?x24?11x?21．（6分）先化简，再求值：?，其中． ???24?x?2x?2?x?2x
22．（6分）如图，一次函数y?kx?b(k?0)的图象与反比例函数y?相交于A、B两点．
（1）根据图象，分别写出点A、B的坐标； （2）求出这两个函数的解析式．
mx(m?0)的图象
y B 1 A O 1 x 16 / 28
参考答案
一、1．A 2．C 3．B 4．C 5．D 6．B 7．C 8．B 9．B *10．A
x?3 13．28° x1?4，x2??4 12．二、11．甲、由、中、田、日等 14．95 15．
*16．(n?3)?n?3?(2n?3)
三、17．解：原式=1?9?4?2 ···························································································· 4分
=?2． ······································································································· 6分
18．解：2x≥x+1，解得x≥1. ························································································ 2分
x?8≥4x-1，解得x≤3． ··············································································· 4分 ∴原不等式组的解集为1≤x≤3． ····································································· 5分 不等式组的解集在数轴上表示如下：
······················································ 6分 -1 0 1 2 3 4
19．解：图略．
（1）正确作出?AOB的角平分线OP． ········································································· 3分 （2）正确作出CD的垂直平分线EF． ··········································································· 6分 20．解：（1）360°?45%?162°； ····················································································· 2分 （2）40?30%?12；图略． ······························································································· 4分 （3）40?12?18?6?4，?100%?10%． ··································································· 6分
40422四、21．解：原式=
x?4x?212?1x?2x2 ···················································································· 2分
=
(x?2)(x?2)x?21x?x(x?2) ······························································································· 6分
= ····································································································································· 8分
14当x?时，原式=
114?4． ·························································································· 10分
22．解：（1）解：由图象知，点A的坐标为(?6，?1)，
点B的坐标为（3，2） ···································································································· 4分 （2）∵反比例函数y?∴2?m3mx的图象经过点B，
，即m?6．
6x∴所求的反比例函数解析式为y?． ·········································································· 6分
∵一次函数y?kx?b的图象经过A、B两点，
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∴???1??6k?b?2?3k?b ·············································································································· 7分
1??k?解这个方程组，得?······························································································ 9分 3 ·
?b?1?∴所求的一次函数解析式为y?
13x?1． ···································································· 10分
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2011年中考数学复习高分冲刺经典习题 (4)
一、填空题：请将答案填写在答题卷中的横线上，本大题共10小题；每小题4分，共40分．
A B1．分解因式：a2＋2a＝ _．
2．如图，在□ABCD中，∠A＝120°，则∠D＝_ °．
DC3．在钦州保税港区的建设中，建设者们发扬愚公移山、精卫填海的精神，每天吹沙填海造地约40亩．据统计，最多一天吹填的土石方达316700方，这个数字用科学计数法表示为_ _方（保留三个有效数字）．
4．如图中物体的一个视图（a）的名称为 ．
5．在不透明的袋子中装有4个红球和7个黄球，每个球除颜色外都相同，从中任意摸出一个球，摸到_ _球的可能性大． 6．钟表分针的运动可看作是一种旋转现象，一只标准时钟的分针匀速旋转，经过15分钟旋转了_ _度．
7．一次函数的图象过点（0，2），且函数y的值随自变量x的增大而增大，请写出一个符合条件的函数解析式：_ _． 8．如图是反比例函数y＝
kx 从正面看 （a） BCy在第二象限内的图象，若图中的矩形OABC
AO的面积为2，则k＝_ _．
9．如图，PA、PB分别与⊙O相切于点A、B，⊙O的切线EF分别交
xPA、PB于点E、F，切点C在⊙O上，若PA长为2，则△PEF的周长是_ _．
10．一组按一定规律排列的式子：－a，
2ECA??POFBa52，－
a83，
a114，…，（a≠0）则第n个式子是
____ （n为正整数）．
二、选择题：本大题共8小题；每小题4分，共32分．在每小题给出的四个选项中，只有
一项是正确的，请将正确答案前的字母填入答题卷中选择题答题卡对应的空格内．每小题选对得3分，选错，不选或多选均得零分． 11．实数1的倒数是（ ） A．0
32B．1
22C．－1
12D．±1
3312．sin30°的值为（ ） A．
B．
C．
D．
13．某校计划修建一座既是中心对称图形又是轴对称图形的花坛，从学生中征集到的设计方
案有等腰三角形、正三角形、等腰梯形、菱形等四种方案，你认为符合条件的是（ ）
A．等腰三角形 A．（－2，－1）
B．正三角形 B．（2，1）
C．等腰梯形 C．（2，－1）
D．菱形 D．（－2，1）
AO14．点P（－2，1）关于 y轴对称的点的坐标为（ ）
15．如图，在等腰梯形ABCD中，AB＝DC，AC、BD交于点O，则图中全等三角形共有（ ）
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DBC
A．2对 C．4对 A．y＝2x2＋3 C．y＝2（x＋3） A．AB垂直平分CD C．AB与CD互相垂直平分
2
B．3对 D．5对 B．y＝2x2－3 D．y＝2（x－3）
B．CD垂直平分AB D．CD平分∠ACB
2
16．将抛物线y＝2x2向上平移3个单位得到的抛物线的解析式是（ ）
C17．如图，AC＝AD，BC＝BD，则有（ ）
ABD18．如图，有一长为4cm，宽为3cm的长方形木板在桌面上做无滑动的翻滚（顺时针方向），
木板上的顶点A的位置变化为A→A1→A2，其中第二次翻滚被桌面上一小木块挡住，使木板边沿A2C与桌面成30°角，则点A翻滚到A2位置时，共走过的路径长为（ ）
A．10cm C．4.5πcm
B．3.5πcm D．2.5πcm
BC AA1A2三、解答题：本大题3题，共28分．解答应写出文字说明或演算步骤． 19．（本题满分8分，每小题4分）
（1）解不等式：x－1＜0，并把它的解集在数轴上表示出来； （2）解方程：
32x?11＝1．
20．（本题满分10分，每小题5分）
（1）当b?0时，比较1＋b与1的大小；
a??3a?（2）先化简，再求值：???a?1a?1?·a?1a2，其中a＝7＋1（精确到0.01）．
21．（本题满分10分，每小题5分）
（1）已知：如图1，在矩形ABCD中，AF＝BE．求证：DE＝CF； （2）已知：如图2，⊙O1与坐标轴交于A（1，0）、B（5，0）两点，点O1的纵坐标为5．求⊙O1的半径．
y F E A B
O1O
A B xBD OA C 图2 图1
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