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2007年福建省宁德市初中毕业、升学考试数学试题（满分：150分，考试时间：120分钟）一、填空题（本大题有10小题，每小题3分，共30分）1．．2．分解因式：．3．若，则．4．如图，，垂足为，则度．5．2007年4月27日，我国公布了第一批19座著名风景名胜山峰高程数据，其中“五岳”山峰高程数据分别是：泰山1532。7米，华山2154。9米，衡山1300。2米，恒山2016。1米，嵩山1491。7米．这五个数据的中位数是米．6．如图，的周长为20，对角线的长为5，则的周长为．7．反比例函数图象如图所示，则随的增大而．8．如图，若把太阳看成一个圆，则太阳与地平线的位置关系是（填“相交”、“相切”、“相离”）．9．按下面程序计算，输入，则输出的答案是． 10．一元二次方程的解是．二、选择题（本大题有6小题，每小题4分，共24分．在每小题给出的四个选项中，只有一个选项是正确的，请把你认为正确选项的代号填写在题中的括号内）11．下列计算错误的是（ ）A．B．C．D．12．北京2008年第29届奥运会火炬接力活动历时130天，传递总里程约13。7万千米．传递总里程用科学记数法表示为（ ）A．千米B．千米C．千米D．千米13．若如图所示的两个四边形相似，则的度数是（ ）A．B．C．D． 14．下列事件是必然事件的是（ ）A．2008年奥运会刘翔能夺得男子110米栏冠军B．这次数学考试李红会得满分C．太阳每天从东方升起D．李大爷买了一注“36选7的体育彩票”会中特等奖15．如图，是的直径，，则的度数是（ ）A．B．C．D． 16．如图1是一个小正方体的侧面展开图，小正方体从如图2所示的位置依次翻到第1格、第2格、第3格，这时小正方体朝上面的字是（ ）A．和B．谐C．社D．会三、解答题（本大题有10小题，共96分）17．（本题满分8分）求值：，其中．18．（本题满分8分）解不等式，并把解集在数轴上表示出来．19．（本题满分8分）如图，已知，垂足分别为．请添加一个适当条件，使，并予以证明．添加条件：．20．（本题满分8分）已知：如图，直线是一次函数的图象．求：（1）这个函数的解析式；（2）当时，的值．21．（本题满分8分）育才中学现有学生2870人，学校为了进一步丰富学生课余生活，拟调整兴趣活动小组，为此进行一次抽样调查．根据采集到的数据绘制的统计图（不完整）如下：请你根据图中提供的信息，完成下列问题：（1）图1中“电脑”部分所对应的圆心角为度；（2）在图2中，将“体育”部分的图形补充完整；（3）爱好“书画”的人数占被调查人数的百分数是；（4）估计育才中学现有的学生中，有人爱好“书画”．22．（本题满分10分）图1是小明在健身器材上进行仰卧起坐锻炼时情景．图2是小明锻炼时上半身由位置运动到与地面垂直的位置时的示意图．已知米，米，米．（1）求的倾斜角的度数（精确到）；（2）若测得米，试计算小明头顶由点运动到点的路径的长度（精确到0。
01米）23．（本题满分10分）我国“八纵八横”铁路骨干网的第八纵通道温（州）福（州）铁路全长298千米．将于2009年6月通车，通车后，预计从福州直达温州的火车行驶时间比目前高速公路上汽车的行驶时间缩短2小时．已知福州至温州的高速公路长331千米，火车的设计时速是现行高速公路上汽车行驶时速的2倍．求通车后火车从福州直达温州所用的时间（结果精确到0。01小时）．24．（本题满分10分）汉字是世界上最古老的文字之一，字形结构体现人类追求均衡对称、和谐稳定的天性．如图，三个汉字可以看成是轴对称图形．（1）请在方框中再写出2个类似轴对称图形的汉字；（2）小敏和小慧利用“土”、“口”、“木”三个汉字设计一个游戏，规则如下：将这三个汉字分别写在背面都相同的三张卡片上，背面朝上洗匀后抽出一张，放回洗匀后再抽出一张，若两次抽出的汉字能构成上下结构的汉字（如“土”“土”构成“圭”）小敏获胜，否则小慧获胜．你认为这个游戏对谁有利？请用列表或画树状图的方法进行分析并写出构成的汉字进行说明． 解：（1）25．（本题满分12分）如图，点是等边内一点，．将绕点按顺时针方向旋转得，连接．（1）求证：是等边三角形；（2）当时，试判断的形状，并说明理由；（3）探究：当为多少度时，是等腰三角形？26．（本题满分14分）已知：矩形纸片中，厘米，厘米，点在上，且厘米，点是边上一动点．按如下操作：步骤一，折叠纸片，使点与点重合，展开纸片得折痕（如图1所示）；步骤二，过点作，交所在的直线于点，连接（如图2所示）（1）无论点在边上任何位置，都有（填“”、“”、“”号）；（2）如图3所示，将纸片放在直角坐标系中，按上述步骤一、二进行操作：①当点在点时，与交于点点的坐标是（，）；②当厘米时，与交于点点的坐标是（，）；③当厘米时，在图3中画出（不要求写画法），并求出与的交点的坐标；（3）点在运动过程，与形成一系列的交点观察、猜想：众多的交点形成的图象是什么？并直接写出该图象的函数表达式．2007年福建省宁德市初中毕业、升学考试数学试题参考答案及评分标准（1）本解答给出了一种或几种解法供参考，如果考生的解法与本解答不同，可参照本答案的评分标准的精神进行评分．（2）对解答题，当考生的解答在某一步出现错误时，如果后续部分的解答未改变该题的立意，可酌情给分；如果有较严重的错误，就不给分．（3）解答右端所注分数表示考生正确作完该步应得的累加分数．（4）评分只给整数分．一、填空题（本大题有10小题，每小题3分，共30分）1．2；2．；3．； 4．40；5．1532。
7；6．15； 7．减少；8．相离；9．3；10．，；或，．二、选择题（本大题有6小题，每小题4分，共24分）11．C；12．B；13．A；14．C；15．A；16．D三、解答题（本大题有10小题，共96分）17．解：原式4分．6分当时，原式8分说明：若考生直接将代入计算，且结果正确不扣分．18．解：．2分．4分．6分解集表示正确．8分19．添加条件：（或，或等）．2分证明：，，．4分又，，．8分20．解：（1）依题意，得4分解得． ……………………4分．6分（2）当时，．8分 21．（1）126；2分（2）画图，如图所示；4分（3）；6分（4）287．8分 22．解：（1）过作，分别交延长线于．，，．四边形为矩形．．2分在中，，．即的倾斜角度数约为．7分（2），．．8分的长（米）．答：小明头顶运动的路径的长约为1。60米．10分 23．解：设通车后火车从福州直达温州所用的时间为小时．1分依题意，得．5分解这个方程，得．8分经检验是原方程的解．9分．答：通车后火车从福州直达温州所用的时间约为1。64小时．10分 24．解：（1）如： 等2分（2）这个游戏对小慧有利．3分每次游戏时，所有可能出现的结果如下：（列表）土口木土（土，土）（土，口）（土，木）口（口，土）（口，口）（口，木）木（木，土）（木，口）（木，木）（树状图）7分总共有9种结果，每种结果出现的可能性相同，其中能组成上下结构的汉字的结果有4种：（土，土）“圭”，（口，口）“吕”，（木，口）“杏”或“呆”，（口，木）“呆”或“杏”．，．9分．游戏对小慧有利．10分说明：若组成汉字错误，而不影响数学知识的考查且结论正确，本题只扣1分25．（1）证明：，，是等边三角形．3分（2）解：当，即时，是直角三角形．5分，．又是等边三角形，．．即是直角三角形．7分（3）解：①要使，需．，，．．②要使，需．，．．③要使，需．．．综上所述：当的度数为，或，或时，是等腰三角形．12分说明：第（3）小题考生答对1种得2分，答对2种得4分．26．（1）．2分（2）①；②．6分③画图，如图所示．8分解：方法一：设与交于点．在中，，．，， ．又，．．．．11分方法二：过点作，垂足为，则四边形是矩形．，．设，则．在中，．．．．．11分（3）这些点形成的图象是一段抛物线．12分函数关系式：．14分说明：若考生的解答：图象是抛物线，函数关系式：均不扣分．Learn General Secretary on "two to learn a" strengthening "four Consciousnesses" important speech caused a strong reaction in the country。
