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    益阳市2015年普通初中毕业学业考试试卷

       

    注意事项:1本学科试卷分试题卷和答题卡两部分;

    2请将姓名、准考证号等相关信息按要求填写在答题卡上;

    3请按答题卡上的注意事项在答题卡上作答,答在试题卷上无效;

    4本学科为闭卷考试,考试时量为90分钟,卷面满分为150分;

    5考试结束后,请将试题卷和答题卡一并交回.

    试 题 卷

    一、选择题本大题共8小题,每小题5分,共40分.在每小题给出的四个选项中,只有一项是符合题目要求的

    1.下列实数中,是无理数的为

         A                    B                       C0                        D

    2.下列运算正确的是

         A                                         B            

         C                                      D

    3.某小组5名同学在一周内参加家务劳动的时间如下表所示,关于“劳动时间”的这组数据,以下说法正确的是

    劳动时间(小时)

    3

    3.5

    4

    4.5

     

    1

    1

    2

    1

         A.中位数是4,平均数是3.75                B.众数是4,平均数是3.75        

         C.中位数是4,平均数是3.8                  D.众数是2,平均数是3.8

    4.一个几何体的三视图如图1所示,则这个几何体是                 

         A.三棱锥              B.三棱柱         C.圆柱               D.长方体

    5.如图2,在矩形ABCD中,对角线ACBD交于点O,以下说法错误的是

    A                                      B         

    C                                           D

    6.下列等式成立的是

    A                                     B 

    C                                D

    7沅江市近年来大力发展芦笋产业,某芦笋生产企业在两年内的销售额从20万元增加到80万元.设这两年的销售额的年平均增长率为x,根据题意可列方程为

                  A20(1+2x) =80                                     B2×20(1+x) =80

                  C20(1+x2) =80                                      D20(1+x)2 =80

    8.若抛物线的顶点在第一象限,则m的取值范围为

                  A                 B                 C            D

    二、填空题本大题共5小题,每小题5分,共25分.把答案填在答题卡中对应题号后的横

    线上

    9.计算:       

    10.已知yx的反比例函数,当x > 0时,yx的增大而减小.请写出一个满足以上条件的函数表达式       

    11.甲、乙、丙三位好朋友随机站成一排照合影,甲没有站在中间的概率为       

    12如图3,正六边形ABCDEF内接于OO的半径为1,则的长为       

                                   

    13.图4是用长度相等的小棒按一定规律摆成的一组图案,第1个图案中有6根小棒,第2个图案中有11根小棒,…,则第n个图案中有        根小棒.

    三、解答题(本大题共2小题,每小题8分,共16

    14.化简

    15如图5,直线ABCDBC平分∠ABD,求的度数.

    四、解答题(本大题共3小题,每小题10分,共30分)

    16.如图6,直线l上有一点P1(21),将点P1先向右平

    1个单位,再向上平移2个单位得到像点P2,点

    P2恰好在直线l上.

       1)写出点P2的坐标;

       2)求直线l所表示的一次函数的表达式;

       3)若将点P2先向右平移3个单位,再向上平移6

    单位得到像点P3.请判断点P3是否在直线l上,并说明理由.

    172014益阳市的地区生产总值(第一、二、三产业的增加值之和)已进入千亿元俱乐部,图7表示2014年益阳市第一、二、三产业增加值的部分情况,请根据图中提供的信息解答下列问题:

    12014年益阳市的地区生产总值为多少亿元?

    2请将条形统计图中第二产业部分补充完整;

    3)求扇形统计图中第二产业对应的扇形的圆心角度数.

    18.如图8,在ABCD中,对角线ACBD相交于点O

    CAB=ACB,过点BBEABAC于点E

    1)求证:ACBD

    2)若AB=14,求线段OE的长

    五、解答题(本大题共2小题,每小题12分,共24

    19.大学生小刘回乡创办小微企业,初期购得原材料若干吨,每天生产相同件数的某种产品,单件产品所耗费的原材料相同.当生产6天后剩余原材料36吨,当生产10天后剩余原材料30吨.若剩余原材料数量小于或等于3吨,则需补充原材料以保证正常生产.

    1)求初期购得的原材料吨数与每天所耗费的原材料吨数;

    2若生产16天后,根据市场需求每天产量提高20%,则最多再生产多少天后必须补充原材料?

