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2016年江苏省南通市中考数学试卷

2016年江苏省南通市中考数学试卷
2016年江苏省南通市中考数学试卷

2016年江苏省南通市中考数学试卷

一、选择题(本大题共10小题,每小题3分,共30分)

1.(3分)(2016?南通)2的相反数是()

A.﹣2 B.﹣C.2 D.

2.(3分)(2016?南通)太阳半径约为696000km,将696000用科学记数法表示为()A.696×103B.69.6×104 C.6.96×105 D.0.696×106

3.(3分)(2016?南通)计算的结果是()

A.B.C.D.

4.(3分)(2016?南通)下列几何图形:

其中是轴对称图形但不是中心对称图形的共有()

A.4个B.3个C.2个D.1个

5.(3分)(2016?南通)若一个多边形的内角和与它的外角和相等,则这个多边形是()A.三角形B.四边形C.五边形D.六边形

6.(3分)(2016?南通)函数y=中,自变量x的取值范围是()

A.x且x≠1 B.x且x≠1 C.x且x≠1 D.x且x≠1

7.(3分)(2016?南通)如图,为了测量某建筑物MN的高度,在平地上A处测得建筑物顶端M的仰角为30°,向N点方向前进16m到达B处,在B处测得建筑物顶端M的仰角为45°,则建筑物MN的高度等于()

A.8()m B.8()m C.16()m D.16()m 8.(3分)(2016?南通)如图所示的扇形纸片半径为5cm,用它围成一个圆锥的侧面,该圆锥的高是4cm,则该圆锥的底面周长是()

A.3πcmB.4πcm C.5πcm D.6πcm

9.(3分)(2016?南通)如图,已知点A(0,1),点B在x轴正半轴上的一动点,以AB 为边作等腰直角三角形ABC,使点C在第一象限,∠BAC=90°,设点B的横坐标为x,点C的纵坐标为y,则表示y与x的函数关系的图象大致是()

A.B.C.D.

10.(3分)(2016?南通)平面直角坐标系xOy中,已知A(﹣1,0)、B(3,0)、C(0,﹣1)三点,D(1,m)是一个动点,当△ACD的周长最小时,△ABD的面积为()

A.B.C.D.

二、填空题(本大题共8小题,每小题3分,共24分)

11.(3分)(2016?南通)计算:x3?x2=______.

12.(3分)(2016?南通)已知:如图直线AB与CD相交于点O,OE⊥AB,∠COE=60°,则∠BOD等于______度.

13.(3分)(2016?南通)某几何体的三视图如图所示,则这个几何体的名称是______.

14.(3分)(2016?南通)如图Rt△ABC中,CD是斜边AB上的中线,已知CD=2,AC=3,则cosA=______.

15.(3分)(2016?南通)已知一组数据5,10,15,x,9的平均数是8,那么这组数据的中位数是______.

16.(3分)(2016?南通)设一元二次方程x2﹣3x﹣1=0的两根分别是x1,x2,则x1+x2(x22﹣3x2)=______.

17.(3分)(2016?南通)如图,BD为正方形ABCD的对角线,BE平分∠DBC,交DC与点E,将△BCE绕点C顺时针旋转90°得到△DCF,若CE=1cm,则BF=______cm.

18.(3分)(2016?南通)平面直角坐标系xOy中,已知点(a,b)在直线y=2mx+m2+2(m >0)上,且满足a2+b2﹣2(1+2bm)+4m2+b=0,则m=______.

三、解答题(本大题共10小题,共96分)

19.(10分)(2016?南通)(1)计算:|﹣2|+(﹣1)2+(﹣5)0﹣;

(2)解方程组:.

20.(8分)(2016?南通)解不等式组,并写出它的所有整数解.

21.(9分)(2016?南通)某水果批发市场新进一批水果,有苹果、西瓜、桃子和香蕉四个品种,统计后将结果绘制成条形图(如图),已知西瓜的重量占这批水果总重量的40%.回答下列问题:

(1)这批水果总重量为______kg;

(2)请将条形图补充完整;

(3)若用扇形图表示统计结果,则桃子所对应扇形的圆心角为______度.

22.(7分)(2016?南通)不透明袋子里装有红色、绿色小球各一个,除颜色外无其他差别,随机摸出一个小球后,放回并摇匀,再随机摸出一个,求两次都摸到红色小球的概率.23.(8分)(2016?南通)列方程解应用题:

某列车平均提速60km/h,用相同的时间,该列车提速前行驶200km,提速后比提速前多行驶100km,求提速前该列车的平均速度.

24.(9分)(2016?南通)已知:如图,AM为⊙O的切线,A为切点,过⊙O上一点B作BD⊥AM于点D,BD交⊙O于点C,OC平分∠AOB.

