2015年北京中考一模五选五试题及答案
2015年北京市通州区中考数学一模试卷带解析答案
灯塔落在地面上的影长为 12 米,然后在同一时刻立一根高 2 米的标杆,测得 标杆影长为 0.5 米,那么燃灯塔高度为 米.
14. (3 分)生物学研究表明在 8﹣17 岁期间,男女生身高增长速度规律呈现如 图所示,请你观察此图,回答下列问题:男生身高增长速度的巅峰期是 岁,在 岁时男生女生的身高增长速度是一样的.
四、解答题(每题 5 分,共 25 分)
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22. (5 分)为了把通州区打造成宜居的北京城市副中心,区政府对地下污水排 放设施进行改造.某施工队承担铺设地下排污管道任务共 2200 米,为了减少 施工对周边交通环境的影响,施工队进行技术革新,使实际平均每天铺设管 道的长度比原计划多 10%,结果提前两天完成任务.求原计划平均每天铺设 排污管道的长度. 23. (5 分)已知菱形 ABCD 的对角线 AC 与 BD 相交于点 E,点 F 在 BC 的延长 线上, 且 CF=BC, 连接 DF, 点 G 是 DF 中点, 连接 CG. 求证: 四边形 ECGD 是矩形.
2. (3 分)北京市为了缓解交通拥堵问题,大力发展轨道交通.据调查,目前轨 道交通日均运送乘客达到 1320 万人次.数据 1320 万用科学记数法表示正确 的是( ) B.13.2×102 万 C.1.32×103 万 D.1.32×104 万 )
A.132×101 万
3. (3 分)某几何体的通州区中考一模数学试卷
一、选择题(每题只有一个正确答案,共 10 个小题,每小题 3 分,共 30 分) 1. (3 分)﹣2 的绝对值是( A.±2 B.2 ) C. D.
A.圆柱
B.三棱柱
C.长方体 ) C.2a2+a2=3a4
2015年北京市东城区中考数学一模试卷带解析答案
源处 费 理 费 第一阶梯 第二阶梯 第三阶梯 0﹣180(含) 181﹣260(含) 260 以上 5.00 7.00 9.00
第 3 页(共 31 页)
2.07 4.07 6.07
1.57 1.36
某户居民从 2015 年 1 月 1 日至 4 月 30 日,累积用水 190 立方米,则这户居民 4
21. (5 分)列方程或方程组解应用题:2015 年“植树节”前夕,某小区为绿化 环境,购进 200 棵柏树苗和 120 棵枣树苗,且两种树苗所需费用相同.每棵 枣树苗的进价比每棵柏树苗的进价的 2 倍少 5 元,每棵柏树苗的进价是多少 元? 22. (5 分)在平面直角坐标系 xOy 中,过点 A(﹣4,2)向 x 轴作垂线,垂足 为 B,连接 AO.双曲线 (1)求反比例函数的解析式; (2)求△BOD 的面积. 经过斜边 AO 的中点 C,与边 AB 交于点 D.
个月共需缴纳水费
元.
15. (3 分)已知女排赛场球网的高度是 2.24 米,某排球运动员在一次扣球时, 球恰好擦网而过,落在对方场地距离球网 4 米的位置上,此时该运动员距离 球网 1.5 米,假设此次排球的运行路线是直线,则该运动员击球的高度是 米.
16. (3 分)在平面直角坐标系 xOy 中,记直线 y=x+1 为 l.点 A1 是直线 l 与 y 轴的交点,以 A1O 为边作正方形 A1OC1B1,使点 C1 落在在 x 轴正半轴上,作 射线 C1B1 交直线 l 于点 A2,以 A2C1 为边作正方形 A2C1C2B2,使点 C2 落在在 x 轴正半轴上, 依次作下去, 得到如图所示的图形. 则点 B4 的坐标东城区中考一模数学试卷
一、选择题(本题共 30 分,每小题 3 分)下面各题均有四个选项,其中只有一 个是符合题意的. 1. (3 分)与﹣2 的和为 0 的数是( A.﹣2 B. ) C. D.2
2015年北京中考英语一模五选五汇编附答案
2015年一模五选五汇编海淀一模通州一模七、阅读短文,根据短文内容,从短文后的五个选项中选出能填入空白处的最佳选项。
(共10分,每小题2分)I often hear some students say that English is difficult, and it gives them a headache so they can’t learn it well. But English is very easy for me. __56__. I’m very glad to tell you something about how I study English.__57__. When I started Grade 3 in primary school, we had a new subject—English. I was interested in it, so I worked hard at it. Soon we had an English exam and I got a very good mark. How happy I was! __58__.Second, I think English is a foreign language. I should learn it well in the following way: __59__, speak bravely, read aloud and learn more words and phrases whenever I can. Then practice again and again and make the process interesting. __60__: Whenever I have a question, I must make it clear by asking our English teacher. How happy I am when I understand!A. I also have a good habitB. I’m good at itC. After that, I learnt English harder and harderD. Listen to the teacher carefullyE. First, interest in English is very important门头沟一模七、阅读短文,根据短文内容,从短文后的五个选项中选出能填入空白处的最佳选项。
2015年北京市顺义区中考数学一模试卷带解析答案
A.2.8×107
3. (3 分)如图是由四个相同的小正方体组成的立体图形,它的俯视图为(
A.
B.
C.
D.
4. (3 分)一名射击爱好者 5 次射击的中靶环数如下:6,7,9,8,9,这 5 个 数据的中位数是( A.6 ) B.7 C.8 ) D.9
5. (3 分)下列图形中是中心对称图形的是(
A.
B.
C. 6. (3 分)函数
D. 中,自变量 x 的取值范围是(
第 1 页(共 28 页)
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A.x≠3
B.x≥3
ቤተ መጻሕፍቲ ባይዱ
C.x>3
D.x≤3
7. (3 分)一个不透明的口袋中,装有 4 个红球,3 个黄球,1 个白球,这些球 除颜色外其余都相同,从口袋中随机摸一个球,则摸到红球的概率为( A. B. C. D. )
根据以上信息解答下列问题: (1)在扇形统计图中,A(经常租用)所占的百分比是 (2)求两次共抽样调查了多少人,并补全折线统计图; (3)根据调查的结果,请你谈谈从 2015 年 1 月底到 2015 年 3 月底,我区居民 使用公租自行车的变化情况. 25. (5 分)如图,AB 是⊙O 的直径,C 是⊙O 上一点,D 是 的中点,过点 D ;
15. (3 分)居民用电计费实行“一户一表”政策,以年为周期执行阶梯电价, 即:一户居民全年不超过 2880 度的电量,执行第一档电价标准为 0.48 元/度; 全年用电量在 2880 度到 4800 度之间(含 4800) ,超过 2880 度的部分,执行 第二档电价标准为 0.53 元/度; 全年用电量超过 4800 度, 超过 4800 度的部分, 执行第三档电价标准为 0.78 元/度. 小敏家 2014 年用电量为 3000 度, 则 2014 年小敏家电费为 元.
北京市西城区2015年初三一模试卷
北京市西城区2015年初三一模试卷数学 2015.4一、选择题(本题共30分,每小题3分)下面各题均有四个选项,其中只有一个是符合题意的。
1.31的相反数是 A. 31 B.-31C. 3D.-32.据市烟花办相关负责人介绍,2015年除夕零时至正月十五24时,全市共销售烟花爆竹约箱,同比下降了32%,将用科学记数法表示应为A.1.96×105B. 1.96×104C. 19.6×104D.0. 196×1063.下列运算正确的是A.3a+3b=6abB.a 3-a=a 2C. (a 2)3=a 6D.a 6÷a 3=a 24.如图是一个 几何体的直观图,则其主视图是5.甲、乙、丙、丁四名选手参加100米决赛,赛场共设1,2,3,4四条跑道,选手以随机抽签的方法决定各自的跑道,若甲首先抽签,则甲抽到1号跑道的概率是A.1B.21 C. 31D. 416.下列图形中,即是轴对称图形又是中心对称图形的是A. B. C. D.7.如图,线段AB 是⊙O 的直径,弦CD ⊥AB,如果∠BOC=70°,那么∠BAD 等于 A. 20° B. 30° C. 35° D. 70°8.在平面直角坐标系xoy 中,第一象限内的点P 在反比例函数的图象上,如果点P 的纵坐标是3,OP=5,那么该函数的表达式为A.y=x 12 B. y=-x 12 C.y=x 15 D.y=-x159.为了解某小区“全民健身”活动的开展情况,某志愿者对居住在该小区50名成年人一周的体育锻炼时间进行了统计,并绘制成如图所示的条形统计图。
这组数据的众数和中位数分别是A.6,4B.6,6C.4,4D.4,610.如图,过半径为6的⊙O 上一点A 作⊙O 的切线l ,P 为⊙O于点H ,连接PA ,如果PA=x ,AH=y ,那么下列图象中,能大致表示y 与x A. B. C. D.A. B. C.二、填空题(本题共18分,每小题3分)11.如果分式51-x 有意义,那么x 的取值范围是 . 12.半径为4cm ,圆心角为60°的扇形的面积为 cm 2. 13.分解因式:12m 2-3= .14.如图,△ABC 中,AB=AC,点D,E 在BC 边上,当 时,△ABD ≌△ACE.(添加一个适当的条件即可).15. 如图是蹊跷板的示意图,立柱OC 与地面垂直,以O 为横板AB 的中点..,AB 绕点O 上下转动,横板AB 的B 端最大高度h 是否会随横板长度的变化而变化呢?一位同学做了如下研究:他先设AB=2m,OC=0.5m,通过计算得到此时的h 1,再将横板AB换成A ′B ′,O 为横板A ′B ′的中点,且A ′B ′=3m ,此时B ′点的最大高度为h 2,由此得到h 1与h 2的大小关系是:h 1 h 2(填“>”、“=”或“<”),可进一步得出h 随横板的长度的变化而 (填“不变 ”或“改变”).16.如图,数轴上,点A 的初始位置表示的数为1,现点A 做如下移动:第1次点A 向左移动3个单位长度至点A 1,第2次从点A 1向右移动6个单位长度至点A 2,第3次从点A 2向左移动9个单位长度至点A 3,…,按照这种移动方式进行下去,点A 4表示的数是 ,如果点A n 与原点的距离不小于20,那么n 的最小值是 。
2015年北京通州初三数学一模试题含答案
通州区2015年初三模拟考试数学试卷一、选择题(每题只有一个正确答案,共10个小题,每小题3分,共30分) 1.2-的绝对值是( )A .2±B .2C .12D .12-2.北京市为了缓解交通拥堵问题,大力发展轨道交通.据调查,目前轨道交通日均运送乘客达到1320万人次.数据1320万用科学计数法表示正确的是( )A .113210⨯万 B .213.210⨯万 C .31.3210⨯万 D .41.3210⨯万 3.某几何体的三视图如图所示,这个几何体是( ) A .圆柱 B .三棱柱 C. 长方体D .圆锥4.下列等式一定成立的是( ). A .22a a a ⋅=B .22=÷a aC .22423a a a +=D .()33a a -=-5.如图,点A 、D 在射线AE 上,直线AB ∥CD ,∠CDE =140°, 那么∠A 的度数为( ) A .140° B .60° C .50°D .40° 6.一个多边形的每一个内角均为108°,那么这个多边形是( )A .七边形B .六边形C .五边形D .四边形7.某学校组织学生进行社会主义核心价值观的知识竞赛,进入决赛的共有20名学生,他们的决赛成绩如下表所示:那么20名学生决赛成绩的众数和中位数分别是( )A .85, 90B .85, 87.5C .90, 85D .95, 908.物理某一实验的电路图如图所示,其中K 1,K 2,K 3 为电路开关,L 1 ,L 2为能正常发光的灯泡.任意闭合开关K 1, K 2, K 3中的两个,那么能让两盏灯泡同时..发光的概率为( ) A .31B .32C .21D .619.如图,AB 是⊙O 的直径,CD 是弦,且CD ⊥AB ,BC =6,AC =8,那么sin ∠ABD 的值是( )A .43 B .34 C .35 D .4510.如图,在Rt △ABC 中,∠ACB =90°,D 为斜边AB 的中点,动点P 从B 点出发,沿B →C →A 运动.如图(1)所示,设S △DPB = y ,点P 运动的路程为x ,若y 与x 之间的函数图象如图(2)所示,则△ABA .4B .6C .12D .14二、填空题:(每题3分,共18分)11.分解因式:2a 2-4a +2=________________.12.使得分式321x -有意义的x 的取值范围是 . 13.燃灯佛舍利塔(简称燃灯塔)是通州八景之一,该塔始建于南北朝北周宇文时期,距今已有1300多年历史.燃灯塔距运河300 米,是通州的象征.某同学想利用相似三角形的有关知识来求 燃灯塔的高度.他先测量出燃灯塔落在地面上的影长为12米, 然后在同一时刻立一根高2米的标杆,测得标杆影长为0.5米, 如图(1)A214.生物学研究表明在8—17岁期间,男女生身高增长速度规律呈现如下图所示,请你观察此图,回答下列问题:男生身高增长速度的巅峰期是 岁,在 岁时男生女生的身高增长速度是一样的.15.如图,在扇形OAB 中,∠AOB =110°,半径OA =18,将扇形OAB 沿着过点B 的直线折叠,点O 恰好落在AB 上的点D 处,折痕交OA 于点C ,则AD 的长等于 . 16.如图,在平面直角坐标系xOy 中,四边形ABOC 是正方形,点A 的坐标为(1,1).¼1AA 是以点B 为圆心,BA 为半径的圆弧;¼12A A 是以点O 为圆心,1OA 为半径的圆弧,¼23A A 是以点C 为圆心,2CA 为半径的圆弧,¼34A A 是以点A 为圆心,3AA 为半径的圆弧,继续以点B 、O 、C 、A 为圆心按上述做法得到的曲线12345AA A A A A ……称为“正方形的渐开线”,那么点5A 的坐标是 , 点A 的坐标是 .第15题图 第16题图 三、解答题(每题5分,共25分)17.如图,点O 是直线l 上一点,点A 、B 位于直线l 的两侧,且∠AOB =90°,OA =OB ,分别过A 、B 两点作AC ⊥l ,交直线l 于点C ,BD ⊥l ,交直线l 于点D . 求证:AC =OD .18()1201512tan 6012-⎛⎫--︒-- ⎪⎝⎭19.解不等式组51342133x x x ->-⎧⎪⎨-≥-⎪⎩,并把不等式组的解集在数轴上表示出来.20.已知:2450x x +-=,求代数式22(1)(1)(2)x x x +---的值.21.如图,一次函数y 1=kx +b 的图象与反比例函数y 2=6x的图象交于A (m ,3),B (-3,n )两点.(1)求一次函数的表达式;(2)观察函数图象,直接写出关于x 的不等式 6x>kx +b四、解答题(每题5分,共25分)22.为了把通州区打造成宜居的北京城市副中心,区政府对地下污水排放设施进行改造.某施工队承担铺设地下排污管道任务共2200米,为了减少施工对周边交通环境的影响,施工队进行技术革新,使实际平均每天铺设管道的长度比原计划多10%,结果提前两天完成任务.求原计划平均每天铺设排污管道的长度.通州区2013年至2014年三期自行车投放数量统计图(单位:辆) 通州区2013年至2014年三期所投放的 自行车租赁点百分比统计图23.已知菱形ABCD 的对角线AC 与BD 相交于点E ,点F 在BC 的延长线上,且CF=BC ,连接DF ,点G 是DF 中点,连接CG .求证:四边形 ECGD 是矩形.24.为倡导“1公里步行、3公里单车、5公里汽车(地铁、轻轨)”出行模式, 2013年5月环保公共自行车正式“驶入”通州,通州区分三期投放白绿环保公共自行车.第一期投放租赁点以八通线通州北苑、梨园站为中心,共投放21个租赁点。
2015.5北京中考东城一模+答案
东城区2014—2015学年第二学期初三综合练习(一) 数学试题 2015.5学校 班级 姓名 考号考生须知1.本试卷共8页,共五道大题,29道小题,满分120分.考试时间120分钟. 2.在试卷上准确填写学校名称、班级、姓名和考号. 3.试题答案一律填涂或书写在答题卡上,在试卷上作答无效. 4.在答题卡上选择题、作图题用2B 铅笔作答,其他试题用黑色字迹签字笔作答. 5.考试结束,请将本试卷和答题卡一并交回. 一、选择题(本题共30分,每小题3分)下面各题均有四个选项,其中只有一个..是符合题意的. 1.与2-的和为0的数是 A .2- B .12-C .12D .22.2015年元旦期间,北京各大公园接待游客达245 000万人次。
