2015年SSAT模拟题--数学篇
2015年模拟考试数学试卷及答案答题卡
2015年模拟数学试题卷（全卷三个大题，共23小题，共6页；满分120分，考试时间120分钟）参考公式：二次函数y=ax 2+bx+c 的顶点坐标是)4ab 4ac ,2a b (2--．一、选择题（本题有8小题，每小题3分，共24分.请选出各题中唯一的正确选项，不选、多选、错选， 均不给分） 1．﹣3的相反数为（ ）A 、3B 、13C 、﹣3D 、13-2．已知地球上海洋面积约为316 000 000km 2，316 000 000这个数用科学记数法可表示为( ) A ．3.16×109 B ．3.16×108 C ．3.16×107 D ．3.16×106 3．如图所示的是零件三通的立体图，则这个几何体的俯视图是（ ）A B C D4．已知反比例函数1y x-=，下列结论中正确的是（ ）A .图象经过点（1，1）B .图象在第一、三象限C .当1>x 时，10y -<<D .当0<x 时，y 随着x 的增大而减小5．如图，在Rt △ABC 中，90C ∠=︒，4AC =，3BC =，则tan A 的值为（ ） A ．34 B ．43 C ．35 D ．456．已知圆锥的母线长为5，底面半径为3，则圆锥的表面积为（ ） A ．15π B ．24π C ．30π D ．39π7．已知⊙O 1和⊙O 2的半径分别为2cm 和5cm ，两圆的圆心距是3cm ，则两圆的位置关系是（ ）A ．内含B ．外切C ．内切D ．相交8．某班体育委员调查了本班46名同学一周的平均每天体育活动时间，并制作了如图所示的频数分布直方图，从直方图中可以看出，该班同学这一周的平均每天体育活动时间的中位数和众数依次是（ ）A ．40分，40分B ．50分，40分C ．50分，50分D ．40分，50分（第5题图）主视方向（第3题图）6(第16题图）二、填空题（本题有6小题，每小题3分，共18分） 9．计算：23()a ．10．如图，已知//,,35AB CD BC ABE C BEC ∠∠=︒∠平分，则的度数是 ． 11．某校艺术节演出中，5位评委给某个节目打分如下：9分，9.2分，8.9分，8.8分，9.1分，则该节目的平均得分是分．12．阳阳从家到学校的路程为2400米，他早晨8点离开家，要在8点30分到8点40分之间到学校，如果用x 表示他的速度（单位：米/分），则x 的取值范围为 ． 13．如图，在平面直角坐标系xoy 中，直线AB 过点A （－4，0），B （0，4），⊙O 的半径O 为坐标原点），点P 在直线AB 上，过点P 作⊙O 的一条切线PQ ，Q 为切点，则切线长PQ 的 最小值为 ．14．如图，已知直线y ＝2x ＋6交y 轴于点A ，点B 是这条直线上的一点，并且位于第一象限，点P 是直线x=8上的一动点，若△APB 是等腰直角三角形，则点B 的坐标为 ．三、简答题(本题有9小题，共78分)15．（本题10分）（1）计算：101()(2013)3π-+-+ （2）解方程：xx x -=+--23123(第8题图)（第12题图）AD(第15题图)16．（本题6分）如图，图①，图②均为76 的正方形网格，点A ，B ，C 在格点（小正方形的顶点）上．（1）在图①中确定格点D ，并画出一个以A ，B ，C ，D 为顶点的四边形，使其为轴对称图形；（2）在图②中确定格点E ，并画出一个以A ，B ，C ，E 为顶点的四边形，使其为中心对称图形．17．（本题8分）如图，在□ABCD 中，分别延长BA ，DC 到点E ，使得AE=AB ，CH=CD ，连接EH ，分别交AD ，BC 于点F ,G 。
SSAT数学考试真题练习(含答案)
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。
2015年6月13日SSAT预测
2015年6月13日SSAT预测2015年6月13日SSAT预测下载地址：/ssat/zt/20150424/xxq-2015n6y13rssatksjj.html?seo=wenku6.069小马老师为了考生能够成功备考2015年6月13日SSAT考试，特发布了2015年6月13日SSAT预测，考生可以进入下载地址免费索取下载使用。
2015年6月13日SSAT预测部分内容：1. Vivian wants to plant a vegetable garden that contains only tomatoes and cucumbers. However, she has a limited amount of space for the garden, and she can only afford to buy a specific number of each vegetable. Vivian has enough space to plant a total of 40 vegetables, and she has a total of $80 to purchase the vegetables. Tomatoes cost $1 per plant and cucumbers cost $3 per plant. Let T represent the number of tomatoes and let C represent the number of cucumbers Vivian will plant in her garden.Which system of linear equations can be used to solve for the number of