深国交入学G1考试模拟试题二

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2020年最新深圳国际交流学院G1入学考试数学训练2

2020年最新深圳国际交流学院G1入学考试数学训练一．选择题（共8小题）1．若a≠b，且a2﹣4a+1＝0，b2﹣4b+1＝0，则的值为（）A．B．1 C．.4 D．32．关于x的方程kx2+2x﹣1＝0有实数根，则k的取值范围是（）A．k≥﹣1 B．k≥﹣1且k≠0 C．k≤﹣1 D．k≤1且k≠0 3．函数y＝与y＝﹣kx2+k（k≠0）在同一直角坐标系中的图象可能是（）A．B．C．D．4．如图，某小区计划在一块长为32m，宽为20m的矩形空地上修建三条同样宽的道路，剩余的空地上种植草坪，使草坪的面积为570m2．若设道路的宽为xm，则下面所列方程正确的是（）A．（32﹣2x）（20﹣x）＝570B．32x+2×20x＝32×20﹣570C．（32﹣x）（20﹣x）＝32×20﹣570D．32x+2×20x﹣2x2＝5705．如图是抛物线y＝ax2+bx+c（a≠0）的部分图象，其顶点坐标为（1，n），且与x轴的一个交点在点（3，0）和（4，0）之间．则下列结论：①a﹣b+c＞0；②3a+b＝0；③b2＝4a（c﹣n）；④一元二次方程ax2+bx+c＝n﹣1有两个不相等的实数根．其中正确结论的个数是（）A．1 B．2 C．3 D．46．甲、乙两车间同时开始加工一批服装．从开始加工到加工完这批服装甲车间工作了9小时，乙车间在中途停工一段时间维修设备，然后按停工前的工作效率继续加工，直到与甲车间同时完成这批服装的加工任务为止．设甲、乙两车间各自加工服装的数量为y （件）．甲车间加工的时间为x（时），y与x之间的函数图象如图所示，则下列结论错误的是（）A．甲车间每小时加工服装80件B．这批服装的总件数为1140件C．乙车间每小时加工服装为60件D．乙车间维修设备用了4小时7．如图，在平面直角坐标系中，A（1，2），B（1，﹣1），C（2，2），抛物线y＝ax2（a≠0）经过△ABC区域（包括边界），则a的取值范围是（）A．a≤﹣1或a≥2 B．≤a≤2C．﹣1≤a＜0或1＜a≤D．﹣1≤a＜0或0＜a≤28．如图，在单位为1的方格纸上，△A1A2A3，△A3A4A5，△A5A6A7，…，都是斜边在x轴上，斜边长分别为2，4，6，…的等腰直角三角形，若△A1A2A3的顶点坐标分别为A1（2，0），A2（1，1），A3（0，0），则依图中所示规律，A2019的坐标为（）A．（﹣1008，0）B．（﹣1006，0）C．（2，﹣504）D．（1，505）二．填空题（共5小题）9．因式分解：x3﹣9x＝．10．已知＝+，则实数A＝．11．如图，菱形ABCD的顶点A，B的横坐标分别为1，4，BD∥x轴、双曲线y＝（x＞0）经过A，B两点，则菱形ABCD的面积为．12．如图是抛物线型拱桥，当拱顶离水面2m时，水面宽4m，水面下降2m，水面宽度增加m．13．已知直线y＝kx（k≠0）经过点（12，﹣5），将直线向上平移m（m＞0）个单位，若平移后得到的直线与半径为6的⊙O相交（点O为坐标原点），则m的取值范围为．三．解答题（共4小题）14．计算：+﹣﹣（）﹣1．15．如图，AB为⊙O的直径，弦CD∥AB，E是AB延长线上一点，∠CDB＝∠ADE．（1）DE是⊙O的切线吗？请说明理由；（2）求证：AC2＝CD•BE．16．某中学计划购买A型和B型课桌凳共200套．经招标，购买一套A型课桌凳比购买一套B型课桌凳少用40元，且购买4套A型和5套B型课桌凳共需1820元．（1）求购买一套A型课桌凳和一套B型课桌凳各需多少元？（2）学校根据实际情况，要求购买这两种课桌凳总费用不能超过40880元，并且购买A 型课桌凳的数量不能超过B型课桌凳数量的，求该校本次购买A型和B型课桌凳共有几种方案？哪种方案的总费用最低？17．如图，二次函数y＝ax2+2x+c的图象与x轴交于点A（﹣1，0）和点B，与y轴交于点C（0，3）．（1）求该二次函数的表达式；（2）过点A的直线AD∥BC且交抛物线于另一点D，求直线AD的函数表达式；（3）在（2）的条件下，在x轴上是否存在一点P，使得以B、C、P为顶点的三角形与△ABD相似？若存在，求出点P的坐标；若不存在，请说明理由．参考答案与试题解析一．选择题（共8小题）1．若a≠b，且a2﹣4a+1＝0，b2﹣4b+1＝0，则的值为（）A．B．1 C．.4 D．3【分析】根据根与系数的关系即可求出答案．【解答】解：由题意可知：a、b是方程x2﹣4x+1＝0的两个不同的实数根，∴由根与系数的关系可知：ab＝1，a+b＝4，∴a2+1＝4a，b2+1＝4b，∴原式＝+＝＝＝1，故选：B．2．关于x的方程kx2+2x﹣1＝0有实数根，则k的取值范围是（）A．k≥﹣1 B．k≥﹣1且k≠0 C．k≤﹣1 D．k≤1且k≠0 【分析】由于k的取值范围不能确定，故应分k＝0和k≠0两种情况进行解答．【解答】解：（1）当k＝0时，﹣6x+9＝0，解得x＝；（2）当k≠0时，此方程是一元二次方程，∵关于x的方程kx2+2x﹣1＝0有实数根，∴△＝22﹣4k×（﹣1）≥0，解得k≥﹣1，由（1）、（2）得，k的取值范围是k≥﹣1．故选：A．3．函数y＝与y＝﹣kx2+k（k≠0）在同一直角坐标系中的图象可能是（）。

