.(3分)2022年10月12日,“天宫课堂”第三课在中国空间站开讲,3名航天员演示了在微重力环境下毛细效应实验、水球变“懒”实验等,相应视频在某短视频平台的点赞量达到150万次,数据150万用科学记数法表示为( )A.1.5×105B.0.15×105C.1.5×106D.1.5×107【分析】科学记数法的表示形式为a×10n的形式,其中1≤|a|<10,n为整数.确定n 的值时,要看把原数变成a时,小数点移动了多少位,n的绝对值与小数点移动的位数相同.当原数绝对值≥10时,n是正数;当原数的绝对值<1时,n是负数.【解答】解:150万=1500000=1.5×106.故选:C.【点评】此题主要考查科学记数法的表示方法.科学记数法的表示形式为a×10n的形式,其中1≤|a|<10,n为整数,表示时关键要正确确定a的值以及n的值.5.(3分)今年3月份某校举行学雷锋志愿服务活动,为了解学生一周学雷锋志愿服务的次数,随机抽取了50名学生进行一周学雷锋志愿服务次数调查,依据调查结果绘制了如图的折线统计图,下列有关该校一周学雷峰志愿服务次数说法正确的是( )A.众数是5B.众数是13C.中位数是7D.中位数是9【分析】从折线图统计中获取信息,通过折线统计图和中位数、众数的定义等知识求解.【解答】解:因为5出现了13次,出现的次数最多,所以该校一周学雷峰志愿服务次数的众数是5;该校一周学雷峰志愿服务次数最中间的两个数字都为6,所以该组数据的中位数为6;故选项A正确,符合题意.故选:A.【点评】本题考查折线统计图、众数及中位数的定义等知识点,掌握众数、中位数的定义,并能从统计图中得到必要的信息是解决本题的关键.6.(3分)分别写有数字﹣1,﹣2,1,3,4的五张卡片,除数字外其他均相同,将它们背面朝上,从中任抽一张,抽到负数的概率是( )A.15B.13C.25D.12【分析】用负数的个数除以数的总数即可求得答案.【解答】解:∵5张卡片中有2张是负数,∴从中任抽一张,抽到负数的概率是2 5,故选:C.【点评】考查了概率的基本计算,用到的知识点为:概率等于所求情况数与总情况数之比.7.(3分)一船向东航行,上午8时到达B处,看到有一灯塔在它的南偏东60°,距离为72海里的A处,上午10时到达C处,看到灯塔在它的正南方向,则这艘船航行的速度为( )A.18海里/小时B.183海里/小时C.36海里/小时D.363海里/小时【分析】首先画图,构造直角三角形,利用勾股定理求出船8时到10时航行的距离,再求速度即可解答.【解答】解:如图在R t△ABC中,∠ABC=90°﹣60°=30°,AB=72海里,故AC=36海里,BC=AB2―AC2=363海里,艘船航行的速度为363÷2=183海里/时.故选:B.【点评】本题考查方位角、直角三角形、锐角三角函数的有关知识.解一般三角形的问题一般可以转化为解直角三角形的问题,解决的方法就是作高线.8.(3分)如图,已知⊙O是△ABC的外接圆,连接AO,若∠B=70°,则∠OAC的度数为( )A.20°B.25°C.50°D.65°【分析】连接CO,由圆周角定理可得∠AOC=2∠B=140°,根据等腰三角形的性质和三角形内角和定理即可求出∠OAC的度数.【解答】解:连接CO,∵∠B=70°,∴∠AOC=2∠B=140°,∵OA=OC,∴∠OAC=∠OCA,∴∠OAC=12(180°﹣140°)=20°.故选:A.【点评】本题考查了三角形的外接圆和圆周角定理,熟练掌握圆周角定理是解决问题的关键.二.填空题(共8小题,满分32分,每小题4分)9.(4分)若102y=25,则10﹣y= 15 .【分析】根据幂的乘方运算的逆运算和负指数幂的运算法则计算.【解答】解:∵102y=25,∴10y=5,∴10﹣y=110y=15.故答案为1 5.【点评】此题的实质是考查幂的乘方运算的逆运算和负指数幂的运算,要根据式子的特点灵活运算.10.(4分)在函数y=12x―1中,自变量x的取值范围是 x≠12 .【分析】函数由分式组成,故分母不等于0是这个函数有意义的条件.【解答】解:根据题意得:2x﹣1≠0,解得x≠1 2.故答案为x≠1 2.【点评】(1)当函数表达式是整式时,自变量可取全体实数;(2)当函数表达式是分式时,考虑分式的分母不能为0;11.(4分)分解因式:a4﹣2a2b2+b4= (a+b)2(a﹣b)2 ;x5﹣x3= x3(x+1)(x﹣1) .【分析】(1)先利用完全平方公式分解因式,再利用平方差公式继续进行因式分解;(2)先提取公因式x3,再利用平方差公式继续进行因式分解.【解答】解:(1)a4﹣2a2b2+b4,=(a2﹣b2)2,=(a+b)2(a﹣b)2;(2)x5﹣x3,=x3(x2﹣1),=x3(x+1)(x﹣1).【点评】本题考查了提公因式法和公式法进行因式分解,一个多项式有公因式首先提取公因式,然后再用其他方法进行因式分解,同时因式分解要彻底,直到不能分解为止.12.(4分)若一个多边形的外角和是内角和的13,则这个多边形的边数是 8 .【分析】根据多边形的内角和的公式(n﹣2)×180°和多边形的外角和公式,解方程即可求出n的值【解答】解:设这个多边形的边数为n,则根据多边形内角和与外角和公式可得方程360°=13(n﹣2)×180°解得n=8故答案为8.【点评】本题考查的是多边形的内角和,利用内角和公式进行列方程解决是本题的关键.13.(4分)关于x的一元二次方程2x2﹣2x+m﹣2=0有正整数根,则正整数m的值为 2 .【分析】利用判别式△≥0,确定m的取值范围,求出m的整数解即可判断.【解答】解:由题意△≥0,∴4﹣8(m﹣2)≥0,解得m≤5 2,∵m是正整数,∴m=1或2,当m=1时,方程:2x2﹣2x﹣1=0,没有正整数根,不合题意舍弃,当m=2时,方程:2x2﹣2x=0,有正整数根符合题意,∴m的值为2,故答案为2【点评】本题考查一元二次方程的根的判别式,解题的关键是理解题意灵活运用所学知识解决问题.14.(4分)如图,为了测量河宽AB(假设河的两岸平行),在河的彼岸选择一点A,在点C 测得∠ACB为30°,点D处测得∠ADB为60°,若CD=60m,则河宽AB为 303 m(结果保留根号).【分析】先根据三角形外角的性质求出∠CAD的度数,判断出△ACD的形状,再由锐角三角函数的定义即可求出AB的值.【解答】解:∵∠ACB=30°,∠ADB=60°,∴∠CAD=30°,∴AD=CD=60m,在R t△ABD中,AB=AD•sin∠ADB=60×32=303(m).