Time, watching "red treasure", the origin of building the party back to power, how to strengthen services for the masses, improve party cohesion, fighting to become the grass-roots party members and masses hot topic。 Grass-roots party organizations "two" is to strengthen the service of party members and cadres, the pioneer spirit。 Distribution of grass-roots party organizations in all walks of people, clothing, shelter, which belongs to the nerve endings of the party organization and comments reputation has a direct perception of the masses。
Strengthen the party ahead of the "pedal" spirit; strengthen the party members and cadres "success does not have to be me" and "the first to bear hardships, the last to" service spirit to set the party's positive image among the people is important。 Grass-roots party organizations "two" is to cleanse all people not happy not to see "stereotypes", establish the honest faithful, diligent faith for the people。 No need to avoid mentioning that, some members of our party can not stand the "money," corrosion of temptation, thin, Xu Zhou, such abuse and corrupt bribery, malfeasance borers, and rats。
Two, is to clean up, thin, Xu, Zhou's solution to restore the party's fresh and natural, solid and honest work style。 Cleansing "take, eat, card," undesirable and behaviour, "cross, hard and cold, push" attitude。 Grass-roots party organizations "two" is to strengthen the sense of ordinary party members, participating in consciousness, unity consciousness。 For reasons known, members of grass-roots party branches less mobile, less resources, and the construction of party organizations have some lag。
Two studies, is to focus on the grass-roots party branches "loose, soft, loose" problem, advance the party members and cadres, "a gang working", "Hong Kong report。" Strong cleanup actions, style and rambling, presumptuous "unqualified" party members, pays special attention to party members and cadres "joining party of thought" problem。 "Party building" is obtained in the long-term development of our party's historical experience accumulated。 Two is our party under the new historical conditions, strengthen the party's construction of a new "rectification movement。
" Grass-roots party organizations should always catch the hard work, results-oriented。 Two educational outcomes are long-term oriented and become an important impetus for the work。 "Two" should have three kinds of consciousness "two" study and education, basic learning lies in the doing。 only the Constitution address the series of party rules, and do solid work, be qualified party members had a solid ideological basis。 only the "learning" and "do" real unity, to form a "learn-learn-do-do" the virtuous cycle, and ultimately achieve the fundamental objective of education。
This requires that the Organization Learn General Secretary on "two to learn a" strengthening "four Consciousnesses" important speech caused a strong reaction in the country。 Time, watching "red treasure", the origin of building the party back to power, how to strengthen services for the masses, improve party cohesion, fighting to become the grass-roots party members and masses hot topic。 Grass-roots party organizations "two" is to strengthen the service of party members and cadres, the pioneer spirit。
Distribution of grass-roots party organizations in all walks of people, clothing, shelter, which belongs to the nerve endings of the party organization and comments reputation has a direct perception of the masses。 Strengthen the party ahead of the "pedal" spirit; strengthen the party members and cadres "success does not have to be me" and "the first to bear hardships, the last to" service spirit to set the party's positive image among the people is important。 Grass-roots party organizations "two" is to cleanse all people not happy not to see "stereotypes", establish the honest faithful, diligent faith for the people。
