2016年陕西数学中考副题

2016年陕西省初中毕业学业考试

数学试卷

一、选择题(共10小题，每小题3分，计30分. 每小题只有一个选项是符合题意的) 01、计算：(－3)×(－1

3

)＝

A.－1

B.1

C.－9

D.9

02、如图，下面的几何体由两个大小相同的正方体和一个圆柱体组成，则它的左视图是

03、计算：(－2x 2y )3＝

A.－8x 6y 3

B.8x 6y 3

C.－6x 6y 3

D.6x 5y 3 04、如图，AB ∥CD .若∠1＝40°，∠2＝65°，则∠CAD ＝

A.50°

B.65°

C.75°

D.85° 05、设点A (－3，a )，B (b ，1

2

)在同一个正比例函数的图象上，则ab 的值为

A.－23

B.－32

C.－6

D.32

06、如图，在△ABC 中，∠BAC ＝90°，AB ＝20，AC ＝15，△ABC 的高AD 与角平分线CF 交于点E ，则

AF

DE

的值为 A.35 B.34 C.12 D.23

07、已知两个一次函数y ＝3x ＋b 1和y ＝－3x ＋b 2. 若b 1＜b 2＜0，则它们图象的交点在

A.第一象限

B.第二象限

C.第三象限

D.第四象限 08、如图，在三边互不相等的△ABC 中，D 、E 、F 分别是AB 、AC 、BC 边的中点.连接DE ，过点C 作CM ∥AB

交DE 的延长线于点M ，连接CD 、EF 交于点N ，则图中全等三角形共有 A.3对 B.4对 C.5对 D.6对 09、如图，在⊙O 中，弦AB 垂直平分半径OC ，垂足为D .若点P 是⊙O 上异于点A 、B 的任意点，则∠APB

＝

A.30°或60°

B.60°或150°

C.30°或150°

D.60°或120° 10、将抛物线M ：y ＝－1

3

x 2＋2向左平移2个单位，再向上平移1个单位，得到抛物线M ′.若抛物线M ′与x

轴交于A 、B 两点，M ′的顶点记为C ，则∠ACB ＝

A.45°

B.60°

C.90°

D.120°

(第4题图) (第6题图) (第8题图) (第9题图)

二、填空题(共4小题，每小题3分，计12分)

11、不等式－2x ＋1＞－5的最大整数解是________. 12、请从以下两个小题中任选一个．．．．

作答，若多选，则按第一题计分. A.如图，五边形ABCDE 的对角线共有________条.

B.用科学计算器计算：373cos81°23′≈________.(结果精确到1) 13、如图，在x 轴上方，平行于x 轴的直线与反比例函数y ＝

x k 1和y ＝x

k

2的图象分别交于A 、B 两点，连接OA 、OB .若△AOB 的面积为6，则k 1－k 2＝________.

14、如图，在正方形ABCD 中，AB ＝4，E 是BC 边的中点，F 是CD 边上的一点，且DF ＝1.若M 、N 分

别是线段AD 、AE 上的动点，则MN ＋MF 的最小值为________.

(第12题A 图) (第13题图) (第14题图)

三、解答题(共11小题，计78分.解答应写出过程) 15、(本题满分5分)

计算： (－3)2＋|2－5|－20. 16、(本题满分5分)

化简：（9

37222--+a a a —34

++a a ）÷33-+a a .

17、(本题满分5分)

如图，已知锐角△ABC ，点D 是AB 边上的一定点，请用尺规在AC 边上求作一点E ， 使△ADE 与△ABC 相似.(作出符合题意的一个点即可，保留作图痕迹，不写作法.) 18、(本题满分5分)

2016年4月23日是我国第一个“全民阅读日”.某校开展了“建设书香校园，捐赠有益图书”活动.我们在参加活动的所有班级中，随机抽取了一个班，已知这个班是八年级5班，全班共50名学生.现将该班捐赠图书情况的统计结果，绘制成如下两幅不完整的统计图.

