SSAT模考数学及答案

2024学年广东省华师附中新世界校中考数学模拟精编试卷注意事项：1．答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。

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回答非选择题时，将答案写在答题卡上，写在本试卷上无效。

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一、选择题（每小题只有一个正确答案，每小题3分，满分30分）1．31 的值是（）A．1 B．﹣1 C．3 D．﹣32．为了解某班学生每周做家务劳动的时间，某综合实践活动小组对该班9名学生进行了调查，有关数据如下表．则这9名学生每周做家务劳动的时间的众数及中位数分别是（）每周做家务的时间（小时）0 1 2 3 4人数（人） 2 2 3 1 1 A．3，2.5 B．1，2 C．3，3 D．2，23．某果园2011年水果产量为100吨，2013年水果产量为144吨，求该果园水果产量的年平均增长率．设该果园水果产量的年平均增长率为x，则根据题意可列方程为（）A．144（1﹣x）2=100 B．100（1﹣x）2=144 C．144（1+x）2=100 D．100（1+x）2=1444．下列计算正确的是()A．a2•a3＝a6B．(a2)3＝a6C．a2+a2＝a3D．a6÷a2＝a35．若（x﹣1）0＝1成立，则x的取值范围是（）A．x＝﹣1 B．x＝1 C．x≠0D．x≠16．已知正方形ABCD的边长为4cm，动点P从A出发，沿AD边以1cm/s的速度运动，动点Q从B出发，沿BC，CD边以2cm/s的速度运动，点P，Q同时出发，运动到点D均停止运动，设运动时间为x（秒），△BPQ的面积为y （cm2），则y与x之间的函数图象大致是（）A ．B ．C ．D ．7．有理数a ，b ，c ，d 在数轴上的对应点的位置如图所示，则正确的结论是（ ）A ．a ＞﹣4B ．bd ＞0C ．|a |＞|b |D ．b +c ＞08．如果340x y -=，那么代数式23()x y y x y-⋅+的值为（ ）A ．1B ．2C ．3D ．49．已知关于x 的一元二次方程（a+1）x 2+2bx+（a+1）=0有两个相等的实数根，下列判断正确的是（ ） A ．1一定不是关于x 的方程x 2+bx+a=0的根 B ．0一定不是关于x 的方程x 2+bx+a=0的根 C ．1和﹣1都是关于x 的方程x 2+bx+a=0的根 D ．1和﹣1不都是关于x 的方程x 2+bx+a=0的根 10．下列各式：①a 0=1 ②a 2·a 3=a 5 ③ 2–2= –14④–(3－5)＋(–2)4÷8×(–1)=0⑤x 2+x 2=2x 2，其中正确的是 ( ) A ．①②③B ．①③⑤C ．②③④D ．②④⑤二、填空题（共7小题，每小题3分，满分21分）11．如图，在△ABC 中，AB=AC ，以点C 为圆心，以CB 长为半径作圆弧，交AC 的延长线于点D ，连结BD ，若∠A=32°，则∠CDB 的大小为_____度．12．已知正比例函数的图像经过点M ( )、、，如果，那么________．（填“＞”、“＝”、“＜”）13．计算：（π﹣3）0﹣2-1=_____．14．如图，在平面直角坐标系中，以坐标原点O 为位似中心在y 轴的左侧将△OAB 缩小得到△OA′B′，若△OAB 与△OA′B′的相似比为2：1，则点B （3，﹣2）的对应点B′的坐标为_____．15．新定义[a ，b]为一次函数（其中a≠0，且a ，b 为实数）的“关联数”，若“关联数”[3，m+2]所对应的一次函数是正比例函数，则关于x 的方程的解为 ．16．从﹣1，2，3，﹣6这四个数中任选两数，分别记作m ，n ，那么点（m ，n ）在函数图象上的概率是 ．17．不等式组2012x x x -≤⎧⎪⎨-<⎪⎩的最大整数解是__________.三、解答题（共7小题，满分69分）18．（10分）如图,矩形ABCD 中,点P 是线段AD 上一动点, O 为BD 的中点, PO 的延长线交BC 于Q .(1)求证: OP OQ =;(2)若=8AD cm ,6AB cm =,P 从点A 出发,以l /cm s 的速度向D 运动(不与D 重合).设点P 运动时间为()t s ,请用t 表示PD 的长;并求t 为何值时,四边形PBQD 是菱形.19．（5分）如图1，三个正方形ABCD 、AEMN 、CEFG ，其中顶点D 、C 、G 在同一条直线上，点E 是BC 边上的动点，连结AC 、AM. （1）求证：△ACM ∽△ABE.（2）如图2，连结BD 、DM 、MF 、BF ，求证：四边形BFMD 是平行四边形.（3）若正方形ABCD 的面积为36，正方形CEFG 的面积为4，求五边形ABFMN 的面积.20．（8分）化简求值：212(1)211x x x x -÷-+++，其中31x =-．21．（10分）如图，M 、N 为山两侧的两个村庄，为了两村交通方便，根据国家的惠民政策，政府决定打一直线涵洞.工程人员为了计算工程量，必须计算M 、N 两点之间的直线距离，选择测量点A 、B 、C ，点B 、C 分别在AM 、AN 上，现测得AM=1千米、AN=1.8千米，AB=54米、BC=45米、AC=30米，求M 、N 两点之间的距离.22．（10分）已知a 2+2a=9，求22212321121a a a a a a a +++-÷+--+的值． 23．（12分） “扬州漆器”名扬天下，某网店专门销售某种品牌的漆器笔筒，成本为30元/件，每天销售量y （件）与销售单价x （元）之间存在一次函数关系，如图所示.（1）求y 与x 之间的函数关系式；（2）如果规定每天漆器笔筒的销售量不低于240件，当销售单价为多少元时，每天获取的利润最大，最大利润是多少？ （3）该网店店主热心公益事业，决定从每天的销售利润中捐出150元给希望工程，为了保证捐款后每天剩余利润不低于3600元，试确定该漆器笔筒销售单价的范围.24．（14分）已知抛物线y ＝ax 2+（3b +1）x +b ﹣3（a ＞0），若存在实数m ，使得点P （m ，m ）在该抛物线上，我们称点P （m ，m ）是这个抛物线上的一个“和谐点”． （1）当a ＝2，b ＝1时，求该抛物线的“和谐点”；（2）若对于任意实数b ，抛物线上恒有两个不同的“和谐点”A 、B ． ①求实数a 的取值范围； ②若点A ，B 关于直线y ＝﹣x ﹣（21a +1）对称，求实数b 的最小值． 参考答案一、选择题（每小题只有一个正确答案，每小题3分，满分30分） 1、B 【解题分析】直接利用立方根的定义化简得出答案． 【题目详解】 因为（-1）3=-1，﹣1．故选：B ． 【题目点拨】此题主要考查了立方根，正确把握立方根的定义是解题关键．, 2、D 【解题分析】试题解析：表中数据为从小到大排列．数据1小时出现了三次最多为众数；1处在第5位为中位数． 所以本题这组数据的中位数是1，众数是1． 故选D ．考点：1.众数；1.中位数. 3、D 【解题分析】试题分析：2013年的产量=2011年的产量×（1+年平均增长率）2，把相关数值代入即可． 解：2012年的产量为100（1+x ），2013年的产量为100（1+x ）（1+x ）=100（1+x ）2， 即所列的方程为100（1+x ）2=144， 故选D ．点评：考查列一元二次方程；得到2013年产量的等量关系是解决本题的关键． 4、B 【解题分析】试题解析：A.235,a a a ⋅=故错误. B.正确.C.不是同类项，不能合并，故错误.D.624.a a a ÷= 故选B.点睛：同底数幂相乘，底数不变,指数相加. 同底数幂相除，底数不变,指数相减. 5、D 【解题分析】试题解析：由题意可知：x-1≠0， x≠1 故选D. 6、B 【解题分析】根据题意，Q 点分别在BC 、CD 上运动时，形成不同的三角形，分别用x 表示即可. 【题目详解】 （1）当0≤x ≤2时， BQ ＝2x14242y x x =⨯⨯=当2≤x ≤4时，如下图()()()()211144448242428222y x x x x x x =-+⨯-⨯---⨯⨯-=-++由上可知 故选：B . 【题目点拨】本题是双动点问题，解答时要注意讨论动点在临界两侧时形成的不同图形，并要根据图形列出函数关系式. 7、C 【解题分析】根据数轴上点的位置关系，可得a ，b ，c ，d 的大小，根据有理数的运算，绝对值的性质，可得答案． 【题目详解】解：由数轴上点的位置，得 a ＜﹣4＜b ＜0＜c ＜1＜d ． A 、a ＜﹣4，故A 不符合题意； B 、bd ＜0，故B 不符合题意；C 、∵|a|＞4，|b|＜2，∴|a|＞|b|，故C 符合题意；D 、b+c ＜0，故D 不符合题意； 故选：C ． 【题目点拨】本题考查了有理数大小的比较、有理数的运算，绝对值的性质，熟练掌握相关的知识是解题的关键 8、A 【解题分析】先计算括号内分式的减法，再将除法转化为乘法，最后约分即可化简原式，继而将3x =4y 代入即可得． 【题目详解】解：∵原式=223x y y x y-•+ =()()3x y x y y x y +-•+=33x y y- ∵3x -4y =0， ∴3x =4y 原式=43y yy-=1 故选：A ． 【题目点拨】本题主要考查分式的化简求值，解题的关键是熟练掌握分式的混合运算顺序和运算法则． 9、D 【解题分析】根据方程有两个相等的实数根可得出b=a+1或b=-（a+1），当b=a+1时，-1是方程x 2+bx+a=0的根；当b=-（a+1）时，1是方程x 2+bx+a=0的根．再结合a+1≠-（a+1），可得出1和-1不都是关于x 的方程x 2+bx+a=0的根． 【题目详解】∵关于x 的一元二次方程（a+1）x 2+2bx+（a+1）=0有两个相等的实数根，∴()()2210{2410a b a +≠-+＝＝， ∴b=a+1或b=-（a+1）．当b=a+1时，有a-b+1=0，此时-1是方程x 2+bx+a=0的根； 当b=-（a+1）时，有a+b+1=0，此时1是方程x 2+bx+a=0的根． ∵a+1≠0， ∴a+1≠-（a+1），∴1和-1不都是关于x 的方程x 2+bx+a=0的根． 故选D ． 【题目点拨】本题考查了根的判别式以及一元二次方程的定义，牢记“当△=0时，方程有两个相等的实数根”是解题的关键． 10、D【解题分析】根据实数的运算法则即可一一判断求解. 【题目详解】①有理数的0次幂，当a=0时，a0=0；②为同底数幂相乘，底数不变，指数相加，正确；③中2–2= 14，原式错误；④为有理数的混合运算，正确；⑤为合并同类项，正确．故选D.二、填空题（共7小题，每小题3分，满分21分）11、1【解题分析】根据等腰三角形的性质以及三角形内角和定理在△ABC中可求得∠ACB=∠ABC=74°，根据等腰三角形的性质以及三角形外角的性质在△BCD中可求得∠CDB=∠CBD=12∠ACB=1°．【题目详解】∵AB=AC，∠A=32°，∴∠ABC=∠ACB=74°，又∵BC=DC，∴∠CDB=∠CBD=12∠ACB=1°，故答案为1．【题目点拨】本题主要考查等腰三角形的性质，三角形外角的性质，掌握等边对等角是解题的关键，注意三角形内角和定理的应用．12、>【解题分析】分析：根据正比例函数的图象经过点M（﹣1，1）可以求得该函数的解析式，然后根据正比例函数的性质即可解答本题．详解：设该正比例函数的解析式为y=kx，则1=﹣1k，得：k=﹣0.5，∴y=﹣0.5x．∵正比例函数的图象经过点A（x1，y1）、B（x1，y1），x1＜x1，∴y1＞y1．故答案为＞．点睛：本题考查了正比例函数图象上点的坐标特征，解答本题的关键是明确题意，利用正比例函数的性质解答．13、【解题分析】分别利用零指数幂a0=1（a≠0），负指数幂a-p=（a≠0）化简计算即可. 【题目详解】解：（π﹣3）0﹣2-1=1-=．故答案为：.【题目点拨】本题考查了零指数幂和负整数指数幂的运算，掌握运算法则是解题关键．14、（-32，1）【解题分析】根据如果位似变换是以原点为位似中心，相似比为k，那么位似图形对应点的坐标的比等于k或−k进行解答．【题目详解】解：∵以原点O为位似中心，相似比为：2：1，将△OAB缩小为△OA′B′，点B（3，−2）则点B（3，−2）的对应点B′的坐标为：（-32，1），故答案为（-32，1）．【题目点拨】本题考查了位似变换：位似图形与坐标，在平面直角坐标系中，如果位似变换是以原点为位似中心，相似比为k，那么位似图形对应点的坐标的比等于k或−k．15、.【解题分析】试题分析：根据“关联数”[3，m+2]所对应的一次函数是正比例函数，得到y=3x+m+2为正比例函数，即m+2=0，解得：m=-2，则分式方程为，去分母得：2-（x-1）=2（x-1），去括号得：2-x+1=2x-2，解得：x=，经检验x=是分式方程的解考点：1.一次函数的定义；2.解分式方程；3.正比例函数的定义．16、．【解题分析】试题分析：画树状图得：∵共有12种等可能的结果，点（m，n ）恰好在反比例函数图象上的有：（2，3），（﹣1，﹣6），（3，2），（﹣6，﹣1），∴点（m，n ）在函数图象上的概率是：=．故答案为．考点：反比例函数图象上点的坐标特征；列表法与树状图法．17、2【解题分析】先求出每个不等式的解集，再确定其公共解，得到不等式组的解集，然后求其整数解．【题目详解】解：2012xxx-≤⎧⎪⎨-<⎪⎩①②，由不等式①得x≤1，由不等式②得x＞-1，其解集是-1＜x≤1，所以整数解为0，1，1，则该不等式组的最大整数解是x=1．故答案为：1．【题目点拨】考查不等式组的解法及整数解的确定．求不等式组的解集，应遵循以下原则：同大取较大，同小取较小，小大大小中间找，大大小小解不了．三、解答题（共7小题，满分69分）18、(1)证明见解析；(2) PD=8-t，运动时间为74秒时，四边形PBQD是菱形．【解题分析】(1)先根据四边形ABCD是矩形，得出AD∥BC，∠PDO=∠QBO，再根据O为BD的中点得出△POD≌△QOB，即可证得OP=OQ ；(2)根据已知条件得出∠A 的度数，再根据AD=8cm ，AB=6cm ，得出BD 和OD 的长，再根据四边形PBQD 是菱形时，利用勾股定理即可求出t 的值，判断出四边形PBQD 是菱形．【题目详解】(1)∵四边形ABCD 是矩形，∴AD ∥BC ，∴∠PDO=∠QBO ，又∵O 为BD 的中点，∴OB=OD ，在△POD 与△QOB 中，PDO QBO OD OBPOD QOB ∠=∠⎧⎪=⎨⎪∠=∠⎩， ∴△POD ≌△QOB ，∴OP=OQ ；(2)PD=8-t ，∵四边形PBQD 是菱形，∴BP=PD= 8-t ，∵四边形ABCD 是矩形，∴∠A=90°，在Rt △ABP 中，由勾股定理得：AB 2+AP 2=BP 2，即62+t 2=(8-t)2，解得：t=74， 即运动时间为74秒时，四边形PBQD 是菱形． 【题目点拨】本题考查了矩形的性质，菱形的性质，全等三角形的判定与性质，勾股定理等，熟练掌握相关知识是解题关键.注意数形结合思想的运用.19、（1）证明见解析；（2）证明见解析；（3）74.【解题分析】(1)根据四边形ABCD 和四边形AEMN都是正方形得AB AC AC AM ==CAB=∠MAC=45°，∠BAE=∠CAM ，可证△ACM∽△ABE；（2）连结AC，由△ACM∽△ABE得∠ACM=∠B=90°，易证∠MCD=∠BDC=45°，得BD∥CM,由MC=2BE，FC=2CE，得MF=BD，从而可以证明四边形BFMD是平行四边形；（3）根据S五边形ABFMN=S正方形AEMN+S梯形ABFE+S三角形EFM求解即可.【题目详解】（1）证明：∵四边形ABCD和四边形AEMN都是正方形，∴12AB ACAC AM==，∠CAB=∠MAC=45°，∴∠CAB-∠CAE=∠MAC-∠CAE，∴∠BAE=∠CAM，∴△ACM∽△ABE.（2）证明：连结AC因为△ACM∽△ABE，则∠ACM=∠B=90°，因为∠ACB=∠ECF=45°，所以∠ACM+∠ACB+∠ECF=180°，所以点M,C,F在同一直线上，所以∠MCD=∠BDC=45°，所以BD平行MF，又因为2BE，2CE，所以2，所以四边形BFMD是平行四边形（3）S 五边形ABFMN =S 正方形AEMN +S 梯形ABFE +S 三角形EFM=62+42+12（2+6）⨯4+12 ⨯2⨯6 =74.【题目点拨】本题主要考查了正方形的性质的应用，解此题的关键是能正确作出辅助线，综合性比较强，有一定的难度． 20、33【解题分析】分析：先把小括号内的通分，按照分式的减法和分式除法法则进行化简，再把字母的值代入运算即可. 详解：原式2112,2111x x x x x x -+⎛⎫=÷- ⎪++++⎝⎭2112,211x x x x x -+-=÷+++ ()211,11x x x x -+=⋅-+ 1.1x =+ 当31x =时，131311x ==+-+ 点睛：考查分式的混合运算，掌握运算顺序是解题的关键.21、1.5千米【解题分析】先根据相似三角形的判定得出△ABC ∽△AMN,再利用相似三角形的性质解答即可【题目详解】在△ABC 与△AMN 中，305549AC AB ==，151.89AM AN ==，∴AC AM AB AN =，∵∠A=∠A ，∴△ABC ∽△ANM ， ∴AC AM BC MN =，即30145MN =，解得MN=1.5(千米) ，因此，M 、N 两点之间的直线距离是1.5千米.【题目点拨】此题考查相似三角形的应用，解题关键在于掌握运算法则22、22(1)a +，15． 【解题分析】试题分析：原式第二项利用除法法则变形，约分后两项通分并利用同分母分式的减法法则计算得到最简结果，把已知等式变形后代入计算即可求出值．试题解析：22212321121a a a a a a a +++-÷+--+=()()()()()211211112a a a a a a a -+-⨯++-++ =()21111a a a --++ =()221a +， ∵a 2+2a =9，∴（a +1）2=1．∴原式=21105=． 23、（1）10700y x =-+；（2）单价为46元时，利润最大为3840元.（3）单价的范围是45元到55元.【解题分析】（1）可用待定系数法来确定y 与x 之间的函数关系式；（2）根据利润=销售量×单件的利润，然后将（1）中的函数式代入其中，求出利润和销售单件之间的关系式，然后根据其性质来判断出最大利润；（3）首先得出w 与x 的函数关系式，进而利用所获利润等于3600元时，对应x 的值，根据增减性，求出x 的取值范围．【题目详解】（1）由题意得：4030055150k b k b +=⎧⎨+=⎩ 10700k b =-⎧⇒⎨=⎩．故y与x之间的函数关系式为：y=-10x+700，（2）由题意，得-10x+700≥240，解得x≤46，设利润为w=（x-30）•y=（x-30）（-10x+700），w=-10x2+1000x-21000=-10（x-50）2+4000，∵-10＜0，∴x＜50时，w随x的增大而增大，∴x=46时，w大=-10（46-50）2+4000=3840，答：当销售单价为46元时，每天获取的利润最大，最大利润是3840元；（3）w-150=-10x2+1000x-21000-150=3600，-10（x-50）2=-250，x-50=±5，x1=55，x2=45，如图所示，由图象得：当45≤x≤55时，捐款后每天剩余利润不低于3600元．【题目点拨】此题主要考查了二次函数的应用、一次函数的应用和一元二次方程的应用，利用函数增减性得出最值是解题关键，能从实际问题中抽象出二次函数模型是解答本题的重点和难点．24、（1）（11,22）或（﹣1，﹣1）；（1）①2＜a＜17②b的最小值是13【解题分析】（1）把x=y=m，a=1，b=1代入函数解析式，列出方程，通过解方程求得m的值即可；（1）抛物线上恒有两个不同的“和谐点”A、B．则关于m的方程m=am1+（3b+1）m+b-3的根的判别式△=9b1-4ab+11a．①令y=9b1-4ab+11a，对于任意实数b，均有y＞2，所以根据二次函数y=9b1-4ab+11的图象性质解答；②利用二次函数图象的对称性质解答即可．【题目详解】（1）当a ＝1，b ＝1时，m ＝1m 1+4m +1﹣4，解得m ＝12或m ＝﹣1． 所以点P 的坐标是（12，12）或（﹣1，﹣1）； （1）m ＝am 1+（3b +1）m +b ﹣3，△＝9b 1﹣4ab +11a ．①令y ＝9b 1﹣4ab +11a ，对于任意实数b ，均有y ＞2，也就是说抛物线y ＝9b 1﹣4ab +11的图象都在b 轴（横轴）上方． ∴△＝（﹣4a ）1﹣4×9×11a ＜2．∴2＜a ＜17．②由“和谐点”定义可设A （x 1，y 1），B （x 1，y 1），则x 1，x 1是ax 1+（3b +1）x +b ﹣3＝2的两不等实根，123122x x b a++=-． ∴线段AB 的中点坐标是：（﹣312b a +，﹣312b a +）．代入对称轴y ＝x ﹣（21a+1），得 ﹣312b a +＝312b a +﹣（21a+1）， ∴3b +1＝1a+a ． ∵a ＞2，1a ＞2，a •1a ＝1为定值， ∴3b +1＝1a +a 1a a＝1， ∴b ≥13． ∴b 的最小值是13． 【题目点拨】此题考查了二次函数综合题，其中涉及到了二次函数图象上点的坐标特征，抛物线与x 轴的交点，一元二次方程与二次函数解析式间的关系，二次函数图象的性质等知识点，难度较大，解题时，掌握“和谐点”的定义是解题的难点．。