其中, “冰雪乐园”吸引了大批游客亲身感受冰雪带来的快乐,一起为北京申办2022年冬奥会助力加油.用科学记数法表示245 000 ,正确的是A .424.510⨯B .52.4510⨯C .62.4510⨯D .60.24510⨯ 3.一个几何体的三视图如图所示,则这个几何体是 A .圆柱 B .球 C .圆锥 D . 棱柱4.在某校初三年级古诗词比赛中,初三(1)班42名学生的成绩统计如下,则该班学生成绩的中位数和众数分别是分数 50 60 70 80 90 100 人数 12813144A . 70,80B . 70,90C . 80,90D . 80,1005. 在六张卡片上分别写有1π,, 1.5,3,0,23-,从中任意抽取一张,卡片上的数为无理数的概率是 A . 16B .13C . 12D . 236.正五边形的每个外角等于A. 36︒B. 60︒C. 72︒D. 108︒ 延长线7.如图,AB 是O 的直径,点C 在O 上,过点C 作O 的切线交AB 的于点D ,连接OC ,AC . 若50D ∠=︒,则A ∠的度数是A. 20︒ B .25︒C .40︒D .50︒8.小李驾驶汽车以50千米/小时的速度匀速行驶1y (单位:千米)与行驶时间t (单位:小时)的函数图象大致如图所示,则接电话后小李的行驶速度为 A. 43.5 B. 50 C. 56 D . 589. 如图,已知∠MON =60°,OP 是∠MON 的角平分线 ,点A 是OP 上一点,过点A 作ON 的平行线交OM 于点B,AB=4.则直线AB 与ON 之间的距离是 A.3 B.2 C.23 D.410. 如图1, ABC △和DEF △都是等腰直角三角形,其中90C EDF ∠=∠=︒,点A 与点D 重合,点E 在AB 上,4AB =,2DE =.如图2,ABC △保持不动,DEF △沿着线段AB 从点A 向点B 移动, 当点D 与点B 重合时停止移动.设AD x =,DEF △与ABC △重叠部分的面积为S ,则S 关于x 的函数图象大致是图1 图22.24A B C D二、填空题(本题共18分,每小题3分)11.分解因式:224mx my -= . 128272+3的结果为 .13. 关于x 的一元二次方程230x x m +-=有两个不相等的实数根,则实数m 的取值范围 是 .14. 北京的水资源非常匮乏,为促进市民节水,从2014年5月1日起北京市居民用水实行阶梯水价,实施细则如下表:北京市居民用水阶梯水价表 单位: 元/立方米分档水量户年用水量(立方米)水价其中自来水费水资源费污水处理费 第一阶梯 0-180(含)第二阶梯 181-260(含) 第三阶梯260以上6.07某户居民从2015年1月1日至4月30日,累积用水190立方米,则这户居民4个月共需缴纳水费 元.15.已知女排赛场球网的高度是2.24米,某排球运动员在一次扣球时,球恰好擦网而过,落在对方场地距离球网4米的位置上,此时该运动员距离球网1.5米,假设此次排球的运行路线是直线,则该运动员击球的高度是 米.ODBC16.在平面直角坐标系xOy 中,记直线1y x =+为l .点1A 是直线l 与y 轴的交点,以1A O 为 边做正方形111A OC B ,使点1C 落在在x 轴正半轴上,作射线11C B 交直线l 于点2A ,以 21A C 为边作正方形2122A C C B ,使点2C 落在在x 轴正半轴上,依次作下去,得到如图点4B 的坐标是 ,点n B 的坐标是 .三、解答题(本题共30分,每小题5分)17.如图,AC 与BD 交于点O ,OA OC =,OB OD =.求证:DC AB ∥.18. 计算:()11336043-⎛⎫--︒+-+- ⎪⎝⎭π.19.解不等式组:()2131,5 4.2x x x x --⎧⎪⎨-+⎪⎩><20.先化简,再求值:222442111a a a a a a -+-+÷+--,其中21a =. 21.列方程或方程组解应用题:2015年“植树节”前夕,某小区为绿化环境,购进200棵柏树苗和120棵枣树苗,且两种的进价比每棵柏树苗的进价的2倍少5元,每棵柏树苗的进价是多少元?22.在平面直角坐标系xOy 中,过点()4,2A -向x 轴作垂线,垂足为B ,连接AO .双曲线 ky x=经过斜边AO 的中点C ,与边AB 交于点D . (1)求反比例函数的解析式; (2)求△BOD 的面积. 四、解答题(本题共20分,每小题5分)23. 如图,ABC △中,90BCA ∠=︒,CD 是边AB 上的中线,分别过点C ,D 作BA ,BC的平行线交于点E ,且DE 交AC 于点O ,连接AE . (1)求证:四边形ADCE 是菱形; (2)若2AC DE =,求sin CDB ∠的值.第15题图 第16题图F24.为弘扬中华传统文化,某学校决定开设民族器乐选修课.为了更贴合学生的兴趣,对学生最喜爱的一种民族乐器进行随机抽样调查,收集整理数据后,绘制出以下两幅未完成的统计图,请根据图1和图2提供的信息,解答下列问题:(1)在这次抽样调查中,共调查 名学生; (2)请把条形图(图1)补充完整;(3)求扇形统计图(图2)中,二胡部分所对应的圆心角的度数; (4)如果该校共有学生1500名,请你估计最喜爱古琴的学生人数.过点,D A 分别25. 如图,在⊙O 中,AB 为直径,OC AB ⊥,弦CD 与OB 交于点F ,作⊙O 的切线交于点G ,且GD 与AB 的延长线交于点E . (1)求证:12∠=∠;(2)已知::1:3OF OB =,⊙O 的半径为3,求AG 的长.26. 在四边形ABCD 中,对角线AC 与BD 交于点O ,E 是OC 上任意一点,AG BE ⊥于点G ,交BD 于点F .(1)如图1,若四边形ABCD 是正方形,判断AF 与BE 的数量关系;明明发现,AF 与BE 分别在AOF △和BOE △中,可以通过证明AOF △和BOE △全等,得到AF 与BE 的数量关系;请回答:AF 与BE 的数量关系是 .(2) 如图2,若四边形ABCD 是菱形, 120ABC ∠=︒,请参考明明思考问题的方法,求AFBE的值.BAG BF EO DCA图1 图2五、解答题(本题共22分,第23题7分,第24题7分,第25题8分)27.在平面直角坐标系xOy 中,抛物线()210y ax bx a =++≠过点()1,0A -,()1,1B ,与y 轴交于点C .(1)求抛物线()210y ax bx a =++≠的函数表达式;(2)若点D 在抛物线()210y ax bx a =++≠的对称轴上,当ACD △的周长最小时,求点D 的坐标;(3)在抛物线()210y ax bx a =++≠的对称轴上是否存在点P ,使ACP △成为以AC 为直角边的直角三角形?若存在,求出点P 的坐标;若不存在,请说明理由.28. 已知:Rt △A ′BC ′和 Rt △ABC 重合,∠A ′C ′B =∠ACB =90°,∠BA ′C ′=∠BAC =30°,现将Rt △A ′BC ′ 绕点B 按逆时针方向旋转角α(60°≤α≤90°),设旋转过程中射线C ′C 和线段AA ′相交于点D ,连接BD . (1)当α=60°时,A ’B 过点C ,如图1所示,判断BD 和A ′A 之间的位置关系,不必证明; (2)当α=90°时,在图2中依题意补全图形,并猜想(1)中的结论是否仍然成立,不必证明; (3)如图3,对旋转角α(60°<α<90°),猜想(1)中的结论是否仍然成立;若成立,请证明你的结论;若不成立,请说明理由.29.定义符号{}min a b ,的含义为:当a b ≥时, {}min a b b =,;当a b <时, {}min a b a =,.如:{}min 122-=-,,{}min 121-=-,.(1)求{}2min x -1,-2;(2)已知2min{2,3}3x x k -+-=-, 求实数k 的取值范围;(3) 已知当23x -≤≤时,22min{215,(1)}215x x m x x x --+=--.直接写出实数m 的取值范围.东城区2014-2015学年第二学期初三综合练习(一)数学试题参考答案及评分标准 2015.5一、选择题(本题共30分,每小题3分)二、填空题(本题共18分,每小题3分) 三、解答题(本题共30分,每小题5分) 17. 证明:∵在ODC △和OBA △中,∵,,,OD OB DOC BOA OC OA =⎧⎪∠=∠⎨⎪=⎩∴ODC OBA △≌△. …………3分 ∴C A ∠=∠. …………4分 ∴DC AB ∥. …………5分()()1118.36043134415-⎛⎫-︒+-+- ⎪⎝⎭=--+=-解:π分分19. ()2131,8x x x x --⎧⎪⎨-+⎪⎩①②>解:5<2,2x 由①得,<,…………2分 1x -由②得,>, …………4分 所以,不等式组的解集为12x -<<. …………5分()()()22224421112211112221131a a a a a a a a a a a a a a a a a -+-+÷+----=+⋅++---=+++=+20.解:分当1a =时,2=原式.…………5分 21.解:设每棵柏树苗的进价是x 元,则每棵枣树苗的进价是()25x -元. …………1分 根据题意,列方程得:200=120(25)x x -, …………3分 解得: 15x =. …………5分 答:每棵柏树苗的进价是15元. 22. 解:(1)过点C 向x 轴作垂线,垂足为E .∵CE x ⊥轴,AB x ⊥轴,()4,2A-,∴CE AB ∥,()4,0B -. ∴12OE OC CE OB OA AB ===. ∵4OB =,2AB =, ∴2OE =,1CE =.∴()2,1C -. …………2分 ∵双曲线ky x=经过点C , ∴2k =-.∴反比例函数的解析式为2y x=-. …………3分 (2)∵点D 在AB 上,∴点D 的横坐标为4-. ∵点D 在双曲线2y x=-上, ∴点D 的纵坐标为12. …………4分 ∴BODS △11141222OB BD =⋅⋅=⨯⨯=.…………5分 四、解答题(本题共20分,每小题5分)23.(1)证明:∵DE BC ∥,CE AB ∥, ∴四边形DBCE 是平行四边形. ∴CE BD =. 又∵CD 是边AB 上的中线,∴BD AD =.∴CE DA =. 又∵CE DA ∥,∴四边形ADCE 是平行四边形.∵90BCA ∠=︒,CD 是斜边AB 上的中线, ∴AD CD =.∴四边形ADCE 是菱形. …………3分(2)解:作CFAB ⊥于点F .由(1) 可知, .BC DE =设BC x =,则2AC x =.在Rt ABC △中,根据勾股定理可求得5AB x =.∵1122AB CF AC BC ⋅=⋅, ∴255AC BC CF x AB ⋅==.F∵152CD AB x ==, ∴4sin 5CF CDB CD ∠==.…………5分 24.解:(1)20÷10%=200(名),…………1分 答:一共调查了200名学生; (2)最喜欢古筝的人数:200×25%=50(名), 最喜欢琵琶的人数:200×20%=40(名); 补全条形图如图; …………3分 (3)二胡部分所对应的圆心角的度数为:60200×360°=108°; …………4分 (4)1500×30200=225(名). …………5分答:1500名学生中估计最喜欢古琴的学生人数为225. 25.(1)证明:连结OD ,如图.∵DE 为⊙O 的切线,OD 为半径, ∴OD DE ⊥.∴90ODE ∠=︒,即290ODC ∠+∠=︒.∵OC OD =, ∴C ODC ∠=∠. ∴290C ∠+∠=︒. 而OC OB ⊥,∴390C ∠+∠=︒. ∴23∠=∠.∵13∠=∠, ∴12∠=∠. …………2分(2)解:∵:1:3OF OB =,⊙O 的半径为3, ∴1OF =. ∵12∠=∠, ∴EF ED =.在Rt ODE △中,3OD =,设DE x =,则EF x =,1OE x =+.∵222OD DE OE +=,∴()22231x x +=+,解得4x =.∴4DE =,5OE =.∵AG 为⊙O 的切线,OA 为半径,GD 为⊙O 的切线, ∴AG AE ⊥,GA GD =.∴90GAE ∠=︒.在Rt AGE △中,设DG t =,则4GE t =+.∵222AG AE GE +=. ∴()22284t t +=+,解得,6t =.∴6AG =. -------------------5分26. 解:(1)AF =BE ; …………1分 (2)AF BE=. …………2分 理由如下:∵四边形ABCD 是菱形,120ABC ∠=︒,∴AC BD ⊥,60ABO ∠=︒.∴90FAO AFO ∠+∠=︒.∵AG BE ⊥,∴90EAG BEA ∠+∠=︒.∴AFO BEA ∠=∠.又∵90AOF BOE ∠=∠=︒,∴AOF BOE △∽△. …………3分∴AF AO BE OB= . ∵60ABO ∠=︒,AC BD ⊥,∴tan 60AO OB=︒=.∴AF BE = …………5分 五、解答题(本题共22分,第27题7分,第28题7分,第29题8分)27.解:(1)∵抛物线()210y ax bx a =++≠过点()1,0A -,()1,1B ,∴10,1 1.a b a b -+=⎧⎨++=⎩∴1,21.2a b ⎧=-⎪⎪⎨⎪=⎪⎩ ∴抛物线的函数关系式为211122y x x =-++. …………2分 (2)∵122b x a =-=,()0,1C∴抛物线211122y x x =-++的对称轴为直线12x =. 设点E 为点A 关于直线12x =的对称点,则点E 的坐标为()2,0. 连接EC 交直线12x =于点D ,此时ACD △的周长最小. 设直线EC 的函数表达式为y kx m =+,代入,E C 的坐标,则2m 0,1.k m +=⎧⎨=⎩解得1,21.k m ⎧=-⎪⎨⎪=⎩所以,直线EC 的函数表达式为112y x =-+. 当12x =时,34y =. ∴ 点D 的坐标为13,24⎛⎫⎪⎝⎭. …………4分 (3)存在.①当点A 为直角顶点时,过点A 作AC 的垂线交y 轴于点M ,交对称轴于点1P . ∵AO OC ⊥,1AC AP ⊥,∴90AOM CAM ∠=∠=︒.∵()0,1C ,()1,0A -,∴1OA OC ==.∴45CAO ∠=︒.∴45OAM OMA ∠=∠=︒.∴1OA OM ==.∴点M 的坐标为()0,1-.设直线AM 对应的一次函数的表达式为11y k x b =+,代入,A M 的坐标,则1110,1.k b b -+=⎧⎨=-⎩ 解得111,1.k b =-⎧⎨=-⎩ 所以,直线AM 的函数表达式为1y x =--. 令12x =,则32y =-. ∴点1P 的坐标为13,22⎛⎫-⎪⎝⎭. …………5分 ②当点C 为直角顶点时,过点C 作AC 的垂线交对称轴于点2P ,交x 轴于点N . 与①同理可得Rt CON △是等腰直角三角形,∴1OC ON ==.∴点N 的坐标为()1,0.∵2CP AC ⊥,1AP AC ⊥,∴21CP AP ∥.∴直线2CP 的函数表达式为1y x =-+. 令12x =,则12y =. ∴点2P 的坐标为11,22⎛⎫ ⎪⎝⎭. …………6分 综上,在对称轴上存在点1P 13,22⎛⎫- ⎪⎝⎭,2P 11,22⎛⎫ ⎪⎝⎭,使ACP △成为以AC 为直角边的直角三角形.…………7分28.解:(1) 当60α=︒时, BD A A '⊥. ------------1分(2)补全图形如图1,BD A A '⊥仍然成立;------------3分(3)猜想BD A A '⊥仍然成立.证明:作AE C C '⊥,A F C C ''⊥,垂足分别为点,E F ,如图2,则90AEC A FC ''∠=∠=︒. ∵BC BC '=,∴BCC BC C ''∠=∠.∵90ACB A C B ''∠=∠=︒,∴90ACE BCC '∠+∠=︒,'90A C F BC C ''∠+∠=︒. ∴ACE A C F ''∠=∠.在AEC △和A FC ''△中,90,,,AEC A FC ACE A C F AC A C ''∠=∠=︒⎧⎪''∠=∠⎨⎪''=⎩∴AEC A FC ''△≌△.∴AE A F '=.在AED △和A FD '△中,90,,,AEC A FD ADE A DF AE A F '∠=∠=︒⎧⎪'∠=∠⎨⎪'=⎩∴AED A FD '△≌△.∴AD A D '=.∵AB A B '=,∴'ABA △为等腰三角形.∴BD A A '⊥------------7分29.解:(1)∵20x ≥,∴2x -1≥-1.∴2-x -1>2.图2图1∴{}2min 2x =--1,-2. ┉┉2分(2) ∵()2211x x k x k -+=-+-2,∴()2111x k k -+--≥.∵2min{2,3}3x x k -+-=-, ∴13k --≥.∴2k -≥.┉┉5分 (3) 37m -≤≤.┉┉8分。
2015北京中考模拟题英语五选五集合
七、阅读短文,根据短文内容,从短文后的五个选项中选出能填入空白处的最佳选项。
每个选项只能用一次。
(共10分,每小题2分)The Same But DifferentMaggie and Sarah are twin sisters. They were born just a few minutes apart, and they look exactly alike. They both have blonde hair and green eyes. 56 . Sometimes other students at school have a hard time telling them apart.Maggie and Sarah like going to the same school. This is because they are not just twin sisters, but best friends too. They have a lot in common. 57 . Both girls spend a lot of time together with their family, and they both like to play with their dog, Callie.58 . Maggie likes to play sports. She is on a soccer team and a basketball team. Sarah doesn’t really like sports. She likes to dance.There are other differences between them too. 59 . Maggie likes to read mystery books, but Sarah likes to read books about animals. Maggie gets better grades in reading and Spanish, but Sarah gets better grades in math and science.Everyone is different in her or his own way. Maggie and Sarah like being different from each other as much as they like being similar. 60 .A. That is what makes them specialB. They are around the same height as wellC. But Maggie and Sarah are also very differentD. Maggie likes the color red, but Sarah likes the color greenE. Both girls enjoy a lot of the same television shows, books, and foodNew words & expressions七、阅读短文,根据短文内容,从短文后的五个选项中选出能填入空白处的最佳选项。
中考英语一模五选五汇编附答案
中考英语一模五选五汇编附答案2015年一模五选五汇编各区一模成绩如下:海淀一模:ABCDE西城一模:AEBCD东城一模:EDCBA朝阳一模:___丰台一模:CDEBA房山一模:BADCE通州一模:未公布阅读理解I often hear some students say that English is difficult。
and it gives them a headache so they can't learn it well。
But for me。
English is very easy。
__56__.When I started Grade 3 in primary school。
we had a new subject - English。
I was interested in it。
so I worked hard at it。
Soon we had an English exam and I got a very good mark。
How happy I was。
__57__.Second。
I think English is a foreign language。
I should learn it well in the following way: __58__ speak bravely。
read aloud。
and learn more words and phrases whenever I can。
Then practice again and again and make the process ___ I have a n。
I must make it clear by asking our English teacher。
How happy I am when I understand!A。
I also have a good habitB。
I'm good at it___。
北京市东城区2015年中考一模数学试题和答案
东城区2014—2015学年第二学期初三综合练习(一) 数学试题 2015.5学校 班级 姓名 考号一、选择题(本题共30分,每小题3分)下面各题均有四个选项,其中只有一个..是符合题意的. 1.与2-的和为0的数是 A .2- B .12-C .12D .22.2015年元旦期间,北京各大公园接待游客达245 000万人次。