请你根据以上信息，解答下列问题：

(1)补全上面的条形统计图和扇形统计图； (2)求八年级5班平均每人捐赠了多少本书？

(3)若该校八年级共有800名学生，请你估算这个年级学生共可捐赠多少本书？ 19、(本题满分7分)

如图，在菱形ABCD 中，点E 是边AD 上一点，延长AB 至点F ， 使BF ＝AE ，连接BE 、CF . 求证：BE ＝CF .

20、(本题满分7分)

某市为了创建绿色生态城市，在城东建了“东州湖”景区.小明和小亮

想测量“东州湖”东西两端A、B间的距离.于是，他们去了湖边，如图，

在湖的南岸的水平地面上，选取了可直接到达点B的一点C，并测得

BC＝350米，点A位于点C北偏西73°方向，点B位于点C北偏东

45°方向.请你根据以上提供的信息，计算“东州湖”东西两端之间

AB的长.(结果精确到1米)

(参考数据：si n73°≈0.9563，cos73°≈0.2924，t an73°≈3.2709，2≈1.414.)

21、(本题满分7分)

上周六上午8点，小颖同爸爸妈妈一起从西安出发回安康看望姥姥，

途中他们在一个服务区休息了半小时，然后直达姥姥家.如图，是小颖

一家这次行程中距姥姥家的距离y(千米)与他们路途所用的时间x(时)

之间的函数图象.

请你根据以上信息，解答下列问题：

(1)求线段AB所对应的函数关系式；

(2)已知小颖一家出服务区后，行驶30分钟时，距姥姥家还有80千米，

问小颖一家当天几点到达姥姥家？

22、(本题满分7分)

孙老师在上《等可能事件的概率》这节课时，给同学们提出了一个问题：“如果同时随机投掷两枚质地均匀的骰子，它们朝上一面的点数和是多少的可能性最大？”同学们展开讨论，各抒己见，其中小芳和小超两位同学给出了两种不同的回答.小芳认为6的可能性最大，小超认为7的可能性最大.你认为他们俩的回答正确吗？请用列表或画树状图等方法加以说明.

(骰子：六个面上分别刻有1，2，3，4，5，6个小圆点的小正方体.)

23、(本题满分8分)

如图，已知⊙O的半径为5，△ABC是⊙O的内接三角形，AB＝8.

过点B作⊙O的切线BD，过点A作AD⊥BD，垂足为D.

(1)求证：∠BAD＋∠C＝90°；

(2)求线段AD的长.

24、(本题满分10分)

如图，在平面直角坐标系中，O为坐标原点，△AOB是等腰直角三角形，

∠AOB＝90°，点A(2，1).

(1)求点B的坐标；

(2)求经过A、O、B三点的抛物线的函数表达式；

(3)在(2)所求的抛物线上，是否存在一点P，使四边形ABOP的面积最大？

若存在，求出点P的坐标；若不存在，请说明理由.

25、(本题满分12分)

(1)如图①，在△ABC中，BC＝6，D为BC上一点，AD＝4，则△ABC面积的最大值是________.

(2)如图②，已知矩形ABCD的周长为12，求矩形ABCD面积的最大值.

(3)如图③，△ABC是葛叔叔家的菜地示意图，其中AB＝30米，BC＝40米，AC＝50米.现在他想利用

周边地的情况，把原来的三角形地拓展成符合条件的面积尽可能大、周长尽可能长的四边形地，用来建鱼塘.已知葛叔叔欲建的鱼塘是四边形ABCD，且满足∠ADC＝60°.你认为葛叔叔的想法能否实现？若能，求出这个四边形鱼塘周长的最大值；若不能，请说明理由.

2016年陕西省初中毕业学业考试数学答案及评分参考

一、选择题(共

二、填空题(共4小题，

三、解答题(共11小题，计15、原式＝9＋5－2－25＝7－ 5.

