2007年湖南省张家界市中考数学真题及答案.doc

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2007 年湖南省张家界市中考数学真题及答案注意事项： 1．答题前，考生务必将自己的姓名、准考证号写在答题卡和该试题卷的封面上，并将准考证号下面对应的信息点用 2B 铅笔涂黑． 2．考生作答时，选择题和非选择题均须写在答题卡上，在草稿纸和本试题卷上答题无效．考生在答题卡上按如下要求答题：（1）选择题部分请用 2B 铅笔把对应题目的答案标号所在方框涂黑，修改时用橡皮擦干净，不留痕迹．（2）非选择题部分（包括填空题和解答题）请按题号用 0.5 毫米黑色墨水签字笔书写，否则作答无效．（3）保持字体工整、笔迹清晰、卡面清洁、不折叠． 3．考试结束后，将本试题卷和答题卡一并交回． 4．本试题卷共 3 页．如缺页，考生须声明，否则后果自负．考生注意：本学科试卷共三道大 25 小题，满分 120 分，考试时量 120 分钟．一、选择题：（本题 8 小题，每小题 3 分，满分 24 分） 1．3 的相反数是（） A．3 B． 3 C． 1 3 D． 3 2．下面是某几何体的三种视图，则该几何体是（）主视图 B．圆台左视图俯视图 A．圆柱 3．数轴上阴影部分表示的是某不等式组的解集，它的具体范围是（ D．直棱柱 C．圆锥 A． x   2 B． 2   ≤ x 1 C． 2  ≤ ≤ x 1 D．  3  2  1 0 1 2 3 ） 1 x ≤ 4．一组数据共 4 个数，其众数为 6，中位数为 5，平均数为 4，则这组数据是（ A．0 6 5．沿着虚线将矩形剪成两部分，既能拼成三角形又能拼成梯形的是（ 5 ） C．1 D．4 B．1 5 6 6 6 6 4 3 6 6 ） 6 Ａ．Ｂ． 6．下列事件中是必然事件的是（ A．明天我市天气晴朗 C．抛一枚硬币，正面朝下Ｃ．Ｄ．） B．两个负数相乘，结果是正数 D．在同一个圆中，任画两个圆周角，度数相等中， ACB  90  ，CD AB ， DE BC ， 7．如图在 ABC△ 那么与 ABC△ A．1 个相似的三角形的个数有（） B．4 个 C．3 个 D．2 个 A C D E B

8．观察一列有规律的数：4，8，16，32，…，它的第 2007 个数是（） A． 20072 B． 20072 1 C． 20082 D． 20062 二、填空题（本题 8 小题，每小题 3 分，满分 24 分） A ，在函数 9．已知点 (3 5) k  x 10．在四边形 ABCD 中， AC  点，则四边形 EFGH 的周长为 y  上，则 k  ． 4cm ， 4.5cm BD  ．，E F G H ，，，分别是边 AB BC CD DA ，，，的中 H A D G C F E B 11．温家宝总理在今年政府工作报告中指出：今后 5 年国家财政新增加义务教育经费累计将达 218200000000 元，用科学记数法表示为元． 12．分解因式 2 2  xy xy   x ． 13．随着中国经济的高速发展，股市持续上涨，到 2007 年 5 月 28 日止，股市的开户人数已达到 1 亿人，同日对股民的市场抽样调查如右图所示，据此估计当日对后市看涨的股民为万人． 14．关于 x 的方程 2 3  x x   的一个根是 1 ，另一根是 0 k 看跌 13.10％看平 20.69％看涨 66.21％． 15．将 ABC△  绕点C 顺时针旋转得到 A B C △  ，已知   ACA  90 ， BC  3 ，则点 B 旋转经过的路线长是． A 16．若 3 2k  有意义，则函数 y kx 1  的图象不经过第象限．三、解答题（本大题 9 小题，满分 72 分） 17．（本小题 6 分）计算： 3 2   2 2   18 tan 45    (4sin 60  0  1)  | 2 3 2 |  ． B A C B 18．（本小题 6 分）如图所示方格纸中，每个方格都是边长为 1 的正方形， ABC△ 小正方形顶点）请按下列要求在答题卡上分别画 A B C  （1）把 ABC△ （2）将 ABC△ △ 向右平移 4 个单位得 A B C   ；关于直线l 作轴反射得 A B C   △ △ ．  的顶点 A B C，，是方格纸中的三个格点（即 △  ， A B C ：  l A B C

19．（本小题 6 分）河边有一条笔直的公路，公路两侧是平坦地带，一次活动课，老师要求测量河的宽度．一同学的测量结果 BCD 如图所示： CD 请你帮助计算河的宽度 AB （结果保留根号）．  BDC 45 ，   30  ，  70 米． B A 45° D 30° C 20．（本小题 6 分）如图，在四边形 ABCD 中， AB AD 中 BE 和 DE 是否相等？若相等，请写出证明过程；若不相等，请说明理由．， BC DC ，E 为 AC 上的一动点（不与 A 重合），在 E 移动过程 A E D B C 21．（本小题 9 分）有两张背面相同的纸牌，其正面分别是正三角形和圆，将这两张纸牌背面朝上洗匀后摸出一张，放回洗匀后，再摸出一张．（1）写出两次摸牌出现的所有可能的结果．（2）求两次摸出都是圆的概率． 22．（本小题 9 分）张桑公路有一隧道，由 A 队单独施工，预计 200 天贯通．为了公路早日通车，由 A，B 两队同时施工，结果 120 天就贯通了．试问：如果由 B 队单独施工，需要多少天才能贯通？