其中, “冰雪乐园”吸引了大批游客亲身感受冰雪带来的快乐,一起为北京申办2022年冬奥会助力加油.用科学记数法表示245 000 ,正确的是A .424.510⨯ B .52.4510⨯C .62.4510⨯ D .60.24510⨯ 3.一个几何体的三视图如图所示,则这个几何体是 A .圆柱 B .球 C .圆锥 D . 棱柱4.在某校初三年级古诗词比赛中,初三(1)班42名学生的成绩统计如下,则该班学生成绩的中位数和众数分别是5. 在六张卡片上分别写有1π,, 1.5,3,0,3-,从中任意抽取一张,卡片上的数为无理数的概率是6.正五边形的每个外角等于A. 36︒B. 60︒C. 72︒D. 108︒ 7.如图,AB 是O 的直径,点C 在O 上,过点C 作O 的切线交AB 的延长线于点D ,连接OC ,AC . 若50D ∠=︒,则A ∠的度数是A. 20︒ B .25︒C .40︒D .50︒8.小李驾驶汽车以50千米/小时的速度匀速行驶1小时后,途中靠边停车接了半小时电话,然后继续匀速行驶.已知行驶路程y (单位:千米)与行驶时间t (单位:小时)的函数图象大致如图所示,则接电话后小李的行驶速度为 A. 43.5 B. 50 C. 56 D . 589. 如图,已知∠MON =60°,OP 是∠MON 的角平分线 ,点A 是OP 上一点,过点A 作ON 的平行线交OM 于点B,AB=4.则直线AB 与ON 之间的距离是A.B.2C.D.410. 如图1, ABC △和DEF △都是等腰直角三角形,其中90C EDF ∠=∠=︒,点A 与点D 重合,点E 在AB 上,4AB =,2DE =.如图2,ABC △保持不动,DEF △沿着线段AB 从点A 向点B 移动, 当点D 与点B 重合时停止移动.设AD x =,DEF △与ABC △重叠部分的面积为S ,则S 关于x 的函数图象大致是A B C D二、填空题(本题共18分,每小题3分)11.分解因式:224mx my -= . 12的结果为 .13. 关于x 的一元二次方程230x x m +-=有两个不相等的实数根,则实数m 的取值范围 是 .14. 北京的水资源非常匮乏,为促进市民节水,从2014年5月1日起北京市居民用水实行阶梯水价,实施细则如下表:北京市居民用水阶梯水价表 单位: 元/立方米某户居民从2015年1月1日至4月30日,累积用水190立方米,则这户居民4个月共需缴纳水费 元.15.已知女排赛场球网的高度是2.24米,某排球运动员在一次扣球时,球恰好擦网而过,落在对方场地距离球网4米的位置上,此时该运动员距离球网1.5米,假设此次排球的运行路线是直线,则该运动员击球的高度是 米.图1 图216.在平面直角坐标系xOy 中,记直线1y x =+为l .点1A 是直线l 与y 轴的交点,以1A O 为 边做正方形111A OC B ,使点1C 落在在x 轴正半轴上,作射线11C B 交直线l 于点2A ,以 21A C 为边作正方形2122A C C B ,使点2C 落在在x 轴正半轴上,依次作下去,得到如图所示的图形.则点4B 的坐标是 ,点n B 的坐标是 .三、解答题(本题共30分,每小题5分)17.如图,AC 与BD 交于点O ,OA OC =,OB OD =.求证:DC AB ∥.18. 计算:()1136043-⎛⎫-︒+-+- ⎪⎝⎭π.19.解不等式组:()2131,5 4.2x x x x --⎧⎪⎨-+⎪⎩><20.先化简,再求值:222442111a a a a a a -+-+÷+--,其中1a =. 21.列方程或方程组解应用题:2015年“植树节”前夕,某小区为绿化环境,购进200棵柏树苗和120棵枣树苗,且两种树苗所需费用相同.每棵枣树苗的进价比每棵柏树苗的进价的2倍少5元,每棵柏树苗的进价是多少元?F(1)求反比例函数的解析式; (2)求△BOD 的面积. 四、解答题(本题共20分,每小题5分)23. 如图,ABC △中,90BCA ∠=︒,CD 是边AB 上的中线,分别过点C ,D 作BA ,BC 的平行线交于点E ,且DE 交AC 于点O ,连接AE . (1)求证:四边形ADCE 是菱形; (2)若2AC DE =,求sin CDB ∠的值.24.为弘扬中华传统文化,某学校决定开设民族器乐选修课.为了更贴合学生的兴趣,对学生最喜爱的一种民族乐器进行随机抽样调查,收集整理数据后,绘制出以下两幅未完成的统计图,请根据图1和图2提供的信息,解答下列问题: (1)在这次抽样调查中,共调查 名学生; (2)请把条形图(图1)补充完整;(3)求扇形统计图(图2)中,二胡部分所对应的圆心角的度数; (4)如果该校共有学生1500名,请你估计最喜爱古琴的学生人数.25. 如图,在⊙O 中,AB 为直径,OC AB ⊥,弦CD 与OB 交于点F ,过点,D A 分别作⊙O 的切线交于点G ,且GD 与AB 的延长线交于点E .(1)求证:12∠=∠;(2)已知::1:3OF OB =,⊙O 的半径为3,求AG 的长.26. 在四边形ABCD 中,对角线AC 与BD 交于点O ,E 是OC 上任意一点,AG BE ⊥于点G ,交BD 于点F .(1)如图1,若四边形ABCD 是正方形,判断AF 与BE 的数量关系;明明发现,AF 与BE 分别在AOF △和BOE △中,可以通过证明AOF △和BOE △全等,得到AF 与BE 的数量关系;请回答:AF 与BE 的数量关系是 .(2) 如图2,若四边形ABCD 是菱形, 120ABC ∠=︒,请参考明明思考问题的方法,求AFBE的值.图1 图2五、解答题(本题共22分,第23题7分,第24题7分,第25题8分)27.在平面直角坐标系xOy 中,抛物线()210y ax bx a =++≠过点()1,0A -,()1,1B ,与y轴交于点C .(1)求抛物线()210y ax bx a =++≠的函数表达式;(2)若点D 在抛物线()210y ax bx a =++≠的对称轴上,当ACD △的周长最小时,求点D 的坐标;(3)在抛物线()210y ax bx a =++≠的对称轴上是否存在点P ,使ACP △成为以AC为直角边的直角三角形?若存在,求出点P 的坐标;若不存在,请说明理由.BAC28. 已知:Rt △A ′BC ′和 Rt △ABC 重合,∠A ′C ′B =∠ACB =90°,∠BA ′C ′=∠BAC =30°,现将Rt △A ′BC ′ 绕点B 按逆时针方向旋转角α(60°≤α≤90°),设旋转过程中射线C ′C 和线段AA ′相交于点D ,连接BD .(1)当α=60°时,A ’B 过点C ,如图1所示,判断BD 和A ′A 之间的位置关系,不必证明; (2)当α=90°时,在图2中依题意补全图形,并猜想(1)中的结论是否仍然成立,不必证明;(3)如图3,对旋转角α(60°<α<90°),猜想(1)中的结论是否仍然成立;若成立,请证明你的结论;若不成立,请说明理由.29.定义符号{}min a b ,的含义为:当a b ≥时, {}min a b b =,;当a b <时,{}min a b a =,.如:{}min 122-=-,,{}min 121-=-,.(1)求{}2min x -1,-2;(2)已知2min{2,3}3x x k -+-=-, 求实数k 的取值范围;(3) 已知当23x -≤≤时,22min{215,(1)}215x x m x x x --+=--.直接写出实数m 的取值范围.东城区2014-2015学年第二学期初三综合练习(一)数学试题参考答案及评分标准 2015.5三、解答题(本题共30分,每小题5分) 17. 证明:∵在ODC △和OBA △中,∵,,,OD OB DOC BOA OC OA =⎧⎪∠=∠⎨⎪=⎩∴ODC OBA △≌△. …………3分 ∴C A ∠=∠. …………4分 ∴DC AB ∥. …………5分()()1118.36043134415-⎛⎫-︒+-+- ⎪⎝⎭=-+=-解:π分分19. ()2131,8x x x x --⎧⎪⎨-+⎪⎩①②>解:5<2,2x 由①得,<, …………2分 1x -由②得,>, …………4分所以,不等式组的解集为12x -<<. …………5分()()()22224421112211112221131a a a a a a a a a a a a a a a a a -+-+÷+----=+⋅++---=+++=+20.解:分当1a =时,2=原式.…………5分 21.解:设每棵柏树苗的进价是x 元,则每棵枣树苗的进价是()25x -元. …………1分 根据题意,列方程得:200=120(25)x x -, …………3分解得: 15x =. …………5分 答:每棵柏树苗的进价是15元. 22. 解:(1)过点C 向x 轴作垂线,垂足为E .∵CE x ⊥轴,AB x ⊥轴,()4,2A-,∴CE AB ∥,()4,0B -. ∴12OE OC CE OB OA AB ===. ∵4OB =,2AB =, ∴2OE =,1CE =.∴()2,1C -. …………2分 ∵双曲线ky x=经过点C , ∴2k =-.∴反比例函数的解析式为2y x=-. …………3分 (2)∵点D 在AB 上,∴点D 的横坐标为4-. ∵点D 在双曲线2y x=-上, ∴点D 的纵坐标为12. …………4分∴BOD S △11141222OB BD =⋅⋅=⨯⨯=.…………5分 四、解答题(本题共20分,每小题5分)23.(1)证明:∵DE BC ∥,CE AB ∥, ∴四边形DBCE 是平行四边形. ∴CE BD =.又∵CD 是边AB 上的中线, ∴BD AD =. ∴CE DA =. 又∵CE DA ∥,∴四边形ADCE 是平行四边形.∵90BCA ∠=︒,CD 是斜边AB 上的中线, ∴AD CD =.∴四边形ADCE 是菱形. …………3分(2)解:作CFAB ⊥于点F .由(1) 可知, .BC DE =设BC x =,则2AC x =.在Rt ABC △中,根据勾股定理可求得AB =.∵1122AB CF AC BC ⋅=⋅,∴5AC BC CF x AB ⋅==.∵122CD AB x ==, ∴4sin 5CF CDB CD ∠==.…………5分 24.解:(1)20÷10%=200(名),…………1分 答:一共调查了200名学生; (2)最喜欢古筝的人数:200×25%=50(名), 最喜欢琵琶的人数:200×20%=40(名); 补全条形图如图; …………3分 (3)二胡部分所对应的圆心角的度数为:60200×360°=108°; …………4分 (4)1500×30200=225(名). …………5分答:1500名学生中估计最喜欢古琴的学生人数为225. 25.(1)证明:连结OD ,如图.∵DE 为⊙O 的切线,OD 为半径, ∴OD DE ⊥.∴90ODE ∠=︒,即290ODC ∠+∠=︒.26. 解:(1)AF =BE ; …………1分(2)AF BE=. …………2分 理由如下:∵四边形ABCD 是菱形,120ABC ∠=︒,∴AC BD ⊥,60ABO ∠=︒.∴90FAO AFO ∠+∠=︒.∵AG BE ⊥,∴90EAG BEA ∠+∠=︒.∴AFO BEA ∠=∠.又∵90AOF BOE ∠=∠=︒,∴AOF BOE △∽△. …………3分∴AF AO BE OB= . ∵60ABO ∠=︒,AC BD ⊥,∴tan 60AO OB=︒=.∴AF BE = …………5分 五、解答题(本题共22分,第27题7分,第28题7分,第29题8分)27.解:(1)∵抛物线()210y ax bx a =++≠过点()1,0A -,()1,1B ,∴10,1 1.a b a b -+=⎧⎨++=⎩∴1,21.2a b ⎧=-⎪⎪⎨⎪=⎪⎩ ∴抛物线的函数关系式为211122y x x =-++. …………2分 (2)∵122b x a =-=,()0,1C ∴抛物线211122y x x =-++的对称轴为直线12x =. 设点E 为点A 关于直线12x =的对称点,则点E 的坐标为()2,0. 连接EC 交直线12x =于点D ,此时ACD △的周长最小. 设直线EC 的函数表达式为y kx m =+,代入,E C 的坐标,则2m 0,1.k m +=⎧⎨=⎩解得1,21.k m ⎧=-⎪⎨⎪=⎩所以,直线EC 的函数表达式为112y x =-+. 当12x =时,34y =. ∴ 点D 的坐标为13,24⎛⎫⎪⎝⎭. …………4分 (3)存在.①当点A 为直角顶点时,过点A 作AC 的垂线交y 轴于点M ,交对称轴于点1P . ∵AO OC ⊥,1AC AP ⊥,∴90AOM CAM ∠=∠=︒.∵()0,1C ,()1,0A -,∴1OA OC ==.∴45CAO ∠=︒.∴45OAM OMA ∠=∠=︒.∴1OA OM ==.∴点M 的坐标为()0,1-.设直线AM 对应的一次函数的表达式为11y k x b =+,代入,A M 的坐标, 则1110,1.k b b -+=⎧⎨=-⎩ 解得111,1.k b =-⎧⎨=-⎩ 所以,直线AM 的函数表达式为1y x =--. 令12x =,则32y =-. ∴点1P 的坐标为13,22⎛⎫-⎪⎝⎭. …………5分 ②当点C 为直角顶点时,过点C 作AC 的垂线交对称轴于点2P ,交x 轴于点N . 与①同理可得Rt CON △是等腰直角三角形,∴1OC ON ==.∴点N 的坐标为()1,0.∵2CP AC ⊥,1AP AC ⊥,∴21CP AP ∥.∴直线2CP 的函数表达式为1y x =-+. 令12x =,则12y =. ∴点2P 的坐标为11,22⎛⎫ ⎪⎝⎭. …………6分 综上,在对称轴上存在点1P 13,22⎛⎫-⎪⎝⎭,2P 11,22⎛⎫ ⎪⎝⎭,使ACP △成为以AC 为直角边的直角三角形.…………7分28.解:(1) 当60α=︒时, BD A A '⊥. ------------1分(2)补全图形如图1,B D A A'⊥仍然成立;------------3分 (3)猜想BD A A '⊥仍然成立. 证明:作AE C C '⊥,A F C C ''⊥,垂足分别为点,E F ,如图2,则90AEC A FC ''∠=∠=︒. ∵BC BC '=,∴BCC BC C ''∠=∠. ∵90ACB A C B ''∠=∠=︒,∴90ACE BCC '∠+∠=︒,'90A C F BC C ''∠+∠=︒. ∴ACE A C F ''∠=∠.在AEC △和A FC ''△中, 图2 图190,,,AEC A FC ACE A C F AC A C ''∠=∠=︒⎧⎪''∠=∠⎨⎪''=⎩∴AEC A FC ''△≌△.∴AE A F '=.在AED △和A FD '△中,90,,,AEC A FD ADE A DF AE A F '∠=∠=︒⎧⎪'∠=∠⎨⎪'=⎩∴AED A FD '△≌△.∴AD A D '=.∵AB A B '=,∴'ABA △为等腰三角形.∴BD A A '⊥------------7分29.解:(1)∵20x ≥,∴2x -1≥-1.∴2-x -1>2.∴{}2min 2x =--1,-2. ┉┉2分(2) ∵()2211x x k x k -+=-+-2, ∴()2111x k k -+--≥.∵2min{2,3}3x x k -+-=-, ∴13k --≥.∴2k -≥. ┉┉5分(3) 37m -≤≤. ┉┉8分。
北京市石景山区2015届九年级5月统一练习(一模)物理试题(扫描版)
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2015年北京怀柔区中考一模数学试题及答案
北京市怀柔区2015年高级中等学校招生模拟考试〔一〕数 学 试 卷 2015.5考生须知 1.本试卷共6页,共五道大题,29道小题,总分值120分.考试时间120分钟。
2.在试卷和答题卡上准确填写学校名称、和准考证号。
3.试题答案一律填涂或书写在答题卡上,在试卷上作答无效。
4. 在答题卡上,选择题用2B 铅笔作答,其他试题用黑色字迹签字笔作答。
5. 考试结束,请将本试卷、答题卡一并交回。
一、选择题〔此题共30分,每题3分〕以下各题均有四个选项,其中只有一个..是符合题意的. 1.把8000用科学计数法表示是A .28010⨯ B .3810⨯ C .40.810⨯ D .4810⨯ 2.数轴上有A ,B ,C ,D 四个点,其中绝对值相等的点是 A.点A 与点D B. 点A 与点C C. 点B 与点C D. 点B 与点D3.以下 软件图标中,既是轴对称图形又是中心对称图形的是A B C D 4. 小华的老师让他在无法看到袋子里小球的情形下,从袋子里模出一个小球. 袋子里各种颜色小球的数量统计如表所示.小华模到褐色小球的概率为 A .101 B .51 C .41D .215. 如图,AD 是∠EAC 的平分线,AD∥BC,∠B=30°,则∠C 为A .30°B .60°C .80°D .120°6.如图,已知⊙O 的半径为10,弦AB 长为16,则点O 到AB 的距离是 A. 3 B. 4 C. 5 D. 67.某校在“中国梦.我的梦”演讲比赛中,有11名学生参加决赛,他们决赛的最终成绩各不相同.其中的一名学生想要知道自己能否进入前6名,不仅要了解自己的成绩,还要了解这11名学生成绩的颜色 红色 橙色 黄色 绿色 蓝色 紫色 褐色 数量 6433225xD CB A 123–1–2–3A .平均数B .众数C .中位数D .方差 8.如图,已知正方形ABCD 中,G 、P 分别是DC 、BC 上的点,E 、F 分别 是AP 、GP 的中点,当P 在BC 上从B 向C 移动而G 不动时, 以下结论成立的是A .线段EF 的长逐渐增大B .线段EF 的长逐渐减小C .线段EF 的长不改变D .线段EF 的长不能确定 9.如图,函数y=2x 和y=ax+4的图象相交于点A 〔m ,3〕, 则不等式2x≥ax+4的解集为 A .x≥B. x≤3 C . x ≤D .x ≥310.如图1,在等边△ABC 中,点E 、D 分别是AC ,BC 边的中点,点P 为AB 边上的一个动点,连接PE ,PD ,PC ,DE .设AP =x ,图1中某条线段的长为y ,假设表示y 与x 的函数关系的图象大致如图2所示,则这条线段可能是图1中的A .线段PDB .线段PC C .线段PED .线段DE 二、填空题〔此题共18分,每题3分〕11.函数y=1x-3中自变量x 的取值范围是_________________. 12.请写出一个过一、三象限的反比例函数的表达式_________________.13.下面有五个图形,与其它图形众不同的是第 个.G FE PD CBA①②③④⑤xy 图2OPEDCBA图114.如图,在矩形ABCD 中,=,以点B 为圆心,BC 长为半径画弧,交边AD 于点E .假设AE •ED =16,则矩形ABCD的面积为 .15.当三角形中一个内角α是另一个内角β的一半时,我们称此三角形为“半角三角形”,其中α称为“半角”. 如果一个“半角三角形”的“半角”为20°,那么这个 “半角三角形”的最大内角的度数为__________.16.2014年5月1日开始,北京市开始实施居民用水阶梯水价.具体方案如下:户年用水量180立方米〔含〕内,每立方米5元;181立方米至260立方米〔含〕内,每立方米7元;260立方米以上,每立方米9元.阶梯水价以日历年〔每年1月1日到12月31日〕为周期计算.小王家2014年4月30日抄表示数550立方米,5月1日起实施阶梯水价,6月抄表时因用户家中无人未见表,8月12日抄表示数706立方米,那么小王家本期用水量为 立方米,本期用水天数104天,日均用水量为 立方米. 如果按这样每日用水量计算,小李家今后每年的水费将到达 元〔一年按365天计算〕.三、解答题〔此题共30分,每题5分〕17.如图,点C ,D 在线段BF 上,AB DE ∥,AB DF =,A F ∠=∠.求证:BC DE =.18. 计算:011(20152014)82cos 45()2--+-︒+19.解不等式组:240,3(1) 2.x x x -<⎧⎨+≥+⎩20.