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初2014级2012—2013学年度下期期末综合能力训练(二)

初2014级2012—2013学年度下期期末综合能力训练(二)
初2014级2012—2013学年度下期期末综合能力训练(二)

初2014级2012—2013学年度下期期末综合能力训练(二) 数 学 试 卷 (全卷共五个大题,满分150分,考试时间120分钟)

一、选择题(每小题4分,共48分) 1.下列运算正确的是( ) A .

y

x y y

x y --

=-- B .

3

232=

++y

x y x

C .y x y

x y x +=++22 D .

y

x y x x y -=

-+12

2

2.下列调查中,适宜采用抽样调查方式的是( ) A .调查我市中学生每天体育锻炼的时间 B .调查某班学生对“五个重庆”的知晓率 C .调查一架“歼20”隐形战机各零部件的质量

D .调查广州亚运会100米决赛参赛运动员兴奋剂的使用情况 3.将方程2

410x x ++=配方后得到的形式是( )

A .()2

23x += B .()2

43x += C .()2

43x +=- D .()2

25x +=- 4.下列因式分解中,结果正确的是( )

A .(

)

2

322

2824m n n n m n

-=- B .()()()2

1213x x x --=--

C .()()2

5632y y y y --=-+ D .()2

2

693ax ax a a x -+=-

5. 若a b >,且c 为有理数,则下列各式正确的是( ) A .ac bc >

B .ac bc <

C .2

2

ac bc <

D .22

ac bc ≥

6.不解方程,判断方程

0131

21

12

=-+

+-

-x

x x 的解是( )

A 0

B 1

C 2

D 3 7.若△ABC ∽△A ′B ′C ′,∠A=40°,∠C=110°,则∠B ′等于( ) A .30° B .50°

C .40°

D .70°

8.如图:在△ABC 中,DE ∥AC , 则DE :AC=( ) A .8:3 B .3:8 C .8:5 D .5:8

9.A 、B 两地相距48千米,一艘轮船从A 地顺流航行至B 地,又立即从B 地逆流返回A 地,共用去9小时,已知水流速度为4千米/时,若设该轮船在静水中的速度为x 千米/时,则可列方程( ) A 、

94

484

48=-+

+x x B 、

9448448=-+

+x

x

C

9448=+x

D

94

964

96=-+

+x x

10. 2013年4月20日08时02分在四川雅安芦山县发生7.0级地震,人民生命财产遭受重大损失.某部队接到上级命令,乘车前往灾区救援,前进一段路程后,由于道路受阻,车辆无法通行,通过短暂休整后决定步行前往.则能反映部队与灾区的距离s (千米)与时间t

(小时)之间函数关系的大致图

A

B

C

D

E

(8题图)

象是( )

11.用边长相等的黑色正三角形与白色正六边形镶嵌图案,按图①②③所示的规律依次下去,则第

10个图案中,所包含的黑色正三角形是( )

① ② ③

A .36

B .38

C .40 12.如图,在直角坐标系中,有菱形OABC ,A 点的坐标为(10,0),双曲线x

k y =

(0>x )经过C 点,且OB ·AC =160,则k 的值

为( )

A .40

B .48

C .64

D .8 二、填空题(每小题4分,共24分) 13.若分式

1

21

-x 有意义,则x 的取值范围是 。

14.分解因式:32

2x x x -+= .

15.关于x 的方程042

=+-mx x 有两个相等实根,则m = . 16.如图,在A 时测得某树的影长为4米,B 时又测得该树的影长为9米,

若两次日照的光线互相垂直,则树的高度为 米. 17.若关于x 的方程

1

11

61

2+=

--

-x x x k 有增根,则k = .

18.采购员用一张1万元的支票去购物,购单价为590元的A 种物品若干件,又购单价为670元的B 种物

品若干件,其中B 的件数多于A 的件数,找回了几张100元和几张10元的钞票,(10元的张数不超过9张),如果把购A 种物品和B 种物品的件数互换,找回的100元和10元的钞票张数也恰好相反,则原来购B 种物品为 件。 三、解答题(每小题7分,共14分) 19.解下列方程:2

44170x x +-=

A 时

B 时

16题图

20.如图,在平面直角坐标系中,△ABC的三个顶点的坐标分别为A(0,1),B(– 1,1),C(– 1,3).

(1) 画出△ABC关于x轴对称的△A1B1C1;

(2) 画出△ABC以O为位似中心,位似比为1:2的位似△A2B2C2;

(3) C1的坐标为,C2的坐标为,

四、解答题(本大题4个小题,每小题10分,共40分)解答时每小题必须给出必要的演

算过程或推理步骤.

21.先化简,再求值:

2

2

1221

1

211

x x x

x

x x x

--

??

-÷--

?

+-+

??

,其中0

1

2=

-

+x

x.