2017年SSAT数学考试真题回顾做一定的SSAT数学真题可以帮助我们快速了解是否掌握这一知识点，下面为大家分享7道2017年SSAT数学考试真题，含答案及解题思路，正在为SSAT数学发愁的同学快来点击查看！1. Sue receives a base salary of $90 weekly plus a 12% commission on all sales. Sue had $3,000 in sales this week. How much did she make total?(苏收到每周90美元的基本工资加上所有销售额的12%的佣金。

苏这个星期有三千美元的销售额。

她总计可以拿多少钱?)A. $375B. $450C. $480D. $510E. $525答案：(B)解题思路：销售额*12%+基本工资=总工资2. If the perimeter of a rectangular house is 25feet, and the length is 22 feet. What is the width?(如果长方形房屋的周长为25英尺，长度为22英尺。

宽度是多少?)A. 16 feetB. 35 feetC. 37 feetD. 40 feetE. 42 feet答案：(A)解题思路：长方形周长=(长+宽)*23. Jimmy made a 15% profit on the sale of a custom designed boat, and the original cost of the boat was $15,000. The boat sold for how much?(吉米在出售一艘定制的船时赚了15%的利润，船的原始价格是15000美元。

船卖了多少钱?)A. $17,250.00B. $16,540.44C. $16,230.34D. $15,980.55E. $15,870.88答案：(A)解题思路：船的原始价格*15%=吉米的利润，吉米的利润+船原始价格=船出售的价格4. A recent study showed that an increase in body weight by 10 kilograms resulted in a 0.15% increase in heart disease. What fraction is equal to 0.15%?(最近的一项研究显示，体重增加10公斤导致心脏病增加了0.15%。

ssat数学练习题
SSAT数学练习题
1. 计算下列表达式的值：\( 3x^2 - 5x + 2 \) 当 \( x = 2 \) 时。

2. 一个矩形的长是宽的两倍，如果宽是10单位，那么矩形的周长是
多少？
3. 如果一个数的25%是50，那么这个数是多少？
4. 一个圆的直径是14厘米，求这个圆的面积。

5. 一个三角形的底边长是12厘米，高是6厘米，求这个三角形的面积。

6. 一个数列的前三项是2，4，8，这个数列的下一个数是什么？
7. 如果一个商品打8折后的价格是160美元，那么这个商品的原价是
多少？
8. 一个直角三角形的两条直角边分别是3厘米和4厘米，求这个三角
形的斜边长。

9. 一个班级有20个学生，其中15个学生喜欢数学，10个学生喜欢科学，5个学生既喜欢数学又喜欢科学，那么有多少学生不喜欢数学也不喜欢科学？
10. 一个数除以5的商是10，这个数是多少？
11. 一个长方形的面积是60平方厘米，长是15厘米，求这个长方形
的宽。

12. 如果一个数的三倍加上4等于26，那么这个数是多少？
13. 一个圆的周长是31.4厘米，求这个圆的半径。

14. 如果一个商品的原价是x美元，打9折后的价格是y美元，那么x 和y之间的关系是什么？
15. 一个等腰三角形的底边长是8厘米，两腰相等，如果这个三角形
的周长是24厘米，那么每条腰的长度是多少？
请在解答这些题目时，仔细阅读题目要求，并确保你的计算过程清晰准确。

2024年上海田家炳中学特色课程班中考第三次模拟数学试题一、单选题1．下列各数中，无理数是（ ）A ．211B ．3.14159CD ．1.2&2．下列多项式分解因式正确的是（ ）A ．()222a b a b -=-B ．()222a b a b +=+ C ．()22323a a a a +-=+- D ．()2422a a -=- 3．下列事件中，必然事件是（ ）A ．随机购买一张电影票，座位号恰好是偶数B ．抛掷一枚质地均匀的硬币，落地后反面朝上C ．在只装有2个黄球和3个白球的盒子中，摸出一个球是红球D ．在平面内画一个三角形，该三角形的内角和等于180︒4．在气象学上，每天在规定时段采集若干气温的平均数是当天的平均气温，连续5天的平均气温在10C ︒以上，这5天中的第1个平均气温大于10C ︒以上的日期即为春天的开始，那么下列表述正确的是（ ）A ．这5天中每天采集的若干气温中最高气温一定都大于10C ︒B ．这5天中每天采集的若干气温中最低气温一定都大于10C ︒C ．这5天中每天采集的若干气温的中位数一定都大于10C ︒D ．这5天中每天采集的若干气温的众数一定都大于10C ︒5．下列命题中，真命题是（ ）A ．对角线相等的四边形是平行四边形B ．对角线相等的平行四边形是矩形C ．对角线互相垂直的四边形是菱形D ．对角线互相垂直且相等的四边形是正方形6．如图，在平行四边形ABCD 中，对角线AC BD 、相交于点O ，过O 作AC 的垂线交AD 于点,E EC 与BD 相交于点F ，且ECD DBC ∠=∠，那么下列结论&&错误的是（ ）A ．EA EC =B ．DOC DCO ∠=∠ C ．4BD DF = D ．BC CD CE BF=二、填空题7．计算：()233a =．8．据国家航天局消息，航天科技集团所研制的天问一号探测器由长征五号运载火箭发射，并成功着陆于火星预选着陆区，距离地球320000000千米，其中320000000用科学记数法表示为．9x =的解为． 10．方程组22520x y x y ⎧+=⎨-=⎩的解是． 11．从1到10这十个自然数中抽取一个数，这个数是素数的概率是．12．《九章算术》中记载：“今有牛五、羊二，直金十九两．牛二、羊五，直金十六两．牛、羊各直金几何？”题目大意是：“5头牛、2只羊共值金19两，2头牛、5只羊共值金16两，每头牛、每只羊各值金多少两？”根据题意，设1头牛值金x 两，1只羊值金y 两，那么可列方程组为．13．一根蜡烛长30厘米，点燃后匀速燃烧，经过50分钟其长度恰为原长的一半．在燃烧的过程中，如果设蜡烛的长为y （厘米），燃烧的时间为t （分钟），那么y 关于t 的函数解析式为（不写定义域）．14．如图，在梯形ABCD 中，AD BC ∥，2BC AD =，点E 、F 分别是边AB 、CD 的中点，连接AC ，设AB a u u u r r =，AC b =u u u r r ，那么用向量a r 、b r 表示向量EF =u u u r ．15．已知两个半径都为4的A e 与B e 交于点C D 、，6CD =，那么圆心距AB 的长是． 16．如图，有一幅不完整的正多边形图案，小明量得图中一边与对角线的夹角15BAC ∠=︒，那么这个正多边形的中心角的余弦值是．17．如图，在ABC V 中，6AB AC ==，4BC =． 已知点D 是边AC 的中点，将ABC V 沿直线BD 翻折，点C 落在点E 处，联结AE ，那么AE 的长是．18．如图，在Rt ABC △中，90C ∠=︒，53AB BC ==，，以点C 为圆心作半径为1的圆C ，P 是AB 上的一个点，以P 为圆心，PB 为半径作圆P ，如果圆C 和圆P 有公共点，那么BP 的取值范围是．三、解答题1910212π-． 20．解方程组：222521x y x xy y +=⎧⎨-+=⎩ 21．阅读下面的材料：如果函数()y f x =满足：对于自变量x 的取值范围内的任意1x ，2x ，（1）若12x x <，都有12()()f x f x <，则称()f x 是增函数；（2）若12x x <，都有12()()f x f x >，则称()f x 是减函数．例题：证明函数6()(0)f x x x=>是减函数． 证明：设120x x <<，()()()21211212121266666x x x x f x f x x x x x x x ---=-==． ∵120x x <<，∴210x x ->，120x x >．∴()211260x x x x ->．即12())0(f x f x ->． ∴12()()f x f x >．∴函数6()(0)f x x x=>是减函数． 根据以上材料，解答下面的问题： 已知函数21()(0)f x x x x =+<， 21(1)(1)0(1)f -=+-=-，217(2)(2)(2)4f -=+-=-- （1）计算：()3f -= ，()4f -= ；（2）猜想：函数21()(0)f x x x x =+<是 函数（填“增”或“减”）； （3）请仿照例题证明你的猜想．22．某款“不倒翁”的主视图如图1，它由半圆O 和等边PAB V 组成，直径8cm AB =，半圆O 的中点为点C ，MN 为桌面，半圆O 与MN 相切于点Q ，拨动“不倒翁”后它在桌面MN 上做无滑动的滚动．(1)如图1，AB MN ∥，请直接写出PC 的长为______cm （结果保留根号）；(2)如图2，当PB MN ⊥时，连接OQ ，OC①直接写出∠COQ 的度数，并求点C 到桌面MN 的距离（结果保留根号）②当PA 或PB 垂直于MN 时“不倒翁”开始折返，直接写出从PB MN ⊥滚动到PA MN ⊥（图2-图3）过程中，点Q 在MN 上移动的距离．23．已知：如图，在菱形ABCD 中，点E 是边DC 上的任意一点（不与点D 、C 重合），AE 交对角线BD 于F ，过点E 作EG BC ∥交BD 于点G ．(1)求证：2=⋅DF FG BF ；(2)当2⋅=⋅BD DF AD DE 时，求证：AE DC ⊥．24．在平面直角坐标系xOy 中，抛物线23y ax bx =+-的图像与x 轴交于点(3,0)A -和点(1,0)B ．与y 轴交于点,C D 是线段OA 上一点．(1)求这条抛物线的表达式和点C 的坐标；(2)如图，过点D 作DG x ⊥轴，交该抛物线于点G ，当D G A D G C ∠=∠时，求GAC △的面积；(3)点P 为该抛物线上第三象限内一点，当1OD =，且45DCB PBC ∠+∠=︒时，求点P 的坐标．25．如图，已知半圆O 的直径为MN ，点A 在半径¼OM 上，B 为¼MN 的中点，点C 在»BN上，以AB 、BC 为邻边作矩形ABCD ，边CD 交MN 于点E ．(1)如果6MN =，2AM =，求边BC 的长；(2)连接CN ，当CEN V 是以CN 为腰的等腰三角形时，求BAN ∠的余切值；(3)连接DO 并延长，交AB 于点P ，如果2BP AP =，求BC AB的值．。