2018年深圳国际交流学院G1入学考试数学数学模拟试卷2

的值为 0，则 x 的取值为（
）
B．x=3
C．x=﹣3 或 x=1 D．x=3 或 x=﹣1
4．若分式 A．m≥1
不论 x 取何值总有意义，则 m 的取值范围是（
）
B．m＞1
C． m≤1
D．m＜1
5．如图，在平面直角坐标系第一象限有一点 P，其横坐标为 3，在 x 轴上有一点
A（﹣1，0）．已知 PA 两点间的距离为2 5，则 P 的纵坐标为（
7
6
23．设 a、b 是任意两个不等实数，我们规定：满足不等式 a≤x≤b 的实数 x 的所有取值的全体叫做闭区间，表示为[a，b]．对于一个函数，如果它的自变量 x 与函数值 y 满足：当 m≤x≤n 时，有 m≤y≤n，我们就称此函数是闭区间[m，n] 上的“闭函数”．（1）反比例函数 y= 是闭区间[1，2013]上的“闭函数”吗？请判断并说明理由；（2）若一次函数 y=kx+b（k≠0）是闭区间[m，n]上的“闭函数”，求此函数的解析式；（3）若二次函数 y= x2﹣ x﹣ 是闭区间[a，b]上的“闭函数”，求实数 a，b 的值．
2�� + 4(�� < −3) −2(−3 ≤ �� ≤ 3)
2�� − 8(�� > 3)
．
12．如图，正六边形的边长为 2，分别以它的三个不相邻的顶点为圆心，2 为半
径画弧，则阴影部分面积为
．
13．若关于 x 的一元二次方程（x﹣2）（x﹣3）=m 有实数根 x1，x2 且 x1≠x2，有下列结论：
）
1
A．2
B．﹣2
C．
D．1
11
6．根据下列表格中的对应值，判断方程 ax2+bx+c=0（a≠0，a，b，c 为常数）

2020年深国交G1入学考试数学模拟试卷2答案(初二新版)

12 解得 x1 6 2 6 ， x2 6 2 6 ． ∴ CD＝| x1 x2 | 4 6 ≈10 ． ∴ BD＝13-6+10＝17(米)．答：他应再向前跑 17 米．
19.(1)如图所示，设第一次落地时，抛物线的表达式为 y a(x 6)2 4 ．由已知当 x＝0 时，y＝1．即1 36a 4，∴ a 1 ．
12 ∴ 表达式为 y 1 (x 6)2 4 ．
12
(2)令 y＝0， 1 (x 6)2 4 0 ． 12
∴ (x 6)2 48．解得 x1 4 3 6 ≈13 ， x2 4 3 6 0 (舍去)． ∴ 足球第一次落地距守门员约 13 米． (3)如图所示，第二次足球弹出后的距离为 CD，根据题意得 CD＝EF(即相当于将抛物线 AEMFC 向下平移了 2 个单位)， ∴ 2 1 ( x 6)2 4 ，
x1
1 时，原方程无意义．∴
x
3 2
是原方程的解．
（2） x4 x2 6 0 ．
解：设 x2 y ，那么原方程可化为 y2 y 6 0
解得 y1 3 ； y2 2 当 y 3 时， x2 3 ； x 3
当 y 2 时， x2 2 不符合题意，舍去．
所以原方程的解为 x1 3 ， x2 3 ．
2020年深国交入学考试
G1 数学试题模拟2（初二新版）
一、选择题（共 10 小题，每小题 4 分，共 40 分）
1-5 BABBA 6-10 DACCA
二、填空题（共 6 小题，每小题 4 分，共 24 分）
11．18
12．－2
13．300°
14．y1＜y21）设生产 A 型桌椅 x 套，则生产 B 型桌椅 (500 x) 套，由题意得 0.5x 0.7 (500 x) ≤302 2x 3 (500 x) ≥1250

2020年最新深圳国际交流学院G1入学考试数学训练试题

2020年最新深圳国际交流学院G1入学考试数学训练知识点1 :函数的定义与自变量的取值范围1．（3分）下列图象能表示y是x的函数的是（）A．B．C．D．2．（3分）在函数y＝+中，自变量x的取值范围是（）A．x≥1B．x≥1且x≠3C．x≠3D．1≤x≤3知识点2 :一次函数的定义，图像与性质3．（3分）若y＝（m﹣1）x2﹣|m| +3是关于x的一次函数，则m的值为（）A．1 B．﹣1 C．±1 D．±24．（3分）以下关于直线y＝2x﹣4的说法正确的是（）A．直线y＝2x﹣4与x轴的交点坐标为（0，﹣4）B．坐标为（3，3）的点不在直线y＝2x﹣4上C．直线y＝2x﹣4不经过第四象限D．函数y＝2x﹣4中，y的值随x的增大而减小5．（3分）A（x1，y1）和B（x2，y2）是一次函数y＝（k2+1）x+2图象上的两点,且x1＜x2，则y与y2的大小关系是（）1A．y1＝y2B．y1＜y2C．y1＞y2D．不确定6．（3分）已知正比例函数y＝kx（k≠0）的图象经过二、四象限，则一次函数y＝kx﹣k的图象大致是（）A．B．C．D．7. （3分）将函数y=2x-3的图象向上平移2个单位得到的函数解析式为。