23．（本小题 9 分）当 a  2 1  时，求 a a   1 a  1 ( a 2 4  2 1)   1 2  1 a 的值． 24. （本小题 9 分）如图，已知 AB 为圆O 的弦（非直径），E 为 AB 的中点，EO 的延长线交圆于点C ，CD AB∥ ，且交 AO 的延长线于点 D ． :EO OC 1: 2 CD  ，求圆O 的半径．， 4  25．（本小题 12 分） A E O C B D 抛物线 y  2 ax  bx  交 x 轴于 A B，两点，交 y 轴于点 C ，对称轴为直线 1x  ，已知： ( 1 0) A  ，， c C ，． (0 3) 2  c  ax （1）求抛物线  的解析式； bx 和 BOC△ y （2）求 AOC△ （3）在对称轴是否存在一个点 P ，使 PAC△ 明理由．的面积的比；的周长最小．若存在，请求出点 P 的坐标；若不存在，请说 y A O 1 x B C

张家界 2007 年初中毕业学业考试数学试卷答案及评分标准一、选择题 1．B 2．A 二、填空题 3．C 4．A 5．D 6．B 7．B 8．C 9． 15 10．8.5cm 11． 11 2.182 10 12． ( x y  1) 2 13．6621 万人 14． 2 15．三、解答题 3 π 2 16．二 17．解：原式 2 3 2 1 1 (3 2 2)        ·························································4 分    2 3 2 1 1 3 2 2  ············································································· 5 分    0 ·············································································································· 6 分 18．（略）每个图形 3 分 19．解：在 Rt ABC△ 中， BCD  30  ， tan 30  AB AC ，··································· 1 分  AC  AB tan 30  3 AB ，···············································································2 分中，在 Rt ABC△ 又 AC AD CD   BDC  45  ， AD AB ．··················································3 分，·····················································································4 分 AB AB   ，······················································································ 5 分 70  3  35 3 35  ．······················································································· 6 分 AB  20．解：相等．·······························································································1 分证明：在 ABC△ AB AD ABC  ，··········································································· 3 分，··················································· 2 分（公共边） BC DC ， AC AC 和 ADC△ (SSS) ADC ≌△ 中， △ BAE DAE    和 ABE△ 在 ADE△ AB AD ， BAE    AE AE ，  DAE ≌△ ADE ABE △ ，，·······················································································4 分中， (SAS) ···············································································5 分  BE DE ．······························································································· 6 分 21．解：（1）正三角形和正三角形正三角形和圆圆和正三角形圆和圆（写对一种情况 1 分）共计 4 分．（2）两张都是圆的概率的 1 4 ．·········································································· 9 分

 1 22．解：设 B 队单独施工需要 x 天才能贯通，·······················································1 分 120 120  ，····························································································· 4 分 200 x 解方程得 300 x  ，························································································· 7 分检验 300 是原方程的根，且符合题意．···························································8 分答： B 队单独施工需要 300 天才能贯通．·····························································9 分 x  23．解：原式  a a a   1 (  1 2)( a  ( 1) a   2 2) (  2 a  1) ·························································3 分  a a a   1 (  1 2)( a  ( 1) a   2 2) (  a  1)( a  1) ···································································· 4 分  ( a  2)( a  ．··························································································· 5 分 2) 当 a  2 1  时，原式 ( 2 1 2)( 2 1 2)      ·········································································· 6 分  ( 2 3) ( 2 1)    ·························································································7 分  ．···································································································9 分 2 2 1  24．解： E 是 AB 的中点， 90  OE AB ，即 AEO   DOE  AB CD∥ ， AOE     AOE ∽△    DOC △ : AE DC OE OC 2 AE 2 OE :   OA OC 1 2  CD 又   AE OE  而 2 2  2 OA ，  ，······································································· 1 分  90  ，······································································ 2 分 OCD ，······················································································ 3 分，··················································································· 4 分  ，··········································································5 分 1: 2  ．························································································ 6 分，··················································································· 7 分  OE 2   4 (2 OE 2 ) ， OE  圆O 的半径 OA  2 OE  2 3 2 3 3 3 2   ，·······························································8 分 4 3 3 ．····················································· 9 分 25．解：（1） A B ，两点关于 1x  对称， B 点坐标为 (3 0)，，···························· 1 分

根据题意得： ··········································································· 2 分 x  ．································································ 3 分 3  0 9 3 a b c        0 a b c    3 c  2 c   ， y 3 2 2    ．  x b a ，解得 1  抛物线的解析式为和 BOC△ | |  OA OC | （2） AOC△ 1 | S 2 | 1 OA  ，| 而| AOC  △ 的面积分别为， S △ BOC  1 | 2 OB OC | |  | ，··············································· 4 分 OB  ，··················································································· 5 分 | 3  S △ AOC : S △ BOC |  OA OB |:| | 1:3  ．································································ 6 分（3）存在一个点 P ．·······················································································7 分 C 点关于 1x  对称点坐标C 为 (2 3)，，··························································· 8 分令直线 AC 的解析式为 y  kx b   3 2 k b         0 k b  ······························································································ 9 分  k   ， 1 b   ，即 AC 的解析式为 1 y x   ．··········································· 10 分 1 为 1x  时， y   ，·····················································································11 分 2  P 点坐标为 (1 2)，．·················································································· 12 分

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2007年湖南省张家界市中考数学真题及答案.doc

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