16、原式＝2a 2＋7a －3－（a ＋4）（a －3）a 2－9÷a ＋3a －3＝2a 2＋7a －3－a 2－a ＋12a 2－9·a －3

a ＋3

＝a 2＋6a ＋9a 2－9·a －3a ＋3＝（a ＋3）2（a ＋3）（a －3）·a －3

a ＋3

＝1

17.、如图①或图②，点E 即为所求.(只要求作其中一种即可)

18、(1)补全的条形统计图和扇形统计图如图所示.

(2)24÷8%＝300，300÷50＝6. ∴八年级5班平均每人捐赠了6本书. (3)6×800＝4800. ∴这个年级学生共可捐赠4800本书.

19、∵四边形ABCD 是菱形， ∴AB ＝BC ，AD ∥BC . ∴∠A ＝∠CBF .

又∵AE ＝BF ， ∴△ABE ≌△BCF . ∴BE ＝CF . 20、如图，在Rt △BCD 中，∠BCD ＝45°，BC ＝350，

∴BD ＝350si n 45°＝175 2. ∴CD ＝BD ＝175 2.

在Rt △ACD 中，∠ACD ＝73°，∴AD ＝175 2 t an 73°. ∴AB ＝AD ＋BD ＝175 2 t an 73°＋1752≈1057(米). 21、(1)设线段AB 所对应的函数关系式为y ＝kx ＋b (k ≠0)，

根据题意得 ??

?=+=,1202320b k b 解之得,320

100

???=-=b k

∴线段AB 所对应的函数关系式为y ＝－100x ＋320(0≤x ≤2).

(注：不写x 的取值范围不扣分)

(2)由题意，当x ＝2.5时，y ＝120； 当x ＝3时，y ＝80. 设线段CD 所对应的函数关系式为y ＝k ′x ＋b ′(k ′≠0)，

根据题意得,80''3120''5.2???=+=+b k b k 解得,320'80

'?

??=-=b k ∴线段CD 所对应的函数关系式为y ＝－80x ＋320.

当y ＝0时，－80x ＋320＝0，∴x ＝4. ∴小颖一家当天中午12点到达姥姥家.

22、小超的回答正确，小芳的回答不正确.理由如下：

由题意得：

6的结果共有5种. 实际上，和为7的结果最多. ∴P (点数和为7)＝636＝16，P (点数和为6)＝536＜1

6.

∴小超的回答正确，小芳的回答不正确.

23、(1)如图，连接BO 并延长交⊙O 于点E ，连接AE .

∵BD 切⊙O 于点B ，∴BE ⊥BD .

又∵AD ⊥BD ，∴AD ∥BE . ∴∠BAD ＝∠1.

又∵BE 是⊙O 的直径，∴∠1＋∠E ＝90°.∴∠BAD ＋∠E ＝90° 又∵∠E ＝∠C ， ∴∠BAD ＋∠C ＝90°.

(2)由(1)得∠BAD ＝∠1， 又∵∠D ＝∠BAE ＝90°，∴△ABD ∽△BEA .

∴

BE AB ＝BA AD ，即810＝8

AD . ∴AD ＝32

5.

24、(1)如图，过点A 作AC ⊥x 轴，垂足为C ，过点B 作BD ⊥y 轴，垂足为D .

∵△AOB 为等腰直角三角形，且A (2，1)， ∴△AOC ≌△BOD . ∴BD ＝AC ＝1，OD ＝OC ＝2，∴B (－1，2).

(2)设经过A 、O 、B 三点的抛物线的函数表达式为y ＝ax 2＋bx (a ≠0)，

则,1242???=+=-b a b a 解之得 ,6765??

???-

==b a ∴经过A 、O 、B 三点的抛物线的函数表达式为y ＝56x 2－76x . (3)存在.理由如下：

设P (m ，56m 2－7

6m )，则0＜m ＜2，如图，过点P 作P Q ∥y 轴交OA 于点Q ，连接OP 、AP. ∵点A (2，1)，∴直线OA ：y ＝12x . ∴点Q(m ，12m ). ∴P Q ＝12m －(56m 2－76m )＝－56m 2＋53m .