知识点3 :一次函数图像与不等式，方程（组）的关系8．（3分）函数y＝kx+b（k、b为常数，k≠0）的图象如图，则关于x的不等式kx+b＜0的解集为（）A．x＞0 B．x＜0 C．x＜2 D．x＞29．（3分）如图，一次函数y＝x+1与y＝2x﹣1图象的交点是（2，3），观察图像，直接写出方程组 y＝x+1 的解为（）y＝2x﹣1A． B．C． D．知识点4 :观察图像，获取信息10．（3分）电话卡上存有4元话费，通话时每分钟话费0.4元，则电话卡上的余额y（元）与通话时间t（分钟）之间的函数图象是图中的（）A．B．C．D．11．（3分）甲、乙两同学骑自行车从A地沿同一条路到B地，已知乙比甲先出发，他们离出发地的距离s/km和骑行时间t/h之间的函数关系如图所示．根据图象信息，以下说法错误的是（）A．他们都骑了20kmB．两人在各自出发后半小时内的速度相同C．甲和乙两人同时到达目的地D．相遇后，甲的速度大于乙的速度12. （3分）一台印刷机每年可印刷的书本数量y（万册）与它的使用时间x（年）成反比例关系，当x=2时，y=20．则y与x的函数图象大致是（）A． B． C． D．知识点5: 分段函数的定义与图像13．（3分）如图是一个运算程序的示意图，若输出y的值为2，则输入的x值可能为（）A．3 B．±1C．1或3 D．±1或314．（3分）小刘下午5点30分放学匀速步行回家，途中路过鲜花店为过生日的妈妈选购了一束鲜花，6点20分到家，已知小刘家距学校3千米，下列图象中能大致表示小刘离学校的距离S（千米）与离校的时间t（分钟）之间的关系的是（）A． B．C． D．15．（9分）某城市出租车的收费标准为：3千米以内（含3千米）收费8元，超过3千米时，超过的部分每千米收费1.4元．（1）写出车费y（元）和行车里程x（千米）之间的关系式；（2）甲乘坐13千米需付多少元钱？若乙付的车费是36元，则他乘坐了多少里程？知识点6: 反比例函数的定义，图像与性质16. （3分）在下列函数中，y是x的反比例函数的是（）A．y＝3x B．y＝C．y＝D．y＝17．（3分）已知函数是反比例函数，且当x＜0时，y随着x的增大而增大，则m的取值是．18．（3分）若点A（﹣3，y1），B（﹣2，y2），C（1，y3）都在反比例函数y＝（k<0）的图象上，则y1，y2，y3的大小关系是（）A．y2＜y1＜y3B．y3＜y2＜y1C．y1＜y2＜y3D．y3＜y1＜y219．（3分）对于反比例函数y＝，下列说法不正确的是（）A．图象分布在第一、三象限B．当x＞0时，y随x的增大而减小C．图象经过点（2，3）D．若点A（x1，y1），B（x2，y2）都在图象上，且x1＜x2，则y1＜y220．（3分）已知函数y＝图象如图，以下结论，其中正确的有（）个：①k＜0；②y随x的增大而增大；③若A（﹣1，a），点B（2，b）在图象上，则a＜b（﹣x，﹣y）也在图象上．④若P（x，y）在图象上，则点P1A．4个 B．3个 C．2个 D．1个21．（3分）已知A（m+3，2），B（3，）是同一个反比例函数图象上的两个点，则m＝知识点7: 反比例函数中K的几何意义22．（3分）反比例函数图象的一支如图所示，△POM的面积为2，则该函数的解析式是（）A．y＝ B．y＝C．y＝﹣ D．y＝﹣23．（3分）如图，在反比例函数y＝（x＞0）的图象上，有点P1、P2、P3、P4，它们的横坐标依次为1，2，3，4．分别过这些点作x轴与y轴作垂线，图中所构成的阴影部分的面积从左到右依次为S1、S2、S3，则S1+S2+S3＝（）A．2 B．2.5C．3 D．无法确定知识点 8:反比例函数的应用24. （3分）某种气球内充满了一定质量的气体，当温度不变时，气球内气体的气压P（kPa）是气球体积V的反比例函数，其图象如图所示，当气球内的气压大于160kPa时，气球将爆炸，为了安全，气球的体积应该（）A．不小于m3 B．小于m3C．不大于m3 D．小于m3知识点 9: 反比例函数与一次函数结合25．（3分）函数y＝﹣2x与函数y＝﹣在同一坐标系中的大致图象是（）A．B．C．D．26．（3分）如图，正比例函数y1=k1x的图象与反比例函数y2=的图象相交于A，B两点，其中点A的横坐标为2，当y1＞y2时，x的取值范围是（）A．x＜﹣2或x＞2 B．x＜﹣2或0＜x＜2C ．﹣2＜x ＜0或0＜x ＜2D ．﹣2＜x ＜0或x ＞227．（12分）如图，直线y ＝kx +b 与反比例函数的图象分别交于点A （﹣1，2），点B （﹣4，n ），直线与x 轴，y 轴分别交于点C ，点D ．（1）求此一次函数和反比例函数的解析式；（2）求△AOB 的面积．28．（10分）如图所示,已知一次函数y=kx+b(k≠0)的图象与x 轴、y 轴分别交于A 、B 两点,且与反比例函数y=mx (m≠0)的图象在第一象限交于C 点, CD 垂直于x 轴,垂足为 D.若OA=OB=OD=1,(1)求点A 、B 、D 的坐标；(2)求一次函数和反比例函数的解析式.yOxDC B A29．（14分）为了预防传染病,某学校对教室采用药薰消毒法进行消毒. 已知药物燃烧时,室内每立方米空气中的含药量y(毫克)与时间x(分钟)成正比例,药物燃烧完后,y与x成反比例(如图所示),现测得药物8分钟燃毕, 此时室内空气中每立方米的含药量为6毫克.请根据题中所提供的信息,解答下列问题:(1)分别求出药物燃烧时及药物燃烧后y 关于x 的函数关系式, 并写出自变量x 的取值范围，(2)研究表明,当空气中每立方米的含药量低于 1.6毫克时学生方可进教室,那么从消毒开始,至少需要经过几分钟后,学生才能回到教室？(3)研究表明,当空气中每立方米的含药量不低于3毫克且持续时间不低于10 分钟时,才能有效杀灭空气中的病菌,那么此次消毒是否有效?为什么?参考答案1.D2.B3.B4.B5.B6.C7.y=2x-1,8.D 9.B 10.D 11.C 12.C 13.C 14.C8 x≤315.(1)y = (2)甲需付22元，乙乘坐了23千米。