tomatoes and cucumbers Vivian will plant in her garden?a. T + C = 40 and T + 3C = 80b. T + 3C = 40 and T + C = 80c. T + C = 80 and T + 3C = 40d. 3T + C = 80 and T + C = 40The base angles of an isosceles triangle are:PerpendicularCongruentComplimentarySupplementaryparallelHow many points are necessary to define a line?a. Oneb. Twoc. Threed. Foure. Infinite2015年6月13日SSAT预测下载地址：/ssat/zt/20150424/xxq-2015n6y13rssatksjj.html?seo=wenku6.069。
2015年上海市初中毕业统一学业考试最新数学模拟试卷
2015年上海市初中毕业统一学业考试最新数学模拟试卷一、选择题（每小题4分，共24分）A ．155°B ．145°C ．110°D ．35°3.下列标志中，可以看作是轴对称图形的是（ ）（A ） （B ） （C ） （D ） 4.如图，在 平行四边形ABCD 中，点E 是边AD 的中点，EC 交对角线BD 于点F ， 则EF ︰FC 等于（ ）（A ）3︰2 （B ）3︰1 （C ）1︰1 （D ）1︰25.某公司欲招聘一名公关人员，对甲、乙、丙、丁四位候选人进行了面试和笔试，他们的成 绩如下表所示：如果公司认为，作为公关人员面试的成绩应该比笔试的成绩更重要，并分别赋予它们6和4的权. 根据四人各自的平均成绩，公司将录取（A ）甲 （B ）乙 （C ）丙 （D ）丁B6．如图，直线y1=x+b与y2=kx﹣1相交于点P，点P的横坐标为﹣1，则关于x的不等式x+b＞kx﹣1的解集在数轴上表示正确的是（）A．B．C．D．二、填空题（每小题4分，共48分）7．分解因式：2x2﹣8= ．8.在函数中，自变量x的取值范围是_________．9.数学小组五名同学在一次测试中的数学成绩分别为98，96，97，100，99，则该小组五名同学该次测试数学成绩的方差为_________．10.现有一圆心角为120°，半径为9cm的扇形纸片，用它恰好围成一个圆锥的侧面（接缝忽略不计），则围成的圆锥的高为_________cm．11.如图所示，以边长为2的等边△ABO的顶点O为坐标原点，点B在x轴上，则经过点A 的反比例函数的表达式为_________．12．不等式组的解集为________．13．观察下列一组数：，，，，，…，它们是按一定规律排列的，那么这一组数的第n个数是_________．14．如图，在Rt△ABC中，∠ABC=90°，AB=3，AC=5，点E在BC上，将△ABC沿AE折叠，使点B落在AC边上的点B′处，则BE的长为_________．15．从﹣1，1，2这三个数字中，随机抽取一个数，记为a，那么，使关于x的一次函数y=2x+a 的图象与x轴、y轴围成的三角形的面积为，且使关于x的不等式组有解的概率为_________．16．如图，正方形ABCD的边长为6，点O是对角线AC、BD的交点，点E在CD上，且DE=2CE，过点C作CF⊥BE，垂足为F，连接OF，则OF的长为________．17．如图，双曲线y=经过Rt△BOC斜边上的点A，且满足=，与BC交于点D，S△BOD=21，求k= ．18．如图，在第1个△A1BC中，∠B=30°，A1B=CB；在边A1B上任取一点D，延长CA1到A2，使A1A2=A1D，得到第2个△A1A2D；在边A2D上任取一点E，延长A1A2到A3，使A2A3=A2E，得到第3个△A2A3E，…按此做法继续下去，则第n个三角形中以A n为顶点的内角度数是。
2015上半年SAT模拟试题：数学
2015上半年SAT模拟试题：数学2015上半年SAT模拟试题：数学1. Which of the following could be a value of x, in the diagram above?A. 10B. 20C. 40D. 50E. any of the above2. Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?A. 10B. 15C. 20D. 253. Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?A. 5 : 1B. 10 : 5C. 15 : 2D. 20 : 2E. 25 : 24. A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?A. 2.5πB. 3πC. 5πD. 4πE. 10π5. Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?A. 4C. 8D. 12E. it cannot be determined from the information given.