故答案为:303.【点评】本题考查的是解直角三角形的应用﹣仰角俯角问题,涉及到三角形外角的性质、等腰三角形的判定与性质、锐角三角函数的定义及特殊角的三角函数值,难度适中.15.(4分)如图,在平面直角坐标系中,R t△OBC的顶点B在x轴的正半轴上,反比例函数y=kx(x>0)的图象与边OC交于点E,CE=13OC,S△OBC=18,则k= 16 .【分析】根据相似三角形的判定和性质得出S△OEFS△OCB=49,进而求出S△OEF=8,再根据反比例函数系数k的几何意义求出结果即可.【解答】解:过点E作EF⊥OB,垂足为F,∵CB⊥OB,∴EF∥BC,∴△OEF∽△OCB,又∵CE=13 OC,∴OE=23 OC,即OEOC=23,∴S△OEFS△OCB=49∵S△OBC=18,∴S△OEF=8=12|k|,∵k>0,∴k=16,故答案为:16.【点评】本题考查反比例函数系数k的几何意义以及相似三角形的判定和性质,理解反比例函数系数k的几何意义,掌握相似三角形的判定和性质是正确解答的前提.16.(4分)如图,在边长为8的正方形ABCD中,对角线ACBD交于点O,点E是边CD 上方一点,且∠CED=90°,若DE=2,则EO的长为 30+2 .【分析】过O作OF⊥EO,交EC的延长线于F,利用正方形的性质,先判定△DOE≌△COF(AAS),即可得出△EOF是等腰直角三角形,再根据勾股定理,即可得到OE的长.【解答】解:如图所示,过O作OF⊥EO,交EC的延长线于F,R t△EOF中,∠CEO+∠F=90°,∵∠CED=90°,∴∠CEO+∠OED=90°,∴∠OED=∠F,∵四边形ABCD是正方形,∴∠COD=∠DOE+∠COE=90°,DO=CO,又∵∠COF+∠COE=90°,∴∠DOE=∠COF,在△DOE和△COF中,∠OED=∠F∠DOE=∠COF,DO=CO∴△DOE≌△COF(AAS),∴EO=FO,DE=CF=2,又∵∠EOF=90°,∴△EOF是等腰直角三角形,∵正方形ABCD的边长为8,∴R t△CDE中,CE=CD2―DE2=82―22=215,∴EF=215+2,∴OE=cos45°EF=22(215+2)=30+2,故答案为:30+2.【点评】本题考查了正方形的性质,全等三角形的判定和性质,等腰直角三角形的性质和判定的综合运用.在应用全等三角形的判定时,要注意三角形间的公共边和公共角,必要时添加适当辅助线构造三角形.三.解答题(共4小题,满分44分)17.(10分)化简求值:(a―1a―a―2a+1)÷2a2―aa2+2a+1;其中a2﹣a﹣1=0.【分析】先把括号内通分和除法运算化为乘法运算,再把分子分母因式分解后约分得到原式=a+1a2,然后把a2=a+1代入计算即可.【解答】解:原式=(a+1)(a―1)―a(a―2)a(a+1)•(a+1)2a(2a―1)=2a―1a(a+1)•(a+1)2a(2a―1)=a+1 a2,∵a2﹣a﹣1=0.∴a2=a+1,∴原式=a+1a+1=1.【点评】本题考查了分式的化简求值:先把分式化简后,再把分式中未知数对应的值代入求出分式的值.在化简的过程中要注意运算顺序和分式的化简.化简的最后结果分子、分母要进行约分,注意运算的结果要化成最简分式或整式.18.(10分)求不等式组x+1≤3x―1<4(x+2)的整数解.【分析】分别求出每一个不等式的解集,根据口诀:同大取大、同小取小、大小小大中间找、大大小小无解了确定不等式组的解集.【解答】解:解不等式x+1≤3,得x≤2,解不等式x﹣1<4(x+2),得x>﹣3,所以原不等式组的解集为﹣3<x≤2,其整数解为﹣2,﹣1,0,1,2.【点评】本题考查的是解一元一次不等式组,正确求出每一个不等式解集是基础,熟知“同大取大;同小取小;大小小大中间找;大大小小找不到”的原则是解答此题的关键.19.(12分)在2021年双11到来之前,某商家为了囤货,投入28000元资金购进A、B两种商品共1000件,两种商品的成本价和销售价如表所示:商品单价(元/件)成本价销售价A2535B3045(1)该商家购进两种商品各多少件?(2)这批商品全部销售完后,该商家共获利多少元?【分析】(1)设购进A种商品x件,购进B种商品y件,由表中数据和投入28000元资金购进A、B两种商品共1000件,列出方程组,解方程组即可;(2)销售额减去成本即可.【解答】解:(1)设购进A种商品x件,购进B种商品y件,根据题意,得x+y=100025x+30y=28000,解得x=400y=600,答:该商家购进A种商品400件,B种商品600件.(2)400×(35﹣25)+600×(45﹣30)=13000(元),答:该商家共获利13000元.【点评】本题考查了二元一次方程组的应用,解题的关键是:找准等量关系,列出二元一次方程组.20.(12分)课前预习是学习的重要缓解,为了了解所教班级学生完成课前预习的具体情况,某班主任对本班部分学生进行了为期半个月的跟踪调查,他将调查结果分为四类:A.优秀,B.良好,C.一般,D.较差,并将调查结果绘制成以下两幅不完整的统计图.(1)本次调查的样本容量是 20 ;其中A类女生有 2 名,D类学生有 2 名;(2)将条形统计图补充完整;(3)若从被调查的A类和D类学生中各随机选取一位学生进行“一帮一”辅导学习,即A类学生辅导D类学生,请用列表法或画树状图的方法求出所选两位同学中恰好是一位女同学辅导一位男同学的概率.【分析】(1)根据B类有6+4=10人,所占的比例是50%,据此即可求得总人数,再求得A类总人数可得A类女生人数,由各类别人数之和为总人数可得D类人数;(2)根据以上所求数据即可补全图形;(3)利用列举法即可表示出各种情况,然后利用概率公式即可求解.【解答】解:(1)本次调查的学生数=(6+4)÷50%=20(名),则A类女生有:20×15%﹣1=2(名),D类学生有20﹣(3+10+5)=2(名),故答案为:20、2、2;(2)补全图形如下:(3)由题意画树形图如下:从树形图看出,所有可能出现的结果共有6种,且每种结果出现的可能性相等,所选一位女同学辅导一位男同学的结果共有2种.所以P(一位女同学辅导一位男同学)=26=13.【点评】本题考查了列表法或树状图法:通过列表法或树状图法展示所有等可能的结果求出n,再从中选出符合事件A或B的结果数目m,然后根据概率公式求出事件A或B 的概率.也考查了统计图.。