【教育资料】【深圳名师】深国交中考自主招生2018-2019G1入学考试数学模拟试题无答案学习专用

教育资源H GCBD E A2019-2019年深圳国际交流学院入学考试G1数学模拟试题（时间：70分钟满分：100分）姓名：_____ 分数：______一．选做题（共10小题，每题3分，共30分）1．若a ≤1，则化简后为（）. （A ）（B ）（C ）（D ）2．阳光中学阅览室在装修过程中，准备用边长相等的正方形和正三角形两种地砖镶嵌地面，在每个顶点的周围正方形、正三角形地砖的块数可以分别是A 、2，2B 、2，3C 、1，2D 、2，13．已知A 、B 两地相距4千米。

上午8:00，甲从A 地出发步行到B 的，8:20乙从B 地出发骑自行车到A 地，甲乙两人离A 地的距离（千米）与甲所用的时间(分)之间的关系如图所示。

由图中的信息可知，乙到达A 地的时间为A 、8:30B 、8:35C 、8:40D 、8:454．如图，在正方形ABCD 的外侧，以AD 为斜边作等腰直角△ADE ，BE 、CE 分别交AD 于点G 、H ，若△GHE 的面积为2，则△CDH 的面积为（）A 、2；B 、22；C 、32；D 、4；5．已知抛物线y =ax 2+bx +c (a ＞0)的对称轴为直线x =－1，与x 轴的一个交点为(x 1，0)，且0＜x 1＜1，下列结论：①9a －3b ＋c ＞0；②b ＜a ；③3a ＋c ＞0。

其中正确结论的个数是A 、0B 、1C 、3D 、36．如图，已知O 是四边形ABCD 内一点，OA OB OC ==，70ABC ADC ∠=∠=°，则DAO DCO ∠+∠的大小是（） A ．70° B ．110° C ．140° D ．150° 7．如图，已知点A 是一次函数y =x 的图象与反比例函数xy 2=的图象在第一象限内的交点，点B 在x 轴的负半轴上，且OA =OB ，那么△AOB 的面积为A 、2B 、22C 、2D 、22 8．如图，在矩形ABCD 中，对角线AC 、BD 相交于点G ，E 为AD 的中点，连接BE 交AC 于点F ，连接FD ，若∠BFA =90°，则下列四对三角形：①△BEA 与△ACD ；②△FED 与△DEB ；③△CFD 与△ABC ；④△ADF 与△CFB 。