答案：1.Correct Answer: BExplanation:The marked angle, ABC must be more than 90 degrees because it is the external angle of triangle BDC, and must be equal to the sum of angles BDC (90) and DCB. Also ABC is not a straight line and must be less than 180. Therefore 90 5x 180 The only value of x which satisfies this relation is 20.2.Correct Answer: AExplanation:20 large cakes will require the equivalent of 10 helpers working for one hour. 700 small cakes will require the equivalent of 20 helpers working for one hour. This means if only one hour were available we would need 30 helpers. But since three hours are available we can use 10 helpers.3.Correct Answer: EExplanation:Indian stamps are common to both ratios. Mulltiply both ratios by factors such that the Indian stamps are represented by the same number. US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2.Now US : Indian = 25 : 10, and Indian : British = 10 : 2 Hence the two ratios can be combined and US : British = 25 : 24.Correct Answer: CExplanation:Draw the diagram. The diagonal of the rectangle is the diameter of the circle. The diagonal is the hypotenuse of a 3,4,5 triangle, and is therefore, 5. Circumference = π.diameter = 5π5.Correct Answer: DExplanation:If two sets of four consecutive integers have one integer in common, the total in the combined set is 7., and we can write the sets as n + (n + 1) + (n + 2) + (n + 3 ) and (n + 3) + (n + 4) + (n + 5) + (n + 6) Note that each term in the second set is 3 more than the equivalent term in the first set. Since there are four terms the total of the differences will be 4 x 3 = 12更多推荐：| | | | |。
2015年高考数学模拟金卷(二)7页word文档
2015年高考数学模拟金卷（二）（说明：本套试卷满分150分，考试时间120分钟）一、选择题：本大题共12小题，每小题5分，共60分， 1. 设i为虚数单位，复数z1=1+i，z2=2i-1，则复数z1?z2在复平面上对应的点在（）A. 第一象限B. 第二象限C. 第三象限D. 第四象限2. 一名同学先后投掷一枚骰子两次，第一次向上的点数记为x，第二次向上的点数记为y，在直角坐标系xOy中，以（x，y）为坐标的点落在直线2x+y=8上的概率为（）A. B. C. D.3. （理）已知曲线C1：x2+y2-2x=0和曲线C2：y=xcosθ-sinθ（θ为锐角），则C1与C2的位置关系可能为（）A. 相交B. 相切C. 相离D. 以上情况均有（文）若实数x，y满足约束条件x+y≥0，x-y+3≥00≤x≤3，，则z=2x-y 的最大值为（）A. -B. 11C.0D. 94. 2015年某中学派出5名优秀教师去某地区的三所中学进行教学交流，每所中学至少派一名教师，则不同的分配方法有（）A. 80种B. 90种C. 120种D. 150种5. 设数列{an}是以2为首项，1为公差的等差数列，{bn}是以1为首项，2为公比的等比数列，则a +a +…+a 等于（）A. 1033B. 1034C. 2057D. 20586. 不等式 0的解集记为q，已知p是q的充分不必要条件，则实数a 的取值范围是（）A. （-2，-1]B. [-2，-1]C.D. [-2，+∞）7. 下面四个命题：①“直线a∥直线b”的充要条件是“a平行于b所在的平面”；②“直线l⊥平面α内所有直线”的充要条件是“l⊥平面α”；③“直线a，b为异面直线”的充分不必要条件是“直线a，b不相交”；④“平面α∥平面β”的必要不充分条件是“α内存在不共线三点到β的距离相等”.其中正确命题的序号是（）A. ①②B. ②③C. ③④D. ②④8. 椭圆 + =1（a>b>0）的两顶点为A（a，0），B（0，b），且左焦点为F，△FAB是以角B为直角的直角三角形，则椭圆的离心率e为（）A. B. C. D.9. 某品牌香水瓶的三视图如图1（单位：cm），则该几何体的表面积为（）图1A. 95-B. 94-C. 94+D. 95+10. 