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1 完形填空 Late one night, a thief crept into a wealthy merchant’s house. He was a young thief, without experience. In fact, this was his first professional 1 . So he had 2 everything carefully. All went marvelously well at first. He found, as he _3 , an unlatched window and got into the room easily. But, stepping his way through the 4 room, he stubbed (碰到) his bare _5 against a table leg. Choking (抑制) back a cry of pain, terrified of waking the merchant, he hit _6 on the forehead and called himself a fool. He had _7 to bring a light. In the darkness, _8 , he was able to see an oil lamp on the table, and lit it, then he gave a _9 of relief. As he 10 the lamp, a small spider came out from under its 11 . “Thank you for saving my life,” said the spider. “Before he went to bed, the merchant set this lamp down on top of me so I couldn’t escape. If you hadn’t come along, I wouldn’t have 12 the night; 13 , I’d have extremely uncomfortable situation for a long time.” “You have saved a life and shown compassion (同情), ”the spider went on, 14 the impatient thief said he had not 15 to do so. “ 16 yet, you have done so without the 17 thought or hope of reward. You have gained more merits (优点) than you could possibly imagine.” “But you’re only a spider,” said the thief. “And you’re only a man.” said the spider. “My dear thief, when you understand that 18 is life, whether on eight legs or 19 , you will have understood much. Your deed, 20 , has got rid of the bad things from your heart. Go from here with a fresh spirit. And good luck to you.” The thief did so and never thought to steal again. 1. A. job B. mistake C. appearance D. finding 2. A. explained B. managed C. planned D. imagined 3. A. expected B. remembered C. reminded D. meant 4. A. dull B. dark C. sitting D. terrible 5. A. head B. shoulder C. hand D. toe 6. A. the merchant B. the spider C. the thief D. himself 7. A. remembered B. forgot C. avoided D. happened 8. A. however B. when C. so that D. but 9. A. applause B. cry C. sigh D. laugh 10. A. woke up B. laid down C. picked up D. turned over 11. A. base B. cap C. cover D. foot 12. A. spent B. lasted C. hated D. worried 13. A. in time B. however C. anyhow D. indeed 14. A. although B. so C. so that D. as if 15. A. said B. led C. cared D. intended 16. A. Better B. Worse C. Natural D. Lucky 17. A. hopeful B. least C. ordinary D. most 18. A. man B. spider C. life D. chance 19. A. three B. two C. a dozen D. a hundred 20. A. in no case B. at ease C. in any case D. without delay 2