深国交G1入学考试英语模拟试题

深国交G1入学考试英语模拟试题(总7页)-CAL-FENGHAI.-(YICAI)-Company One1-CAL-本页仅作为文档封面，使用请直接删除1. “Tommy, run! Be quick! The house is on fire!” the mothershouted, with clearly ________ in her voice．A．anger B．rudeness C．regret D．panic2．The two girls are so alike that strangers find ______ difficult to tell one from the other．A．it B．them C．her D．that3． Planning so far ahead _____ no sense—so many things will have changed by next year．．A．made B．is making C．makesD．has made4．Tom______ in the library every night over the last three months．A．works B．workedC．has been working D．had been working5．—Bob has gone to California．—Oh, can you tell me when he _________A．has left B．left C．is leaving D．wouldleaving6．The next thing he saw was smoke ______ from behind the house．A．rose B．rising C．to rise D．risen7．Sarah pretended to be cheerful, ______nothing about the argument．A．says B: said C．to sayD．saying8．The rare fish, _____ from the cooking pot, has been returned to the sea．A．saved B．saving C．to be saved D．havingsaving9．When Mom looked back on the early days of their marriage, she wondered how they had managed with ______ money．A．so few B．such few C．so little D．suchlittle10．Mr. Stevenson is great to work for—I really couldn't ask for a＿boss．A．better B．goodC．best D．still better11．I can _____ the house being untidy, but I hate it if it’s not clean．A．come up with B．put up with C．turn toD．stick to12．____ Barbara Jones offers to her fans is honesty and happiness．A．Which B．What C．That D．Whom13. In my opinion, what he told us just now about the affair simply doesn’t make any .A. ideaB. meaningC. senseD. point14. I didn’t like the story, , it’s too long, als o it was written by a writer I don’t knowA. for one thingB. for a thingC. althoughD. in one hand15. It is strongly suggested that measures students to cheat in the exams.A. be taken to preventB. be taken to forbidC. are taken to preventD. are taken to forbid1.My mother is not satisfied with my _____________(explain).2._____________(practise) makes perfect.3.The book written by him is really worth_____________(read) again.4.Golf has gained ____________(popular) among the wealthy in my country.5.The boy finally___________(success) in passing the test.6.He is an ___________(energy) boy.7.The famous pop singer sang many songs, ______________(include) some of my favorite.8.He is busy____________(prepare) for the coming test.9.She could not wait any ___________(long).10.Jim was deeply ___________(influence) by his mother.11.She felt very sorry about her children's bad ____________(behave).12.We'll go for a picnic if it _____________(not rain) tomorrow.13.It's important to exercise______________(regular).14.Much to his ______________(surprising), she gave him her phone number.15. His father's ______________(die) made him very sad.16. Nowadays blogs are much more useful than __________diaries. (tradition)17. In the end, the young man came up with a _____________(wonder) idea.18. They _____(not hear) of that thing yet.19. I happened _________(meet) my old friend in the street yesterday. bike needs _________(repair)thought the young man was a queue _______________(jump).Xiang is the ____________(proud) of the Chinese people.23. The film The promise which (direct) by Chen doesn’t interest me as much.24. It is said that at least 23 people (kill) in the gas explosion in a coal mine in Shaanxi Province.25. They (make) to stay at home all day because of the bad weather.Ⅱ完形填空Number sense is not the ability to count. It is the ability to recognize a 1 in number. Human beings are born with this ability.2 , Experiments show that many animas are, too. For example, many birds have good number sense. If a nest has four eggs and you remove one, the bird will not3 . However, if you remove two, the bird4 leaves. This means that the bird knows the5 between twoand three.Another interesting experiment showed a bird’s 6 number sense. A man was trying to take a photo of a crow(乌鸦) that had anest in a tower, but the crow always left when she saw him coming.The bird did not 7 until the man left the tower. The man had an8 . He took another man with him to the tower. One man left andthe other stayed, but they did not 9 the bird. The crow stayed away until the second man left, too. The experiment was 10 with three men and then with four men. But the crow did not return to the nest until all the men were 11 . It was not until five men wentinto the tower and only four left that they were 12 able tofool the crow.How good is a human’s number senseIt’s not very good. For example, babies about fourteen months old almost always notice if something is taken away from a 13 group. But when the number goes beyond three or four, the children are14 fooled.It seems that number sense is something we have in common withmany animals in this world, and that our human 15is not much better than a crow’s.1. A. rise B. pattern C. changeD. trend2. A. Importantly B. Surprisingly C. Disappointedly D. Fortunately3. A. survive B. care C. hatchD. notice4. A. generally B. sincerely C. casuallyD. deliberately5. A. distance B. range C.difference D. interval6. A. amazing B. annoying C. satisfyingD. disturbing7. A. relax B. recover C. reactD. return8. A. appointment B. excuse C. ideaD. explanation9. A. fool B. hurt C. catchD. kill10. A. reported B. repeated C. designedD. approved11. A. confused B. gone C. tiredD. drunk12. A. gradually B. luckily C.strangely D. finally13. A. single B. small C. localD. new14. A. seldom B. temporarily C. merelyD. often15. A. sight B. nature C. abilityD. beliefⅢ阅读理解A．Imagination and fantasy can play an important role in achievingthe things we fear. Children know this very well. Fred Epstein, inhis book I Make It to Five, tells a story he heard from one of his friends about Tom, a four-year-old boy with a cancer in his back bone. He came through several operations and a lot of pain by mastering his imagination.Tom loved to pretend, and he particularly loved to play superheroes. Dr. Epstein explained that it was actually a brilliant way for his young mind to handle the terrifying and painful life he led.The day before his third trip to the operating room, Tom wasterribly afraid. “ Maybe I could go as Superman,” he whispered tohis mom. Hearing this, the mother hesitated for while. She hasavoided buying the expensive costume(戏装), but finally she agreed.The next day Tom appeared as the powerful Superman, showing off through the hospital halls and coolly waving his hand to the people greeting him along the way. And Tom, with the strength of his fantasy, successfully made it through the operation.The power of imagination need not be reserved for children only. We all have the power to use our fantasies to attempt things we never thought possible, to go through those things that seem impossible,and to achieve what we never believed we could. Just as Dr. Epstein puts it, “If you can dream it, you can do it.”It doesn’t mean that y ou should dress as a superhero for yournext job interview. But, next time you are tested in a way that seems impossible, imagine what it would take to overcome it. Become the person you need to become to win over your challenge and do it inyour mind first. So, let your imagination run wild, and dare to dream.26. What do we know about Tom?A. He was seriously ill.B. He was a dishonest boy.C. He was crazy about magic.D. He was Dr. Epstein’s patient.27. What can be inferred about Tom’s motherA. She was a rich lady.B. She refused Tom’s request.C. She wanted Tom to be a superhero.D. She wanted to get Tom through the pain.28. When Tom went for the third operation, he_________.A. pretended to be painfulB. acted like a superheroC. appeared in poor spiritsD. argued with his mother29. In the last paragraph, you are advised________.A. to go through some difficult testsB. towake up from your wild dreamsC. to become a powerful person in your mindD. to wear expensive clothes for job interviews30. What is the purpose of the passage?A. To tell us an interesting story.B. Tohelp us make right decisions.C. To advise us to care about children.D. To encourage us to use our imagination.B.Some people think that success is only for those with talent or those who grow up in the right family, and