(1)求∠AOB的度数;

(2)当⊙O的半径为2cm,求CD的长.

25.(8分)(2016?南通)如图,将?ABCD的边AB延长到点E,使BE=AB,连接DE,交边BC于点F.

(1)求证:△BEF≌△CDF;

(2)连接BD、CE,若∠BFD=2∠A,求证:四边形BECD是矩形.

26.(10分)(2016?南通)平面直角坐标系xOy中,已知抛物线y=x2+bx+c经过(﹣1,

m2+2m+1)、(0,m2+2m+2)两点,其中m为常数.

(1)求b的值,并用含m的代数式表示c;

(2)若抛物线y=x2+bx+c与x轴有公共点,求m的值;

(3)设(a,y1)、(a+2,y2)是抛物线y=x2+bx+c上的两点,请比较y2﹣y1与0的大小,并说明理由.

27.(13分)(2016?南通)如图,△ABC中,∠ACB=90°,AC=5,BC=12,CO⊥AB于点O,D是线段OB上一点,DE=2,ED∥AC(∠ADE<90°),连接BE、CD.设BE、CD的中点分别为P、Q.

(1)求AO的长;

(2)求PQ的长;

(3)设PQ与AB的交点为M,请直接写出|PM﹣MQ|的值.

28.(14分)(2016?南通)如图,平面直角坐标系xOy中,点C(3,0),函数y=(k>0,

x>0)的图象经过?OABC的顶点A(m,n)和边BC的中点D.

(1)求m的值;

(2)若△OAD的面积等于6,求k的值;

(3)若P为函数y═(k>0,x>0)的图象上一个动点,过点P作直线l⊥x轴于点M,直线l与x轴上方的?OABC的一边交于点N,设点P的横坐标为t,当时,求t的值.

2016年江苏省南通市中考数学试卷

参考答案与试题解析

一、选择题(本大题共10小题,每小题3分,共30分)

1.(3分)(2016?南通)2的相反数是()

A.﹣2 B.﹣C.2 D.

【分析】依据相反数的定义求解即可.

【解答】解:2的相反数是﹣2.

故选:A.

2.(3分)(2016?南通)太阳半径约为696000km,将696000用科学记数法表示为()A.696×103B.69.6×104 C.6.96×105 D.0.696×106

【分析】科学记数法的表示形式为a×10n的形式,其中1≤|a|<10,n为整数.确定n的值时,要看把原数变成a时,小数点移动了多少位,n的绝对值与小数点移动的位数相同.当原数绝对值>1时,n是正数;当原数的绝对值<1时,n是负数.

【解答】解:将696000用科学记数法表示为:6.96×105.

故选:C.

3.(3分)(2016?南通)计算的结果是()

A.B.C.D.

【分析】根据同分母的分式相加的法则:分母不变,分子相加.

【解答】解:原式==,

故选D.

4.(3分)(2016?南通)下列几何图形:

其中是轴对称图形但不是中心对称图形的共有()

A.4个B.3个C.2个D.1个

【分析】根据轴对称图形与中心对称图形的概念求解.

【解答】解:正方形和圆既是中心对称图形,也是轴对称图形;

等边三角形是轴对称图形,不是中心对称图形;

正五边形是轴对称图形,不是中心对称图形.

故选C.

5.(3分)(2016?南通)若一个多边形的内角和与它的外角和相等,则这个多边形是()A.三角形B.四边形C.五边形D.六边形

【分析】根据多边形的内角和公式(n﹣2)?180°与多边形的外角和定理列式进行计算即可得解.

【解答】解:设多边形的边数为n,根据题意得

(n﹣2)?180°=360°,

解得n=4.

故这个多边形是四边形.

故选B.

6.(3分)(2016?南通)函数y=中,自变量x的取值范围是()

A.x且x≠1 B.x且x≠1 C.x且x≠1 D.x且x≠1

【分析】根据二次根式的被开方数为非负数且分母不为0,列出不等式组,即可求x的范围.【解答】解:2x﹣1≥0且x﹣1≠0,

解得x≥且x≠1,

故选B.

7.(3分)(2016?南通)如图,为了测量某建筑物MN的高度,在平地上A处测得建筑物顶端M的仰角为30°,向N点方向前进16m到达B处,在B处测得建筑物顶端M的仰角为45°,则建筑物MN的高度等于()

A.8()m B.8()m C.16()m D.16()m

【分析】设MN=xm,由题意可知△BMN是等腰直角三角形,所以BN=MN=x,则AN=16+x,在Rt△AMN中,利用30°角的正切列式求出x的值.