No need to avoid mentioning that, some members of our party can not stand the "money," corrosion of temptation, thin, Xu Zhou, such abuse and corrupt bribery, malfeasance borers, and rats。 Two, is to clean up, thin, Xu, Zhou's solution to restore the party's fresh and natural, solid and honest work style。 Cleansing "take, eat, card," undesirable and behaviour, "cross, hard and cold, push" attitude。 Grass-roots party organizations "two" is to strengthen the sense of ordinary party members, participating in consciousness, unity consciousness。
For reasons known, members of grass-roots party branches less mobile, less resources, and the construction of party organizations have some lag。 Two studies, is to focus on the grass-roots party branches "loose, soft, loose" problem, advance the party members and cadres, "a gang working", "Hong Kong report。" Strong cleanup actions, style and rambling, presumptuous "unqualified" party members, pays special attention to party members and cadres "joining party of thought" problem。 "Party building" is obtained in the long-term development of our party's historical experience accumulated。
Two is our party under the new historical conditions, strengthen the party's construction of a new "rectification movement。" Grass-roots party organizations should always catch the hard work, results-oriented。 Two educational outcomes are long-term oriented and become an important impetus for the work。 "Two" should have three kinds of consciousness "two" study and education, basic learning lies in the doing。 only the Constitution address the series of party rules, and do solid work, be qualified party members had a solid ideological basis。
only the "learning" and "do" real unity, to form a "learn-learn-do-do" the virtuous cycle, and ultimately achieve the fundamental objective of education。 This requires that the Organization learning education, need three kinds of consciousness: one is to establish an integrated awareness。 "Learning" and "do" what car isTwo-wheel, bird wings, need to go hand in hand, one end can be neglected。 Communist theoretician and man。 only by closely combining theory and practice together in order to truly realize their value。
"Learning" is the Foundation, the Foundation is not strong, shaking; " "Is the key to net to net thousands of accounts。 "Two" education, "" lay the basis, going to "do" the key grip, so that the "learning" and "doing" back to standard, so that the majority of party members "learn" learning theory of nutrients, in the "doing" practice party's purposes。 Second, to establish a sense of depth。 "Learning" and "do" not Chu drawn, entirely different, but the organic unity of the whole。 "Two" learning education, we need to explore integrating "learning" in "do", exhibit "do" in "Science"。
To avoid the "learning" into simple room instruction, "do" into a monotone for doing。 Should exploration "learn" in the has "do", "do" in the has "learn" of education and practice of carrier, makes general grass-roots members can in "learn" in the has "do" of achievements sense, in "do" in the has "learn" of get sense, real makes party of theory brain into heart, put for people service concept outside of Yu shaped。 Third, to adhere to long-term the awareness。 Style construction on the road forever, "two" had to catch the long-term。
