最新高新区数学二诊试题

最新高新区数学二诊试题
最新高新区数学二诊试题

2017-2018学年下期初2015级第二次诊断性检测

数学试题

(时间:120分钟,总分:150分)

A卷(共100分)

一、选择题(每小题3分,共30分, 在下面每一个小题给出四个选项中,只有一项是正确的.)1.计算9的结果为()

A.3 B.﹣3 C.6 D.﹣9

2.下列运算正确的是()

A.a+a=a2B.a3÷a=a3 C.a2?a=a3D.(a2)3=a5

3.如图是由六个相同的小正方体搭成的几何体,这个几何体的主视图是()

A .

B .

C .

D .

4.把0.0813写成a×10n(1≤a<10,n为整数)的形式,则n为()

A.1 B.﹣2 C.2 D.8.13

5.谜语:干活两腿脚,一腿勤,一腿懒,一脚站,一脚转.打一数学学习用具,谜底为()A.量角器B.直尺C.三角板D.圆规

6.在一次中学生田径运动会上,参加男子跳高的15名运动员的成绩如下表所示:

A.1.70、0.25 B.1.75、3 C.1.75、0.30 D.1.70、3

7.将抛物线y=﹣x2向左平移2个单位长度,再向下平移3个单位长度,则平移后所得到的抛物线解析式是()

A.B.C.D.

8.若关于x的一元二次方程(m﹣

2)x2﹣2x+1=0有实根,则m的取值范围是()A.m<3 B.m≤3 C.m<3且m≠2 D.m≤3且m≠2 9.如图:有一块含有45°的直角三角板的两个顶点放在直尺的对边上,如果∠1=20°,那么∠2的度数是()

A.30°B.25°C.20°D.15°

10.如图,正五边形ABCDE内接于⊙O,若⊙O的半径为5,则的长度为()

A.πB.2πC.5πD.10π

第Ⅱ卷

二、填空题(每小题4分,共16分)

11.因式分解:=

+

+49

14

2x

x.

12.如图,在“3×3”网格中,有3个涂成黑色的小方格.若再从余下的6个小方格中随机选取1个涂成黑色,则完成的图案为轴对称图案的概率是.

13.如图,?ABCD中,点E在边AD上,以BE为折痕,将△ABE向上翻折,点A正好落在CD上的F点,若△FDE的周长为8 cm,△FCB的周长为20cm,则FC的长为cm.

14.把直线y=﹣x+3向上平移m个单位后,与直线y=2x+4的交点在第一象限,则m的取值范围是.

三、解答题(本题共54分)

15. (每小题6分,共12分)

(1

)计算:()o45

cos

2

3

4

1

|2

1|0

1

-

-

+

?

?

?

?

?

-

+

-

-

π

(2)解不等式组

()

??

?

?

?

-

<

-

+

-

x

x

x

x

6

1

3

1

2

1

,并把解集在数轴上表示出来.

第9题图

第10题图

第12题图

第13题图

16.(本小题6分)先化简,再求值:

??

?

??---÷--225262x x x x ,其中12-=x . 17.(本小题8分)为了测量白塔的高度AB ,在D 处用高为1.5米的测角仪 CD ,测得塔顶A 的仰角为42°,再向白塔方向前进12米,又测得白塔的顶端A 的仰角为61°,求白塔的高度AB .(参考数据sin42°≈0.67,tan42°≈0.90,sin61°≈0.87,tan61°≈1.80,结果保留整数)

18.(本小题8分)某销售公司年终进行业绩考核,人事部门把考核结果按照A ,B ,C ,D 四个等级,绘制成两个不完整的统计图,如图1,图2.

(1)参加考试人数是 ,扇形统计图中D 部分所对应的圆心角的度数是 ,请把条形统计图补充完整;

(2)若考核为A 等级的人中仅有2位女性,公司领导计划从考核为A 等级的人员中选2人交流考核意见,请用树状图或表格法,求所选人员恰为一男一女的概率;

(3)为推动公司进一步发展,公司决定计划两年内考核A 等级的人数达到30人,求平均每年的增长率.(精确到0.01,

=2.236)

19.(本小题10分)如图,已知A (3,m ),B (﹣2,﹣3)是直线AB 和某反比例函数的图象的两个交点.

(1)求直线AB 和反比例函数的解析式;

(2)观察图象,直接写出当x 满足什么范围时,直线AB 在双曲线的下方; (3)反比例函数的图象上是否存在点C ,使得△OBC 的面积等于△OAB 的面积?如果不存在,说明理由;如果存在,求出满足条件的所有点C 的坐标.

20.(本小题10分)如图, ⊙O ABC Rt ?的外接圆,o

90=∠C ,2

1

tan =

B ,过点B 的直线l 是 ⊙O 的切线,点D 是直线l 上一点,过点D 作CB DE ⊥交CB 延长线于点E ,连结AD ,交⊙O 于点

F ,连结BF 、CD 交于点

G .

(1)ACB ?∽BED ? (2)当AC AD ⊥时,求

CG

DG

的值; (3)若CD 平分ACB ∠,AC =2,连结CF,求线段CF 的长.