已知32a b =,求代数式2243(3)9a b a b a b++-的值.21.列方程或方程组解应用题:为了培育和践行社会主义核心价值观,引导学生广泛阅读古今文学名著,传承优秀传统文化,我区某校决定为初三学生购进相同数量的名著《三国演义》和《红岩》.其中《三国演义》的单价比《红岩》的单价多28元.假设学校购买《三国演义》用了1200元,购买《红岩》用了400元,求《三国演义》和《红岩》的单价各多少元.22.已知:关于x 的一元二次方程2(41)330kx k x k -+++=〔k 是整数〕.(1)求证:方程有两个不相等的实数根;〔2〕假设方程的两个实数根都是整数,求k 的值.FEDCB A四、解答题〔此题共20分,每题5分〕23. 如图,BD 是△ABC 的角平分线,点E ,F 分别在BC ,AB 上,且DE ∥AB ,BE =AF . 〔1〕求证:四边形ADEF 是平行四边形;〔2〕假设∠ABC =60°,BD =4,求平行四边形ADEF 的面积.24.某公司有5个股东,每个股东的利润相同,有100名工人,每名工人的工资相同.2015年第一个季度工人的工资总额与公司的股东总利润情况见右表:该公司老板根据表中数据,作出了图1,并声称股东利润和工人工资同步增长,公司和工人做到了“有福同享”.针对老板的说法,解决以下问题:〔1〕这三个月工人个人的月收入分别是 万元;〔2〕在图2中,已经做出这三个月每个股东利润统计图,请你补出这三个月工人个人月收入的统计图; 〔3〕通过完成第〔1〕,〔2〕问和对图2的观察,你如何看待老板的说法?〔用一两句话概括〕25. 如图,AB 是⊙O 的直径,C 是弧AB 的中点,D 是⊙O 的切线CN 上一点,BD 交AC 于点E ,且BA= BD . 〔1〕求证:∠ACD=45°;〔2〕假设OB=2,求DC 的长.月份 工人工资总额〔万元〕 股东总利润〔万元〕1 28 142 30 163 32 18N EC BA O 股东利润工人工资(万元)总额图1 123股东(万元)个人收入图226.阅读下面材料:小聪遇到这样一个有关角平分线的问题:如图1,在△ABC 中, ∠A =2∠B,CD 平分∠A CB ,AD=2.2,AC=3.6 求BC 的长.小聪思考:因为CD 平分∠A CB ,所以可在BC 边上取点E ,使EC=AC ,连接DE. 这样很容易得到△DEC ≌△DAC ,经过推理能使问题得到解决〔如图2〕. 请答复:〔1〕△BDE 是_________三角形.〔2〕BC 的长为__________.参考小聪思考问题的方法,解决问题:如图3,已知△ABC 中,AB=AC, ∠A =20°, BD 平分∠ABC,BD=2.3,BC=2.求AD 的长. 五、解答题〔此题共22分,第27题7分,第28题7分,第29题8分〕27.在平面直角坐标系xOy 中,二次函数y=〔a-1〕x 2+2x+1与x 轴有交点,a〔1〕求a 的值. 〔2〕将二次函数y=〔a-1〕x 2+2x+1的图象向右平移m 个单位,向下平移m 2+1个单位,当 -2≤x ≤1时,二次函数有最小值-3求实数m 的值.28.在等边△ABC 外侧作直线AP ,点B 关于直线AP 的对称点为D ,连接BD,CD ,其中CD 交直线AP 于点E .〔1〕依题意补全图1;〔2〕假设∠PAB=30°,求∠ACE 的度数;〔3〕如图2,假设60°<∠PAB <120°,判断由线段AB,CE,ED 可以构成一个含有多少度角的三角形,并证明.C ED C B A BC 27题图29. 对某种几何图形给出如下定义: 符合一定条件的动点所形成的图形,叫做符合这个条件的点的轨迹.例如,平面内到定点的距离等于定长的点的轨迹,是以定点为圆心,定长为半径的圆.〔1〕如图1,在△ABC 中,AB=AC ,∠BAC=90°,A(0,2),B 是x 轴上一动点,当点B 在x 轴上运动时,点C 在坐标系中运动,点C 运动形成的轨迹是直线DE ,且DE ⊥x 轴于点G. 则直线DE 的表达式是 .〔2〕当△ABC 是等边三角形时,在〔1①当点B 运动到如图2的位置时,AC ∥x 轴,则C 点的坐标是 . ②在备用图中画出动点C 形成直线的示意图,并求出这条直线的表达式.③设②中这条直线分别与x,y 轴交于E,F 两点,当点C 在线段EF 上运动时,点H 在线段OF 上运动,〔不与O 、F 重合〕,且CH=CE,则CE 的取值范围是 .ABCP ABCP怀柔区2014—2015学年度中考模拟练习〔一〕数学试卷答案及评分参考二、填空题〔此题共18分,每题3分〕三、解答题〔此题共30分,每题5分〕 17.〔本小题总分值5分〕 证明:∵ AB ∥DE∴ ∠B = ∠EDF ;在△ABC 和△F DE 中A F AB DFB EDF ∠=∠⎧⎪=⎨⎪∠=∠⎩…………………………3分 ∴△ABC ≌△FDE (ASA),…………………4分 ∴BC=DE. …………………………………5分 18.解:原式=1+-222+……………………………………4分 =1++2…………………………………………………………5分 19. 解①得:x<2,…………………………………………………………2分解②得:x ≥1-2,……………………………………………………4分 所以不等式组的解集为:1-2≤x<2. ……………………………5分20. 解:2243(3)9a ba b a b ++-43(3)(3)(3)a b a b a b a b +=++- 433a ba b +=-……………………………………………3分∵32a b =, ∴23a b =. ………………………………………………4分∴原式=662aa a =--. ……………………………………5分21.解:设《红岩》的单价为x 元,则《三国演义》的单价为(x+28)元. ……………1分. 由题意,得120040028x x=+……………………………………3分. 解得x=14. ……………………………………4分.经检验,x=14是原方程的解,且符合题意. ∴x+28=42.答:《红岩》的单价为14元,《三国演义》的单价为42元. ……………………5分.22.〔1〕证明:△2(41)4(33)k k k =+-+2(21)k =-·………………………………………1分.∵2(41)330kx k x k -+++=是一元二次方程,∴k ≠0, ∵k 是整数 ∴12k ≠即210k -≠. ∴△2(21)0k =->∴方程有两个不相等的实数根. ………………………………………2分〔2〕解方程得:2(41)(21)2k k x k+±-=……………………………………3分.∴3x =或11x k=+………………………………………4分∵k 是整数,方程的根都是整数,∴k =1或-1…………………………………5分.四、解答题〔此题共20分,每题5分〕23. 〔1〕证明:∵BD 是△ABC 的角平分线, ∴∠ABD =∠DBE ,∵DE ∥AB , ∴∠ABD =∠BDE , ∴∠DBE =∠BDE ,∴BE=DE; ∵BE =AF ,∴AF=DE;∴四边形ADEF 是平行四边形. ………………………………………2分〔2〕解:过点D 作DG ⊥AB 于点G ,过点E 作EH ⊥BD 于点H , ∵∠ABC =60°,BD 是∠ABC 的平分线, ∴∠ABD =∠EBD =30°,∴DG =BD =×4=2,………………………………………3分 ∵BE =DE ,∴BH =DH =2,∴BE ==433,∴DE =433,………………………………………4分 ∴四边形ADEF 的面积为:DE •DG =833.………………………………………5分 24. 解:〔1〕0,28,0.3,0.32. ……………………………3分〔2〕补图如右图:………………………………4分 〔3〕答案不唯一.…………………………………5分25. 〔1〕证明:∵C 是弧AB 的中点,∴弧AC=弧BC,∴AC=BC.∵AB 是⊙O 的直径,∴∠ACB=90°,∴∠BAC=∠CBA=45°, 连接OC, ∵OC=OA, ∴∠AC0=45°. ∵CN 是⊙O 切线,∴∠OCD=90°,∴∠ACD=45°. ………………………………2分.(2) 解:作BH ⊥DC 于H 点,…………………………3分. ∵∠ACD=45°,∴∠DCB=135°, ∴∠BCH=45°, ∵OB=2,∴BA= BD=4,AC= BC=. ∵BC=,∴BH= CH=2, 设DC=x,在Rt △DBH 中,利用勾股定理:2222)24x ++=(,………4分. 解得:x=2-±,∴x=2-+∴DC的长为:2-+5分. 26.解:〔1〕△BDE 是等腰三角形. ………………………1分. 〔2〕BC 的长为5.8.………………………………2分. ∵△ABC 中,AB=AC, ∠A =20°, ∴∠A BC=∠C= 80°,∵BD 平分∠B. ∴∠1=∠2= 40°,∠BDC= 60°,.在BA 边上取点E ,使BE=BC=2,连接DE ,. (3)则△DEB ≌△DBC ,∴∠BED=∠C= 80°, ∴∠4=60°,∴∠3=60°,在DA 边上取点F ,使DF=DB ,连接FE ,…………………………4则△BDE ≌△FDE ,∴∠5=∠1= 40°,BE=EF=2, ∵∠A =20°,∴∠6=20°,∴AF=EF=2,∵BD=DF=2.3, ∴AD = BD+BC=4.3.…………………………5分.五、解答题〔此题共22分,第27题7分,第28题7分,第29题27.解:〔1〕∵二次函数y=〔a-1〕x 2+2x+1与x 轴有交点,令y=0,则〔a-1〕x 2+2x+1=0,∴=4-4(a-1)0∆≥,解得a ≤2. …………………………………1分. ∵a 为正整数. ∴a=1、2又∵y=〔a-1〕x 2+2x+1是二次函数,∴a-1≠0,∴a ≠1, ∴a 的值为2. ………………………………………2分〔2〕∵a=2,∴二次函数表达式为y=x 2+2x+1,将二次函数y=x 2+2x+1化成顶点式y=〔x+1〕2二次函数图象向右平移m 个单位,向下平移m 2+1个单位后的表达式为y=〔x+1-m 〕2-〔m 2+1〕.此时函数的顶点坐标为〔m-1, -m 2-1〕. …………………………………4分 当m-1<-2,即m <-1时, x=-2时,二次函数有最小值-3,∴-3=〔-1-m 〕2-〔m 2+1〕,解得32m =-且符合题目要求. ………………………………5分 当 -2≤m-1≤1,即-1≤m ≤2,时,当 x= m-1时,二次函数有最小值-m 2-1=-3,解得m =.∵m =-1≤m ≤2的条件,舍去.∴m =.……………………………………6分当m-1>1,即m >2时,当 x=1时,二次函数有最小值-3, ∴-3=〔2-m 〕2-〔m 2+1〕,解得32m =,不符合m >2的条件舍去. 综上所述,m 的值为32-……………………………………7分 28.解:〔1〕补全图形,如图1所示. …………………………… 1分〔2〕连接AD ,如图2.∵点D 与点B 关于直线AP 对称,∴AD=AB ,∠DAP = ∠BAP =30°.∵AB=AC, ∠BAC =60°. ∴AD=AC, ∠DAC =120°.∴2∠ACE+60°+60°=180°∴∠ACE =30°…………………………… 3分〔3〕线段AB,CE,ED 可以构成一个含有60°角的三角形. …………………………… 4分 证明:连接AD ,EB ,如图3.∵点D 与点B 关于直线AP 对称, ∴AD=AB ,DE=BE , 可证得∠EDA = ∠E BA .∵AB=AC,AB=AD.∴AD=AC, ∴∠ADE = ∠ACE.∴∠ABE = ∠ACE.设AC ,BE 交于点F,又∵∠AFB = ∠CFE.∴∠B AC = ∠BEC=60°.∴线段AB,CE,ED 可以构成一个含有60°角的三角形.………7分29. 解:〔1〕x=2. …………………………1分.〔2〕①C 点坐标为:2)…………………………3分.P E D C BA P E D C BA②由①C点坐标为: ,23()再求得其它一个点C1〕,或〔0,-2〕等代入表达式y=kx+b,解得b=-2 k⎧⎪⎨=⎪⎩∴直线的表达式是2y=-.………………………5分.动点C运动形成直线如下图.……………6分.EC≤<…………………………8分.11北京中考网-北达教育旗下 beijing518 名师一对一辅导 400-668-7882北京中考网—北达教育旗下 :// beijing518 名师一对一辅导 400-668-788212 相关信息链接:北达教育|百度百科|百度贴吧北达教育北达教育总部位于北京大学校内,分校普及北京各城区40多所,多年来被家长认可的教育机构,法制晚报曾报道:是什么让北达教育成为京城良好口碑课外辅导品牌?为此北达教育被法制晚报评为:公众最信赖知名教育品牌!曾多次被新浪网,中国网评为课外绿色发展机构!北达教育为中央电视台推荐品牌。
北京2015中考一模各区完型及答案
2015海淀一模The LakeThe day when Robert was born was the happiest day of my life. Unfortunately my wife decided she no longer wanted to be married to me. My little boy and I had to 31 , only getting to see each other every other weekend.One day, I decided to go fishing with my son, who was about 5 years old, at a nearby lake. We arrived at the lake early. Getting out of the car, we brought out all of the fishing equipment and our life jackets and the cooler that had our tasty lunch in it. I could just 32 the day in my mind in hopes that it would never end. We both went out onto the dock(船坞)and I thought, “Do I put his life jacket on first or load the boat first?” I saw him skipping rocks on the water, so I decided to load the boat first.I was just finishing up when I heard the splash. I turned and looked quickly expecting to see Robert 33 standing there, but I did not see him anywhere. I jumped into the water to save my son immediately. I searched and searched but found him nowhere. I came up for a breath hoping to see him above water, now wondering how I could find him in the murky (浑浊的)water. I finally decided to go all the way to the bottom and 34 around, not coming up until I found him.Finally, there on the bottom he was, his arms wrapped around the wooden pole that holds up the dock. I brought him to the 35 and put him on the bank. While both of us were coughing and spitting out water, I just hugged him and was 36 that I had found him in time.When things finally calmed down, I asked one simple question, “Robert, why were you 37 onto that pole on the bottom of the lake?” He looked at me with the most innocent and loving eyes and simply replied, “I was waiting for you, Daddy. I knew you would come to 38 me.”I thought that I could not be any 39 or any madder at the same time and I just told him, “I sure do love you, sweetheart.” He replied, “I love you too, Dad.”There is no amount of money or cars or jobs or any material thing that could replace being loved and 40 someone so much. I am lucky to have the ability to love on such a high level, and the ability to forgive on the same level.31. A. back B. part C. argue D. move32. A. picture B. enjoy C. show D. spend33. A. carefully B. happily C. safely D. quietly34. A. walk B. look C. hear D. feel35. A. surface B. centre C. front D. corner36. A. thoughtful B. regretful C. hopeful D. thankful37. A. jumping B. holding C. stepping D. pointing38. A. call B. awake C. save D. remind39. A. funnier B. prouder C. sadder D. cooler40. A. missing B. touching C. loving D. Changing2015.4 西城一模The hugThe phone rang. It was Lisa, my 86-year-old friend, calling. Lisa was wondering if I could take her to Flint to see the __31__. I promised her I could, so on the date of the appointment (预约) I drove over to her home to pick her up.Lisa’s eyesight was __32__, so she wasn’t able to drive her car any more. However, she still kept her old white Cadillac and insisted that I drive it whenever we went anywhere. Lisa’s appointment went __33__ and she was really satisfied with her doctor. Then, we were on our way to get a bite to eat. It was a cloudy day without any rain or snow, but the road was