others believe thatsuccess mostly comes down to luck. I’m not going to say luck, talent, and circumstances don’t come into play because they do. Some people are born into the right family while others are born with great intelligence, and that’s just the reality of how life is.However, to succeed in life, one first needs to set a goal andthen gradually make it more practical. And, in addition to that, in order to get really good at something, one needs to spend at least 10,000 hours studying and practicing. To become great at certain things, it’ll require even more time, time that most people won’t put in.This is a big reason why many successful people advise you to do something you love. If you don’t enjoy what you do, it is going to feel like unbearable pain and will likely make you quit well before you ever become good at it.When you see people exhibiting some great skills or having achieved great success, you know that they have put in a huge part of their life to get there at a huge cost. It’s sometimes easy to think they got lucky or they were born with some rare talent, but thinking that way does you no good, and there’s a huge chance that you’re wrong anyway.Whatever you do, if you want to become great at it, you need to work day in and day out, almost to the point of addiction, and over a long period of time. If you’re not willing to put in the time and work, don’t expect to receive any rewards. Consistent, hard work won’t guarantee you the level of success you may want, but it will guarantee that you will become rally good at whatever it is you putall that work into.31. Paragraph 1 mainly talks about__________.A. the reasons for successB. the meaning of successC. the standards of successD. the importance of success32. Paragraph 2, the underlined word that refers to__________.A. being good at somethingB. setting a practical goalC. putting in more timeD. succeeding in life33. Successful people suggest doing what one lovesbecause_____________.A. work makes one feel painB. one tends to enjoy his workC. one gives up his work easilyD. it takes a lot of time to succeed34. What can be infer from Paragraph 4?A. Successful people like to show their great skills.B. People sometimes succeed without luck or talent.C. People need to achieve success at the cost of life.D. It helps to think that luck or talent leads to success.35. What is the main theme of the passage?A. Having a goal is vital to success.B. Being good is different from being great.C. One cannot succeed without time and practice.D. Luck, talent and family help to achieve success.C.One day, when I was working as a psychologist in England, an adolescent boy showed up in my office. It was David. He kept walingup and down restlessly, his face pale, and his hands shaking slightly. His head teacher had referred him to me. “This boy has lost his family,” he wrote. “He is understandably very sad and refuses totalk to others, and I’m very worried about him. Can I help?”I looked at David and showed him to a chair. How could I help himThere are problems psychology doesn’t have the answer to, and which no wards can describe. Sometimes the best thing one can do isto listen openly and sympathetically.The first two times we met, David didn’t say a word. He sat there, only looking up to look at the children’s drawings on thewall behind me. I suggested we play a game of chess. He nodded. After that he played chess with me every Wednesday afternoon---in complete silence and without looking at me. It’s not easy to cheat in chess, but I admit I made sure David won once or twice.Usually, he arrived earlier than agreed, took the chess board and pieces from the shelf and began setting them up before I even got a chance to sit down. It seemed as if he enjoyed my company. But whydid he never look at me?“Perhaps he simply needs someone to share his pain with,” I thought. “Perhaps he senses that I respect his suffering.” Some months later, when we were playing chess, he looked up at me suddenly.“It’s your turn,” he said.After that day, David started talking. He got friends in school and joined a bicycle club. He wrote to me a few times, about hisbiking with some friends, and about his plan to get into university. Now he had really started to live his own life.Maybe I gave David something. But I also learned that one---without any words---can reach out to another person. All it takes isa hug, a shoulder to cry on, a friendly touch, and an ear that listens.36. When he first met the author, David_________.A. felt a little excitedB. walked energeticallyC. looked a little nervousD. showed up with his teacher37. As a psychologist, the author __________.A. was ready to listen to DavidB. was skeptical about psychologyC. was able to describe David’s problemD. was sure of handling David’s problem38. David enjoyed being with the author because he____________.A. wanted to ask the author for adviceB. needed to share sorrow with the authorD. beat the author many times in the chess game39. What can be inferred about David?A. He recovered after months of treatment.B. He liked biking before he lost his family.C. He went into university soon after starting to talk.D. He got friends in school before he met the author.40. What made David change?A. His teacher’s help.B. Theauthor’s friendship.C. His exchange of letters with the author.D. The author’s silent communication with him.D.While Jennifer was at home taking an online exam for her businesslaw class, a monitor(监控器) a few hundred miles away was watchingher every move.Using a web camera equipped in Jennifer’s Los Angeles apartment,the monitor in Phoenix tracked how frequently her eyes moved from the computer screen and listened for the secret sounds of a possiblehelper in the room. Her Internet access was locked---remotely---toprevent Internet searches, and her typing style was analyzed to makesure she was who she said she was; Did she enter her student numberat the same speed as she had in the past Or was she slowing down In the battle against cheating, this is the cutting edge and akey to encourage honestly in the booming field of on line education.The technology gives trust to the entire system, to the institutionand to online education in general. Only with solid measures against cheating, experts say, can Internet universities show that theirexams and diplomas are valid---that students haven’t searched theInternet to get the right answers.Although online classes have existed for more than a decade, the concern over cheating become sharper in the last year with the growthof “open online courses.” Private colleges, public universities and corporations are jumping into the online education field, spendingmillions of dollars to attract potential students, while also takingsteps to help guarantee honesty at a distance.Aside from the web cameras, a number of other high-tech methodsare becoming increasingly popular. Among them are programs that check student’s identities using personas information, such as thetelephone numbers they once used.Other programs can produce unique exams by drawing on a largelist of questions and can recognize possible cheaters by analyzingwhether difficult test questions are answered at he same speed aseasy ones. As in many university classes, term papers are scannedagainst some large Internet data banks for cheating.41. Why was Jennifer watched by a monitor in an online exam?42. The underlined expression cutting edge in Paragraph 3 is closestin meaning to _______.A. advanced techniqueB. sharpening toolC. effective ruleD. dividing line43. For Internet universities, exams and diplomas will be validif__________.A. they can attract potential studentsB. they can defeat academic cheatingC. they offer students online helpD. they offer many online courses44. Some programs can find out possible cheaters by_________.A. checking the question answering speedB. producing a large number of questionsC. scanning the Internet test questionsD. giving difficult test questions45. Which of the following is the best title of this passage?A. The Advantages of Online ExamsB. The High-tech Methods in Online CoursesC. The Fight against Cheating in Online EducationD. The War against the Booming of Online EducationⅣ。