【解答】解:设MN=xm,

在Rt△BMN中,∵∠MBN=45°,

∴BN=MN=x,

在Rt△AMN中,tan∠MAN=,

∴tan30°==,

解得:x=8(+1),

则建筑物MN的高度等于8(+1)m;

故选A.

8.(3分)(2016?南通)如图所示的扇形纸片半径为5cm,用它围成一个圆锥的侧面,该圆锥的高是4cm,则该圆锥的底面周长是()

A.3πcmB.4πcm C.5πcm D.6πcm

【分析】根据题意首先求出圆锥的底面半径,进而利用圆周长公式得出答案.

【解答】解:∵扇形纸片半径为5cm,用它围成一个圆锥的侧面,该圆锥的高是4cm,

∴圆锥的底面半径为:=3(cm),

∴该圆锥的底面周长是:2π×3=6π(cm).

故选:D.

9.(3分)(2016?南通)如图,已知点A(0,1),点B在x轴正半轴上的一动点,以AB 为边作等腰直角三角形ABC,使点C在第一象限,∠BAC=90°,设点B的横坐标为x,点C的纵坐标为y,则表示y与x的函数关系的图象大致是()

A.B.C.D.

【分析】根据题意作出合适的辅助线,可以先证明△ADC和△AOB的关系,即可建立y与x的函数关系,从而可以得到哪个选项是正确的.

【解答】解:作AD∥x轴,作CD⊥AD于点D,若右图所示,

由已知可得,OB=x,OA=1,∠AOB=90°,∠BAC=90°,AB=AC,点C的纵坐标是y,

∵AD∥x轴,

∴∠DAO+∠AOD=180°,

∴∠DAO=90°,

∴∠OAB+∠BAD=∠BAD+∠DAC=90°,

∴∠OAB=∠DAC,

在△OAB和△DAC中,

∴△OAB≌△DAC(AAS),

∴OB=CD,

∴CD=x,

∵点C到x轴的距离为y,点D到x轴的距离等于点A到x的距离1,

∴y=x+1(x>0).

故选:A.

10.(3分)(2016?南通)平面直角坐标系xOy中,已知A(﹣1,0)、B(3,0)、C(0,﹣1)三点,D(1,m)是一个动点,当△ACD的周长最小时,△ABD的面积为()

A.B.C.D.

【分析】先根据△ACD的周长最小,求出点C关于直线x=1对称的点E的坐标,再运用待定系数法求得直线AE的解析式,并把D(1,m)代入,求得D的坐标,最后计算,△ABD 的面积.

【解答】解:由题可得,点C关于直线x=1的对称点E的坐标为(2,﹣1),

设直线AE的解析式为y=kx+b,则

解得,

∴y=﹣x﹣,

将D(1,m)代入,得

m=﹣﹣=﹣,

即点D的坐标为(1,﹣),

∴当△ACD的周长最小时,△ABD的面积=×AB×|﹣|=×4×=.

故选(C)

二、填空题(本大题共8小题,每小题3分,共24分)

11.(3分)(2016?南通)计算:x3?x2=x5.

【分析】根据同底数的幂的乘法即可求解.

【解答】解:原式=x5.

故答案是:x5.

12.(3分)(2016?南通)已知:如图直线AB与CD相交于点O,OE⊥AB,∠COE=60°,则∠BOD等于30度.

【分析】根据垂线的定义,可得∠ACE的度数,根据余角的性质,可得∠AOC的度数,根据对顶角相等,可得答案.

【解答】解:由垂线的定义,得

∠AOE=90°,

由余角的性质,得

∠AOC=∠AOE﹣∠COE=30°,

由对顶角相等,得

∠BOD=∠AOC=30°,

故答案为:30.

13.(3分)(2016?南通)某几何体的三视图如图所示,则这个几何体的名称是圆柱.

【分析】由主视图和左视图确定是柱体,锥体还是球体,再由俯视图确定具体形状.

【解答】解:根据主视图和左视图为长方形判断出是柱体,根据俯视图是圆形可判断出这个几何体应该是圆柱,

故答案为:圆柱.

14.(3分)(2016?南通)如图Rt△ABC中,CD是斜边AB上的中线,已知CD=2,AC=3,

则cosA=.

【分析】首先根据直角三角形斜边上的中线等于斜边的一半,即可求得AB的长,然后利用余弦函数的定义求解.