"Two" study and education, by no means, assault-style wind-sport, but the recurrent education within the party。 In recent years, the party's mass line education practice and "three-three" special education in grass-roots borne rich fruits, vast numbers of party members and cadres withstood the baptism of the spirit。 "Two" greater need to focus on longer hold long-term, to establish and perfect the effective mechanism of the education, focusing on the creation of long-term education, strive to make the vast number of party members to maintain their vanguard Color, maintain the party's advanced nature and purity。
Awareness-raising, antennas and atmosphere – a discussion on how leading cadres of party members "two" current, "two" activity is in full swing up and down the country, party cadres as a "key minority" is both a barometer and impetus。 The "two" meaning enough deep, is to determine the party cadres can resolve to study hard first。 In the "two" in the process, some cadres of himself, standing long, high awareness, that Constitution Party rules is simple, its not worth bothering some party cadres think speak series has nothing to do with the grass-roots work, water business learning series of speeches seen as window dressing。
These "lazy, casual, and decadent" ideas learning lacks motivation, a serious impediment to "two" effect。 John Stuart Mill once said, only a basic element of human thought patterns change dramatically, human destiny can make great improvement。 The same, only party members and learning education, need three kinds of consciousness: one is to establish an integrated awareness。 "Learning" and "do" what car isTwo-wheel, bird wings, need to go hand in hand, one end can be neglected。 Communist theoretician and man。
only by closely combining theory and practice together in order to truly realize their value。 "Learning" is the Foundation, the Foundation is not strong, shaking; " "Is the key to net to net thousands of accounts。 "Two" education, "" lay the basis, going to "do" the key grip, so that the "learning" and "doing" back to standard, so that the majority of party members "learn" learning theory of nutrients, in the "doing" practice party's purposes。 Second, to establish a sense of depth。 "Learning" and "do" not Chu drawn, entirely different, but the organic unity of the whole。
"Two" learning education, we need to explore integrating "learning" in "do", exhibit "do" in "Science"。 To avoid the "learning" into simple room instruction, "do" into a monotone for doing。 Should exploration "learn" in the has "do", "do" in the has "learn" of education and practice of carrier, makes general grass-roots members can in "learn" in the has "do" of achievements sense, in "do" in the has "learn" of get sense, real makes party of theory brain into heart, put for people service concept outside of Yu shaped。
Third, to adhere to long-term the awareness。 Style construction on the road forever, "two" had to catch the long-term。 "Two" study and education, by no means, assault-style wind-sport, but the recurrent education within the party。 In recent years, the party's mass line education practice and "three-three" special education in grass-roots borne rich fruits, vast numbers of party members and cadres withstood the baptism of the spirit。 "Two" greater need to focus on longer hold long-term, to establish and perfect the effective mechanism of the education, focusing on the creation of long-term education, strive to make the vast number of party members to maintain their vanguard Color, maintain the party's advanced nature and purity。
