21. 解决本题的关键是弄清楚极差=最大值-最小值；中位数为先排序后取中的原则；从图中
获得的信息可以从发展趋势，每年各类达到的数目，比例等去解答.
22．（本题8分）某商场为了吸引顾客，设计了一种促销活动：在一个不透明的箱子里放有4个相同的小球，球上分别标有“0元”、“10元”、“20元”和“30元”的字样．规定：顾客在本商场同一日内，每消费满200元，就可以在箱子里先后摸出两个球（第一次摸出后不放回）．商场根据两小球所标金额的和返还相应价格的购物券，可以重新在本商场消费．某顾客刚好消费200元．
（1）该顾客至少可得到 元购物券，至多可得到 元购物券；
（2）请你用画树状图或列表的方法，求出该顾客所获得购物券的金额不低于30元的概率． 全品中考网 全品中 考网
22. 本题主要考查概率知识.解决本题的关键是弄清题意，满200元可以摸两次，但摸出一个后不放回，概率在变化. 23．（本题8分）有一水库大坝的横截面是梯形ABCD，AD∥BC，EF为水库的水面，点E在DC上，某课题小组在老师的带领下想测量水的深度，他们测得背水坡AB的长为12米，迎水坡上DE的长为2米，?BAD?135°，?ADC?120°，求水深．（精确到0.1米，2?1.41，3?1.73）
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B （第23题） A D E F 水深 C 23. 本题主要考查三角函数及解直角三角形的有关知识.解决本题的关键是作出辅助线. 24．（本题8分）某批发市场批发甲、乙两种水果，根据以往经验和市场行情，预计夏季某一段时间内，甲种水果的销售利润y甲（万元）与进货量x（吨）近似满足函数关系
y甲?0.3x；乙种水果的销售利润y乙（万元）与进货量x（吨）近似满足函数关系y乙?ax?bx（其中a?0，a，b为常数），且进货量x为1吨时，销售利润y乙为1.4
2万元；进货量x为2吨时，销售利润y乙为2.6万元． （1）求y乙（万元）与x（吨）之间的函数关系式．
（2）如果市场准备进甲、乙两种水果共10吨，设乙种水果的进货量为t吨，请你写出这两种水果所获得的销售利润之和W（万元）与t（吨）之间的函数关系式．并求出
这两种水果各进多少吨时获得的销售利润之和最大，最大利润是多少？
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24. 解决本题的关键是从现实问题中抽象出函数模型，然后解答.特别要注意数量间的关系. 25．（本题12分）在△ABC中，AB?BC?2，?ABC?120°，将△ABC绕点B顺时针
旋转角?(0°???90°)得△A1BC1，A1B交AC于点E，A1C1分别交AC、BC于
D、F两点．
（1）如图1，观察并猜想，在旋转过程中，线段EA1与FC有怎样的数量关系？并证明你的结论；
D A1 C F C C1
A1 D E F C1
E B
（第25题 图1）
A A B
（第25题 图2）
（2）如图2，当??30°时，试判断四边形BC1DA的形状，并说明理由； （3）在（2）的情况下，求ED的长． 全品中考网 全品中 考网 25. 本题主要考查旋转、全等三角形、特殊平行四边形、解直角三角形等知识.解决本题的关
键是结合图形，大胆猜想.
26．（本题14分）如图，已知直线l1:y?23x?83与直线l2:y??2x?16相交于点C，l1、l2分别交x轴于A、B两点．矩形DEFG的顶点D、E分别在直线l1、l2上，顶点F、G都在x轴上，且点G与点B重合． （1）求△ABC的面积；
（2）求矩形DEFG的边DE与EF的长；
（3）若矩形DEFG从原点出发，沿x轴的反方向以每秒1个单位长度的速度平移，设移动时间为t(0≤t≤12)秒，矩形DEFG与△ABC重叠部分的面积为S，求yS关于l2 l1t的函数关系式，并写出相应的t的取值范围．
E D C
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A O （G）B x F （第26题）
26. 本题属于大综合题目，主要考查的知识点有一次函数、二次函数、方程组与平移、三角
形的面积、三角形的相似等知识点.解决本题的关键是理顺各知识点间的关系，还要善于分解，化整为零，各个击破.