still busy. The __34__ stop and go as we were in an area by the market. We were at a __35__ stop when someone hit us from behind. Lisa was very angry, and she even started to say some dirty words in a low voice. I could __36__ this situation could get very bad. There re ally wasn’t any reason why someone could rear end (追尾) the car so I wasn’t sure what was going on when I pulled over. I was feeling a little __37__ when I got out of the car. As I walked around the car a young woman got out of the car with anger! I could see all the other doors on her car starting to open. For some unknown__38__, I walked over to the young woman and got my arms around her and gave her a hug. When I gave her a hug all the other doors shut!Lisa got out and when she saw me hugging the girl she __39__ down. I called the police and they came out and took a report. I really don’t know what was actually going on that day, I do know that I just wanted to hug this girl in my mind and I believe it __40__ us all from what could have been a very ugly scene.31. A. eye doctor B. house cleaner C. music teacher D. office worker32. A. hurting B. failing C. changing D. improving33. A. badly B. well C. late D. quietly34. A. traffic B. crowd C. Rain D. bus35. A. sudden B. slow C. complete D. quick36. A. understand B. recognize C. show D. tell37. A. comfortable B. tired C. painful D. nervous38. A. reason B. excuse C. purpose D. answer39. A. looked B. cooled C. fell D. walked40. A. separated B. taught C. benefited D. Saved2015.5朝阳一模During summer vacations, I would volunteer at the pet rescue (救助) centre, so I could see a lot of dogs. Minnie was the funniest-looking dog I'd ever seen by far. Her body looked like a sausage. Her hair was too thin to 31 her body. Her eyes always seemed sur prised, and her tail was so short that it looked like a rat’s tail.She looked so strange that her 32 didn’t want her any more. She was brought to the centre. But I thought, “Minnie was kind and sweet. No one should laugh at her strange looking.” So I gave Minnie a good bath and 33 her in the newspaper: “Funny-looking dog, kind and sweet, needs loving 34 .”Later, a boy called me, but I warned him that Minnie was 35 . However, the boy told me that his grandfather’s sixteen-year-old dog had just died. They wanted to keep Minnie very much. Hearing these words, I said that they could take Minnie away. I combed (梳) her hair, and gave her a good bath. Then we waited for them to arrive.At last, an old car stopped in front of the pet rescue centre. Two kids 36 to the door. They put Minnie into their arms and rushed out to their grandfather, who was waiting in the car. I hurried behind them to see his reaction (反应).Inside the car, the grandfather put Minnie in his arms and 37 her soft hair. Shelooked very relaxed and happy. “She’s perfect, and I like her!” the old man said. I was 38 that Minnie had found a good owner. Just at that time, I saw that the grandfather’s eyes were a milky white color—he was blind.After that summer vacation, I missed Minnie so much. So I went back to the grandfather’s house. The grandfather was walking in the garden with Minnie 39 the way. I could see both of them were happy. “Minnie is the most beautiful dog in my eyes,” said the grandfather, “I’ve 40 felt happier before!” Hearing this, I was pretty happy!31. A. hide B. warm C. protect D. cover32. A. owner B. leader C. teacher D. partner33. A. introduced B. reported C. praised D. advertised34. A. school B. family C. hospital D. zoo35. A. sick B. dirty C. ugly D. dangerous36. A. jumped B. stepped C. walked D. raced37. A. tidied B. cleaned C. touched D. pulled38. A. peaceful B. thankful C. careful D. powerful39. A. leading B. taking C. giving D. making40. A. just B. ever C. never D. still2015 丰台一模“Class,this is David Evans,” Mrs. Parmele introduced him to us, trying to give him a warm welcome. We saw a boy in old clothes and shoes. David looked around and smiled, hoping somebody would 31 back. Nobody did. He kept on smiling anyway.I held my breath, hoping Mrs. Parmele wouldn’t notice the empty 32 next to mine. She did, and pointed him in that direction. He looked over at me as he sat down, but I looked away.By the end of his first week, David was at the bottom of our school’s social ladder. “It’s his own fault,”I told my mother one evening at dinner. “He 33 even knows how to count.”As I ate lunch with him the next day and listened to him, however, I realized that David was very pleasant to be around. After lunch, I 34 that I would be David’s friend.One night, as Mother tucked me into bed, I said, “Mom, tomorrow is David’s birthday, and he’s not going to get anything. Nobody even cares.”“Don’t worry,” Mom said as she kissed me goodnight. “I’m sure everything will be 35 .”At breakfast the next morning, I said I wasn’t feeling well.“How would you like it if your only friend didn’t show up on your birthday?”Mother asked gently. I thought it over for a moment and then kissed her goodbye.I wished David a happy birthday first thing in the morning, and his embarrassed smile showed me that he was glad I had 36 .By mid-afternoon I had almost decided that birthdays weren’t that 37 . Then, as Mrs. Parmele was writing on the blackboard, I heard a familiar voice singing the birthday song.Moments later, Mother came through the door with a tray(托盘) of cupcakes. She was also taking a 38 in her hand.Mrs. Parmele joined in. Mother found David looking like a deer in car headlights. She put the cupcakes and the gift on his desk and said, “Happy birthday, David.”My friend kindly shared his cupcakes with the class, taking the tray from desk to desk. I caught Mother 39 me. She smiled and winked(使眼色).David Evans moved on shortly thereafter, and I never heard from him again. But whenever I hear that familiar song, I remember the soft tones of my mother’s voice, the 40 in a boy’s eyes, and the taste of the sweetest cupcake.31. A. look B. smile C. wave D. call32. A. desk B. box C.basket D. bottle33. A. quickly B. suddenly C. hardly D. probably34. A. refused B. guessed C. regretted D. decided35. A. terrible B. fine C. easy D. difficult36. A. discovered B. explained C. remembered D. mentioned37. A. important B. popular C. interesting D. different38. A. bag B. letter C. card D. gift39. A. watching B. calling C. pushing D. encouraging40. A. surprise B. happiness C. kindness D. friendship2015 东城一模An Imperfect PaintingMy parents always wanted me to be “on top”, so from early on I had the 31 to be the best in everything, from getting the highest score on a spelling test to running fastest in a race.In middle school, I realized how many other smarter and faster people there were. It became 32 that I was not the best any more, but my parents still held on to their hope and forced me to try hard. To their disappointment, I became less confident and didn’t want to work hard because, to me, there was no point in making any more 33 if I was unable to be number one. My grades began to fall; I never practiced the piano; I 34 painting. It was all because my motivation(动力) to do anything had dropped much.When high school started, I was at a new school in a new city. I 35 to get back my motivation and start over. So I picked up my ever favorite hobby again and enrolled(报名) myself in the art course. 36 , our art teacher, Mr. Grady, gave us more freedom with our art projects. He would always encourage us to realize our potential(潜力).My first painting was simply a bee sitting on a sunflower. I made every effort, but still found it hard to feel satisfied with it. I knew it was not 37 and could hardly get a good grade. But I showe d it to Mr. Grady. He didn’t 38 it in a rush. Instead, he gave me advice which only motivated me to work harder on it. For the first time I was happy with the 39 of my painting rather than disappointed about its imperfection. I finished all the other projects with higher grades, but I hung the first painting in my room at the end of the term.My parents thought 40 me to be number one would motivate me. Instead, it discouraged me much when I was not number one, for I had gone to school only to get a grade, not knowledge, let alone progress. Actually, it is okay not to be the best ateverything as long as you continue to try your best.31. A. ability B. chance C. goal D. way32. A. strange B. obvious C. acceptable D. impossible33. A. efforts B. choices C. promises D. wishes34. A. regretted B. considered C. continued D. stopped35. A. failed B. refused C. decided D. waited36. A. Naturally B. Similarly C. Normally D. Luckily37. A. famous B. modern C. perfect D. special38. A. name B. grade C. hang D. finish39. A. progress B. meaning C. style D. title40. A. instructing B. helping C. encouraging D. pushing2015 石景山一模“Mommy, look!” cried my daughter, Darla, pointing to a chicken hawk in the air.