如图2所示的程序框图输出的结果是（）A. 6B. -6C. 5D. -5图211. △ABC中，∠A=60°，∠A的平分线AD交边BC于D，已知AB=3，且= +λ （λ∈R），则AD的长为（）A. 1B.C. 2D. 312. 已知函数f（x）的定义域为[-1，5]，部分对应值如表1， f（x）的导函数y=f ′（x）的图象如图3所示，下列关于函数f（x）的命题：①函数f（x）的值域为[1，2]；②函数f（x）在[0，2]上是减函数；③如果当x∈[-1，t]时，f（x）的最大值是2，那么t的最大值为4；④当1 A. 4个 B. 3个 C. 2个 D. 1个图3二、填空题：本大题共4小题，每小题5分，共20分，13. （理）某中学200名考生的高考数学成绩近似服从正态分布N（120，100），则此校数学成绩在140分以上的考生人数约为_______.（注：正态总体N（μ，σ2）在区间（μ-2σ，μ+2σ）内取值的概率约为0.954）（文）某校现有高一、高二、高三三个年级共48个教学班，各年级学生数分别是1000，1050，1200，若按分层抽样从全校抽出65名学生，则高二年级比高一年级多抽出_______名学生.14. （理）若锐角α，β满足（1+ tanα）（1+ tanβ）=4，则α+β=_________.（文）函数f（x）=sinx?cosx-sin2x的最小正周期是_________.15. 设a，b均为大于1的正数，且ab+a-b-10=0，若a+b的最小值为m，则m=_________，满足3x2+2y2≤m的整点（x，y）的个数为_________.16. 如图4中的三角形称为希尔宾斯基三角形，在四个三角形中，黑色三角形的个数依次构成数列{an}的前四项，依此着色方案继续对三角形着色，图4（1）黑色三角形的个数的通项公式an=_________；（2）若数列{bn}满足bn= ?an+1，记M=C +C +C ?b1+C ?b2+…+C ?b19，则M的个位数是_________.三、解答题：本大题共6小题，共70分，17. （本小题满分12分）已知单调递增的等比数列{an}满足：a2+a3+a4=28，且a3+2是a2，a4的等差中项.（1）求数列{an}的通项公式；（2）设bn=anlog an，求数列{bn}的前n项和Sn.18. （本小题满分12分）如图5，四棱柱ABCD-A1B1C1D1的底面ABCD 是平行四边形，且AA1⊥底面ABCD，AB=2，AA1=BC=4，∠ABC=60°，点E 为BC中点，点F为B C 中点.（1）求证：平面A1ED⊥平面A1AEF；（2）（理）设二面角A1-ED-A的大小为α，直线AD与平面A1ED所成的角为β，求sin（α+β）的值.（文）求三棱锥E-A1FD的体积.19. （本小题满分12分）某市为“市中学生知识竞赛”进行选拔性测试，且规定：成绩大于或等于90分的有参赛资格，90分以下（不包括90分）的则被淘汰. 若现有500人参加测试，学生成绩的频率分布直方图如图6所示：（1）求获得参赛资格的人数；（2）根据频率直方图，估算这500名学生测试的平均成绩；（3）（理）若知识竞赛分初赛和复赛，在初赛中每人最多有5次选题答题的机会，累计答对3题或答错3题即终止，答对3题者方可参加复赛，已知参赛者甲答对每一个问题的概率都相同，并且相互之间没有影响，已知他连续两次答错的概率为，求甲在初赛中答题个数的分布列及数学期望.（文）若知识竞赛分初赛和复赛，在初赛中每人最多有5次选题答题的机会，累计答对3题或答错3题即终止，答对3题者方可参加复赛，已知参赛者甲答对每一个问题的概率都相同，并且相互之间没有影响，已知他连续两次答错的概率为，求甲在初赛中答题个数为3时的概率.20. （本小题满分12分）如图7，曲线C1是以原点O为中心，F1，F2为焦点的椭圆的一部分，曲线C2是以O为顶点，F2（1，0）为焦点的抛物线的一部分，A ，是曲线C1和C2的交点.（1）求曲线C1和C2所在的椭圆和抛物线的方程.（2）过F2的一条与x轴不垂直的直线，分别与曲线C1，C2依次交于B，C，D，E四点.①求△CDF1面积的取值范围.②（只理科做）若G为CD中点，H为BE中点， ? 是否为定值？若是，求出此定值；若不是；请说明理由.21. （本小题满分12分）（理）函数f（x）=x3+ax2+bx的图象C与x 轴相切于不同于原点的一点，且f（x）的极小值为-4.（1）求函数f（x）的解析式及单调区间；（2）过曲线C上一点P1（x1，y1）（P1不是C的对称中心）作曲线C 的切线，切C于不同于P1（x1，y1）的另一点P2（x2，y2），再过P2（x2，y2）作曲线C的切线，切C于不同于P2（x2，y2）的另一点P3（x3，y3），…，过Pn（xn，yn）作曲线C的切线，切C于不同于Pn（xn，yn）的另一点Pn+1（xn+1，yn+1）. 令x1=-1，求{xn}的通项公式.（文）函数f（x）=x3+ax2+bx的图象与x轴相切于点（-3，0），且函数存在极值.（1）求函数f（x）的解析式及单调区间；（2）过函数y=f（x）图象上一点P1（x1，y1）（P1不是y=f（x）图象的对称中心）作曲线的切线，切于不同于P1（x1，y1）的另一点P2（x2，y2），再过P2（x2，y2）作曲线的切线，切于不同于P2（x2，y2）的另一点P3（x3，y3），…，过Pn（xn，yn）作曲线的切线，切于不同于Pn（xn，yn）的另一点Pn+1（xn+1，yn+1），求xn与xn+1的关系.选做题请考生在第22、23、24三题中任选一题作答，若多做，则按所做的第一题记分.22. （本小题满分10分）选修4-1：几何证明选讲如图8，△ABC内接于⊙O，且AB=AC，过点A的直线交⊙O于点P，交BC的延长线于点D.（1）求证：AC2=AP?AD；（2）若∠ABC=60°，⊙O的半径为1，且P为的中点，求AD的长.23. （本小题满分10分）选修4-4：坐标与参数方程已知直线l经过点P（1，1），且l的一个方向向量v=（，1）.（1）写出直线l的参数方程；（2）设l与圆x2+y2=9相交于两点A，B，求点P到A，B两点间的距离之积.24. （本小题满分10分）选修4-5：不等式选讲已知x-a希望以上资料对你有所帮助，附励志名3条：1、积金遗于子孙，子孙未必能守；积书于子孙，子孙未必能读。