Awareness-raising, antennas and atmosphere – a discussion on how leading cadres of party members "two" current, "two" activity is in full swing up and down the country, party cadres as a "key minority" is both a barometer and impetus。 The "two" meaning enough deep, is to determine the party cadres can resolve to study hard first。 In the "two" in the process, some cadres of himself, standing long, high awareness, that Constitution Party rules is simple, its not worth bothering some party cadres think speak series has nothing to do with the grass-roots work, water business learning series of speeches seen as window dressing。
These "lazy, casual, and decadent" ideas learning lacks motivation, a serious impediment to "two" effect。 John Stuart Mill once said, only a basic element of human thought patterns change dramatically, human destiny can make great improvement。 The same, only party members and Learn General Secretary on "two to learn a" strengthening "four Consciousnesses" important speech caused a strong reaction in the country。 Time, watching "red treasure", the origin of building the party back to power, how to strengthen services for the masses, improve party cohesion, fighting to become the grass-roots party members and masses hot topic。
Grass-roots party organizations "two" is to strengthen the service of party members and cadres, the pioneer spirit。 Distribution of grass-roots party organizations in all walks of people, clothing, shelter, which belongs to the nerve endings of the party organization and comments reputation has a direct perception of the masses。 Strengthen the party ahead of the "pedal" spirit; strengthen the party members and cadres "success does not have to be me" and "the first to bear hardships, the last to" service spirit to set the party's positive image among the people is important。
Grass-roots party organizations "two" is to cleanse all people not happy not to see "stereotypes", establish the honest faithful, diligent faith for the people。 No need to avoid mentioning that, some members of our party can not stand the "money," corrosion of temptation, thin, Xu Zhou, such abuse and corrupt bribery, malfeasance borers, and rats。 Two, is to clean up, thin, Xu, Zhou's solution to restore the party's fresh and natural, solid and honest work style。 Cleansing "take, eat, card," undesirable and behaviour, "cross, hard and cold, push" attitude。
Grass-roots party organizations "two" is to strengthen the sense of ordinary party members, participating in consciousness, unity consciousness。 For reasons known, members of grass-roots party branches less mobile, less resources, and the construction of party organizations have some lag。 Two studies, is to focus on the grass-roots party branches "loose, soft, loose" problem, advance the party members and cadres, "a gang working", "Hong Kong report。" Strong cleanup actions, style and rambling, presumptuous "unqualified" party members, pays special attention to party members and cadres "joining party of thought" problem。
"Party building" is obtained in the long-term development of our party's historical experience accumulated。 Two is our party under the new historical conditions, strengthen the party's construction of a new "rectification movement。" Grass-roots party organizations should always catch the hard work, results-oriented。 Two educational outcomes are long-term oriented and become an important impetus for the work。 "Two" should have three kinds of consciousness "two" study and education, basic learning lies in the doing。