“Uh huh,” I answered, driving, lost in thought about the timetable of my day.31 filled her face.“What’s the matter, sweetheart?” I asked.“Nothing,” my seven-year-old daughter said. The moment was gone.Dinner, baths and phone calls 32 the hours until bedtime.“Come on, Darla, time for bed!” She raced past me up the stairs. Tired, I kissed her and tucked her in.“Mom, I forgot to give you something!” she said.“Give it to me in the morning.” I said. My 33 was gone. I could hardly stay cool.“You won’t have time in the morning!” she talked back quickly.“I’ll take time,”I answered. Sometimes no matter how hard I tried, time was never enough.She wasn’t ready to 34 up yet. “No, you won’t! It will be just like today when I told you to look at the chicken hawk. You didn’t 35 listen to what I said.”I was too tired to argue; she hit too 36 to the truth. “Good night!” I shut her door in anger.Later though, her gray-blue eyes filled my vision as I thought about how little time we really had until she was grown and gone. My husband asked me what was going on and I told him.“Maybe she was not asleep yet. Why don’t you 37 ?” he said.I followed his advice, 38 it was my own idea. I opened her door gently. In Darla’s hand I could see her paper all crumpled (弄皱的) up. She had torn into small pieces a big red heart with a poem she had written titled, “Why I Love My Mother?”Why I Love My MotherAlthough you’re busy, and you work so hard,You always take time to play with me,I love you Mommy,Because I am the biggest part of your busy day!Tears filled my eyes. When I softly touched her face, she awakened from a dreamless sleep and asked, “Why are you 39 , Mommy?”“You ARE the most important part of my busy day!”She smiled and then went back to sleep, not really understanding how strongly I 40 what I said.31. A. Disappointment B. Worries C. Fear D. Enjoyment32. A. cost B. filled C. lasted D. took33. A. belief B. attitude C. attention D. patience34. A. give B. build C. call D. clear35. A. just B. even C. yet D. almost36. A. heavily B. badly C. close D. hard37. A. watch B. exam C. test D. check38. A. realizing B. thinking C. wishing D. guessing39. A. crying B. laughing C. shouting D. touching40. A. considered B. expressed C. inferred D. meant 2015 房山一模40 A get B join C see D leave海淀31 B 32. A 33. C 34. D 35. A 36. D 37. B 38. C 39. B 40. C西城31. A 32. B 33. B 34. A 35. C 36. D 37. D 38. A 39. B 40. D朝阳31. D 32. A 33. D 34. B 35.C 36. D 37. C 38. B 39. A 40.C 丰台31. B 32.A 33.C 34. D 35. B 36. C 37. A 38. D 39. A 40. B东城31. C 32. B 33. A 34. D 35. C36. D 37. C 38. B 39. A 40. D石景山31. A 32. B 33. D 34. A 35. B36. C 37. D 38. C 39. A 40. D房山31C 32 B 33 A 34 C 35 B 36 D 37 D 38 A 39 B 40 A。
北京市西城区2015年初三一模数学试卷参考答案及评分标准
北京市西城区2015年初三一模试卷数学试卷参考答案及评分标准 2015. 4一、选择题(本题共30分,每小题3分)二、填空题(本题共18分,每小题3分)三、解答题(本题共30分,每小题5分) 17()01112π2008()6tan302--+-︒=3362132⨯-++………………………………………………………… 4分 =32332-+=3.…………………………………………………………………………………… 5分 18.证明:如图1.∵ ∠EAC =∠DAB ,∴ 11EAC DAB ∠+∠=∠+∠.即 ∠BAC =∠DAE . …………………… 1分 在△ABC 和△ADE 中,,,,C E BAC DAE AB AD ∠=∠⎧⎪∠=∠⎨⎪=⎩………………………3分∴ △ABC ≌△ADE .…………………………………………………………… 4分 ∴ BC = DE.…………………………………………………………………… 5分 19.解:()2035148.x x x -≤⎧⎪⎨+>-⎪⎩,由①,得2x ≥. ………………………………………………………………… 2分由②,得 15348x x +>-.移项,合并,得 1111x >-.系数化1,得 1x >-. ………………………………………………………… 4分所以原不等式组的解集为2x ≥.…………………………………………………5分20.解: 223312111a a a a a a a ++÷-++++=()()2331111a a a a a a ++÷-+++……………………………………………………………2分 ()()2311311a a a a a a ++=⋅-+++ =111+-+a a a …………………………………………………………………………3分 =11a a -+.………………………………………………………………………………4分 当2=a 时,原式=311212=+-.………………………………………………………5分 21.解:设普通列车的平均速度为x 千米/时.…………………………………………… 1分 则高铁的平均速度是2.5x 千米/时.依题意,得40052032.5x x+=.…………………………………………………… 2分 解得 120=x .……………………………………………………………………3分 经检验,120=x 是原方程的解,且符合题意.……………………………… 4分 所以 30052=x ..答:高铁的平均速度是300千米/时.………………………………………………… 5分 22.(1)证明: []22(1)4(2)m m m ∆=--++ 2248448m m m m =-+++284m =+.……………………………………………………………………1分∵ 28m ≥0,∴ 284m +>0.………………………………………………………………2分∴ 方程总有两个不相等的实数根. ……………………………………… 3分(2)解:∵ 2x =-是此方程的一个根,∴ 2(2)2(2)(1)(2)0m m m --⨯---+=.整理得 220m m -=.解得 10m =,22m =.……………………………………………………… 5分四、解答题(本题共20分,每小题5分) 23.(1)证明:∵ ADE BAD ∠=∠,∴ AB ∥ED .…………………………………………………………… 1分 ∵ BD 垂直平分AC ,垂足为F , ∴ BD AC ⊥,AF=FC .又∵ AE AC ⊥,∴ 90EAC DFC ∠=∠=︒. ∴AE ∥BD .∴ 四边形ABDE 是平行四边形.…………………………………………2分(2)解:如图2,连接BE 交AD 于点O . ∵ DA 平分∠BDE ,∴ ∠ADE=∠1.又∵ ADE BAD ∠=∠, ∴ ∠1=∠BAD .∴ AB= BD .………………………………3分 ∴ ABDE 是菱形. ∵ AB=5,AD=6,∴ BD=AB=5,AD BE ⊥,132OA AD ==. 在Rt △OAB 中,224OB AB OA -=.∵ 1122ABD S AD OB BD AF =⋅=⋅V , ∴ 645AF ⨯=.解得 4.8AF =. …………………………4分∵ BD 垂直平分AC ,∴ 29.6AC AF ==.……………………5分 注:其他解法相应给分. 24.解:(1)补全扇形图如图3所示.…………………1分 (2)2号线,52<x ≤72 ,22.2.(各1分)………………………………………… 4分 (3)30.……………………………………… 5分 25.解:(1)依题意,补全图形如图4.……………… 1分 (2)BAD ∠.…………………………………… 2分 证明:如图5,连接BC ,CD .∵ 直线l 与直线MA 关于直线MD 对称, ∴ 12∠=∠.………………………3分 ∵ AB 为⊙O 的直径,∴ 90ACB ∠=︒,即BC MA ⊥. 又∵ BE l ⊥,∵ cos 1MC MB =⋅∠,cos 2ME MB =⋅∠, ∴ MC=ME . 又∵ C ,E 两点分别在直线MA 与直线l 上, 可得C ,E 两点关于直线MD 对称.图3∴ 3BED ∠=∠. ………………… 4分 又∵ 3BAD ∠=∠,∴ BAD BED ∠=∠. ……………… 5分26.解:45. …………………………………………………1分画图见图6. ………………………………………3分 45.………………………………………………… 5分五、解答题(本题共22分,第23题7分,第24题7分,第25题8分) 27.解:(1)∵ 二次函数21y x bx c =++的图象1C 经过(1,0)-,∴10,3.b c c -+=⎧⎨=-⎩ ………………………………1分解得2,3.b c =-⎧⎨=-⎩…………………………………2分∴ 抛物线1C 的函数表达式为3221--=x x y . …………………………………… 3分 (2)∵ 22123=(1)4y x x x =----,∴ 抛物线1C 的顶点为(1,4)- ∴ 平移后抛物线2C 的顶点为(0,0),它对应的函数表达式为22y x =.… 5分 (3)a ≥1-(见图7).………………………………………………………………7分28.解:(1)90,12.……………………………………………………………………… 2分 (2)结论:90AHB ∠=︒,AF BE . 证明:如图8,连接AD .∵ AB =AC ,∠BAC =60°, ∴ △ABC 是等边三角形. ∵ D 为BC 的中点, ∴ AD ⊥BC . ∴ ∠1+∠2=90°.又∵ DE ⊥AC ,∴ ∠DEC =90°. ∴ ∠2+∠C =90°. ∴ ∠1=∠C =60°. 设AB =BC=k (0k >),则124kCE CD ==,DE =. ∵ F 为DE 的中点,∴ 12DF DE ==,AD AB ==.∴AD BC =,DF CE =. ∴ =BC AD CE DF .…………………………………………………………3分 又∵ ∠1=∠C ,∴ △ADF ∽△BCE .………………………………………………… 4分∴AF AD BE BC ==,………………………………………………… 5分 ∠3=∠4. 又∵ ∠4+∠5=90°,∠5=∠6, ∴ ∠3+∠6=90°.∴ 90AHB ∠=︒.………………………………………………………6分(3)1tan 9022α︒-().………………………………………………………………7分注:写1cos 2sin αα+或其他答案相应给分.29.解:(1)313.(每空各1分)…………………………………………………… 2分(2)-1.…………………………………………………………………………… 4分(3)①如图9,过点O 分别作射线OE 、OF 的垂线OG 、OH ,则图形M 为:y 轴正半轴,∠GOH 的边及其内部的所有点(图中的阴影部分).……………………………………………………………………………… 7分 说明:(画图2分,描述1分)(图形M 也可描述为:y 轴正半轴,直线x y 33=下方与直线x y 33-=下方重叠的部分(含边界)) ②34.…………………………………………………………………………8分。
北京市顺义区2015年中考数学一模试卷及答案解析(pdf版)
2015年北京市顺义区中考数学一模试卷一、选择题(本题共30分,每小题3分)下面各题均有四个选项,其中只有一个是符合题意的.2.(3分)(2015•顺义区一模)2014年11月北京主办了第二十二届APEC (亚太经合组织)领导人会议,“亚太经合组织”联通太平洋两岸,从地理概念上逐渐变成了一个拥有28000000人口的经济合作体,把“28000000”用科学记数法表示正确的是( )3.(3分)(2015•宜兴市二模)如图是由四个相同的小正方体组成的立体图形,它的俯视图为( ).4.(3分)(2014•舟山)一名射击爱好者5次射击的中靶环数如下:6,7,9,8,9,这5.6.(3分)(2014•来宾)函数中,自变量x 的取值范围是( )7.(3分)(2015•顺义区一模)一个不透明的口袋中,装有4个红球,3个黄球,1个白球, .8.(3分)(2015•顺义区一模)如图,⊙O 的半径为5,AB 为⊙O 的弦,OC ⊥AB 于点C .若OC=3,则AB 的长为( )9.(3分)(2015•顺义区一模)若正多边形的一个外角为60°,则这个正多边形的中心角的度数是( )10.(3分)(2015•顺义区一模)如图,菱形ABCD 的对角线AC ,BD 相交于点O ,AC=6,BD=8,动点P 从点B 出发,沿着B ﹣A ﹣D 在菱形ABCD 的边上运动,运动到点D 停止,点P ′是点P 关于BD 的对称点,PP ′交BD 于点M ,若BM=x ,△OPP ′的面积为y ,则y 与x 之间的函数图象大致为( ).B .C .D二、填空题(本题共18分,每小题3分)11.(3分)(2015•郴州)分解因式:2a 2﹣2= . 12.(3分)(2015•顺义区一模)质量检测部门对甲、乙两工厂生产的同样产品抽样调查,计算出甲厂的样本方差为0.99,乙厂的样本方差为1.22.由此可以推断出生产此类产品,质量比较稳定的是 厂.13.(3分)(2015•顺义区一模)在综合实践课上,小明同学设计了如图测河塘宽AB 的方案:在河塘外选一点O ,连结AO ,BO ,测得AO=18m ,BO=21m ,延长AO ,BO 分别到D ,C 两点,使OC=6m ,OD=7m ,又测得CD=5m ,则河塘宽AB= m .14.(3分)(2015•顺义区一模)写出一个当自变量x>0时,y随x的增大而增大的反比例函数表达式.15.(3分)(2015•顺义区一模)居民用电计费实行“一户一表”政策,以年为周期执行阶梯电价,即:一户居民全年不超过2880度的电量,执行第一档电价标准为0.48元/度;全年用电量在2880度到4800度之间(含4800),超过2880度的部分,执行第二档电价标准为0.53元/度;全年用电量超过4800度,超过4800度的部分,执行第三档电价标准为0.78元/度.小敏家2014年用电量为3000度,则2014年小敏家电费为元.16.(3分)(2015•顺义区一模)规定:在平面直角坐标系xOy中,“把某一图形先沿x轴翻折,再沿y轴翻折”为一次变化.如图,已知正方形ABCD,顶点A(1,3),C(3,1).若正方形ABCD经过一次上述变化,则点A变化后的坐标为,如此这样,对正方形ABCD连续做2015次这样的变化,则点D变化后的坐标为.三、解答题(本题共30分,每小题5分)17.(5分)(2015•顺义区一模)计算:.18.(5分)(2015•顺义区一模)解不等式组:.19.(5分)(2015•顺义区一模)如图,C,D为线段AB上两点,且AC=BD,AE∥BF.AE=BF.求证:∠E=∠F.20.(5分)(2015•顺义区一模)已知b=a﹣3,求代数式的值.21.(5分)(2015•顺义区一模)已知关于x的一元二次方程kx2﹣3x﹣2=0有两个不相等的实数根.(1)求k的取值范围;(2)若k为小于2的整数,且方程的根都是整数,求k的值.22.(5分)(2015•顺义区一模)列方程或方程组解应用题:在练习100米跑步时,小丽为了帮助好朋友小云提高成绩,让小云先跑7.5秒后自己再跑,结果两人同时到达终点,这次练习中小丽的平均速度是小云的1.6倍,求小云这次练习中跑100米所用的时间.四、解答题(本题共20分,每小题5分)23.(5分)(2015•顺义区一模)如图,平行四边形ABCD中,点E是AD边上一点,且CE⊥BD 于点F,将△DEC沿从D到A的方向平移,使点D与点A重合,点E平移后的点记为G.(1)画出△DEC平移后的三角形;(2)若BC=,BD=6,CE=3,求AG的长.24.(5分)(2015•顺义区一模)为了提倡“绿色”出行,顺义区启动了公租自行车项目,为了解我区居民公租自行车的使用情况,某校的社团把使用情况分为A(经常租用)、B(偶尔租用)、C(不使用)三种情况.先后在2015年1月底和3月底做了两次调查,并根据调查结果绘制成了如下两幅不完整的统计图:根据以上信息解答下列问题:(1)在扇形统计图中,A(经常租用)所占的百分比是;(2)求两次共抽样调查了多少人,并补全折线统计图;(3)根据调查的结果,请你谈谈从2015年1月底到2015年3月底,我区居民使用公租自行车的变化情况.25.(5分)(2015•顺义区一模)如图,AB是⊙O的直径,C是⊙O上一点,D是的中点,过点D作⊙O的切线,与AB,AC的延长线分别交于点E,F,连结AD.(1)求证:AF⊥EF;(2)若tan∠CAD=,AB=5,求线段BE的长.26.