SSAT数学练习题测试讲解
SSAT数学练习题测试讲解SSAT数学练习题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 $__ 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. 13 b. 14 c. 15 d. 16 e. 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 + 1/3E. 3x + 3 1/311 In a classroom of 35 students, 14 our male. What percentof 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 adishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage ofa 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 the following?A. 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 cost of an instrument. During a back to school sale an additional 15% is taken off the discounted price. Julie, a student at the local high school, purchases a flute 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 angles of a triangle measure 15° and 85 °. What is the measure for the third 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 to how 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 swimming lessons 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. __37 On a Map, 1 inch represents 20 miles. The distance between 2 towns is 6 1/5 inches. 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 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. 4339 Sarah is twice as old as her youngest brother. If the difference between their ages is 15 years. How old is her youngest brother?A. 10B. 15C. 20D. 25E. 3040 Which of the following fractions is equal to 5/6?A. 20/30B. 15/24C. 25/30D. 40/54E. 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. $224.51B. $237.60C. $246.55D. $271.38E. $282.3242 In a writing competition, the first place winner receives of the prizemoney. 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. $18,50043 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 treein a straight line?A. 50 feetB. 75 feetC. 120 feetD. 130 feetE. 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 rate 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 edging your flower bed that is 6 yards by 1 yard. How much will edging you flower bed cost?A. $32.48B. $64.96C. $97.44D. $129.92E. $194.8846 If 3x=6x-15 then x + 8=A. 5B. 10C. 11D. 12E. 1347 The number of milliliters in 1 liter is。