22.某蔬菜店第一次用800元购进某种蔬菜,由于销售状况良好,该店又用1400元第二次购进该品种蔬菜,所购数量是第一次购进数量的2倍,但进货价每千克少了0.5元.

(1)第一次所购该蔬菜的进货价是每千克多少元?

(2)蔬菜店在销售中,如果两次售价均相同,第一次购进的蔬菜有3% 的损耗,第二次购进的蔬菜有5% 的损耗,若该蔬菜店售完这些蔬菜获利不低于1244元,则该蔬菜每千克售价至少为多少元?

23.某校九年级为了解学生课堂发言情况,随机抽取该年级部分学生,对他们某天在课堂上发言的次数进行了统计,其结果如下表,并绘制了如图所示的两幅不完整的统计图,已知B 、E 两组发言的人数比为

10:3,请结合图中相关数据回答下列问题:

(1) A 组有 人,C 组有 人,E 组有 人,并补全直方图; (2) 该年级共有学生600人,请估计全年级在这天发言次数不少于20的人数;

(3) 已知A 组发言的学生中恰有一位女生,E 组发言的学生中恰有两位男生,现从A 组与E 组中分别..

抽一位学生写报告,求所抽的两位学生至多有一位男生的概率.

24.已知,矩形ABCD 中,延长BC 至E ,使BE = BD ,F 为DE 的中点,连结AF 、CF .

(1) 若AB = 3,AD = 4,求CF 的长; (2) 求证:∠ADB = 2∠DAF .

五、解答题:(每题12分,共24分) 25. 如图,已知点A(2,4)在反比例函数(0)k y x x

=>的图象S 1上,将双曲线S 1沿y 轴翻折后得到的是

反比例函数k y x

=-

的图象S 2,直线AB 交y 轴于点B(0,3),交x 轴于点C ,P 为线段BC 上的一个动点

(点P 与B 、C 不重合),过P 作x 轴的垂线与双曲线S 2在第二象限相交于点E . (1)求双曲线S 2和直线AB 的解析式.

(2)设点P 的横坐标为m ,线段PE 的长为h ,求h 与m 之间的函数关系,并写出自变量m 的取值范围. (3)在线段BC 上是否存在点P ,使得P 、E 、A 为顶点的三角形与BOC ?相似?

若存在,请求出点P 的坐标;若不存在,请说明理由.

A B

26.如图,在直角梯形ABCD 中,AD ∥BC ,90B ∠=?, 6AD =, 8BC =

,AB =点M 是BC

的中点.点P 从点M 出发沿MB 以每秒1个单位长的速度向点B 匀速运动,到达点B 后立刻以原速度沿BM 返回;点Q 从点M 出发以每秒1个单位长的速度在射线MC 上匀速运动.在点P 、Q 的运动过程中,以PQ 为边作等边三角形EPQ ,使它与梯形ABCD 在射线BC 的同侧.点P 、Q 同时出发,当点P 返回到点M 时停止运动,点Q 也随之停止.设点P 、Q 运动的时间是t 秒(0t >). (1)设PQ 的长为y ,在点P 从点M 向点B 运动的过程中,写出y 与t 之间的函数关系式(不必写t 的取值范围);

(2)当 1BP =时,求EPQ △与梯形ABCD 重叠部分的面积;

(3)随着时间t 的变化,线段AD 会有一部分被EPQ △覆盖,被覆盖线段的长度在某个时刻会达到最大值,请回答:该最大值能否持续一个时段?若能,直接写出t 的取值范围;若不能,请说明理由.

A

B

解:(1)y = 2t ;(2)当BP = 1时,有两种情形:

①如图6,若点P 从点M 向点B 运动,有 MB = BC 2

1

= 4,MP = MQ = 3,∴PQ = 6.连接EM ,

∵△EPQ 是等边三角形,∴EM ⊥PQ .∴33=EM . ∵AB = 33,∴点E 在AD 上.

∴△EPQ 与梯形ABCD 重叠部分就是△EPQ ,其面积为39.

②若点P 从点B 向点M 运动,由题意得 5=t .PQ = BM + M Q -BP = 8,PC = 7.

设PE 与AD 交于点F ,Q E 与AD 或AD 的延长线交于点G ,过点P 作PH ⊥AD 于点H ,则

HP = 33,AH = 1.在Rt △HPF 中,∠HPF = 30°,

∴HF = 3,PF = 6.∴FG = FE = 2.又∵FD = 2,∴点G 与点D 重合,

7.此时△EPQ 与梯形ABCD 的重叠部分就是梯形FPCG ,其面积为

32

27.

(3)能.4≤t ≤5.

图7

图6

2013年12月大学英语四级听力真题(附原文及答案解析)

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2013年上学期《电工基础》期中考试卷

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2012年12月四级听力真题原文

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