(5分)(2015•顺义区一模)阅读、操作与探究:小亮发现一种方法,可以借助某些直角三角形画矩形,使矩形邻边比的最简形式(如4:6的最简形式为2:3)为两个连续自然数的比,具体操作如下:如图1,Rt△ABC中,BC,AC,AB的长分别为3,4,5,先以点B为圆心,线段BA的长为半径画弧,交CB的延长线于点D,再过D,A两点分别作AC,CD的平行线,交于点E.得到矩形ACDE,则矩形ACDE的邻边比为.请仿照小亮的方法解决下列问题:(1)如图2,已知Rt△FGH中,GH:GF:FH=5:12:13,请你在图2中画一个矩形,使所画矩形邻边比的最简形式为两个连续自然数的比,并写出这个比值;(2)若已知直角三角形的三边比为(2n+1):(2n2+2n):(2n2+2n+1)(n为正整数),则所画矩形(邻边比的最简形式为两个连续自然数的比)的邻边比为.五、解答题(本题共22分,第23题7分,第24题7分,第25题8分)27.(7分)(2015•顺义区一模)在平面直角坐标系xOy中,抛物线y=+2x﹣a+1与y轴交于C点,与x轴交于A,B两点(点A在点B左侧),且点A的横坐标为﹣1.(1)求a的值;(2)设抛物线的顶点P关于原点的对称点为P′,求点P′的坐标;(3)将抛物线在A,B两点之间的部分(包括A,B两点),先向下平移3个单位,再向左平移m(m>0)个单位,平移后的图象记为图象G,若图象G与直线PP'无交点,求m的取值范围.28.(7分)(2015•顺义区一模)如图,△ABC中,AB=AC,点P是三角形右外一点,且∠APB=∠ABC.(1)如图1,若∠BAC=60°,点P恰巧在∠ABC的平分线上,PA=2,求PB的长;(2)如图2,若∠BAC=60°,探究PA,PB,PC的数量关系,并证明;(3)如图3,若∠BAC=120°,请直接写出PA,PB,PC的数量关系.29.(8分)(2015•顺义区一模)已知:如图1,抛物线的顶点为M,平行于x轴的直线与该抛物线交于点A,B(点A在点B左侧),根据对称性△AMB恒为等腰三角形,我们规定:当△AMB为直角三角形时,就称△AMB为该抛物线的“完美三角形”.(1)①如图2,求出抛物线y=x2的“完美三角形”斜边AB的长;②抛物线y=x2+1与y=x2的“完美三角形”的斜边长的数量关系是;(2)若抛物线y=ax2+4的“完美三角形”的斜边长为4,求a的值;(3)若抛物线y=mx2+2x+n﹣5的“完美三角形”斜边长为n,且y=mx2+2x+n﹣5的最大值为﹣1,求m,n的值.2015年北京市顺义区中考数学一模试卷参考答案与试题解析一、选择题(本题共30分,每小题3分)下面各题均有四个选项,其中只有一个是符合题意的.2.(3分)(2015•顺义区一模)2014年11月北京主办了第二十二届APEC (亚太经合组织)领导人会议,“亚太经合组织”联通太平洋两岸,从地理概念上逐渐变成了一个拥有28000000人口的经济合作体,把“28000000”用科学记数法表示正确的是( )3.(3分)(2015•宜兴市二模)如图是由四个相同的小正方体组成的立体图形,它的俯视图为().4.(3分)(2014•舟山)一名射击爱好者5次射击的中靶环数如下:6,7,9,8,9,这5个数据的中位数是().6.(3分)(2014•来宾)函数中,自变量x的取值范围是()解:∵有意义的条件是:7.(3分)(2015•顺义区一模)一个不透明的口袋中,装有4个红球,3个黄球,1个白球,.∴从口袋中随机摸一个球,则摸到红球的概率为:=8.(3分)(2015•顺义区一模)如图,⊙O的半径为5,AB为⊙O的弦,OC⊥AB于点C.若OC=3,则AB的长为()AC==49.(3分)(2015•顺义区一模)若正多边形的一个外角为60°,则这个正多边形的中心角的∴正多边形的边数为其中心角为10.(3分)(2015•顺义区一模)如图,菱形ABCD 的对角线AC ,BD 相交于点O ,AC=6,BD=8,动点P 从点B 出发,沿着B ﹣A ﹣D 在菱形ABCD 的边上运动,运动到点D 停止,点P ′是点P 关于BD 的对称点,PP ′交BD 于点M ,若BM=x ,△OPP ′的面积为y ,则y 与x 之间的函数图象大致为( ).B .C .DAC=3∴,即=y=OM=×﹣二、填空题(本题共18分,每小题3分)11.(3分)(2015•郴州)分解因式:2a2﹣2=2(a+1)(a﹣1).12.(3分)(2015•顺义区一模)质量检测部门对甲、乙两工厂生产的同样产品抽样调查,计算出甲厂的样本方差为0.99,乙厂的样本方差为1.22.由此可以推断出生产此类产品,质量比较稳定的是甲厂.13.(3分)(2015•顺义区一模)在综合实践课上,小明同学设计了如图测河塘宽AB的方案:在河塘外选一点O,连结AO,BO,测得AO=18m,BO=21m,延长AO,BO分别到D,C两点,使OC=6m,OD=7m,又测得CD=5m,则河塘宽AB=15m.根据题意得出=解:∵==3=∴=∴=14.(3分)(2015•顺义区一模)写出一个当自变量x>0时,y随x的增大而增大的反比例函数表达式(答案不唯一).﹣(15.(3分)(2015•顺义区一模)居民用电计费实行“一户一表”政策,以年为周期执行阶梯电价,即:一户居民全年不超过2880度的电量,执行第一档电价标准为0.48元/度;全年用电量在2880度到4800度之间(含4800),超过2880度的部分,执行第二档电价标准为0.53元/度;全年用电量超过4800度,超过4800度的部分,执行第三档电价标准为0.78元/度.小敏家2014年用电量为3000度,则2014年小敏家电费为1446元.16.(3分)(2015•顺义区一模)规定:在平面直角坐标系xOy中,“把某一图形先沿x轴翻折,再沿y轴翻折”为一次变化.如图,已知正方形ABCD,顶点A(1,3),C(3,1).若正方形ABCD经过一次上述变化,则点A变化后的坐标为(﹣1,﹣3),如此这样,对正方形ABCD连续做2015次这样的变化,则点D变化后的坐标为(﹣3,﹣3).三、解答题(本题共30分,每小题5分)17.(5分)(2015•顺义区一模)计算:.×﹣18.(5分)(2015•顺义区一模)解不等式组:.19.(5分)(2015•顺义区一模)如图,C,D为线段AB上两点,且AC=BD,AE∥BF.AE=BF.求证:∠E=∠F.20.(5分)(2015•顺义区一模)已知b=a﹣3,求代数式的值.解:===21.(5分)(2015•顺义区一模)已知关于x的一元二次方程kx2﹣3x﹣2=0有两个不相等的实数根.(1)求k的取值范围;(2)若k为小于2的整数,且方程的根都是整数,求k的值.∴)知道的根22.(5分)(2015•顺义区一模)列方程或方程组解应用题:在练习100米跑步时,小丽为了帮助好朋友小云提高成绩,让小云先跑7.5秒后自己再跑,结果两人同时到达终点,这次练习中小丽的平均速度是小云的1.6倍,求小云这次练习中跑100米所用的时间.依题意,得四、解答题(本题共20分,每小题5分)23.(5分)(2015•顺义区一模)如图,平行四边形ABCD中,点E是AD边上一点,且CE⊥BD 于点F,将△DEC沿从D到A的方向平移,使点D与点A重合,点E平移后的点记为G.(1)画出△DEC平移后的三角形;(2)若BC=,BD=6,CE=3,求AG的长.=3AD=BC=2AD=3224.(5分)(2015•顺义区一模)为了提倡“绿色”出行,顺义区启动了公租自行车项目,为了解我区居民公租自行车的使用情况,某校的社团把使用情况分为A(经常租用)、B(偶尔租用)、C(不使用)三种情况.先后在2015年1月底和3月底做了两次调查,并根据调查结果绘制成了如下两幅不完整的统计图:根据以上信息解答下列问题:(1)在扇形统计图中,A(经常租用)所占的百分比是20%;(2)求两次共抽样调查了多少人,并补全折线统计图;(3)根据调查的结果,请你谈谈从2015年1月底到2015年3月底,我区居民使用公租自行车的变化情况.25.(5分)(2015•顺义区一模)如图,AB是⊙O的直径,C是⊙O上一点,D是的中点,过点D作⊙O的切线,与AB,AC的延长线分别交于点E,F,连结AD.(1)求证:AF⊥EF;(2)若tan∠CAD=,AB=5,求线段BE的长.为BD=AD=的中点,∵∴BD=AD=∴∴∴.26.(5分)(2015•顺义区一模)阅读、操作与探究:小亮发现一种方法,可以借助某些直角三角形画矩形,使矩形邻边比的最简形式(如4:6的最简形式为2:3)为两个连续自然数的比,具体操作如下:如图1,Rt△ABC中,BC,AC,AB的长分别为3,4,5,先以点B为圆心,线段BA的长为半径画弧,交CB的延长线于点D,再过D,A两点分别作AC,CD的平行线,交于点E.得到矩形ACDE,则矩形ACDE的邻边比为1:2.请仿照小亮的方法解决下列问题:(1)如图2,已知Rt△FGH中,GH:GF:FH=5:12:13,请你在图2中画一个矩形,使所画矩形邻边比的最简形式为两个连续自然数的比,并写出这个比值;(2)若已知直角三角形的三边比为(2n+1):(2n2+2n):(2n2+2n+1)(n为正整数),则所画矩形(邻边比的最简形式为两个连续自然数的比)的邻边比为n:(n+1).五、解答题(本题共22分,第23题7分,第24题7分,第25题8分)27.(7分)(2015•顺义区一模)在平面直角坐标系xOy中,抛物线y=+2x﹣a+1与y轴交于C点,与x轴交于A,B两点(点A在点B左侧),且点A的横坐标为﹣1.(1)求a的值;(2)设抛物线的顶点P关于原点的对称点为P′,求点P′的坐标;(3)将抛物线在A,B两点之间的部分(包括A,B两点),先向下平移3个单位,再向左平移m(m>0)个单位,平移后的图象记为图象G,若图象G与直线PP'无交点,求m的取值范围.)在抛物线∴,则的坐标为∴∴28.(7分)(2015•顺义区一模)如图,△ABC中,AB=AC,点P是三角形右外一点,且∠APB=∠ABC.(1)如图1,若∠BAC=60°,点P恰巧在∠ABC的平分线上,PA=2,求PB的长;(2)如图2,若∠BAC=60°,探究PA,PB,PC的数量关系,并证明;(3)如图3,若∠BAC=120°,请直接写出PA,PB,PC的数量关系.)结论:PD=∴29.(8分)(2015•顺义区一模)已知:如图1,抛物线的顶点为M,平行于x轴的直线与该抛物线交于点A,B(点A在点B左侧),根据对称性△AMB恒为等腰三角形,我们规定:当△AMB为直角三角形时,就称△AMB为该抛物线的“完美三角形”.(1)①如图2,求出抛物线y=x2的“完美三角形”斜边AB的长;②抛物线y=x2+1与y=x2的“完美三角形”的斜边长的数量关系是相等;(2)若抛物线y=ax2+4的“完美三角形”的斜边长为4,求a的值;(3)若抛物线y=mx2+2x+n﹣5的“完美三角形”斜边长为n,且y=mx2+2x+n﹣5的最大值为﹣1,求m,n的值.中,得到,得到点坐标为,所以,所以=AB=∴∴点坐标为,,得∴∴。
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朝阳一模Kevin Pearce, snowboard athlete (运动员), has come a long way since his accident on December 31, 2009.56 ,,when he fell and hurt his head. Luckily, he was wearing a helmet (头盔). 57 . He stayed in hospital for four months. He still can‟t remember several weeks of his life after the accident.Today, Pearce is still working hard to get his health back to 100%. 58 . A year ago, he couldn‟t walk straight. Now, he can not only walk, but he can also drive again.Pearce says he must thank his fans, his friends and especially his family. His parents and elder brothers have been by his side since the accident. 59 . He said he couldn‟t have got well so quickly without them.These days, Pearce is back on the snowboarding circuit (巡回比赛). 60 . He is on the road again and it is a丰台一模A new pet shop called Turtle Dove opened on First Street. It sold two kinds of animals. 56 , Bill and Bob. They moved here from the northern California, where they owned an ant farm store. That store was so successful that they sold it after four years and got a lot of money.They took it easy for a few years. Traveling through the state. “We visited almost every zoo in the country, 57 , and partly because we were looking for support for our next business,” said Bill. They finally decided on turtles and doves(白鸽). “They‟re easy to feed and care for, 58 .” said Bob.The store will be open from 9 a.m. to 9 p.m. Wednesdays through Saturdays. “We think those are hours that our customers will find very convenient. What‟s more, the three days off gives us a chance to go into the woods and find more little animals. 59 , we always try to collect them from the wild. That way our customers can save more money. Of course, by removing these animals from the nature, we protect them from being eaten by their nature enemies. So our customers are happy, our animals are happy, 60 .It‟s a win-win for all of us.”石景山一模High school life can be terrible if you get it all wrong. Find out how to survive high school with a few easy tips.◆56. ________.High school is a fun time to make new friends and meet new people. Make friends with all kinds of people and not just a group which you are comfortable with. Socialize, but by judging who you can connect to. You will find friends, but stay away from the ones who don‟t want to be your friends.◆Be yourself.Do your own things, and don‟t just follow others. 57. ________. Just be yourself and create a strong self-image.◆Be positive (积极的).There is nothing better than having a smile on your face whenever you can. 58. ________. Just be brave enough to meet new people or do something you‟ve never tried. Meanwhile, respect your teachers and classmates and try to be helpful if you want the same in return.◆Be confident.When you believe in yourself, others will believe in you. 59. ________. And people respect you for that. Make sure you won‟t easily get influenced by others.◆Love high school.60. ________. Make the most out of it, and you will never get those moments back. Come up with funny ideas, top顺义一模What a day通州一模西城一模Following Their DreamsFlorence lived in the countryside of Kenya (肯尼亚)in Africa. When she was 12, she wanted nothing more than to finish school. But for many girls like her, school is not a choice.___56___. Families will probably spend money educating boys. Many girls are forced to marry.___57___. It was Beads for Education, started by Lisa Stevens, that helped realize her dream. Beads has provided many girls with the best education possible. Florence was the first of 320 Kenyan girls in third grade.___58___. During her visit, she heard that many women made and sold baskets. They used the money to send their daughters to school. Two years later, she started to help sell the Kenyan crafts in the U. S. In 1998, Stevens began helping girls continue their education.