SSAT考试数学5套题+答案SSAT考试数学练习题(1)1. Add 0.98 + 45.102 + 32.3333 + 31 + 0.00009A. 368.573B. 210.536299C. 109.41539D. 99.9975E. 80.87695432. Find 0.12 ÷ 1A. 12B. 1.2C. .12D. .012E. .00123. (9 ÷ 3) x (8 ÷ 4) =A. 1B. 6C. 72D. 576E. 7524. 6 x 0 x 5A. 30B. 11C. 25D. 0E. 275. 7.95 ÷ 1.5A. 2.4B. 5.3C. 6.2D. 7.3E. 7.56. -32 + 7 equals:A. -25B. 25C. -26D. 26E. 277. -37 + -47 equals:A. 64B. -84C. 65D. -75E. -668. 41% equals:A. 4.1B. .41C. .041D. .0041E. .00415答案：1.B 2.C 3.B 4.0 5.B 6.A 7.B 8.B1. Round 907.457 to the nearest tens place.A. 908.0B. 910C. 907.5D. 900E. 907.462. At a certain high school, the respective weights for the following subjects are: Mathematics 3, English 3, History 2, Science 2 and Art 1.What is a student's average whose marks were the following: Geometry 89, American Literature 92, American History 94, Biology 81, and Sculpture 85?A. 85.7B. 87.8C. 88.9D. 89.4E. 90.23. Ginger over the course of an average work-week wanted to see how much she spent on lunch daily. On Monday and Thursday, she spent $5.43 total. On Tuesday and Wednesday, she spent $3.54 on each day. On Friday, she spent $7.89 on lunch. What was her average daily cost?A. $3.19B. $3.75C. $3.90D. $4.08E. $4.234. What is 1230.932567 rounded to the nearest hundredths place?A. 1200B. 1230.9326C. 1230.93D. 1230E. 1230.9335. Subtract the following numbers rounded to the nearesttenths place.134.679-45.548-67.8807A. 21.3B. 21.25C. -58.97D. -59.0E. 16. What is the absolute value of -9?A. -9B. 9C. 0D. -1E. 17. What is the median of the following list of numbers? 4, 5, 7, 9, 10, 12A. 6B. 7.5C. 7.8D. 8E. 98. What is the mathematical average of the number of weeks in a year, seasons in a year, and the number of days in January?A. 36B. 33C. 32D. 31E. 299. In a college, some courses contribute more towards anoverall GPA than other courses. For example, a science class is worth 4 points; mathematics is worth 3 points; history is worth 2 points; and English is worth 3 points. The values of the grade letters are as follows, A= 4, B=3, C=2, D=1, F=0. What is the GPA of a student who made a “C” in Trigonometry, a “B” in American History, an “A” in Botany, and a “B” in Microbiology?A. 2.59B. 2.86C. 3.08D. 3.33E. 3.6710. Over the course of a week, Fred spent $28.49 on lunch. What was the average cost per day?A. $4.07B. $3.57C. $6.51D. $2.93E. $5.4111. A roast was cooked at 325° F in the oven for 4 hours. The internal temperature rose from 32° F to 145° F. What was the average rise in temperature per hour?A. 20.2° F/hrB. 28.25° F/hrC. 32.03° F/hrD. 37° F/hrE. 37.29° F/hr12. In the number 743.25 which digit represents the tenths space?A. 2B. 3C. 4D. 5E. 6正确答案：1. B 2. C 3. D 4. C 5. A 6. B 7. D 8. E 9. C 10. A 11.B 12. AAnalogies 11. DRIP : GUSHA. cry : laughB. curl : rollC. stream : tributaryD. dent : destroyE. bend : angle2. WALK : LEGSA. blink : eyesB. chew : mouthC. dress : hemD. cover : bookE. grind : nose3. ENFRANCHISE : SLAVERYA. equation : mathematicsB. liberate : confineC. bondage : subjugationD. appeasement : unreasonableE. anatomy : physiology4. UNION JACK : VEXILLOLOGYA. toad : ornithologyB. turtle : microbiologyC. gymnosperms : botanyD. friend : home economicsE. algae : zoology5. TOPAZ : YELLOWA. diamond : caratB. jeweler : clarityC. sapphire : redD. amethyst : purpleE. amber : blue6. LUMEN : BRIGHTNESSA. candle : lightB. density : darknessC. nickel : metalD. inches : lengthE. color : hue7. MACERATION : LIQUIDA. sublimation : gasB. evaporation : humidityC. trail : pathD. erosion : weatherE. decision : distraction8. CLUMSY : BOTCHA. wicked :insinuateB. strict:pamperC. willful:heedD. clever:eradicateE. lazy:shirk9. FUGITIVE : FLEEA. parasite:fosterB. braggart:boastC. sage:stifleD. bystander:procureE. firebrand:quibble10. CHRONOLOGICAL : TIMEA. virtual:truthB. abnormal:valueC. marginal:knowledgeD. ordinal:placeE. coincidental:health11. SOOT : GRIMYA. frost:transparentB. sunshine:fruitlessC. rain:soddenD. pall:gaudyE. dust:radiant12. MORBID : UNFAVORABLEA. reputable:favorableB. maternal:unfavorableC. disputatious:favorableD. vigilant:unfavorableE. lax:favorable13. SULLEN : BROODA. lethargic:cavortB. regal:cringeC. docile: obeyE. despondent:laugh14. AUTHOR : LITERATEA. cynic:guillibleB. hothead:prudentC. saint:notoriousD. judge:impartialE. doctor:fallible15. MASSIVE : BULKA. ultimate:magnitudeB. trival:importanceC. anonymous:lusterD. interminable:legacyE. gigantic:size16. ENTICE : REPELA. germinate:sproutB. flourish:fadeC. officiate:presideD. lubricate:greaseE. implore:entreat17. HUMDRUM : BOREA. grim:amuseB. nutritious:sickenC. stodgy:exciteD. heartrending:moveE. pending:worry18. HOSPITABLE : COURTESYA. morbid:cheerfulnessB. vindictive:spiteC. leisurely:hasteD. infamous:honorE. despondent:glee19. REINFORCE : STRONGERA. abound: lesserB. dismantle: longerC. wilt: higherD. shirk: greaterE. erode: weaker20. BRAGGART : MODESTYA. fledgling:experienceB. embezzler: greedC. wallflower: timidityE. candidate:ambititonAnswer Key1. D2. B3. B4. C5. D6. D7. D8. E9. B10. D11. C12. A13. C14. D15. E16. B17. D18. B19. E20. ASSAT数学练习题(2)Algebra 2 Practice Questions1. If the average of three numbers is V. If one of the numbers is Z and another is Y, what is the remaining number?A. ZY - VB. Z/V - 3 - YC. Z/3 - V - YD. 3V- Z - YE. V- Z - Y2. Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?A. 2 hoursB. 4 ? hoursC. 5 ? hoursD. 6 hoursE. 7 ? hours3. Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ? hours. How quickly can all three fill the pool together?A. 12 minutesB. 15 minutesC. 21 minutesD. 23 minutesE. 28 minutes4. Mary is reviewing her algebra quiz. She has determined that one of her solutions is incorrect. Which one is it?A. 2x + 5 (x-1) = 9, x = 2B. p - 3(p-5) = 10, p = 2.5C. 4 y + 3 y = 28, y = 4D. 5 w + 6 w - 3w = 64, w = 8E. t - 2t - 3t = 32, t = 85. What simple interest rate will Susan need to secure to make $2,500 in interest on a $10,000 principal over 5 years?A. 4%B. 5%C. 6%D. 7%E. 8%6. Which of the following is not a rational number?A. -4B. 1/5C. 0.8333333...D. 0.45E.7. A study reported that in a random sampling of 100 women over the age of 35 showed that 8 of the women were married 2 or more times. Based on the study results, how many women in a group of 5,000 women over the age of 35 would likely be married 2 or more times?A. 55B. 150C. 200D. 400E. 6008. John is traveling to a meeting that is 28 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time?A. 25 mphB. 37 mphC. 41 mphD. 49 mphE. 56 mph9. If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?A. 2 minutes and 44 secondsB. 2 minutes and 58 secondsC. 3 minutes and 10 secondsD. 3 minutes and 26 secondsE. 4 minutes and 15 seconds10. If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam,Lisa, and Tom worked together to complete it?A. 0.8 daysB. 1.09 daysC. 1.23 daysD. 1.65 daysE. 1.97 days11. Jim has 5 pieces of string. He needs to choose the piece that will be able to go around his 36-inch waist. His belt broke, and his pants are falling down. The piece needs to be at least 4 inches longer than his waist so he can tie a knot in it, but it cannot be more that 6 inches longer so that the ends will not show from under his shirt. Which of the following pieces of string will work the best?A. 3 feetB. 3 ? feetC. 3 ? feetD. 3 ? feetE. 2 ? feet12. The last week of a month a car dealership sold 12 cars. A new sales promotion came out the first week of the next month and the sold 19 cars that week. What was the percent increase in sales from the last week of the previous month compared to the first week of the next month?A. 58%B. 119%C. 158%D. 175%E. 200%13. If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directlynorth at 150 mph and the other travels directly west at 200 mph?A. 50 milesB. 100 milesC. 500 milesD. 700 milesE. 1,000 miles14. During a 5-day festival, the number of visitors tripled each day. If the festival opened on a Thursday with 345 visitors, what was the attendance on that Sunday?A. 345B. 1,035C. 1,725D. 3,105E. 9,315Answer Key1. D2. B3. B4. E5. B6. E7. D8. E9. A10. B11. C12. A14. ESSAT数学练习题(3)SSAT Basic Algebra1. If Lynn can type a page in p minutes, what piece of the page can she do in 5 minutes?A. 5/pB. p - 5C. p + 5D. p/5E. 1- p + 52. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?A. 2 hours and 24 minutesB. 3 hours and 12 minutesC. 3 hours and 44 minutesD. 4 hours and 10 minutesE. 4 hours and 33 minutes3. Employees of a discount appliance store receive an additional 20% off of the lowest price on an item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally cost $450?A. $280.90B. $287C. $292.50D. $306E. $333.894. The sales price of a car is $12,590, which is 20% off the original price. What is the original price?A. $14,310.40B. $14,990.90C. $15,290.70D. $15,737.50E. $16,935.805. Solve the following equation for A : 2A/3 = 8 + 4AA. -2.4B. 2.4C. 1.3D. -1.3E. 06. If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue?B. 10C. 14D. 19E. 217. Alfred wants to invest $4,000 at 6% simple interest rate for5 years. How much interest will he receive?A. $240B. $480C. $720D. $960E. $1,2008. Jim is able to sell a hand-carved statue for $670 which wasa 35% profit over his cost. How much did the statue originally cost him?A. $496.30B. $512.40C. $555.40D. $574.90E. $588.209. The city council has decided to add a 0.3% tax on motel and hotel rooms. If a traveler spends the night in a motel roomthat costs $55 before taxes, how much will the city receive in taxes from him?A. 10 centsB. 11 centsC. 15 centsD. 17 centsE. 21 cents10. A student receives his grade report from a local community college, but the GPA is smudged. He took the following classes: a 2 hour credit art, a 3 hour credit history, a 4 hour credit science course, a 3 hour credit mathematics course, and a 1 hour science lab. He received a “B” in the art class, an “A” in the history class, a “C” in the science class, a “B” in the mathematics class, and an “A” in the science lab. What was his GPA if the letter grades are based on a 4 point scale? (A=4, B=3, C=2, D=1, F=0)A. 2.7B. 2.8C. 3.0D. 3.1E. 3.211. Simon arrived at work at 8:15 A.M. and left work at 10: 30 P.M. If Simon gets paid by the hour at a rate of $10 and time and ? for any hours worked over 8 in a day. How much did Simon get paid?A. $120.25B. $160.75C. $173.75D. $180E. $182.5012. Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?A. 4B. 8C. 12D. 13E. 1613. If r = 5 z then 15 z = 3 y, then r =A. yB. 2 yC. 5 yD. 10 yE. 15 y14. If 300 jellybeans cost you x dollars. How many jellybeans can you purchase for50 cents at the same rate?A. 150/xB. 150xC. 6xD. 1500/xE. 600x15. Lee worked 22 hours this week and made $132. If she works 15 hours next week at the same pay rate, how much will she make?A. $57B. $90C. $104D. $112E. $12216. If 8x + 5x + 2x + 4x = 114, the 5x + 3 =A. 12B. 25C. 33D. 47E. 8617. You need to purchase a textbook for nursing school. The book cost $80.00, and the sales tax where you are purchasing the book is 8.25%. You have $100. How much change will you receive back?A. $5.20B. $7.35C. $13.40D. $19.95E. $21.2518. You purchase a car making a down payment of $3,000 and 6 monthly payments of $225. How much have you paid so far for the car?A. $3225B. $4350C. $5375D. $6550E. $639819. Your supervisor instructs you to purchase 240 pens and 6 staplers for the nurse's station. Pens are purchased in sets of 6 for $2.35 per pack. Staplers are sold in sets of2 for 12.95. How much will purchasing these products cost?A. $132.85B. $145.75C. $162.90D. $225.25E. $226.7520. If y = 3, then y3(y3-y)=A. 300B. 459C. 648D. 999E. 1099参考答案1. A2. A3. D4. D5. A6. A7. E8. A9. D10. C11. C12. D13. A14. A15. B16. C17. C18. B19. A20. CSSAT模拟题11.How many cubed pieces of fudge that are 3 inches on an edge can be packed into a Christmas tin that is 9 inches deep by 12 inches wide by 8 inches high with the lid still being able to be closed?A. 18B. 24C. 32D. 36E. 432. Sarah is twice as old as her youngest brother. If the difference between their ages is15 years. How old is her youngest brother?A. 10B. 15C. 20D. 25E. 303. Which of the following fractions is equal to 5/6?A. 20/30B. 15/24C. 25/30D. 40/54E. 2/74. What will it cost to tile a kitchen floor that is 12 feet wide by 20 feet long if the tile cost $8.91 per square yard?A. $224.51B. $237.60C. $246.55E. $282.325. In a writing competition, the first place winner receives ? of the prize money. The second runner up receives ? of what the winner won. What was the total amount of prize money distributed if the winner receives $6,000?A. $6,000B. $8,500C. $12,000D. $15,000E. $18,5006. You are lying 120 ft away from a tree that is 50 feet tall. You look up at the top of the tree. Approximately how far is your hear from the top of the tree in a straight line?A. 50 feetB. 75 feetC. 120 feetD. 130 feetE. 150 feet7. A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist’s average rate for the round trip in miles per hour?A. 8.1B. 8.3C. 8.6D. 8.9E. 9.08 If edging cost $2.32 per 12-inch stone, and you want a double layer of edging your flower bed that is 6 yards by 1 yard. How much will edging you flower bed cost?B. $64.96C. $97.44D. $129.92E. $194.889. If 3x=6x-15 then x + 8=?A. 5B. 10C. 11D. 12E. 1310. The number of milliliters in 1 liter is?A. 10,000B. 1,000C. 0.1D. 0.01E. 0.001Answer Key1. (B)2. (B)3. (C)4. (B)5. (C)6. (D)7. (D)8. (E)9. (E) 10. (B) 11. (D)1. Sue receives a base salary of $90 weekly plus a 12% commission on all sales. Sue had $3,000 in sales this week. How much did she make total?B. $450C. $480D. $510E. $5252 If the perimeter of a rectangular house is 25 1/3 yards, and the length is 22 feet. What is the width?A. 16 feetB. 35 feetC. 37 feetD. 40 feetE. 42 feet3. Jimmy made a 15% profit on the sale of a custom designed boat, and the original cost of the boat was $15,000. The boat sold for how much?A. $17,250.00B. $16,540.44C. $16,230.34D. $15,980.55E. $15,870.884. A recent study showed that an increase in body weight by 10 kilograms resulted in a 0.15% increase in heart disease. What fraction is equal to 0.15%?A. 3/2000B. 2/750C. 7/4000D. 5/3462E. 1/5005. 6.334 x 104 =?A. 0.0006334B. 0.06334C. 6334D. 63340E. 6334006. If 3x + 5x = -8, then x + 1 =?A. -2B. -1C. 0D. 1E. 27. Two angle in a triangle equal 120°. What is the measure of the third angle?A. 60°B. 70°C. 80°D. 90°E. 120°8 Which of the following would be an appropriate unit to measure sugar for a cookie recipe?A. litersB. cupsC. quartsD. kilogramsE. poundsAnswer key1. (B)2. (A)3. (A)4. (A)5. (D)6. (C)7. (A)8. (B)1、What is the average (arithmetic mean) of 4x + 5, 7x-6,and -8x+2?A. x + 1B. x + 1/3C. 3x + 1D. 3x + 1/3E. 3x + 3 1/32、In a classroom of 35 students, 14 our male. What percent of the classroom is male?A. 14%B. 20%C. 30%D. 40%E. 50%3、If the area of a triangle is 24 and its base is 6, what is the length of the altitude to that base?A. 3B. 6C. 8D. 10E. unknown4、If Jeff and Jimmy have less than 22 dollars between them, and Jeff has 8 dollars, which of the following could be the number of dollars that Jimmy has?Ⅰ12Ⅱ14Ⅲ16B. III onlyC. I & III.D. I & IIE. Neither I, II, nor III is correct.5、Stephanie drove at an average rate of 50 miles per hour for two hours and then increased her average rate by 50% for the next 3 hours. Her average rate of speed for the 5 hours was t miles per hour. What is the value of t?A. 55 mphB. 60 mphC. 65 mphD. 70 mphE. 75 mph6、If 1 alpha = 2 betas and 1 beta = 3 gammas, how many alphas are equal to 36 gammas?A. 6B. 12C. 36D. 72E. 108SSAT模拟题21. There are 8 ounces in a 1/2 pound. How many ounces are in 7 3/4 lbs?A. 12 ouncesB. 86 ouncesC. 119 ouncesD. 124 ouncesE. 138 ounces2. If the value of x and y in the following fraction are both tripled, how does the value of the fraction change? XZ YA. increases by halfB. decreases by halfC. triplesD. doublesE. remains the same3. Which of the following fractions is the equivalent of 0.5%。