    20已知点P是线段AB上与点A不重合的一点,且AP<PBAP绕点A逆时针旋转

    得到AP1BP绕点B顺时针也旋转角得到BP2,连接PP1PP2

    1)如图9-1,当时,求的度数;

    2)如图9-2当点P2AP1的延长线上时,求证:

    3)如图9-3,过BP的中点El1BP ,过BP2的中点Fl2BP2l1l2交于点Q,连接PQ,求证:P1PPQ

    六、解答题(本题满分15

    21已知抛物线E1经过点A(1m),以原点为顶点的抛物线E2经过点B(22),点AB关于y 轴的对称点分别为点

    1m的值及抛物线E2所表示的二次函数的表达式

    2如图10-1,在第一象限内,抛物线E1上是否存在点Q,使得以点QB为顶点的三角形为直角三角形?若存在,求出点Q的坐标;若不存在,请说明理由;

    3如图10-2P为第一象限内的抛物线E1上与点A不重合的一点,连接OP并延长与抛物线E2相交于点,求的面积之比.

    益阳市2015年普通初中毕业学业考试

    数学参考答案及评分标准

    一、选择题本大题共8小题,每小题5分,共40分).

    题号

    1

    2

    3

    4

    5

    6

    7

    8

    答案

    A

    C

    C

    B

    D

    C

    D

    B

    二、填空题本大题共5小题,每小题5分,共25分).

    9410(不唯一)111213

    三、解答题(本大题共2小题,每小题8分,共16).

    14解:原式=·············································································· 6

      =. ································································································· 8

        15解:∵ABCD

    . ············································ 4

    ········································································ 6

    ·············································································· 8

    四、解答题(本大题共3小题,每小题10分,共30

    16解:(1P2(33)·························································································· 3

            2)设直线l所表示的一次函数的表达式为

    ∵点P1(21)P2(33)在直线l

      ,解得.

    直线l所表示的一次函数的表达式为. ······························ 7

    3)点P3在直线l上.

    由题意知点P3的坐标为(69)∴点P3在直线l上. 10

    17:1(亿元)································································· 3

    2)第二产业的增加值为(亿元)画图如下:

                                              

                                                                                      ······························ 7

    3)扇形统计图中第二产业部分的圆心角为·············· 10

    18.解:(1)∵,∴

    ABCD是菱形.

                  ······················································································· 3

    2)在RtAOB中,

             

    RtABE中,

    ·············································································· 9

    ························································ 10

    五、解答题(本大题共2小题,每小题12分,共24

    19解:1初期购得原材料a吨,每天所耗费的原材料为b吨,

    根据题意得:.································································ 3

    解得

    答:初期购得原材料45吨,每天所耗费的原材料为1.5吨.················ 6

    2设再生产x天后必须补充原材料,

    依题意得: ······································· 9

    解得:.

    : 最多再生产10天后必须补充原材料.········································ 12

    20.解:1)由旋转的性质得:AP = AP1BP = BP2

    均为等腰直角三角形,

    . ·············································· 3

    2)由旋转的性质可知均为顶角为的等腰三角形,

    ················ 5

    中,

    ··········································································· 7

    3)如图,连接QB.

    l1l2分别为PBP2B的中垂线,

    .

    BP=BP2

                                      

    RtQBERtQBF

    RtQBERtQBF

    ······················································· 9

      由中垂线性质得:

    由(2)知,

    ,

    P1PPQ···················································································· 12

    六、解答题(本题满分15

    21.解:1抛物线E1经过点A(1m)

    m=12=1

                抛物线E2的顶点在原点,可设它对应的函数表达式为()

                 又点B(22)抛物线E2上,,解得:

    抛物线E2所对应的二次函数表达式为······························· 3

    2)假设在第一象限内 ,抛物线E1上存在点Q,使得△为直角三角形,由图象可知直角顶点只能为点B或点Q

    ①当点B为直角顶点时,过B抛物线E1Q

    则点QB的横坐标相等且为2,将x=2代入y=x2y=4

    ∴点Q的坐标为(24) ··································································· 5

    ②当点Q为直角顶点时,则有,过点QG

    设点Q的坐标为(tt2)( )

           则有

           整理得:,

           , ,解得(舍去)

    ∴点Q的坐标为(3)

    综合①②,存在符合条件的点Q坐标(24)(3)······················· 9

    3过点PPCx,垂足为点CPC交直线于点E,过点Dx,垂足为点DD交直线于点F

    依题意可设P(cc2)(d) (c >0)

    d=2c······································ 12

    =2=4

    ··························· 15

    21题解图1                          21题解图2



      
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