2020年最新深圳国际交流学院G1入学考试数学训

2020年最新深圳国际交流学院G1入学考试数学训练1．如图是由 4 个完全一样的小正方体组成的几何体，这个几何体的主视图是（）A ．B ．C ．D ．2．设 a 为正整数，且＜a +1，则 a 的值为（）A ．5B ．6C ．7D ．83．下列图形中，不是轴对称图形的是（）A ．B ．C ．D ．4．九年级参展作品中有 4 件获得一等奖，其中有 2 名作者是男生，2 名作者是女生．现在要在抽两人去参加学校总结表彰座谈会，求恰好抽中一男一女的概率（）A ．B ．C ．D ． 5．若在实数范围内有意义，则 x 的取值范围是（）A ．B ．x ＜ 2D ．x ≥06．下列事件中，是必然事件的是（）A ．掷一次骰子，向上一面的点数是 6B ．13 个同学参加一个聚会，他们中至少有两个同学的生日在同一个月C ．射击运动员射击一次，命中靶心D ．经过有交通信号灯的路口，遇到红灯7．如图，l 1∥l 2，等边△ABC 的顶点 A 、B 分别在直线 l 1、l 2，则∠1+∠2＝（）A ．30°B ．40°C ．50°D ．60°第 7 题第 8 题第 10 题8．Rt △ABC 中，AB ＝4，则 cos B 的值是（）A ．B ．C ．D ．9．《九章算术》是我国古代数学名著，有题译文如下：今有门，不知其高宽；有竿，不知其长短．横放，竿比门宽长出 4 尺；竖放，竿比门高长出 2 尺；斜放，竿与门对角线长恰好相等．问门高、宽和对角线的长各是多少？设门对角线的长为 x 尺，下列方程符合题意的是（） A ．（x +2）2+（x ﹣4）2＝x 2 B ．（x ﹣2）2+（x ﹣4）2＝x 2 C ．x 2+（x ﹣4）2＝（x ﹣4）2D ．（x ﹣2）2+x 2＝（x +4）210．如图所示，在平面直角坐标系中，直线 y 1＝2x +4 分别与 x 轴，y 轴交于 A ，B 两点，以线段 OB 为一条边向右侧作矩形 OCDB ，且点 D 在直线 y 2＝﹣x +b 上，若矩形 OCDB 的面积为 20，直线 y 1＝2x +4 与直线 y 2＝﹣x +b 交于点 P ．则 P 的坐标为（） A ．（2，8）B ．C ．D ．（4，12）11．3x （x ﹣5）+2（5﹣x ）分解因式的结果为．12．将抛物线 y ＝2x 2 向下平移 1 个单位，再向左平移 3 个单位得到的抛物线的解析式是．13．如图：在 Rt △ABC 中，∠B ＝90°，以顶点 C 为圆心，适当长为半径画弧，分别交 AC 、BC 于点 E 、F ，再分别以点 E 、F 为圆心，大于 EF 的长为半径画弧，两弧交于点 P ，作射线 CP 交 AB 于点 D ，若 BD ＝ 2，AC ＝6，则△ACD 的面积为．第 13 题第 14 题14．如图，若△ABC 内接于半径为 6 的⊙O ，且∠A ＝60°，连接 OB 、OC ，则边 BC 的长为．15.（每小题 6 分，共 12 分）（2）解不等式组：，并求出所有整数解之和．16.（6 分）已知 x ，y 满足方程组，求代数式（x ﹣y ）2﹣（x +2y ）（x ﹣2y ）的值．17.（本小题 8 分）某校组织学生到恩格贝 A 和康镇 B 进行研学活动，澄澄老师在网上查得，A 和 B 分别位于学校 D 的正北和正东方向，B 位于 A 南偏东 37°方向，校车从 D 出发，沿正北方向前往 A 地，行驶到 15 千米的 E 处时，导航显示，在 E 处北偏东 45°方向有一服务区 C ，且 C 位于 A ，B 两地中点处．（1）求 E ，A 两地之间的距离；（2）校车从A地匀速行驶 1 小时 40 分钟到达 B 地，若这段路程限速 100 千米/时，计算校车是否超速？（参考数据，cos37°＝，tan37°＝）18.（本小题 8 分）为了了解本校学生对新闻、体育、动画、娱乐、戏曲五类电视节目的喜爱情况，课题小组随机选取该校部分学生进行了问卷调査（问卷调査表如图 1 所示），并根据调查结果绘制了图 2、图 3两幅统计图（均不完整），请根据统计图解答下列问题．（1）本次接受问卷调查的学生有名．（2）补全条形统计图．（3）扇形统计图中 B 类节目对应扇形的圆心角的度数为．（4）该校共有 2000 名学生，根据调查结果估计该校最喜爱新闻节目的学生人数．19.（10 分）如图，在平面直角坐标系中，直线 AB 与 y 轴交于点 B （0，7），与反比例函数 y ＝在第二象限内的图象相交于点 A （﹣1，a ）．（1）求直线 AB的解析式；（2）将直线 AB 向下平移 9 个单位后与反比例函数的图象交于点 C 和点 E ，与 y 轴交于点 D ，求△ACD 的面积；（3）设直线 CD 的解析式为 y ＝mx +n ，根据图象直接写出不等式 mx +n ≤ 的解集．20.（本题10 分）如图，△ABC 内接于⊙O，∠CBG＝∠A，CD 为直径，OC 与AB 相交于点E，过点E 作EF⊥BC，垂足为F，延长CD 交GB 的延长线于点P，连接BD．（1）求证：PG 与⊙O 相切；（2）＝，的值；（3）在（2）的条件下，若⊙O 的半径为8，PD＝OD，求OE 的长．21．已知关于x 的方程a（x+m）2+b＝0（a、b、m 为常数，a≠0）的解是x1＝2，x2＝﹣1，那么方程a（x+m+2）2+b＝0 的解．22．有六张正面分别标有数字﹣2，﹣1，0，2，3，4 的不透明卡片，它们除数字不同外其余均相同．现它们背面朝上，洗匀后从中任取一张，将该卡片上的数字记为m，则使关于x 的分式方程有正整数解的概率为．23．如图，在△ABC 中，AB＝AC，点A 在y 轴上，点C 在x 轴上，BC⊥x 轴．延长AC 到点D，过点D 作DE⊥x 轴于点G，且DG＝GE，连接CE，反比例函数（k≠0）的图象经过点B，和CE 交于点F，且CF：FE＝2：1．若△ABE 面积为6，则点D 的坐标为．第23 题第24 题第25 题24．如图，在菱形ABCD 中，∠B＝60°，点P 是△ACD 内一点，连接PA、PC、PD，若PA＝5，PD＝12，PC＝13，则AC•BD＝．25．矩形ABCD 的边AB＝4，边AD 上有一点M，连接BM，将MB 绕M 点逆时针旋转90°得MN，N 恰好落在CD 上，过M、D、N 作⊙O，⊙O 与BC 相切，Q 为⊙O 上的动点，连BQ，P 为BQ 中点，连AP，则AP 的最小值为．26.（本题 8 分）为响应成都市“创建全国文明城市”号召，某单位不断美化环境，拟在一块矩形空地上修建绿色植物园，其中一边靠墙，可利用的墙长不超过18m，另外三边由36m 长的栅栏围成．设矩形ABCD 空地中，垂直于墙的边AB＝xm，面积为ym2（如图）．（1）求y 与x 之间的函数关系式，并写出自变量x 的取值范围；（2）若矩形空地的面积为160m2，求x 的值；（3）若该单位用8600 元购买了甲、乙、丙三种绿色植物共400 棵（每种植物的单价和每棵栽种的合理用地面积如下表）．问丙种植物最多可以购买多少棵？此时，这批植物可以全部栽种到这块空地上吗？请说明理由．甲乙丙单价（元/棵）141628合理用地（m2/棵）0.410.427.（10分）（1）证明推断：如图（1），在正方形ABCD中，点E，Q分别在边BC，AB上，DQ⊥AE于点O，点G，F 分别在边CD，AB 上，GF⊥AE．①求证：DQ＝AE；②推断的值为；（2）类比探究：如图（2），在矩形ABCD中，＝k（k为常数）．将矩形ABCD沿GF折叠，使点A 落在BC 边上的点E 处，得到四边形FEPG，EP 交CD 于点H，连接AE 交GF 于点O．试探究GF 与AE 之间的数量关系，并说明理由；（3）拓展应用：在（2）的条件下，连接CP，当k＝时，若tan∠CGP＝，GF＝2 ，求CP 的长．。