SSATLower Level Math Practice Test 1SECTION1Time – 30 Minutes25 QuestionsEach problem in this section contains five suggested answers. Work out the problem in your head or in the space provided at the right side of the page. Then choose the best answer.Sample Question:300 –550 =(B)(C) (D)(E) (A) 250350850-250-850ANSWER: D1. 10 + 15 – 24 = USE THIS SPACE FOR FIGURING .(A) 0(B) 1(C) 2(D) 3(E) 42. What is the perimeter of the square shown in Figure 1? (D) 8(E) 12Figure 1Ivy Globalhttp://www.ivyglobal.ca EDUCATION CONSULTINGSSATLower Level Math Practice Test 23. How many odd numbers are there between the USE THIS SPACE FOR FIGURING .numbers 0 and 10?(A) 3(B) 4(C) 5(D) 6(E) 74. Which of the following sets of numbers is in theright order, from smallest to largest?(A) 1, 2, 2.5, 3, -5(B) 1, 3.1, 2, 4, 5(C) -1, 0, 4, -6, 8(D) 1, 2, 0.3, 0.4, 0.5(E) 3, 5, 7, 9, 9.15. Sam had 3 van models, 4 truck models, and 6 racecarmodels. Today, his father gave him one model of eachtype. How many models does he have in his collectionnow?(A) 16(B) 17(C) 18(D) 196. If the polygon in Figure 2 is equal-sided and its perimeteris 24, what is the length of each side?(A) 3(B) 3.5(C) 4(D) 4.5(E) 5Ivy Global EDUCATION CONSULTING Figure 2http://www.ivyglobal.caSSATLower Level Math Practice Test 37 . According to the graph in Figure 3, howmany more TV’s did Jack sell in 2005than in 2003?(A) 0(B) 3(C) 5(D) 7(E) 20USE THIS SPACE FOR FIGURING .2181614121Jack's Annual TV Sales2002 2003 2004 2005 2006 2007Figure 38 . If a number is subtracted by 5, the difference is 1.If the same number is divided by 2, the answer is?(A) 0(B) 1(C) 2(D) 3(E) 49 . Sarah divides her $8 snack money to be spent equallybetween candies, chocolates, and potato chips. About how much will she spend on potato chips?(A) $1.00Ivy Global(B) $1.50(C) $2.30(D) $2.50(E) $2.70 Ivy GlobalSSATLower Level Math Practice Test 41+3 +5 +710. = USE THIS SPACE FOR FIGURING.10−5−3−1(A) 9(B) 16(C) 17(D) 18(E) 2011. What is the value of x, shown in Figure 4?(A) 45o(B) 50o(C) 55o(D) 60o(E) 65 oFigure 4112. Which of the following fractions is closest to ?2(A)(B)(C) (D)XIvy Global3 6 5 8919202 (E) 13Ivy GlobalSSATLower Level Math Practice Test 513. If 20 + 15 – ! = 40, then ! =(A) 0(B) 5(C) -5(D) 10(E) - 10USE THIS SPACE FOR FIGURING .14. Which number comes next in the sequence of1, 4, 9, 16?(A) 17(B) 19(C) 23(D) 24(E) 25Questions 15 – 17 refer to the graph in Figure 5.15. What is the average amount the baseball teamraised per quarter?(A) $30(B) $40(E) $6016. How much did all threeteams raise for the 4thquarter in total?(A) $75(D) $100(E) $150Ivy Global EDUCATION CONSULTINGValley HighFundraising1st Qtr2nd Qtr3rd Qtr4th Qtr20 40 60DollarsRaisedFigure 5http://www.ivyglobal.caBaseballH ockeyBasketbal80 100SSAT Lower Level Math Practice Test 617. During which quarter did the teams raised the most USE THIS SPACE FOR FIGURING . funds together?(A) First(B) Second(C) Third(D) Fourth(E) Not enough information givenA + B18 . If A♠B = , then ♠6 =A −B 5(A) 5(B) - 1(C) 0(D) 11(E) - 1 119. Which of the following figures CANNOT be drawnwithout lifting the pencil or retracing?(A) (B)Ivy Global(C) (D)(E) None of the aboveIvy GlobalSSATLower Level Math Practice Test 7USE THIS SPACE FOR FIGURING20. If (M + N) × 4 = 28 and both M and N are non-zero whole numbers, then M could NOT be(A) 1(B) 3(C) 5(D) 7(E) Not enough information given21. What is the eighth term in the sequence0, 1, 1, 2, 3, 5, …?(A) 13(B) 21(C) 34(D) 55(E) 8922. At the Fantastic Zoo, the ratio of tigers to leopardsis 5 to 1. Which of the following could NOT bethe total number of tigers and leopards at the zoo?(A) 6(B) 16(C) 18(D) 36Ivy Global(E) 60Ivy GlobalSSATLower Level Math Practice Test 8USE THIS SPACE FOR FIGURING .5A3× 10152, 82323. In the multiplication problem above, A representswhich digit?(A) 0(B) 1(C) 2(D) 4(E) 624. To which of the following is 1.23 closest?(A) 12.0(B) 120(C) 1.2(D) 1.25(E) 1.2225. Two people can paint two houses in three days.How many people are needed to paint three housesin three days?Ivy Global(A) 1.5(B) 2(C) 2.5(D) 3(E) 4STOPIF YOU FINISH BEFORE THE ALLOTED TIMEYOU MAY CHECK YOUR ANSWERS ONLY FOR THIS SECTIONDO NOT TURN TO OTHER SECTIONS OF THIS TEST Ivy GlobalSSAT Lower Level Math Practice Test 9SECTION2Time – 30 Minutes25 QuestionsEach problem in this section contains five suggested answers. Work out the problem in your head or in the space provided at the right side of the page. Then choose the best answer.Sample Question:25 × 8 ÷10 = (B)(C)(D)(E) (A) 2025301902000ANSWER: A1. If 2000 + 5000 + ♦ = 7,040, then ♦ = USE THIS SPACE FOR FIGURING .(A) 4(B) 40(C) 400(D) 6740(E) 70302. Which of the following is an odd integer that liesbetween 51 and 56?(B) 51(C) 52(D) 53(E) 54Ivy Globalhttp://www.ivyglobal.ca EDUCATION CONSULTINGSSAT Lower Level Math Practice Test 10 3. Each person contributed to the sameamount towards a lottery ticket. If theticket cost $100, what cannot be theamount that each gave?(A) $5(B) $10(C) $15(D) $20(E) $25USE THIS SPACE FOR FIGURING .4. What is the area of the triangle shown in Figure1?(A) 3.5(B) 7(C) 9(D) 14(E) 28 72 Figure 15. (110 – 90) ÷ 4 =(A) 2.5(B) 4(C) 5(D) 20(E) 24Ivy Global6. The perimeter of a square with an area of 64 is(A) 80(B) 64(C) 48(D) 40(E) 32Ivy GlobalSSAT Lower Level Math Practice Test 117. An airplane with a capacity of 200 passengers has68 percent of its seats filled. What is the numberof passengers?(A) 34(B) 68(C) 106(D) 136(E) 168USE THIS SPACE FOR FIGURING .8. What is the next number in the sequence of1, 3, 5, 7, …?(A) 2(B) 4(C) 5(D) 6(E) 99 . According to the graph in Figure 2, how muchdid the drama club spend on costumes?(A) $20(B) $25(C) $35(D) $45(E) $504321HOW THE DRAMA CLUB SPENT ITSBUDGETCostumesAudioVi plieDecorations10. If K = 17, then 1 less than 3 × K is equal to(A) 50(B) 47(C) 33(D) 19(E) 16Ivy Globalhttp://www.ivyglobal.ca EDUCATION CONSULTINGSSAT Lower Level Math Practice Test 1211. Which of the following statements is NOT true?(A) 10 < 15 and 1.2 < 1.25(B) 0.3 < 0.333 and 51 > 0.511(C) 0.25 = 1 ÷ 4 and 3.1 < 30(D) - 12 < 1 and -45 > -56(E) None of the aboveUSE THIS SPACE FOR FIGURING .12. 20 percent of $100 is equal to(A) 15% of $150(B) 25% of $90(C) 30% of $60(D) 40% of $50(E) 50% of $35Questions 13 – 15 refers to Figure 313. How many different paths are there from A to B,that takes on a distance of 7.5?(A) 1(B) 2(C) 3(D) 4(E) 5 14.Harryisinahurry. He wants to travel a path fromA toB that is shorter than 7.5.How many choicesdoes he have?AIvy GlobalIvy GlobalFigure 3B(A) 4 (B) 3 (C) 2 (D) 1 (E) 04433.564SSAT Lower Level Math Practice Test 13USE THIS SPACE FOR FIGURING .15. John wants to start from A, travel all thepaths exactly once, then come back to A.How much distance will he need to travel?(A) 29(B) 30.5(C) 32(D) Not enough information isgiven. (E) It is impossible to do.16. Cindy bought a dress at 50% discount off the saleprice, which is already $20 off the regular price.She paid $35. How much was the regular price ofthe dress?(A) $30(B) $50(C) $70(D) $90(E) $11017. If an empty wine glass is placed up-side down, as(C) (D)shown in Figure 4, which of the following describesall the points where the glass touches the table?(A) (B)(E)Ivy GlobalEDUCATION CONSULTINGFigure 4http://www.ivyglobal.caSSAT Lower Level Math Practice Test 14USE THIS SPACE FOR FIGURING .18. If x ♫y = x × (x ÷ y), then 3 ♫ 2 =(A) 2.5(B) 3(C) 4.5(D) 5(E) 6.519. Of the following, 33% of $9.95 is closest to(A) $3.15(B) $3.30(C) $3.45(D) $3.50(E) $3.6020. A polygon has perimeter of 84 and the average lengthis 7. How many sides does the polygon have?(A) 1 1(B) 12(C) 13(D) 91(E) 588Ivy Global21. A person started at point A. He traveled 2km north,2km east, 2km south, and 3km west. How far is he from where he started?(A) 1km north(B) 3km west(C) 2km south(D) 1km east(E) 1km westIvy GlobalSSAT Lower Level Math Practice Test 1522. Cities X and Y are separated by a distance of20km. Jim left City X and biked the first half ofthis distance at a speed of 10km/hour, then hewalked the rest of the distance. If Jim took 3hours to travel from X to Y, how fast does hewalk?(A) 3.3km/hour(B) 5km/hour(C) 6.7km/hour(D) 10km/hour(E) Not enough information givenUSE THIS SPACE FOR FIGURING .23. In Figure 5, what is the area of theUNSHADED region, ifDFGH is a square?(A) 8(B) 12(C) 16(D) 24(E) 28 444 4Figure 524. If f+ g is divisible by 9, which of the following mustalso be divisible by 9?(A) (7 × f) + (7 × g)(B) 9 + (f × g)Ivy Global(C) f+ g ÷ 9(D) 8 × (f+ g) + 1(E) (f+ g) ÷ 9 Ivy GlobalSSATLower Level Math Practice Test 1625. How many numbers can be found between thenumbers 1 and 100 that contains the digit 3? USE THIS SPACE FOR FIGURING .(A) 10(B) 1 1(C) 19(D) 20(E) 21Ivy GlobalSTOPIF YOU FINISH BEFORE THE ALLOTED TIMEYOU MAY CHECK YOUR ANSWERS ONLY FOR THIS SECTIONDO NOT TURN TO OTHER SECTIONS OF THIS TEST Ivy Global。