2015年初中毕业班学业水平考试暨高中招生模拟测试数学附答案
2015年初中毕业班学业水平考试暨高中招生模拟测试数学 全卷分为第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分.第Ⅰ卷1至2页，第Ⅱ卷3至6页.满分120分，考试时间共120分钟.注意事项：1．答题前，考生务必将自己的姓名、座位号、报名号（考号）写在答题卡上，并将条形码贴在答题卡上对应的虚线框内.同时在答题卡背面第3页顶端用2B 铅笔涂好自己的座位号.2．第Ⅰ卷每小题选出的答案不能答在试卷上，必须用2B 铅笔在答题卡上把对应题目．．．．的答案标号涂黑，如需改动，用橡皮擦擦净后，再选涂其它答案.第Ⅱ卷必须用0.5mm 黑色墨水签字笔书写在答题卡上的指定位置.不在指定区域作答的将无效.3．考试结束，监考人员只将答题卡收回.第Ⅰ卷（选择题 共30分）一、选择题：（每题3分，共30分）1、9的算术平方根是（ ）A ．±3B ．-3C ．3D ．±812、下列各式计算正确的是（ ）A ．222)（x y x y -=- B ．32-x x x = C ．235()x x = D ．54x x x ÷=3、右图是由四个相同的小长方体组成的立体图形，这个立体图形的正视图是（ ）4、下列说法正确的是 （ ）A ．为了了解我市今年夏季冷饮市场冰淇淋的质量，可采用普查的调查方式B ．打开电视机，正在播广告是必然事件C ．销售某种鞋，销售商最感兴趣的是所销售的鞋的尺码的平均数D ．当我市考查人口年龄结构时，符合这一条件的所有资阳市的公民的年龄就是一个样本5、如图1，把一块直角三角板的直角顶点放在直尺的一边上，若∠1=32°，则∠2的度数是（ ）；A ．32°B ．58°C ．68°D ．60° 6、一件商品的原价是100元，经过两次提价后的价格为121元，如果每次提价的百分率都是x ，根据题意，下面列出的方程正确的是（ ）A ．100(1)121x +=B ．100(1)121x -=图数学第1页C ．2100(1)121x +=D ．2100(1)121x -=7、如图2，A 、B 两点在数轴上表示的数分别为a 、b ，下列式子成立的是（ ）A ．ab ＞0B ．a +b ＜0C ．（b ﹣1）（a +1）＞0D ．（b ﹣1）（a ﹣1）＞08、如图3，⊙O 是△ABC 的外接圆，∠BAC =60°，若⊙O 的半径0C 为2，则弦BC 的长为（ ）A ．1 BC ．2 D．9、如图4，△ABD 是等边三角形，以AD 为边向外作△ADE ，使∠AED=30°，且AE =3,DE =2，连接BE ，则BE 的长为（ ）A ．4 BC ．5 D10、如图5，二次函数y=ax 2+bx+c (a ≠0)的图象与x 轴交于A 、B 两点，与y 轴交于C 点，且对称轴为直线x =1，点B 坐标为(－1，0)．则下面的四个结论：①2a +b =0；②8a +c ＜0；③abc ＞0；④当y ＜0时，x ＜－1或x ＞2，⑤对任意实数m ，()m am b a b +≤+.其中正确的结论有（ ）个A ．2B ．3C ．4D ．5第Ⅱ卷（非选择题 共90分）注意事项：1．请用0.5毫米的黑色签字笔在答题卡相应区域作答，超出答案区域的答案无效.2．试卷中标“▲”及方框处是需要你在第Ⅱ卷答题卡上作答的内容或问题.请注意准确理解题意、明确题目要求，规范地表达、工整地书写解题过程或结果.二、填空题：（每题3分，共18分）11、PM2.5是指大气中直径小于或等于0.0000025米的颗粒物，0.0000025米用科学记数图 2 图3法表示应为 米；12、有一组数据：5、2、6、5、4，它们的中位数是 ；13、已知：P A 、PB 与⊙O 相切于A 点、B 点，OA ＝1，P A ＝3，则图6中阴影部分的面积是 （结果保留π）；14、若关于x 的一元二次方程2(1)320m x x -+-=总有两个不相等的实数根，则实数m 的取值范围是 ；15、如图7所示，在三角形ABC 中，点D 、E 分别是边AB 、AC 的中点，DF 过EC 的中点G 并与BC 的延长线交于点F ，BE 与DE 交于点O ．若△ADE 的面积为2，则四边形BOGC 的面积为 ；16、如图8，()111P ,x y ，()222P ,x y ，……()P ,n n n x y 在函数()10y x x =>的图象上，△11POA 、△212P A A 、△323P A A 、……△1n n n P A A -都是等腰直角三角形，斜边1OA 、12A A 、23A A 、，……1n n A A -都在x 轴上（n 是大于或等于2的正整数），则点n P 的坐标是 .（用含n 的式子表示）．三、解答题：（共72分）17、（7分）解方程：11322x x x-+=-- ；18、（8分）某校开展了以“人生观、价值观”为主题的班队活动，活动结束后，初三（2）班数学兴趣小组提出了5个主要观点并在本班50名学生中进行了调查（要求每位同学只选自己最认可的一项观点），并制成了如图9所示的扇形统计图.（1）该班学生选择“和谐”观点的有 人，在扇形统计图中，“和谐”观点所在扇形区域的圆心角是 度.（2）如果该校有1500名初三学生，利用样本估计选择“感恩”观点的初三学生约有 人. 图6 图7 图8 图9（3）如果数学兴趣小组在这5个主要观点中任选两项观点在全校学生中进行调查，求恰好选到“和谐”和“感恩”观点的概率（用树状图或列表法分析解答）19.