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200年山西省初中毕业学业考试试卷
数 学
一、选择题（每小题2分，共20分）
1．＞ 2．7.393?1010 3．答案不唯一，如x2?1 4．3 5．30 6．210 7．（9，0） 8．8 9．?3?y?0 10．3n?2
二、选择题（在下列各小题中，均给出四个备选答案，其中只有一个正确答案，请将正确答案的字母号填入下表相应的空格内，每小题3分，共24分） 题 号 答 案
11 D
12 C
13 D
14 D
15 B
16 A
17 A
18 B
三、解答题（本题共76分）
19．（1）解：原式=x2?6x?9??x2?3x?2? ···································································（2分） =x2?6x?9?x2?3x?2 ·······································································（3分） =9x?7． ·······························································································（4分） （2）解：原式=
x?x?2??2x?2?x?2??x?2?xx?2?2x?2 ············································································（2分）
= ··························································································（3分）
=1． ··········································································································（4分）
2（3）解：移项，得x?2x?3，配方，得?x?1??4， ·····················································（2分）
2 ∴x?1??2，∴x1??1，x2?3． ···································································（4分） （注：此题还可用公式法，分解因式法求解，请参照给分）
20．解：（1）π?2； ··········································································································（2分）
（2）答案不唯一，以下提供三种图案．
（第20题 图2） ········································ （6分）
（注：如果花边图案中四个图案均与基本图案相同，则本小题只给2分；未画满四个“田”字格的，每缺1个扣1分．）
21．（1）935.7，859.0； ·······································································································（4分） （2）解：①2004~2008移动电话年末用户逐年递增．
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②2008年末固定电话用户达803.0万户．························································（8分） （注：答案不唯一，只要符合数据特征即可得分）
22．解：（1）10，50；·········································································································（2分） （2）解：解法一（树状图）：
第一次 第二次 10 和
10
0 20 30 0
10 20
30 0 40 20
20 10 30 0 30 50 30
30 10 40
20 50
20 30 10 30
·····································································································································（6分）
从上图可以看出，共有12种可能结果，其中大于或等于30元共有8种可能结果，因此P（不低于30元）=解法二（列表法）：
第一次
第二次
0
10 20
0 10 20
10 10 30
20 20 30 812?23 ·········································································（8分） ．30 30 40 50 30 30 40 50 ·····························································································································（6分） （以下过程同“解法一”） ·····················································································（8分）
23．解：分别过A、D作AM?BC于M，DG?BC于G．过E作
EH?DG于H，则四边形AMGD为矩形．
A D E H F 水深 ?AD∥BC,?BAD?135°，?ADC?120°．∴?B?45°，?DCG?60°，?GDC?30°．
·sinB?12?在Rt△ABM中，AM?AB22?62．
B G M （第23题）
C ∴DG?62． ··············································································································（3分）
32·cos?EDH?2?在Rt△DHE中，DH?DE?3． ············································（6分）
∴HG?DG?DH?62-3≈6?1.41?1.73≈6.7． ··············································（7分） 答：水深约为6.7米． ··································································································（8分） （其它解法可参照给分）
?a?b?1.4，?a??0.1，?b?1.5．24．解：（1）由题意，得：??4a?2b?2.6．解得? ················································（2分）
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∴y乙??0.1x2?1.5x．······················································································（3分）
（2）W?y甲?y乙?0.3?10?t????0.1t2?1.5t?．
∴W??0.1t2?1.2t?3． ···················································································（5分） W??0.1?t??62?∴·····························（7分） 6．.6t?6时，W有最大值为6.6. ·
∴10?6?4（吨）.
答：甲、乙两种水果的进货量分别为4吨和6吨时，获得的销售利润之和最大，最大利润是6.6万元. ······················································································（8分）
25．解：（1）EA1?FC． ·····································································································（1分）
??A??C．证明：（证法一）?AB?BC，
由旋转可知，AB?BC1，?A??C1，?ABE??C1BF，
∴△ABE≌△C1BF． ····························································（3分） ∴BE?BF，又?BA1?BC，
∴BA1?BE?BC?BF．即EA1?FC．····································（4分）
??A??C．（证法二）?AB?BC，
由旋转可知，?A1??C，A1B=CB，而?EBC??FBA1，
∴△A1BF≌△CBE．·····························································（3分） ∴BE?BF，∴BA1?BE?BC?BF，
即EA1?FC． ··········································································（4分）
（2）四边形BC1DA是菱形. ·················································································（5分）
?A1C1∥AB，证明：??A1??ABA1?30°，同理AC∥BC1．
∴四边形BC1DA是平行四边形. ··························································（7分） 又?AB?BC1，∴四边形BC1DA是菱形. ············································（8分）
（3）（解法一）过点E作EG?AB于点G，则AG?BG?1．
在Rt△AEG中，
AE?AGcosA?1cos30°?233．??（10分）
A1 C D E G
B
F C1
A - 10 -
2009年山西省中考数学试题（含答案及详细解析）