SSAT数学考试真题练习（含答案）SSAT为美国中学入学考试，适用于美国、加拿大私立中学的入学，下面为广大正在备考的考生整理了6道SSAT 数学考试真题，并提供了答案，具体详情如下：1.Jamee is five years older than Rachel. In 15 years, their combined ages will be 45. How old is Jamee right now?(A) 5(B) 10(C) 20(D) 25(E) 45答案：B2. If X + = 29，then X =(A) 41(B) 27(C) 17(D)-17(E)-41答案：C3. The paperboy needs to deliver 30 sacks of newspapers to the houses in hisneighborhood. If each sack weighs the same amount, and the total weight ofhis load is 150 pounds when he leaves his house, what is the weight of his loadafter he delivers 15 of the sacks?(A)115 pounds(B)105 pounds(C)75 pounds(D)65 pounds(E)50 pounds答案：C4. The average of five consecutive whole numbers is 18. What is the smallest ofthese numbers?(A) 14(B) 15(C) 16(D) 17(E) 18答案：C5. The least common multiple of 8, 5, and 12 is:A: 100B: 90C: 135D: 120答案：D6. The town of Cedar Hill has 750 television sets. If there are 1.5 television setsfor each person, what is the population of Cedar Hill?A: 1100B: 1125C: 500D: 1000答案：C如何更加快速有效的搞定SSAT数学题目，不妨看看我们整理的SSAT数学解题策略：一、需要明白题目的英文表述。

SSAT模考试题预览说明:预览图片所展示的格式为文档的源格式展示,下载源文件没有水印,内容可编辑和复制模拟试题130分钟60题Section 1 Analogies1. Abstruse is to comprehension asA wholesome is to healthB indiscernible is to visionC articulate is to speechD convoluted is to zealE voracious is to gorge2. Obstruct is to progress asA yearn is to warfareB assuage is to pleasureC stunt is to growthD wrinkle is to skinE warp is to gift3. Abate is to force asA update is to softwareB unearth is to fragranceC forecast is to weatherD annoy is to alcoholE attenuate is to thickness4. Author is to novel asA wrongdoer is to aircraftB outlaw is to shotgunC virtuoso is to pianoD sculptor is to statueE vocalist is to anthem5. Cloth is to tabletop asA yarn is to oasisB saw is to scarfC lathe is to assembling lineD curtain is to windowE framework is to building6. Constellation is to star asA word is to sentenceB dam is to riverC archipelago is to islandD boulder is to marbleE graphite is to granite7. Pilot is to airplane as (Kaplan P180 31-39)A team is to playersB horse is to cartC captain is to shipD passenger is to trainE army is to country8. Snake is to python as dog is toA terrierB canineC petD mammalE quadruped9. Mayor is to city asA governor is to stateB member is to unionC board is to districtD secretary is to committeeE citizen is to legislature10. Paper is to novel asA person is to pollB paint is to brushC canvas is to portraitD back is to chairE color is to palette11. Refined is to vulgar asA calm is to placidB submissive is to recalcitrantC happy is to ecstaticD helpful is to victoriousE tranquil is to forgivable12. Whip is to lash asA stick is to throwB shoe is to walkC saddle is to sitD food is to eatE club is to beat13. Migrate is to swallow asA hibernate is to ground hogB pet is to dogC reproduce is to fishD sting is to beeE pounce is to cat14. Weather is to meteorologist as vegetation is toA driverB artistC oceanographerD hunterE botanist15. Track is to horse racing asA circus is to elephantB court is to tennisC net is to basketballD goal is to footballE air is to bird16. Digress is to topic asA detour is to routeB repatriate is to metropolisC surmount is to glacierD impulse is to journeyE amuse is to nightmare17. Insomnia is to sleep asA aroma is to anvilB fervor is to hallucinationC acrophobia is to heightD amnesia is to memoryE dyslexia is to hearing18. Subtle is to ignore asA wry is to abjectB vivid is to perishC fugacious is to disappearD avaricious is to accommodateE fallacious is to flee19. Mentor is to guide as supervisor is toA contrastB disturbC overseeD competeE perpetrate20. Illuminate is to darkness asA precede is to pollB educate is to ignoranceC intend is to embezzlementD misjudge is to reservoirE exult is to jingoism21. Chorus is to sing as troupe is toA performB irkC outrageD ireE rasp22. Inflate is to balloon asA pirate is to conservatoryB proliferate is to numberC constrict is to syllabusD vex is to vehicleE impel is to puzzle23. Marsh is to sodden asA insulin is to innateB desert is to aridC peninsula is to nonporousD islet is to normalE mortar is to frozen24. Milk is to protein as juice is toA offspringB oysterC toxinD peelE vitamin25. Smile is to pleasure as blush is toA shrugB petroleumC deityD embarrassmentE anguish26. Liar is to honesty asA gangster is to optimismB fanatic is to abhorrenceC coward is to intrepidD prodigal is to renownedE pest is to ungenerous27. Fragile is to break as inflammable is toA accoladeB occludeC burnD supplantE tarnish28. Apathetic is to emotion asA susceptible is to exclaimB imprudent is to discretionC implausible is to platterD baleful is to omenE obsolete is to narcissism29. Sterile is to bacteria asA enigmatic is to mythsB nonchalant is to benchesC sloppy is to beamsD unscrupulous is to brooksE impeccable is to flaws30. Accrete is to reside asA conspire is to plotB coerce is to murmurC comfort is to mutterD compress is to underscoreE compute is to ascend Section 2 Synonyms31. CONTRADICTA opposeB placateC creditD alterE assume32. BENEFITA affectionB diversityC antipathyD rigidityE advantage33. DETRAACTA convictB refineC concealD diminishE conflict34. PONDERA deliberateB resolveC compromiseD denyE resist35. FLEETINGA speedyB ephemeralC impartialD controversialE redundant36. FRANKA tortuousB straightforwardC superficialD insensitiveE esteemed 37. HOSTILITYA amateurB generosityC exaggerationD animosityE ambiguity38. CULTIV ATEA mollifyB fosterC ignoreD alleviateE acknowledge39. BLAMEA complimentB advocateC adhereD rejectE condemn40. DEHYDRATEA contemptB disperseC desiccateD confrontE undermine41. ALIAS (p288 1-10)A formal relationshipB assumed nameC blatant falsehoodD presumed locationE deep emotion42. PHOBIAA illuminationB retractionC anxietyD heightE dismissal43. PROPELA intendB belieC flyD projectE repel44. HEADSTRONGA foreignB delicateC stubbornD uselessE hysterical45. CODDLEA babyB waddleC carryD riddleE assume46. KEENA sharpB niceC forgivingD denseE rotund47. MURKYA religiousB mustyC sentimentalD gloomyE forgetful48. TRYINGA impossibleB strenuousC easyD weatheredE morose 49. ADHERE A connectB alterC stickD listenE complete50. ENIGMATICA attractiveB confusedC happyD mysteriousE unfortunate51. IMMINENT (p243 25-15)A intenseB impressiveC properD observableE forthcoming52. DEXTERITYA secrecyB equalityC reserveD nimblenessE determination53. GREGARIOUSA sloppyB sociableC happyD intelligentE talented54. CATASTROPHEA illusionB disasterC indicationD warningE estimate55. CONVENEA clarifyB serveC assembleD electE dignify56. CANDORA majestyB daringC honestyD perceptionE fatigue57. MARVELA discardB usurpC confuseD pointE wonder 58. BREVITYA ambitionB consistencyC conflictD imaginationE shortness59. LUNGEA pursueB turnC thrustD restoreE startle60. CAMOUFLAGEA obstacleB rangeC emergencyD disguiseE amount模拟试题230分钟60题Section 1 Analogies1. Stutter is to talk asA glitter is to lollB giggle is to milkC vaccinate is to revokeD stagger is to walkE babble is to trace2. Crease is to folding asA slack is to braveryB modulate is to epithetC perforate is to holeD exorcise is to symbolE boost is to vagary3. Stride is to mince asA bury is to interB gorge is to nibbleC impoverish is to obstructD strive is to railE sip is to gormandize4. Scribble is to write asA chuckle is to evacuateB dazzle is to feignC barter is to persecuteD mumble is to speakE malinger is to attend5. Fear is to phobia asA fond is to maniaB levy is to dyspepsiaC dog is to cynophobiaD eclipse is to tuberculosisE blockade is to measles6. Creek is to river asA envelop is to torqueB hurricane is to tornadoC slipper is to lizardD threat is to libertineE pebble is to landslide7. Harsh is to sound asA brazen is to etiquetteB minuscule is to odorC glaring is to lightD nautical is to tasteE nocturnal is to ellipse8. Mercurial is to mood asA prolix is to griefB impromptu is to paymentC versatile is to temperamentD venal is to greenhouseE variable is to consolidation9. Antibiotic is to infection asA artifice is to summaryB encyclopedia is to knowledgeC coagulant is to bleedingD astringent is to stitchE laxative is to profusion10. Spurious is to authenticity as (Kaplan P247 60-)A lavish is to expenseB abject is to subjectivityC affluent is to characterD laughable is to seriousnessE totalitarian is to completeness11. Philanthropic is to benevolence asA smooth is to surfaceB ostentatious is to reserveC miserly is to stinginessD devout is to maliceE realistic is to plan12. Auditorium is to lecture asA theater is to concertB attic is to storageC temple is to religionD cafeteria is to foodE target is to arrow13. Amplify is to sound as bolster is toA smellB courageC insomniaD lightE silence14. Ravenous is to hunger asA pliable is to obstinacyB agitated is to placidityC concerned is to apathyD smart is to tenacityE furious is to indignation15. Tact is to diplomat asA parsimony is to philanthropistB agility is to gymnastC vulnerability is to victimD training is to physicianE bias is to judge16. Illegible is to read asA invisible is to seeB illegal is to actC broken is to fixD irreparable is to breakE intense is to strain17. Irk is to soothing as support is toA conciliatingB elevatingC underminingD irritatingE vilifying18. Nose is to olfactory as ear is toA beautifulB edibleC auditoryD raspyE allergic19. Building is to foundation as plant is toA paneB grottoC primerD floorE root20. Contempt is to sneer asA shame is to shrugB anger is to laughC enjoyment is to groanD agreement is to grimaceE displeasure is to frown21. Electricity is to wire asA sound is to radioB water is to aqueductC music is to instrumentD light is to bulbE river is to bank22. Irrigate is to dry asA soften is to unevenB smooth is to coarseC purify is to distastefulD depend is to supportiveE ferment is to salty23. Jar is to contain as pillar is toA standB ascentC prepareD supportE swingA bat is to wingB horse is to tailC skunk is to odorD oyster is to pearlE tiger is to stripe25. Weight is to scale asA distance is to speedometerB number is to slide rule(计算尺)C length is to thermometerD reading is to gaugeE altitude is to altimeter26. Ore is to mine asA apple is to peelB water is to purifyC batter is to stirD grain is to plowE oil is to drill27. Milk is to sour as bread is toA bentB staleC foldedD bakedE hot28. Canal is to river asA boat is to driftwoodB puddle is to lakeC hammer is to malletD mine is to cavernE telephone is to computerA miter is to popeB bench is to judgeC lobby is to doormanD armchair is to generalE ship is to captain30. Cartographer is to map as chef is toA flowerB silverwareC tableD mealE ingredientSection 2 Synonyms31. DISTINCTA austereB indifferentC awkwardD cynicalE discrete32. HINDERA impedeB challengeC disputeD embellishE enervate33. VERIFYA devoteB modifyC overlookD confirmE devour34. TACITURNA volatileB reticentC loquaciousD randomE garrulous35. PARDONA restoreB gratitudeC provokeD condoneE evaluate36. QUESTIONINGA subtleB unbelievableC anomalousD pragmaticE skeptical 37. ENHANCEA augmentB suppressC minimizeD repudiateE antagonize38. FOCUSA arbitrateB forgeC promoteD avoidE concentrate39. SOLITARYA mindfulB carelessC friendlyD aloneE troubled40. ANTIDOTEA fantasyB remedyC substituteD awardE decoration41. RETARDA turn aroundB push apartC slow downD change positionE see through42. TUMULTA annoyanceB commotionC insignificanceD disagreementE blockage43. SUMMITA plateauB landscapeC slopeD islandE peak44. RANSACKA search thoroughlyB act quicklyC cover completelyD make secureE denounce publicly45. SEVEREA frozenB extremeC longD limitedE essential46. QUENCHA completeB compareC demeanD satisfyE withdraw47. EXPUNGE (p 179 30-24)A eraseB handleC labelD assaultE keep48. TERMINATEA extendB renewC finalizeD sellE end 49. LIMBERB rejectC founderD dominateE deserve50. DINA outlineB clamorC improvementD demonstrationE pressure51. ADAGEA permissionB disdainC humorD preventionE proverb52. CAPRICEA ideaB mistakeC whimD decisionE guess53. LIMPIDA plausibleB essentialC lucidD malleableE meticulous54. GULLB swindleC demonstrateD disparageE bolster55. CONCISEA lethargicB stygianC ambidextrousD conspicuousE laconic56. PRAISEA benevolenceB confusionC simplicityD approbationE aversion57. V AGUEA unsophisticatedB spontaneousC sporadicD transparentE dim58. PLACATEA contestB patterC betrayD consoleE constitute59. SUFFOCATEA give instructionB pull outC make willingD surround completelyE deprive of air60. AGHASTA shockedB swollenC irritatedD nastyE rude。