___59___. In January, 2015, she opened the fourth one. "I want to provide the girls with the best education possible and prepare them for college and beyond," Stevens said.The new high school is named Tembea, which means "to walk". Florence is walking toward a bright future. ___60___ . "Florence is the first in her family to finish high school and college," says Stevens. "She is an example for all girls in Kenya."东城一模Doctors in Germany have warned people that headbanging could be bad for your health. __________ (56). Dancers shake their heads ba ck to front, and from side to side, very quickly.Doctors say this would injure(伤害) the brain. __________ (57). The man had no history of head injuries but had been headbanging for many years.He began to have bad headaches after going to a heavy metal concert. __________ (58) They gave him a brain scan(扫描) and found bleeding in his brain. He needed an operation to repair it. Doctors made a hole in his brain to take out some blood. __________ (59) Doctors said the risk of injury to the brain from headbanging is low and heavy metal fans do not need to stop doing the dance completely. The head doctor, Ariyan Pirayesh, said: "We are not against headbanging. Rock 'n'roll will never die. __________ (60). We just think if our patient had gone to a classical (古典的) concert,this would not have happened."海淀一模The Same But DifferentMaggie and Sarah are twin sisters. They were born just a few minutes apart,and they look exactly alike. They both have blonde hair and green eyes.56 . Sometimes other students at school have a hard time telling them apart.Maggie and Sarah like going to the same school. This is because they are notjust twin sisters, but best friends too. They have a lot in common. 57 . Bothgirls spend a lot of time together with their family, and they both like to play withtheir dog, Callie.58 . Maggie likes to play sports. She is on a soccer team and a basketball team. Sarah doesn‟t really like sports. She likes to dance.There are other differences between them too. 59 . Maggie likes to read mystery books, but Sarah likes to read books about animals. Maggie gets better grades in reading and Spanish, but Sarah gets better grades in math and science.Everyone is different in her or his own way. Maggie and Sarah like being different from each other as much as they like being similar. 60 .A. That is what makes them specialB. They are around the same height as wellC. But Maggie and Sarah are also ve ry differentD. Maggie likes the color red, but Sarah likes the color greenE. Both girls enjoy a lot of the same television shows, books, and food房山一模It is a very common thing for a person to have a good friend. My good friend is Diana. She is a rich and proud girl. 56 . So nobody wants to be her friend.One day after school, I was waiting for Diana when Jane came up to me. She gave me a biscuit. I accepted it. 57 , and had very good time. From then on, I began to spend more time with Jane than with Diana. I felt a little uneasy.After a few days, I went to see Diana for a good talk when Jane came and sat with me. She offered me a sandwich. 58 . She walked away. I was angry with Diana for being so rude and thoughtless.“Never mind,” Jane said, “I‟m used to it .”After school, I tried to catch up with Diana. 59 , but she would not listen to me. She said, “Go and join your …dear‟ Jane. I know you make new friends and forget the old ones.”For the next few weeks, we did not talk to each other. Then , one day, Diana came to Jane and me, saying, “I‟m really sorry about what I did. I‟m a spoiled(宠坏) girl, but I also need good friends just like you. Would you please forgive me?” Jane and I looked at each other and smiled.60 .A.We talked and jokedB.She often thinks that she is too good for anyoneC.While walking home, I tried to correct her attitudeD.She also offered one to Diana , but Diana refused itE.From then on, Diana , Jane and I have been best friends怀柔一模If asked to recite a poem right now, which one would first come to mind? Most of you may say Jing Ye Si (Thoughts in the Silent Night). 56. As one of the most famous Chinese poems, almost every Chinese kid has learned it at school and can recite it.57. To remember World Poetry Day every March 21, the UN issues (发行) a set of six stamps that have six poems in six major languages. This year, Jing Ye Si is one of them.According to the UN, each theme(主题)shows a universal truth —the fading of time, forgiveness, longing (渴望), love, wisdom, and nature.Jing Ye Si is a poem with one of the above themes. 58. And it is catchy and easy for readers to understand the writer‟s longing for his home.The poem was written more than a thousand years ago. 59. Chen Bo, 14, from Inner Mongolia is now st udying in Guangzhou, a city far from his hometown. “Sometimes when I think of my hometown, I remember this poem,” he said.60. Here is a translation by Chinese translators Yang Xianyi and his wife Gladys Yang: “Beside my bed a pool of light —Is it hoarfrost (霜) on the ground? I lift my eyes and see the moon, I bend my head and think of home.” Do you like it?门头沟一模Chinese love to eat because food is thought to be the most important way to communicate. So some people often order so many dishes that they can‟t eat them up. Chinese government asks the public not to waste food anytime. 56 .The managers of some restaurants are doing what they can to help people to reduce (减少) food waste.57 , the waiters should remind them to reduce the number of dishes kindly, or the waiters should ask them to take the leftover with them.Zhong Li, a famous woman, said,“58 , even sometimes we can order a half so that we won‟t waste.” Once Zhong Li ordered half a Beijing Duck and some vegetables. She believed that saving food didn‟t mean losing face.59 . We call it “cleaning the plates”. Xu Jun has done it for years. He said, “60 . However, many people have thrown away a whole chicken or fish.” Cleaning the plates is not only to save food, but also to protect the environment and our health.门头沟一模My mother is a diligent and kind woman. She is very busy from morning till night. As a teacher, sheworks hard. 56 .Both my brother and I love her dearly as she loves us.My mother has been teaching math at a middle school in my hometown. She goes to work early in the morning and does not return home until late in the afternoon. 57 . She treats them with patience and teaches them well. For her excellent quality and very good teaching results, she has been elected as a model teacher several times.58 . Every day, when she comes back home from work, she sets about doing housework, sweeping the living room and bedrooms or cleaning the furniture, and putting everything in good order. 59 . As she has been very busy working every day, she looks older than her age. But she looks as cheerful and happy as ever. Mother never buys expensive dresses for herself, but she often buys some inexpensive but high quality clothes for us. She never goes to expensive restaurants to enjoy meals.She just eats a plain meal outside when she is too busy to cook herself. She lives a busy yet simple life, without any complaints.Ofte n she says to us, “Work whi le you work, and play while you play. That is the way to be happy and gay. If you do not work, you will become lazy and be of no use to society”. What a piece of good advice thisis!60 .This advice of hers will always serve as a guide to my behavior. My mother is great indeed, and I always feel proud of her.燕山一模Water rides — Something that really attracts you!The water rides are the most popular rides. 56__ The boat slides down very fast into the water! You can buy your ticket before you go to the theme park. Then you do not have to stand in a long line. 57 _ If more than 10 people go to the theme park together, it costs less. There is a ticket machine beside each ride. You can stand in line for your turn. Or you can take a ticket that gives a time you can go on that ride. Then you can do something else while you are waiting.58__ This is because when you are scared, your knuckles become white! It is a strange idea to pay more money to be scared, but many people do that because they want to enjoy the excitement of the rides! Sometimes they laugh and scream! At the theme parks, there are special rides for young children. Of course, the children‟s rides are not fast or high or scary. 59__ The children are safe when they sit inside the teacups and the ride goes around very slowly.Sometimes there are animals like rabbits and sheep for children to see at a theme park. So there are lots to do and see. You will sleep very well after you have been to a theme park for the day! 60__ Or would you be too scared? Do you think that your mother and father would enjoy this ride?答案朝阳DCABE 丰台CDEBA 西城AEBCD 东城EDCBA 海淀BECDA 房山BADCE 怀柔ECADB 门头沟CAEDB 平谷EACDB 燕山BADEC。