阅读理解 阅读下列短文,从每题所给的四个选项(A、B、C和D)中,选出最佳选项,并在答题卡上将该项涂黑。 A When I was 11, I threw a glance into Dad’s lunch box and made the unexpected discovery that my mother still showed her love towards my father. The evidence, a napkin resting on top of the sandwiches packed in wax paper, was certain “Love you!” she had written on the napkin. “ Meat loaf for supper!” Mom penned all kinds of messages to Dad on those paper napkins, and he saved a whole pile of them. What embarrassed me as a kid has become a precious memory of my parents. It also started my own brand of lunch box notes. When my kids were young, I’d glue little drawings on their lunches. Lots of sketches(素描) of our dog, Max, along with smiling flowers. When they were teenagers, I’d copy words of wisdom from great people, Einstein, for example, or Bruce Springsteen. Then, my kids grew up making their own handwritten notes. And my husband writes me love notes on recycled paper, because he’s all about being green. Friends who know about my lunch box notes eagerly share stories of their own family traditions. So many focus on food. Maura’s mom always drew hearts on the shells of hard-boiled eggs. Melinda wrote messages on her kids’ bananas. We’re into the third generation of lunch box notes in our home. Whenever my 3-year-old grandson, Clayton, spends the night, he knows his lunch is going to have a napkin note from Grandma in the morning. Last week, I drew a picture of me, waving widely and shouting his name. He took one look at it and screamed, “ Where’s Grandpa?” I added a man in a clean shirt. “ You forgot his tie,” he said. I quickly drew a line of stripes(条纹) down the front of the shirt. Clayton smiled. “Grandpa,” he whispered, running his fingers across the napkin. “It’s you!” 21. When the author first saw Dad’s lunch box notes, she felt ______. A. moved B. awkward C. proud D. nervous 22. What did the author put in the lunch boxes when her kids were in their teens? A. Words of love. B. Pictures of flowers. C. Drawings of their favorite animals. D. Famous words of wisdom 23. It can be inferred that ________. A. the author’s grandson likes drawing pictures on napkins. B. the author’s children dislike making lunch box notes. C. the author’s husband is an environmentalist. D. the author’s friends all had their brand of lunch box notes. 24. What’s the best title for the text? A. Old generation’s way of expressing love. B. Different brands of lunch box notes. C. Lunches packed with love. D. Some interesting family traditions. B Living near the beach may come with an extra perk (利益): better health. A new study analyzed information from more than 48 million people in England and found that the nearer they lived to the coast, the more likely people were to report good health within the past year. Living near the coast may be associated with better health because the seaside environment reduces stress, the researchers said. They pointed to another British study that found that people