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深国交入学G1考试模拟试题二
一、选择题
1．27的立方根是（）
A ．3
B ．3-
C ．9
D ．9-
2．函数y ＝－
x
x －1
中自变量x 的取值范围是( )
A ．x ≥0
B ．x <0且x ≠1
C ．x <0
D ．x ≥0且x ≠1
3
）
A ．π13
B ．π14
C ．π15
D ．π16
4．某市为处理污水需要铺设一条长为4000米的管道，为了尽量减少施工对交通所造成的影
响，实际施工时每天比原计划多铺设10米，结果提前20天完成任务.设原计划每天铺设管道x 米，则可得方程（） A.204000104000=--x x B. 20104000
4000=--x x C.204000104000=-+x x D. 2010
4000
4000=+-x x
5、小明家的钟表在7点20分时，时针与分针的夹角为（） A 、︒120 B 、︒110 C 、︒100 D 、︒90
6．已知：a 、b 、c 是△ABC 三边长，且M ＝(a ＋b ＋c)(a ＋b －c)(a －b －c)，那么 ( )
A ．M ＞0
B ．M ＝0
C ．M ＜0
D ．不能确定
二、填空题
1．因式分解：ab 2－2ab ＋a ＝ .
主视图
左视图
俯视图
2．如果点P (4，－5)和点Q (a ，b )关于y 轴对称，则a 的值为
3．如图，抛物线y ＝－x 2＋2x ＋m (m ＜0)与x 轴相交于点A (x 1,0)、B (x 2,0)，点A 在点B 的左侧．当x ＝x 2－2时，y 0(填“＞”，“＝”或“＜”号)．
4．如图，从⊙O 外一点A 引圆的切线AB ，切点为B ，连接AO 并延长交圆于点C ，连接BC .
若∠A ＝26°，则∠ACB 的度数为度．
5、观察按下列顺序排列的等式：
9011⨯+=； 91211⨯+=； 92321⨯+=； 93431⨯+=； 94541⨯+=； ……
猜想：第n 个等式（n 为正整数）用n 表示，可以表示成________________.
三、解答题
1．计算：
12－⎝ ⎛⎭
⎪⎪⎫－12－1
－tan 60°＋3－8＋⎪
⎪⎪⎪3－2.
2．先化简，再求值：x －y x ÷⎝
⎛⎭
⎪⎪
⎫x －2xy －y 2x ，其中x ＝2，y ＝－1.
3．如图，在边长为1个单位长度的小正方形组成的网格中，△ABC 与△DFE 关于点O 成中心对称，△ABC 与△DFE 的顶点均在格点上，请按要求完成下列各题．
(1)在图中画出点O 的位置；
(2)将△ABC 先向右平移4个单位长度，再向下平移2个单位长度，得到△A 1B 1C 1，
请画出△A 1B 1C 1；
(3)在网格中画出格点M ，使A 1M 平分∠B 1A 1C 1.
4．省射击队为从甲、乙两名运动员中选拔一人参加全国比赛，对他们进行了六次测试，测试成绩如下表(单位：环)：
第一次第二次第三次第四次第五次第六次甲 10 8 9 8 10 9 乙
10
7
10
10
9
8
(1)根据表格中的数据，计算出甲的平均成绩是______环，乙的平均成绩是______环； (2)分别计算甲、乙六次测试成绩的方差；
(3)根据(1)、(2)计算的结果，你认为推荐谁参加全国比赛更合适，请说明理由． ⎩⎪⎨⎪
⎧⎭
⎪⎬⎪⎫计算方差的公式：s 2＝1n [x 1－x 2＋
x 2－x 2＋…＋x n －x 2]
5．如图，已知反比例函数y＝k
x的图象经过第二象限内的点
A(－1，m)，AB⊥x轴于点B，△AOB
的面积为2.若直线y＝ax＋b经过点A，并且经过反比例函数y＝k
x的图象上另一点
C(n，－2)．
(1)求直线y＝ax＋b的解析式；
(2)设直线y＝ax＋b与x轴交于点M，求AM的长．
6．已知：如图，在△ABC中，BC＝AC，以BC为直径的⊙O与边AB相交于点D，DE⊥AC，垂足为点E.
(1)求证：点D是AB的中点；
(2)判断DE与⊙O的位置关系，并证明你的结论；
(3)若⊙O的直径为18，cos B＝1
3
，求DE的长．
7、如图，已知二次函数图象的顶点坐标为C(1,0)，直线m
=与该二次函数的图象交于A、
y+
x
B两点，其中A点的坐标为(3,4)，B点在轴y上.
（1）求m的值及这个二次函数的关系式；
（2）P为线段AB上的一个动点（点P与A、B不重合），过P作x轴的垂线与这个二次函数的图象交于点E点，设线段PE的长为h，点P的横坐标为x，求h与x之间的
函数关系式，并写出自变量x的取值范围；
（3）D为直线AB与这个二次函数图象对称轴的交点，在线段AB上是否存在一点P，使得四边形DCEP是平行四形？若存在，请求出此时P点的坐标；若不存在，请说明
理由.
1、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. 8.1
B. 8.3
C. 8.6
D. 8.9
E. 9.0
2、A large square is made up of small squares. How many squares are
there?
A.9
B.10
C.11
D.14
3、The height h of water in a cylindrical container with radius r = 5 cm is equal to 10 cm. Peter needs to measure the volume of a stone with a complicated shape and so he puts the stone inside the container with water. The height of the water inside the container rises to 13.2 cm. What is the volume of the stone in cubic cm?
.
4、Initially the rectangular prism on the left was full of water. Then water was poured in the right cylindrical container so that the heights of water in both containers are
equal. Find the height h of water in both containers.(round your answer to the nearest tenth of a cm).
.。