第17题图

第18题图

第19题图

第20题图

B卷(50分)

一、填空题(每小题4分,共20分)

21.某班体育委员对本班学生一周锻炼时间(单位:小时)进行了统计,绘制了如图所示的折线统

计图,则该班这些学生一周锻炼时间的中位数是小时.

22.若

?

?

?

-

=

=

2

1

b

a

是关于b

a,的二元一次方程7

=

-

+b

ay

ax 的一个解,代数式1

22

2-

+

+y

xy

x的值

是.

23.如图,同心圆的半径为6cm,8cm,AB为小圆的弦,CD为大圆的弦,且ABCD为矩形,若矩形

ABCD面积最大时,矩形ABCD的周长为cm.

24.如图,在矩形ABCD中,将∠ABC绕点A按逆时针方向旋转一定角度后,BC的对应边B'C'交CD

边于点G.连接BB'、CC'.若AD=7,CG=4,AB'=B'G,则=(结果保留根号).

25.在平面直角坐标系,对于点P(x,y)和Q(x,y′),给出如下定义:若y′=,则称

点Q为点P的“可控变点”.例如:点(1,2)的“可控变点”为点(1,2),点(﹣1,3)的“可控变

点”为点(﹣1,﹣3).点(﹣5,﹣2)的“可控变点”坐标为;若点P在函数y=﹣x2+16(﹣

5≤x≤a)的图象上,其“可控变点”Q的纵坐标y′的取值范围是﹣16≤y′≤16,实数a的取值范围为

______________.

二、解答题(本题共30分)

26.(本小题8分)为进一步缓解城市交通压力,成都大力支持共享单车的推广,并规范共享单车

定点停放,某校学生小明统计了周六校门口停车点各时段的借、还自行车数,以及停车点整点时刻

的自行车总数(称为存量)情况,表格中x=1时的y的值表示8:00点时的存量,x=2时的y值表

示9:00点时的存量…以此类推,他发现存量y(辆)与x(x为

整数)满足如图所示的一个二次函数关系.

根据所给图表信息,解决下列问题:

(1)m=,解释m的实际意义:

(2)求整点时刻的自行车存量y与x之间满足的二次函数关系式;

(3)已知10:00﹣11:00这个时段的还车数比借车数的2倍少4,求此时段的借车数.

27.(本小题10分)在正六边形ABCDEF中,N、M为边上的点,BM、AN相交于点P

(1)如图1,若点N在边BC上,点M在边DC上,BN=CM,求证:BP?BM=BN?BC;

(2)如图2,若N为边DC的中点,M在边ED上,AM∥BN,求的值;

(3)如图3,若N、M分别为边BC、EF的中点,正六边形ABCDEF的边长为2,请直接写出AP的

长.

28.(本小题12分)如图,直线l:3

3+

-

=x

y与x轴、y轴分别相交于A、B两点,抛物线

4

2

2+

+

-

=a

ax

ax

y()0

(1)求该抛物线的函数表达式;

(2))已知点M是抛物线上的一个动点,并且点M在第一象限内,连接AM、BM,设点M的横坐

标为m,△ABM的面积为S,求S与m的函数表达式,并求出S的最大值及此时动点M的坐标;

(3)将点A绕原点旋转得点A′,连结CA′、BA′,在旋转过程中,一动点M从点B出发,沿线段BA′

以每秒3个单位的速度运动到A′,再沿线段A′C以每秒1个单位的速度运动到C后停止,求点M在

整个运动过程中用时最少是多少秒?

时段x 还车数

借车数存量

y

7:00﹣8:00

1

7 5 15

8:00﹣9:00 2

8

7 n

……………

第21题图第23题图第24题图

第26题图

第27题图

C C 第28题图

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成都市高新区二诊数学试题(标准答案)

成都市高新区二诊数学试题(答案)

————————————————————————————————作者:————————————————————————————————日期:

2018年九年级第二次诊断性考试试题 数学 (满分150分,时间:120分钟) 第Ⅰ卷 A卷(100分) 一、选择题(每小题3分,共30分, 在下面每一个小题给出的四个选项中,只有一项是正确的.)1.计算9的结果为(A) A.3 B.﹣3 C.6 D.﹣9 2.下列运算正确的是(C) A.a+a=a2B.a3÷a=a3C.a2?a=a3D.(a2)3=a5 3.如图是由六个相同的小正方体搭成的几何体,这个几何体的主视图是(B) A.B. C. D. 4.把0.0813写成a×10n(1≤a<10,n为整数)的形式,则n为( B ) A.1 B.﹣2 C.2 D.8.13 5.谜语:干活两腿脚,一腿勤,一腿懒,一脚站,一脚转.打一数学学习用具,谜底为(D)A.量角器B.直尺C.三角板D.圆规 6.在一次中学生田径运动会上,参加男子跳高的15名运动员的成绩如下表所示: 成绩/m 1.50 1.60 1.65 1.70 1.75 1.80 人数 2 3 2 3 4 1 则这些运动员成绩的众数、极差分别为(C)

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