2016年江苏省南通市中考数学试卷(含解析版)

2016年江苏省南通市中考数学试卷 一、选择题(本大题共10小题,每小题3分,共30分) 1.(3分)(2016?南通)2的相反数是() A.﹣2 B.﹣C.2 D. 2.(3分)(2016?南通)太阳半径约为696000km,将696000用科学记数法表示为() A.696×103B.69.6×104C.6.96×105D.0.696×106 3.(3分)(2016?南通)计算的结果是() A.B.C.D. 4.(3分)(2016?南通)下列几何图形: 其中是轴对称图形但不是中心对称图形的共有() A.4个B.3个C.2个D.1个 5.(3分)(2016?南通)若一个多边形的内角和与它的外角和相等,则这个多边形是() A.三角形B.四边形C.五边形D.六边形

6.(3分)(2016?南通)函数y=中,自变量x的取值范围是()A.x且x≠1 B.x且x≠1 C.x且x≠1 D.x且x≠1 7.(3分)(2016?南通)如图,为了测量某建筑物MN的高度,在平地上A处测得建筑物顶端M的仰角为30°,向N点方向前进16m到达B处,在B处测得建筑物顶端M的仰角为45°,则建筑物MN的高度等于() A.8()m B.8()m C.16()m D.16()m 8.(3分)(2016?南通)如图所示的扇形纸片半径为5cm,用它围成一个圆锥的侧面,该圆锥的高是4cm,则该圆锥的底面周长是() A.3πcm B.4πcm C.5πcm D.6πcm 9.(3分)(2016?南通)如图,已知点A(0,1),点B在x轴正半轴上的一动点,以AB为边作等腰直角三角形ABC,使点C在第一象限,∠BAC=90°,设点B的横坐标为x,点C的纵坐标为y,则表示y与x的函数关系的图象大致是()

2020年南通市中考英语试卷(含答案)

南通市中考英语试卷 第Ⅰ卷(选择题共60分) 第Ⅰ卷共45小题,请按要求将答案填涂在答题卡上。 一、单项选择(本题共15小题;每小题1分,满分15分) 从A、B、C、D四个选项中,选出可以填入空白处的最佳选项,并在答题卡上将该项涂黑。 1. ---Who's _______ woman in blue, do you know? ---Oh, she's _______ friend of Anna's. A. the; a B. an; the C. a; the D. the; an 2. --- Which of the two shirts would you like? --- . I don't like their styles. A. Either B. Both C. None D. Neither 3. ---I didn't see you at the beginning of the party last night. Where were you? ---I on my history report at that time. A. worked B. work C. was working D. am working 4. Although Flight MH370 has been missing for months, we do believe it ______ some day in the future. A. will find B. won't find C. will be found D. won't be found 5. ---I forgot to bring my e-dictionary. Could I use yours? --- Yes, you . A. can B. must C. could D. should

2016南通数学中考试卷+答案

2016年南通市中考数学试卷 1、2的相反数是(▲) A ﹒-2 B ﹒12 - C ﹒2 D ﹒ 12 2、太阳半径约为696000km ,将696000用科学记数法表示为(▲) A ﹒696×103 B ﹒69.6×104 C ﹒6.96×105 D ﹒0.696×106 3、计算 32 x x -的结果是(▲) A ﹒26 x B ﹒6x C ﹒ 5 2x D ﹒ 1x 4、下列几何图形: 等腰三角形 正方形 正五边形其中是轴对称图形但不是中心对称图形的共有(▲) A ﹒4个 B ﹒3个 C ﹒2个 D ﹒1个 5、若一个多边形的外角和与它的内角和相等,则这个多边形是(▲) A ﹒三角形 B ﹒四边形 C ﹒五边形 D ﹒六边形 6x 的取值范围是(▲) A ﹒12x ≤且x ≠1 B ﹒1 2x ≥且x ≠1 C ﹒12x >且x ≠1 D ﹒1 2 x <且x ≠1 7、如图,为了测量某建筑物MN 的高度,在平地上A 处测得建筑物 顶端M 的仰角为30°,向N 点方向前进16m 到达B 处,在B 处 测得建筑物顶端M 的仰角为45°,则建筑物MN 的高度等于(▲) A ﹒1)m B ﹒1)m C ﹒1)m D ﹒1)m 8、如图所示的扇形纸片半径为5cm ,用它围成一个圆锥的侧面,该圆 锥的高是4cm ,则该圆锥的底面周长是(▲) A ﹒3πcm B ﹒4πcm C ﹒5πcm D ﹒6πcm 9、如图,已知点A (0,1),点B 是x 轴正半轴上的一动点,以 AB 为边作等腰直角三角形ABC ,使点C 在第一象限,∠BAC=90°﹒ 设点B 的横坐标为x ,点C 的纵坐标为y ,则表示y 与x 的函数关系 (第7题)

【真题】2016年南通市中考英语试卷含答案解析(Word版)(2)

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