上海市杨思高中2025届高三下学期一模考试数学试题注意事项1．考生要认真填写考场号和座位序号。

2．试题所有答案必须填涂或书写在答题卡上，在试卷上作答无效。

第一部分必须用2B 铅笔作答；第二部分必须用黑色字迹的签字笔作答。

3．考试结束后，考生须将试卷和答题卡放在桌面上，待监考员收回。

一、选择题：本题共12小题，每小题5分，共60分。

在每小题给出的四个选项中，只有一项是符合题目要求的。

1．已知某几何体的三视图如右图所示，则该几何体的体积为（ ）A ．3B ．103C ．113D ．832．已知点(m ,8)在幂函数()(1)n f x m x =-的图象上，设,(ln ),()m a f b f c f n n π⎛⎫=== ⎪⎝⎭，则（ ） A ．b ＜a ＜c B ．a ＜b ＜cC ．b ＜c ＜aD ．a ＜c ＜b3．设复数z 满足i(i i2i z z -=-为虚数单位)，则z =（ ） A ．13i 22- B ．13i 22+ C ．13i 22--D ．13i 22-+ 4．若直线不平行于平面，且，则（ ）A ．内所有直线与异面B ．内只存在有限条直线与共面C ．内存在唯一的直线与平行D ．内存在无数条直线与相交5．已知双曲线C ：()222210,0x y a b a b -=>>的焦距为2c ，焦点到双曲线C 的渐近线的距离为32，则双曲线的渐近线方程为（） A ．3y x =B ．2y x =±C ．y x =±D ．2y x =±6．设命题:p 函数()x x f x e e -=+在R 上递增，命题:q 在ABC ∆中，cos cos A B A B >⇔<，下列为真命题的是（ ） A ．p q ∧B ．()p q ∨⌝C ．()p q ⌝∧D ．()()p q ⌝∧⌝7．直线l 过抛物线24y x =的焦点且与抛物线交于A ，B 两点，则4||||AF BF +的最小值是 A ．10B ．9C ．8D ．78．复数1z 在复平面内对应的点为()22,3,2,z i =-+则12z z =（ ） A ．1855i -+ B ．1855i -- C ．815i -+D ．815i --9．设1tan 2α=，4cos()((0,))5πββπ+=-∈，则tan 2()αβ-的值为（ ）A ．724-B ．524-C ．524D ．72410．已知函数()2ln e x f x x =，若关于x 的方程21[()]()08f x mf x -+=有4个不同的实数根，则实数m 的取值范围为（ ） A ．3(0,)4B ．2(0,)2C ．23(,)24D ．2(,1)211．己知全集为实数集R ，集合A ={x |x 2 +2x -8>0}，B ={x |log 2x <1}，则()RA B ⋂等于（ ）A ．[-4,2]B ．[-4,2)C ．(-4,2)D ．(0,2)12．已知集合3{|0}2xA x Z x -=∈≥+，B ＝{y ∈N |y ＝x ﹣1，x ∈A }，则A ∪B ＝（ ） A ．{﹣1，0，1，2，3}B ．{﹣1，0，1，2}C ．{0，1，2}D ．{x ﹣1≤x ≤2}二、填空题：本题共4小题，每小题5分，共20分。

上海师范大学附属外国语中学2025届高考数学三模试卷注意事项1．考试结束后，请将本试卷和答题卡一并交回．2．答题前，请务必将自己的姓名、准考证号用0．5毫米黑色墨水的签字笔填写在试卷及答题卡的规定位置． 3．请认真核对监考员在答题卡上所粘贴的条形码上的姓名、准考证号与本人是否相符．4．作答选择题，必须用2B 铅笔将答题卡上对应选项的方框涂满、涂黑；如需改动，请用橡皮擦干净后，再选涂其他答案．作答非选择题，必须用05毫米黑色墨水的签字笔在答题卡上的指定位置作答，在其他位置作答一律无效． 5．如需作图，须用2B 铅笔绘、写清楚，线条、符号等须加黑、加粗．一、选择题：本题共12小题，每小题5分，共60分。

在每小题给出的四个选项中，只有一项是符合题目要求的。

1．已知ABC 的内角A 、B 、C 的对边分别为a 、b 、c ，且60A =︒，3b =，AD 为BC 边上的中线，若72AD =，则ABC 的面积为（ ） AB．4C ．154D．42．已知函数()()()1sin,13222,3100x x f x f x x π⎧-≤≤⎪=⎨⎪-<≤⎩，若函数()f x 的极大值点从小到大依次记为12,?··n a a a ，并记相应的极大值为12,,?··n b b b ，则()1niii a b =+∑的值为（ ）A ．5022449+B ．5022549+C ．4922449+D ．4922549+3．已知正方体1111ABCD A B C D -的棱长为2，E ，F ，G 分别是棱AD ，1CC ，11C D 的中点，给出下列四个命题: ①1EF B C ⊥;② 直线FG 与直线1A D 所成角为60︒;③ 过E ，F ，G 三点的平面截该正方体所得的截面为六边形; ④ 三棱锥B EFG -的体积为56. 其中，正确命题的个数为（ ） A ．1B ．2C ．3D ．44．下列函数中，既是奇函数，又是R 上的单调函数的是( ) A ．()()ln 1f x x =+B ．()1f x x -=C ．()()()222,02,0x x x f x x x x ⎧+≥⎪=⎨-+<⎪⎩D ．()()()()2,00,01,02x xx f x x x ⎧<⎪⎪⎪==⎨⎪⎛⎫⎪-> ⎪⎪⎝⎭⎩5．已知四棱锥P ABCD -中，PA ⊥平面ABCD ，底面ABCD 是边长为2的正方形，5PA =，E 为PC 的中点，则异面直线BE 与PD 所成角的余弦值为（ ） A ．1339-B ．1339C ．155-D ．1556．若向量(1,5),(2,1)a b ==-，则(2)a a b ⋅+=（ ） A ．30B ．31C ．32D ．337．执行如图所示的程序框图，输出的结果为（ ）A ．193B ．4C ．254D ．1328．若实数x 、y 满足21y x y y x ≤⎧⎪+≥⎨⎪≥⎩，则2z x y =+的最小值是（ ）A ．6B ．5C ．2D ．329．抛物线的焦点是双曲线的右焦点，点是曲线的交点，点在抛物线的准线上，是以点为直角顶点的等腰直角三角形，则双曲线的离心率为（ ） A ．B ．C ．D ．10．已知函数2,0()4,0x x f x x x -⎧⎪=⎨+>⎪⎩，若()02f x <，则0x 的取值范围是（ ）A ．(,1)-∞-B ．(1,0]-C ．(1,)-+∞D ．(,0)-∞11．已知复数12iz i-=-（i 为虚数单位）在复平面内对应的点的坐标是（ ） A ．31,55⎛⎫- ⎪⎝⎭B ．31,55⎛⎫-- ⎪⎝⎭C ．31,55⎛⎫ ⎪⎝⎭D ．31,55⎛⎫- ⎪⎝⎭12．在ABC 中，AD 为BC 边上的中线，E 为AD 的中点，且||1,||2AB AC ==，120BAC ∠=︒，则||EB =（ ）A ．194B ．114C ．32D ．74二、填空题：本题共4小题，每小题5分，共20分。

上海培佳双语学校2025届高三3月份第一次模拟考试数学试卷请考生注意：1．请用2B 铅笔将选择题答案涂填在答题纸相应位置上，请用0．5毫米及以上黑色字迹的钢笔或签字笔将主观题的答案写在答题纸相应的答题区内。

写在试题卷、草稿纸上均无效。

2．答题前，认真阅读答题纸上的《注意事项》，按规定答题。

一、选择题：本题共12小题，每小题5分，共60分。

在每小题给出的四个选项中，只有一项是符合题目要求的。

1．三棱柱111ABC A B C -中，底面边长和侧棱长都相等，1160BAA CAA ︒∠=∠=，则异面直线1AB 与1BC 所成角的余弦值为（ ）A ．33B ．66C ．34D ．362．若函数()2xf x e mx =-有且只有4个不同的零点，则实数m 的取值范围是（ ）A ．2,4e ⎡⎫+∞⎪⎢⎣⎭B ．2,4e ⎛⎫+∞ ⎪⎝⎭C ．2,4e ⎛⎫-∞ ⎪⎝⎭D ．2,4e ⎛⎤-∞ ⎥⎝⎦3．如图，在三棱柱111ABC A B C -中，底面为正三角形，侧棱垂直底面，148AB AA ==，.若E F ，分别是棱1BB CC，上的点，且1BE B E =，1114C F CC =，则异面直线1A E 与AF 所成角的余弦值为（ ）A ．210B 26C 13D 13 4．学业水平测试成绩按照考生原始成绩从高到低分为A 、B 、C 、D 、E 五个等级．某班共有36名学生且全部选考物理、化学两科，这两科的学业水平测试成绩如图所示．该班学生中，这两科等级均为A 的学生有5人，这两科中仅有一科等级为A 的学生，其另外一科等级为B ，则该班（ ）A ．物理化学等级都是B 的学生至多有12人 B ．物理化学等级都是B 的学生至少有5人C ．这两科只有一科等级为B 且最高等级为B 的学生至多有18人D ．这两科只有一科等级为B 且最高等级为B 的学生至少有1人5．在正方体1AC 中，E 是棱1CC 的中点，F 是侧面11BCC B 内的动点，且1A F 与平面1D AE 的垂线垂直，如图所示，下列说法不正确．．．的是（ ）A ．点F 的轨迹是一条线段B ．1A F 与BE 是异面直线C ．1A F 与1DE 不可能平行D ．三棱锥1F ABD -的体积为定值6．已知函数()()2,211,22x a x x f x x ⎧-≥⎪=⎨⎛⎫-<⎪ ⎪⎝⎭⎩，满足对任意的实数12x x ≠，都有()()12120f x f x x x -<-成立，则实数a 的取值范围为（ ） A ．()1,+∞B ．13,8⎛⎤-∞ ⎥⎝⎦C ．13,8⎛⎫-∞ ⎪⎝⎭D ．13,8⎛⎫+∞⎪⎝⎭7．已知集合U ＝{1，2，3，4，5，6}，A ＝{2，4}，B ＝{3，4}，则()()UU A B ＝（ ）A ．{3，5，6}B ．{1，5，6}C ．{2，3，4}D ．{1，2，3，5，6}8．已知函数()f x 的图象如图所示，则()f x 可以为（ ）A ．3()3x f x x=-B ．e e ()x xf x x --= C ．2()f x x x =-D ．||e ()xf x x=9．已知()4sin 5πα+=，且sin 20α<，则tan 4πα⎛⎫- ⎪⎝⎭的值为（ ）A ．7B ．7-C ．17D ．17-10．在ABC 中，AD 为BC 边上的中线，E 为AD 的中点，且||1,||2AB AC ==，120BAC ∠=︒，则||EB =（ ）A ．194B ．114C ．32D ．7411．若点位于由曲线与围成的封闭区域内（包括边界），则的取值范围是（ ）A ．B ．C ．D ．12． 若数列{}n a 满足115a =且1332n n a a +=-，则使10k k a a +⋅<的k 的值为( ) A ．21B ．22C ．23D ．24二、填空题：本题共4小题，每小题5分，共20分。

美国SSAT数学考试练习题美国SSAT数学考试练习题想要申请美国高中的同学，对于美国的中考SSAT考试并不陌生。

在SSAT考试中，数学是很重要的一部分内容，因此本文简要介绍美国中学SSAT考试数学习题，希望对想要申请美国高中的同学有所帮助。

1. If the average of three numbers is V. If one of the numbers is Z and another is Y, what is the remaining number?A. ZY - VB. Z/V - 3 - YC. Z/3 - V - YD. 3V- Z - YE. V- Z - Y2. Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?A. 2 hoursB. 4 ? hoursC. 5 ? hoursD. 6 hoursE. 7 ? hours3. Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ? hours. How quickly can all three fill the pool together?A. 12 minutesB. 15 minutesC. 21 minutesD. 23 minutesE. 28 minutes4. Mary is reviewing her algebra quiz. She has determined that one of her solutions is incorrect. Which one is it?A. 2x + 5 (x-1) = 9, x = 2B. p - 3(p-5) = 10, p = 2.5C. 4 y + 3 y = 28, y = 4D. 5 w + 6 w - 3w = 64, w = 8E. t - 2t - 3t = 32, t = 85. What simple interest rate will Susan need to secure to make $2,500 in interest on a $10,000 principal over 5 years?A. 4%B. 5%C. 6%D. 7%E. 8%6. Which of the following is not a rational number?A. -4B. 1/5C. 0.8333333...D. 0.457. A study reported that in a random sampling of 100 women over the age of 35 showed that8 of the women were married 2 or more times. Based on the study results, how many women in a group of 5,000 women over the age of 35 would likely be married 2 or more times?A. 55B. 150C. 200D. 400E. 6008. John is traveling to a meeting that is 28 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time?A. 25 mphB. 37 mphC. 41 mphD. 49 mphE. 56 mph9. If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?A. 2 minutes and 44 secondsB. 2 minutes and 58 secondsC. 3 minutes and 10 secondsD. 3 minutes and 26 secondsE. 4 minutes and 15 seconds10. If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it?A. 0.8 daysB. 1.09 daysC. 1.23 daysE. 1.97 days11. Jim has 5 pieces of string. He needs to choose the piece that will be able to go around his 36-inch waist. His belt broke, and his pants are falling down. The piece needs to be at least 4 inches longer than his waist so he can tie a knot in it, but it cannot be more that 6 inches longer so that the ends will not show from under his shirt. Which of the following pieces of string will workthe best?A. 3 feetB. 3 ? feetC. 3 ? feetD. 3 ? feetE. 2 ? feet12. The last week of a month a car dealership sold 12 cars. A new sales promotion came out the first week of the next month and the sold 19 cars that week. What was the percent increase in sales from the last week of the previous month compared to the first week of the next month?A. 58%B. 119%C. 158%D. 175%E. 200%13. If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph?A. 50 milesB. 100 milesC. 500 milesE. 1,000 miles14. During a 5-day festival, the number of visitors tripled each day. If the festival opened on a Thursday with 345 visitors, what was the attendance on that Sunday?A. 345B. 1,035C. 1,725D. 3,105E. 9,315Answer Key1. D2. B3. B4. E5. B6. E7. D8. E9. A10. B11. C12. A13. C14. E以上是对美国中学SSAT数学考试习题的一个简要介绍，想要申请美国高中并担心美国高中数学的同学可以参考借鉴一下。