only the Constitution address the series of party rules, and do solid work, be qualified party members had a solid ideological basis。 only the "learning" and "do" real unity, to form a "learn-learn-do-do" the virtuous cycle, and ultimately achieve the fundamental objective of education。 This requires that the Organization learning education, need three kinds of consciousness: one is to establish an integrated awareness。 "Learning" and "do" what car isTwo-wheel, bird wings, need to go hand in hand, one end can be neglected。
Communist theoretician and man。 only by closely combining theory and practice together in order to truly realize their value。 "Learning" is the Foundation, the Foundation is not strong, shaking; " "Is the key to net to net thousands of accounts。 "Two" education, "" lay the basis, going to "do" the key grip, so that the "learning" and "doing" back to standard, so that the majority of party members "learn" learning theory of nutrients, in the "doing" practice party's purposes。 Second, to establish a sense of depth。
"Learning" and "do" not Chu drawn, entirely different, but the organic unity of the whole。 "Two" learning education, we need to explore integrating "learning" in "do", exhibit "do" in "Science"。 To avoid the "learning" into simple room instruction, "do" into a monotone for doing。 Should exploration "learn" in the has "do", "do" in the has "learn" of education and practice of carrier, makes general grass-roots members can in "learn" in the has "do" of achievements sense, in "do" in the has "learn" of get sense, real makes party of theory brain into heart, put for people service concept outside of Yu shaped。
Third, to adhere to long-term the awareness。 Style construction on the road forever, "two" had to catch the long-term。 "Two" study and education, by no means, assault-style wind-sport, but the recurrent education within the party。 In recent years, the party's mass line education practice and "three-three" special education in grass-roots borne rich fruits, vast numbers of party members and cadres withstood the baptism of the spirit。 "Two" greater need to focus on longer hold long-term, to establish and perfect the effective mechanism of the education, focusing on the creation of long-term education, strive to make the vast number of party members to maintain their vanguard Color, maintain the party's advanced nature and purity。
Awareness-raising, antennas and atmosphere – a discussion on how leading cadres of party members "two" current, "two" activity is in full swing up and down the country, party cadres as a "key minority" is both a barometer and impetus。 The "two" meaning enough deep, is to determine the party cadres can resolve to study hard first。 In the "two" in the process, some cadres of himself, standing long, high awareness, that Constitution Party rules is simple, its not worth bothering some party cadres think speak series has nothing to do with the grass-roots work, water business learning series of speeches seen as window dressing。
These "lazy, casual, and decadent" ideas learning lacks motivation, a serious impediment to "two" effect。 John Stuart Mill once said, only a basic element of human thought patterns change dramatically, human destiny can make great improvement。 The same, only party members and D B A C 1 2 第4题图 A B C D 第6题图 x y 第7题图 O 第8题图 输入 平方答案第13题图 A B C O 第15题图 图1 图2 第16题图0 1 2 3 4 5 A B C D E F1 2 3 41 2 3 4书画 电脑35% 音乐 体育 人数（人） 电脑 体育 音乐 书画 兴趣小组 282420161284 图1 图2 图2 B C E D A MN 图1 土 口 木 A B C D OA P B C M D (P)E B C 图1 0(A) B C D E 6 12 18 24 x y 6 12 18图3 A N P B C M D E Q T 图20 1 2 3 4 5 人数（人） 电脑 体育 音乐 书画 兴趣小组 28 24 20 16 12 8 4 B C E D A MN F H 一 回 土 口 木 开始 土（土，土） 口（土，口） 木（土，木） 土（口，土） 口（口，口） 木（口，木） 土（木，土） 口（木，口） 木（木，木） 0(A) B C D E 6 12 18 24 x y 6 12 18F M G P