∴S △AOP ＝12×2×(－56m 2＋53m )＝－56m 2＋5

3

m .

又∵S △AOB ＝12×(5)2＝52， ∴S 四边形ABOP ＝S △AOP ＋S △AOB ＝－56m 2＋53m ＋52＝－56(m －1)2＋10

3.

∵－56＜0，∴当m ＝1时，四边形ABOP 的面积最大，此时P (1，－1

3).

25、(1)12.

(2)设矩形ABCD的两邻边长分别为m、n，面积为S. 由题意得2(m＋n)＝12.∴n＝6－m.(3分)

∴S＝mn＝m(6－m)＝－(m－3)2＋9.∴当m＝3时，S的最大值为9.

(3)能实现.理由如下：

如图，在△ABC的另一侧作等边△AEC，再作△AEC的外接圆⊙O，

则满足∠ADC＝60°的点D在优弧AEC上(点D不与A、C重合).

当点D与点E重合时，S△ADC的最大值＝S△AEC.

又∵S△ABC为定值，∴此时，四边形ABCD的面积最大.

设点D′是优弧AEC上任一点，连接AD′、CD′，延长AD′至点F，使D′F＝D′C，则AD′＋D′C＝AF.

连接CF，则∠AFC＝30°. 以点E为圆心，AE长为半径作⊙E，则点F在⊙E上.

∴当点D′与圆心E重合，即AF为⊙E的直径时，AD′＋D′C最长，此时AD′＋D′C＝2AE＝100.

综上，当四边形ABCD的顶点D与点E重合时，其面积最大，同时周长最长.

∴四边形ABCD周长的最大值＝30＋40＋100＝170(米).

2016年河南省中考英语试卷含答案及详细解析

2016年河南省中考英语试卷 一、听力理解（20小题，每小题1分，共20分）第一节听下面5段对话．每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳答案，并将其标号填入题前括号内．每段对话读两遍． 1．（1分）（2016?河南）Who is going to Canada？ A．Jack． B．Chris． C．Julie． 2．（1分）（2016?河南）When can Linda probably come to the party？ A．At 6：30． B．At 7：00． C．At 7：30． 3．（1分）（2016?河南）What did Eric do last weekend？ A．He read a book． B．He stayed at home． C．He went swimming． 4．（1分）（2016?河南）Why does Peter look unhappy？ A．Because he has a math problem． B．Because he failed in the math test． C．Because he's lost his math textbook． 5．（1分）（2016?河南）How many people are there in the boy's family？A．Two． B．Three． C．Four． 第二节听下面几段对话或独白．每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳答案，并将其标号填入题前括号内．每段对话或独自读两遍．

6．（2分）（2016?河南）听下面一段对话，回答第6至第7两个小题．6．How doesthe womanlike dogs？ A．They are noisy． B．They are peaceful． C．They are easy to train． 7．What will the woman have as a pet？ A．A cat． B．A dog． C．A bird． 8．（2分）（2016?河南）听下面一段对话，回答第8至第9两个小题．8．Where is the woman going？ A．To the bus station． B．To the train station． C．To the airport． 9．How much does the woman pay？ A．﹩40． B．﹩45． C．﹩50． 10．（3分）（2016?河南）听下面一段独白，回答第10至第12三个小题．10．How ofen does Dennis buy a new story book？ A．Every day． B．Every week． C．Every month． 11．What does Dennis think of reading？ A．Fantastic． B．Boring． C．Relaxing． 12．What does Dennis want to be when he grows up？ A．A teacher．

陕西省2016年中考英语试题含答案

2016年陕西省初中毕业学业考试试题 英语试卷 第I卷（共65分） A 卷 听力部分（20分）

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