SSAT数学题库SSAT数学专项练习1. Describe the following sequence in mathematical terms. 144, 72, 36, 18, 9A. Descending arithmetic sequenceB. Ascending arithmetic sequenceC. Descending geometric sequenceD. Ascending geometric sequenceE. Miscellaneous sequence2. Which of the following is not a whole number followed by its square?A. 1, 1B. 6, 36C. 8, 64D. 10, 100E. 11, 1443. A nurse has to record her temperatures in Celsius but her thermometer reads Fahrenheit. A patient's temperature is 100.7° F. What is the temperature in °C?A. 32° CB. 36.5° CC. 38.2° CD. 213.3° CE. 223.7° C4. Art realized that he had 2 more quarters than he had originally thought in his pocket. If all of the change in his pocket is quarters and it totals to $8.75, how many quarters did he originally think were in his pocket?A. 27B. 29C. 31D. 33E. 355. There are 12 more apples than oranges in a basket of 36 apples and oranges. How many apples are in the basket?A. 12B. 15C. 24D. 28E. 366. Which of the following correctly identifies 4 consecutive odd integers where the sum of the middle two integers is equal to 24?A. 5, 7, 9, 11B. 7, 9, 11, 13C. 9, 11, 13, 15D. 11, 13, 15, 17E. 13, 15, 17, 197. What is the next number in the sequence? 6, 12, 24, 48, ___A. 72B. 96C. 108D. 112E. 1248. Which of the following numbers could be described in the following way: an integer that is a natural, rational and whole number?A. 0B. 1C. 2.33D. -3E. none of the above9. What is the next number in the following pattern? 1, 1/2, 1/4, 1/8, ___A. 1/10B. 1/12C. 1/14D. 1/15E. 1/1610. Of the following units, which would be most likely to measure the amount of sugar needed in a recipe for 2 dozen cookiesA. degrees CelsiusB. millilitersC. quartsD. kilogramsE. cupsSSAT数学题库SSAT数学综合练习题1. How long will Lucy have to wait before for her $2,500 invested at 6% earns $600 in simple interest?A. 2 yearsB. 3 yearsC. 4 yearsD. 5 yearsE. 6 years2. Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?A. 4B. 8C. 12D. 13E. 163. If r = 5 z then 15 z = 3 y, then r =A. yB. 2 yC. 5 yD. 10 yE. 15 y4. What is 35% of a number if 12 is 15% of a number?A. 5B. 12C. 28D. 33E. 625. A computer is on sale for $1600, which is a 20% discount off the regular price. What is the regular price?A. $1800B. $1900C. $2000D. $2100E. $22006. A car dealer sells a SUV for $39,000, which represents a 25% profit over the cost. What was the cost of the SUV to the dealer?A. $29,250B. $31,200C. $32,500D. $33,800E. $33,9997. After having to pay increased income taxes this year, Edmond has to sell his BMW. Edmond bought the car for $49,000, but he sold it for a 20% loss. What did Edmond sell the car for?A. $24,200B. $28,900C. $35,600D. $37,300E. $39,2008. If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it?A. 0.8 daysB. 1.09 daysC. 1.23 daysD. 1.65 daysE. 1.97 days9. Find 0.12 ÷12A. 100B. 10C. 1D. 0.01E. 0.00110. Divide x5 by x2A. x25B. x10C. x7D. x3E. x2.511. Which of the following numbers could be described in the following way: an integer that is a natural, rational and whole number?A. 0B. 1C. 2.33D. -3E. none of the above12. Find the mode of the following list of numbers: 2, 4, 6, 4, 8, 2, 9, 4, 3, 8A. 2B. 3C. 4D. 5E. 613. In the fraction 3/x, x may not be substituted by which of the following sets?A. {1, 2, 4}B. {-2,-3,-4}C. {1, 3, 7}D. {0, 10, 20}E. {1.8, 4.3}14. Sarah needs to make a cake and some cookies. The cake requires 3/8 cup of sugar and the cookies require 3/5 cup of sugar. Sarah has 15/16 cups of sugar. Does she have enough sugar, or how much more does she need?A. She has enough sugar.B. She needs 1/8 of a cup of sugar.C. She needs 3/80 of a cup of sugar.D. She needs 4/19 of a cup of sugar.E. She needs 1/9 of a cup of sugar.15. At a company fish fry, 1/2 in attendance are employees. Employees' spouses are 1/3 of the attendance. What is the percentage of the people in attendance who are not employees or employee spouses?A. 10.5%B. 16.7%C. 25%D. 32.3%E. 38%16. In a college, some courses contribute more towards an overall GPA than other courses. For example, a science class is worth 4 points; mathematics is worth 3 points; History is worth 2 points; and English is worth 3 points. The values of the grade letters are as follows, A= 4, B=3, C=2, D=1, F=0. What is the GPA of a student made a “C〞in Trigonometry, a “B〞in American History, an “A〞in Botany, and a “B〞in Microbiology?A. 2.59B. 2.86C. 3.08D. 3.33E. 3.6717. There are 8 ounces in a ½ pound. How many ounces are in 7 3/4 lbs?A. 12 ouncesB. 86 ouncesC. 119 ouncesD. 124 ouncesE. 138 ounces18. If the value of x and y in the fraction XZ/Y are both tripled, how does the value of the fraction change?A. increases by halfB. decreases by halfC. triplesD. doublesE. remains the same19. What is the next number in the following pattern? 1, 1/2, 1/4, 1/8, ___A. 1/10B. 1/12C. 1/14D. 1/15E. 1/1620. Of the following units which would be more likely used to measure the amount of water in a bathtub?A. kilogramsB. litersC. millilitersD. centigramsE. volts21. If a match box is 0.17 feet long, what is its length in inches the most closely comparable to the following?A. 5 1/16 inch highlighterB. 3 1/8 inch jewelry boxC. 2 3/4 inch lipstickD. 2 3/16 inch staple removerE. 4 1/2 inch calculator22. Which of the following fractions is the equivalent of 0.5%?A. 1/20B. 1/200C. 1/2000D. 1/5E. 1/50023. In the graph below, no axes or origin is shown. If point B's coordinates are (10,3), which of the following coordinates would most likely be A's?A. (17, -2)B. (10, 6)C. (6, 8)D. (-10, 3)E. (-2, -17)24. Over the course of a week, Fred spent $28.49 on lunch. What was the average cost per day? A. $4.07 B. $3.57 C. $6.51 D. $2.93 E. $5.4125. Of the following units, which would be most likely to measure the amount of sugar needed in a recipe for 2 dozen cookies?A. degrees CelsiusB. millilitersC. quartsD. kilogramsE. cups26. Jim has 5 pieces of string. He needs to choose the piece that will be able to go around his 36-inch waist. His belt broke, and his pants are falling down. The piece needs to be at least 4 inches longer than his waist so he can tie a knot in it, but it cannot be more that 6 inches longer so that the ends will not show from under his shirt. Which of the following pieces of string will work the best?A. 3 4/5 feetB. 3 2/3 feetC. 3 3/8 feetD. 3 1/4 feetE. 2 1/2 feet27. After purchasing a flat screen television for $750, John realizes that he got a great deal on it and wishes to sell it for a 15% profit. What should his asking price be for the television?A. $800.30B. $833.60C. $842.35D. $862.50E. $970.2528. If 300 jellybeans cost you x dollars. How many jellybeans can you purchase for 50 cents at the same rate?A. 150/xB. 150xC. 6xD. x/6E. 1500x29. If 6 is 24% of a number, what is 40% of the same number?A. 8B. 10C. 15D. 20E. 2530. Lee worked 22 hours this week and made $132. If she works 15 hours next week at the same pay rate, how much will she make?A. $57B. $90C. $104D. $112E. $12231. The last week of a month a car dealership sold 12 cars. A new sales promotion came out the first week of the next month and the sold 19 cars that week. What was the percent increase in sales from the last week of the previous month compared to the first week of the next month?A. 58%B. 119%C. 158%D. 175%E. 200%32. If 8x + 5x + 2x + 4x = 114, the 5x + 3 =A. 12B. 25C. 33D. 47E. 8633. If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph? A. 50 miles B. 100 miles C. 500 miles D. 700 miles E. 1,000 miles34. What is the cost in dollars to steam clean a room W yards wide and L yards long it the steam cleaners charge 10 cents per square foot?A. 0.9WLB. 0.3WLC. 0.1WLD. 9WLE. 3WL35. Find 8.23 x 109A. 0.B. 0.000000823C. 8.23D. 8230000000E. 036. During a 5-day festival, the number of visitors tripled each day. If the festival opened on a Thursday with 345 visitors, what was the attendance on that Sunday?A. 345B. 1,035C. 1,725D. 3,105E. 9,31537. Which of the following has the least value?A. 0.27B. 1/4C. 3/8D. 2/11E. 11%SSAT数学题库〔一〕SSAT数学综合练习题1 What is the perimeter of a rectangle with side lengths of 8 and 3?a. 6b. 11 c, 16 d. 22 e. 252 The base angles of an isosceles triangle are:PerpendicularCongruentComplimentarySupplementaryparallel3 How many points are necessary to define a line?a. Oneb. Twoc. Threed. Foure. Infinite4 Two cars start from the same place two hours apart. The first car travels at 10 miles per hour and the second travels at 15 miles per hour. How many hours after the second car leaves does it take for the second car to catch up?a. 1b. 2c. 3d. 4e. 55 What interest rate is necessary to get $1000 in interest over 2 years on a $10000 investment?a. 4%b. 5%c. 6%d. 7%e. 8%6 The sum of 14 consecutive integers is 217. What is the sixth number in the series?a. 13b. 14c. 15d. 16e. 177 Paul needs to be at a meeting in 20 minutes. If his office is 15 miles away, how fast does he need to drive to get there on time, in miles per hour?a. 15b. 20c. 30d. 40e. 458 The base angles of an isosceles triangle are:PerpendicularCongruentComplimentarySupplementaryParallel9 If A $ B = A * B - ( A + B), what is 3 $ (2 $ 1)?A. -5B. -3C. 0D. 1E. 410 What is the average (arithmetic mean) of 4x + 5, 7x-6,and -8x+2?A. x + 1B. x + 1/3C. 3x + 1D. 3x + 1/311 In a classroom of 35 students, 14 our male. What percent of the classroom is male?A. 14%B. 20%C. 30%D. 40%E. 50%12 If the area of a triangle is 24 and its base is 6, what is the length of the altitude to that base?A. 3B. 6C. 8D. 10E. unknown13 If Jeff and Jimmy have less than 22 dollars between them, and Jeff has 8 dollars, which of the following could be the number of dollars that Jimmy has?Ⅰ12Ⅱ14Ⅲ16A. I onlyB. III onlyC. I & III.D. I & IIE. Neither I, II, nor III is correct.14 Stephanie drove at an average rate of 50 miles per hour for two hours and then increased her average rate by 50% for the next 3 hours. Her average rate of speed for the 5 hours was t miles per hour. What is the value of t?A. 55 mphB. 60 mphC. 65 mphD. 70 mphE. 75 mph15 If 1 alpha = 2 betas and 1 beta = 3 gammas, how many alphas are equal to 36 gammas?A. 6B. 12C. 36D. 72E. 10816 At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $8.50 per hour, how much less than a manager does a chef earn each hour?A. $5.95B. $4.25C. $5.10D. $3.25E. $3.4017 A florist buys roses at $0.50 a piece and sells them for $1.00 a piece. If there are no other expenses, how many roses must be sold in order to make a profit of $300?A. 100B. 150C. 200D. 300E. 60018 A certain pump can drain a full 375-gallon tank in 15 minutes. At this rate, how many more minutes would it take to drain a full 600-gallon tank?A. 9B. 15C. 18D. 24E. 2519 Lenny's average score after 3 tests is 88. What score on the 4th test would bring Lenny's average up to exactly 90?A. 92B. 93C. 94D. 95E. 9620 If an integer is divisible by 6 and by 9, then the integer must be divisible by which of theA. 12B. 18C. 24D. 36E. 5421 A certain machine can make 3 widgets every 2 seconds. At this rate, how many widgets will be made in 1 minute?A. 90B. 110C. 150D. 180E. 22022 What is the average of the first 50 positive integers?A. 25B. 25.5C. 26D. 26.5E. 2723 If ab is negative, which of the following CANNOT be negative?A. b-aB. a-bC. a2bD. ab2E. a2b224 In a certain set of numbers, the ratio of integers to nonintegers is 1:4. What percent of the numbers in the set are integers?A. 20%B. 25%C. 40%D. 75%E. 80%25 What is the smallest positive number that leaves a remainder of 2 when the number is divided by 3, 4, or 5?A. 42B. 82C. 22D. 62E. 12226 Which is greater?Column A Column B3-5+6-8-4+7 -2A. the quantity in Column B is greaterB. the relationship cannot be determined from the information givenC. the quantity in Column A is greaterD. the two quantities are equal27 If a die is tossed twice the probability of getting a 3 on both tosses is:A. 1/4B. 1/36C. 1/12D. 1/6E. 1/2528 An instrument store gives a 10% discount to all students off the original costof an instrument. During a back to school sale an additional 15% is taken offthe discounted price. Julie, a student at the local high school, purchases aflute for $306. How much did it originally cost?A. $325B. $375C. $400D. $408E. $42529 If y(x-1)=z then x=A. y-zB. z/y + 1C. y(z-1)D. z(y-1)E. 1-zy30 Which of the following values is NOT equal to 34(58+9)?A. 34 x 67B. 58(34+9)C. 34 x 58 + 34 x 9D. 1,972 + 306E. (9 + 58) 3431 Two angle s of a triangle measure 15° and 85 °. What is the measure for thethird angle?A. 50°B. 55°C. 60°D. 80°E. 90°32 If 5 ounces is equal to 140 grams, then 2 pounds of ground meat is equal tohow many grams?A. 863B. 878C. 896D. 915E. 93233 Which year did the most children take swimming lessons?A. 1990B. 1991C. 1992D. 1994E. 199534 Between which year did the largest decrease in children taking swimminglessons occur?A. 1990-1991B. 1991-1992C. 1992-1993D. 1993-1994E. 1994-199535 What was the average number of children taking swim lessons from 1990 to 1995?A. 250B. 308C. 385D. 450E. 1,85036 Which of the following is equal to 5.93 x 10-2?A. 0.0593B. 0.00593C. 593D. 5930E. 5930037 On a Map, 1 inch represents 20 miles. The distance between 2 towns is 6 1/5inches. How many miles are actually between the two towns?A. 65 milesB. 84 milesC. 124 milesD. 138 milesE. 145 miles38 How many cubed pieces of fudge that are 3 inches on an edge can be packed intoa Christmas tin that is 9 inches deep by 12 inches wide by 8 inches high withthe lid still being able to be closed? A. 18 B. 24 C. 32 D. 36 E. 4339 Sarah is twice as old as her youngest brother. If the difference between theirages is 15 years. How old is her youngest brother? A. 10 B. 15 C. 20 D.25 E. 3040 Which of the following fractions is equal to 5/6? A. 20/30 B. 15/24 C. 25/30 D. 40/54 E. 2/741 What will it cost to tile a kitchen floor that is 12 feet wide by 20 feet longif the tile cost $8.91 per square yard? A. $224.51 B. $237.60C. $246.55D. $271.38E. $282.3242 In a writing competition, the first place winner receives ½ of the prizemoney. The second runner up receives ¼ of what the winner won. What was thetotal amount of prize money distributed if the winner receives $6,000? A. $6,000 B. $8,500 C. $12,000 D. $15,000 E. $18,50043 You are lying 120 ft away from a tree that is 50 feet tall. You look up at thetop of the tree. Approximately how far is your hear from the top of the treein a straight line? A. 50 feet B. 75 feet C. 120 feet D. 130 feet E. 150 feet44 A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist’s average ra te for the round trip in miles per hour?A. 8.1B. 8.3C. 8.6D. 8.9E. 9.045 If edging cost $2.32 per 12-inch stone, and you want a double layer of edgingyour flower bed that is 6 yards by 1 yard. How much will edging you flower bedcost? A. $32.48 B. $64.96 C. $97.44 D. $129.92 E. $194.8846 If 3x=6x-15 then x + 8= A. 5 B. 10 C. 11 D. 12 E. 1347 The number of milliliters in 1 liter is A. 10,000 B. 1,000 C. 0.1 D. 0.01 E. 0.001SSAT数学题库SSAT数学专项训练1. If the average of three numbers is V. If one of the numbers is Z and another is Y, what is the remaining number?A. ZY - VB. Z/V - 3 - YC. Z/3 - V - YD. 3V- Z - YE. V- Z - Y2. Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?A. 2 hoursB. 4 ½ hoursC. 5 ¾ hoursD. 6 hoursE. 7 ½ hours3. Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together?A. 12 minutesB. 15 minutesC. 21 minutesD. 23 minutesE. 28 minutes4. Mary is reviewing her algebra quiz. She has determined that one of her solutions is incorrect. Which one is it?A. 2x + 5 (x-1) = 9, x = 2B. p - 3(p-5) = 10, p = 2.5C. 4 y + 3 y = 28, y = 4D. 5 w + 6 w - 3w = 64, w = 8E. t - 2t - 3t = 32, t = 85. What simple interest rate will Susan need to secure to make $2,500 in interest on a $10,000 principal over 5 years?A. 4%B. 5%C. 6%D. 7%E. 8%6. Which of the following is not a rational number?A. -4B. 1/5C. 0.8333333...D. 0.45E.7. A study reported that in a random sampling of 100 women over the age of 35 showed that 8 of the women were married 2 or more times. Based on the study results, how many women in a group of 5,000 women over the age of 35 would likely be married 2 or more times?A. 55B. 150C. 200D. 400E. 6008. John is traveling to a meeting that is 28 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time?A. 25 mphB. 37 mphC. 41 mphD. 49 mphE. 56 mph9. If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?A. 2 minutes and 44 secondsB. 2 minutes and 58 secondsC. 3 minutes and 10 secondsD. 3 minutes and 26 secondsE. 4 minutes and 15 seconds10. If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it?A. 0.8 daysB. 1.09 daysC. 1.23 daysD. 1.65 daysE. 1.97 days11. Jim has 5 pieces of string. He needs to choose the piece that will be able to go around his 36-inch waist. His belt broke, and his pants are falling down. The piece needs to be at least 4 inches longer than his waist so he can tie a knot in it, but it cannot be more that 6 inches longer so that the ends will not show from under his shirt. Which of the following pieces of string will work the best? A. 3 feet B. 3 ¾ feet C.3 ½ feet D. 3 ¼ feet E. 2 ½ feet12. The last week of a month a car dealership sold 12 cars. A new sales promotion came out the first week of the next month and the sold 19 cars that week. What was the percent increase in sales from the last week of the previous month compared to the first week of the next month?A. 58%B. 119%C. 158%D. 175%E. 200%13. If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph?A. 50 milesB. 100 milesC. 500 milesD. 700 milesE. 1,000 miles14. During a 5-day festival, the number of visitors tripled each day. If the festival opened on a Thursday with 345 visitors, what was the attendance on that Sunday?A. 345B. 1,035C. 1,725D. 3,105E. 9,315SSAT数学题库SSAT数学专项练习题1. If Lynn can type a page in p minutes, what piece of the page can she do in 5 minutes?A. 5/pB. p - 5C. p + 5D. p/5E. 1- p + 52. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?A. 2 hours and 24 minutesB. 3 hours and 12 minutesC. 3 hours and 44 minutesD. 4 hours and 10 minutesE. 4 hours and 33 minutes3. Employees of a discount appliance store receive an additional 20% off of the lowest price on an item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally cost $450?A. $280.90B. $287C. $292.50D. $306E. $333.894. The sales price of a car is $12,590, which is 20% off the original price. What is the original price?A. $14,310.40B. $14,990.90C. $15,290.70D. $15,737.50E. $16,935.805. Solve the following equation for A : 2A/3 = 8 + 4AA. -2.4B. 2.4C. 1.3D. -1.3E. 06. If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue?A. 8B. 10C. 14D. 19E. 217. Alfred wants to invest $4,000 at 6% simple interest rate for 5 years. How much interest will he receive?A. $240B. $480C. $720D. $960E. $1,2008. Jim is able to sell a hand-carved statue for $670 which was a 35% profit over his cost. How much did the statue originally cost him?A. $496.30B. $512.40C. $555.40D. $574.90E. $588.209. The city council has decided to add a 0.3% tax on motel and hotel rooms. If a traveler spends the night in a motel room that costs $55 before taxes, how much will the city receive in taxes from him?A. 10 centsB. 11 centsC. 15 centsD. 17 centsE. 21 cents10. A student receives his grade report from a local community college, but the GPA is smudged. He took the following classes: a 2 hour credit art, a 3 hour credit history, a 4 hour credit science course, a 3 hour credit mathematics course, and a 1 hour science lab. He received a B in the art class, an B in the history class, a C in the science class, a A in the mathematics class, and an A in the science lab. What was his GPA if the letter grades are based on a 4 point scale? (A=4, B=3, C=2, D=1, F=0)A. 2.7B. 2.8C. 3.0D. 3.1E. 3.211. Simon arrived at work at 8:15 A.M. and left work at 10: 30 P.M. If Simon gets paid by the hour ata rate of $10 and time and ½ for any hours worked over 8 in a day. How much did Simon get paid?A. $120.25B. $160.75C. $173.75D. $180E. $182.5012. Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?A. 4B. 8C. 12D. 13E. 1613. If r = 5 z then 15 z = 3 y, then r =A. yB. 2 yC. 5 yD. 10 yE. 15 y14. If 300 jellybeans cost you x dollars. How many jellybeans can you purchase for 50 cents at the same rate?A. 150/xB. 150xC. 6xD. 1500/xE. 600x15. Lee worked 22 hours this week and made $132. If she works 15 hours next week at the same pay rate, how much will she make?A. $57B. $90C. $104D. $112E. $12216. If 8x + 5x + 2x + 4x = 114, the 5x + 3 =A. 12B. 25C. 33D. 47E. 8617. You need to purchase a textbook for nursing school. The book cost $80.00, and the sales tax where you are purchasing the book is 8.25%. You have $100. How much change will you receive back?A. $5.20B. $7.35C. $13.40D. $19.95E. $21.2518. You purchase a car making a down payment of $3,000 and 6 monthly payments of $225. How much have you paid so far for the car?A. $3225B. $4350C. $5375D. $6550E. $639819. Your supervisor instructs you to purchase 240 pens and 6 staplers for the nurse's station. Pens are purchased in sets of 6 for $2.35 per pack. Staplers are sold in sets of 2 for 12.95. How much will purchasing these products cost?A. $132.85B. $145.75C. $162.90D. $225.25E. $226.7520. If y = 3, then y3(y3-y)=A. 300B. 459C. 648D. 999E. 1099SSAT数学题库〔五〕SSAT数学专项练习题答案1. A 2. A 3. D 4. D 5. A 6. A 7. E 8. A 9. D 10. C 11.C 12.D 13. A 14. A 15. B 16. C 17. C 18. B 19. A 20. CSSAT数学题库SSAT数学专项练习题1. 104 is not equal to which of the following?A. 100,000B. 0.1 x 105C. 10 x 10 x 10 x 10D. 102 x 102E. 10,0002. Multiply 104 by 102A. 108B. 102C. 106D. 10-2E. 1033. Divide x5 by x2A. x7B. x4C. x10D. x3E. x2.54. Find 8.23 x 109A. 0.B. 0.000000823C. 8.23D. 8230000000E. 05. 83,000 equals:A. 83.0 x 104B. 8.3 x 104C. 8.3 x 103D. 83.0 x 105E. 83.0 x 1026. .00875 equals:A. 8.75 x 10-2B. 8.75 x 10-3C. 8.75 x 10-4D. 87.5 x 10-3E. 875 x 10-4SSAT数学题库〔六〕SSAT数学专项练习题答案1. A2. C3. D4. D5. B6. BSSAT数学题库〔七〕SSAT数学专项练习题1. If a discount of 20% off the retail price of a desk saves Mark $45, how much did he pay for the desk?B. $160C. $180D. $210E. $2152. A customer pays $1,100 in state taxes on a newly purchased car. What is the value of the car if state taxes are 8.9% of the value?A. $9.765.45B. $10,876.90C. $12,359.55D. $14,345.48E. $15,745.453. How many years does Steven need to invest his $3,000 at 7% to earn $210 in simple interest?A. 1 yearB. 2 yearsC. 3 yearsD. 4 yearsE. 5 years4. Sabrina's boss states that she will increase Sabrina's salary from $12,000 to $14,000 per year if she enrolls in business courses at a local community college. What percent increase in salary will result from Sabrina taking the business courses?B. 16.7%C. 17.2%D. 85%E. 117%5. 35% of what number is 70?A. 100B. 110C. 150D. 175E. 2006. What number is 5% of 2000?A. 50B. 100C. 150D. 200E. 2507. What percent of 90 is 27?A. 15%B. 20%C. 30%E. 41%8. Jim works for $15.50 per hour for a health care facility. He is supposed to get a 75 cent per hour raise at one year of service. What will his percent increase in hourly pay be?A. 2.7%B. 3.3%C. 133%D. 4.8%E. 105%9. If 45 is 120% of a number, what is 80% of the same number?A. 30B. 32C. 36D. 38E. 4110. How long will Lucy have to wait before her $2,500 invested at 6% earns $600 in simple interest?A. 2 yearsB. 3 yearsC. 4 yearsD. 5 yearsE. 6 years。