（8分）关于x 的不等式组23(2)24x a x x -≥-⎧⎨-<⎩ （1）若2a =.求这个不等式组的解集.（2）若这个不等式组的整数解有3个，求a 的取值范围.20、（8分）如图10，在⊙O 中，AB =AC ，BD 为直径，弦AD 与BC 相交于点E ，延长DA 到F ，使∠ABF =∠ABC .（1）求证：BF 是⊙O 的切线；（2）若AD=8，tan ∠ABF =34，求DE 的长．21、（9分）如图11，在平面直角坐标系中，直线l 与x 轴相交于点M （3,0），与y 轴相交于点N （0，-4），反比例函数k y x =（x ＞0）的图象经过线 段MN 的中点A ，（1）求直线l 和反比例函数的解析式；（2）在函数k y x=（x ＞0）的图象上取异于点A 的一点B ， 作BC ⊥x 轴于点C ，连接OB 交直线l 于点P ．若△ONP 的 面积是△OBC 面积的3倍，求点P 的坐标．图10图1122、（9分）如图12，一艘船以每小时60海里的速度自A向正北方向航行，船在A处时，灯塔S在船的北偏东30°，航行1小时后到B处，此时灯塔S在船的北偏东75°，（运算结果保留根号）（1）求船在B处时与灯塔S的距离；（2）若船从B处继续向正北方向航行，问经过多长时间船与灯塔S的距离最近．23、（11分）如图13所示，现有一张边长为4的正方形纸片ABCD，点P为正方形AD 边上的一点（不与点A、点D重合）将正方形纸片折叠，使点B落在P处，点C落在G处，PG交DC于H，折痕为EF，连接BP、BH．（1）求证：∠APB=∠BPH；（2）当点P在边AD上移动时，△PDH的周长是否发生变化？并证明你的结论；（3）设AP为x，四边形EFGP的面积为S，求出S与x的函数关系式，试问S是否存在最小值？若存在，求出这个最小值；若不存在，请说明理由．24、（12分）如图14-1，在直角坐标系中，O是坐标原点，点A在y轴正半轴上，二次函数y=ax2+16x+c的图象F交x轴于B、C两点，交y轴于M点，其中B（﹣3，0），M（0，﹣1）．已知AM=BC．（1）求二次函数的解析式；（2）证明：在抛物线F上存在点D，使A、B、C、D四点连接而成的四边形恰好是平行四边形，并请求出直线BD的解析式；（3）在（2）的条件下，设直线l过D且分别交直线BA、BC于不同的P、Q两点，AC、BD相交于N．①若直线l⊥BD，如图1，试求11BP BQ的值；图12图13②若l为满足条件的任意直线，如图14-2．①中的结论还成立吗？若成立，证明你的猜想；若不成立，请举出反例。
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沃邦教育2015年SSAT数学练习题1 What is the perimeter of a rectangle with side lengths of 8 and 3?a. 6b. 11c, 16d. 22e. 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 + 1/3E. 3x + 3 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 the following?A. 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 angles of a triangle measure 15° and85 °. 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. 18B. 24C. 32D. 36E. 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. 10B. 15C. 20D. 25E. 3040 Which of the following fractions is equal to 5/6?A. 20/30B. 15/24C. 25/30D. 40/54E. 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. $224.51B. $237.60C. $246.55D. $271.38E. $282.3242 In a writing competition, the first pl ace winner receives ½ of the prizemoney. The second runner up receives ¼ 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. $18,50043 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 tree in a straight line?A. 50 feetB. 75 feetC. 120 feetD. 130 feetE. 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 rate 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 bed cost?A. $32.48B. $64.96C. $97.44D. $129.92E. $194.8846 If 3x=6x-15 then x + 8=A. 5B. 10C. 11D. 12E. 1347 The number of milliliters in 1 liter isA. 10,000B. 1,000C. 0.1D. 0.01E. 0.001。