自主招生数学全真模拟试卷(七)一．填空题1.如图，在△ABC 中，AB=9，BC=8，CA=7，AD 为内角平分线，以AD 为弦作一圆与BC 相切，且与AB 、AC 分别交于点M 、N ，则MN=________.2.如图，在Rt△ABC 中，∠ACB=90°，在斜边AB 上分别截取AD=AC ，BE=BC ，DE=6，O 是△CDE 的外心，则O 到△ABC 三边距离之和是_______3.对于三个数a 、b 、c ，用min{a,b,c }表示这三个数中最小的数，例如min{-1,2,3}=-1,min{-1,2,a }=,11,1{aa a ≤-->-,那么min{21,(1),2x x x +--}的最大值为______. 4. 如图，在矩形OABC 中，OA=6，OC=5，反比例函数的图像与AB 、BC 分别交于点E 、F ，且CF<FB,OEF 与BFE 的面积之差等于11530，则此反比例函数的解析式为_________ 5. 设实数x 不等于0和1，则4231x x y x x-+=-的取值范围是________.6. 已知12345,,,,x x x x x 是非负实数，且12345100x x x x x ++++=，M 是12233445,,,x x x x x x x x ++++的最大值，则M 的最小值m=_________.7. 从1，2，3......20这20个整数中，每次取3个数，组成一个有序实数对(a,b,c ),使b 为a ，c 的比例中项，则不同的有序实数对(a,b,c )共有________对.8. 在矩形ABCD 中，AB=4，AD=3，从AB 中点P 0射出的光线到达边BC 的点经反射到达边CD 上的点P 2，再经反射到达边DA 上的点P 3，最后经反射到达边AB 上的点P 4，若P 0P 4=1，则tan ∠BP 0P 1=_________.二．解答题9. 已知正方形ABCD 的边长为5，P 为正方形内一点，且PC=5，求PB 的长.10. 用[x]表示不超过x 的最大整数(如[3.1]=3,[-3.1]=-4),设实数x 不为整数，且，求x 的值.11. 已知m 、n 都是实数，且3331m n mn ++=，求m+n 的值.12. 如图所示，在ABC 中，BC 边上依次有B 、D 、E 、C ，AC 边上依次有A 、G 、F 、C ，满足BD=CE=14BC ，CF=AG=14AC ，BF 交AE 于点J ，交AD 于点I ，BG 交AE 于点K ，交AD 于点H ，且ABC S ∆=1，求KHIJ S .参考答案1. 如图，连接DM ，由∠BDM=∠BAD=∠CAD=∠CMN ，得MN||BC 则△AMN~△ABC ，易知BD=92，又因为BM ∙BA=BD 2，所以BM ∙9=29()2得BM=94，从而有AM=274，又MN AM 3BC AB 4==因此MN=6. 2. 如图，连接OA 、OB 、OC 、OD 、OE ，由OC=OD 知O 在CD 的垂直平分线上，又AD=AC ，则OA 平分CAD ，同理OB 平分CBD ，故O 是ABC 的内心，因此O 到ABC 的三边距离均与ABC 的内切圆的半径相等，半径为1()32AC BC AB +-=，故所求之和为9.3. 分别作出21,(1),2y x y x y x =+=-=-的图像如图所示，由图像知2min{1,(1),2}x x x +--的最大值为14. 由已知得A(6,0),B(6,5)，C(0,5),设此反比例函数为k y x =，则E(6,6k )F(5,5k ),故1S S ,(5)(6)256OAE OCF BEFk k k S ∆∆∆+==--，所以2F BE 161S -S 3030OE F k k ∆∆=-+=解得k=7或23，因为CF<FB 所以35k <，故反比例函数为7y x= 5. 显然2211x x y x x -=+-令t 1=21x x-则2110x t x --=其判别式2114t ∆=+，可知t1可取遍每一个非零实数，再令12111(0)t t t t +=≠则212110t t t -+=，判别式2124t ∆=-得2||2t ≥即||2y ≥，所以2211x x y x x -=+-的取值范围是2y ≥或2y ≤- 6. 依题意有12M x x ≥+，23M x x ≥+，45M x x ≥+，三式相加得23100M x ≥+即1003M ≥,当241351000,3x x x x x =====，此时1003M =，故M 的最小值为10037. 因为222214,319,.......12916818=⨯=⨯=⨯=⨯，每个等都有两组有序实数对(a,b )产生，所以共有22对.8. 当点P 4在点P 0左侧时，由对称性得图，因为P0P4=1，P 0为AB 的中点，且AB=4，AD=3，则AP 4=1，EA=1,EF=6,FG=10,P 0H=7，所以tan ∠BP 0P 1=76,同理，当P 4在点P 0的左侧时，有tan ∠BP 0P 1=32.9. 如图，作PE△AB 于点E ，PF△BC 于点F ，设PE=m ，PF=n ，在Rt△PAE 和Rt△PCF 中，分别由勾股定理得5)5(25)5(2222{=-+=+-n m n n 得m=n -2,代入得n=3或n=4；当n=3时，m=1,得PB=10；当n=4时m=2得PB=52，综上PB=10或5210. 去分母得0)113][])([(113][][113][22=--→+=+x x x x x x x x x x ,x 不是整数，故0][≠-x x ，0113][=-x x ，令)10(][<<+=t t x x ,代入得0113][][2=-+x t x 解得][][1132x x t -=，易知[x ]=-11，t =118,故11310-=x 11. 由已知01)()()(22233=-+++--+n m n mn m n m 即有0)1)(1()1)((22=++-++-++-n m n m n m n mn m 即0])1()1())[(1(222=++++--+n m n m n m 得1,01=+=-+n m n m ；10)1()1()(222-===++++-n m n m n m 时，，故m+n=1或-212.由梅涅劳斯定理有1AC FA JF BJ BE CE =⋅⋅又，，43AC FA 31BE CE ==则14JF BJ =即54BF BJ =同理可得，，，74BG BH 134BF BI 1312BG BK ===由共角比例定理得有6548131254S S BJK =⋅=⋅=∆∆BG BK BF BJ BFG 同理9116S S BFG BIH =∆∆故455256S S S S S HIH BJK HIJK =-=∆∆∆∆BFG BFG 四而21S S ABC BFG =∆∆，故455128S HIJK =四。