昌平区2008—2009学年第二学期初三年级第二次统一练习
数学试卷答案及评分参考 2009.6
一、选择题（共8道小题，每小题4分，共32分） 题号 答案 1 B 2 C 3 D 4 C 5 A 6 C 7 B 8 B
二、填空题（共4道小题，每小题4分，共16分） 题号 答案 9 10 611 1 12 2.4?10 线段、等腰三角形等 1 3三、解答题（共5道小题，每小题5分，共25分）
?1?13．解：12????cos45????3?
?3??23?3?2·············································································································· 4分 ?3 ·
2?1?23?2． ······················································································································· 5分 2214．解：ax?4ax?4a
=a(x2?4x?4) ······················································································································ 2分 =a(x?2)2． ··························································································································· 5分 15．解：=
2x1? x2?1x?12xx?1······························································································ 2分 ?(x?1)(x?1)?x?1??x?1?2x?(x?1) ························································································································ 3分
(x?1)(x?1)x?1 ························································································································ 4分
(x?1)(x?1)1．·································································································································· 5分 x?1=
=
=
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16．证明：∵同弧所对的圆周角相等，
??A??C,?D??B． ???????????????????????2分
在△ADE和△CBE中，
??A??C，?···························································································································· 3分 ?AD?CB，??D??B,??△ADE≌△CBE． ··········································································································· 4分 ?AE?CE． ························································································································ 5分
217．解：x?x?1??x?y??2
??x2?x?x2?y2??2，???????????????????????1分
x?y?2． ······································································································ 2分
x2?y2?xy ∴
2x2?y2?2xy= ······················································································································ 3分
2(x?y)2= ······························································································································· 4分
2?2． ······································································································································ 5分
四、解答题（共2道小题，每小题5分，共10分） 18．（1）证明：如图，连接OC． ∵PC切半?O于点C，
C??PCO?90?．???????1分 D∵AB?2PA，
P?PA?OA?OB?OC．
AOBOC1?． ·在Rt△PCO中，sin?P?·············································································· 2分 OP2（2）过点O作OD?BC于点D，则BC?2BD．·························································· 3分
1?sin?P?，
2??P?30?， ??POC?60?． ∵OC?OB，
??B??OCB?30?． 在Rt△OBD中，OB?2，
································································································ 4分 ?BD?OB?cos30??3． ·
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······················································································································ 5分 ?BC?23． ·
19．解：（1）由题意，得0.5?∴a?a 33， 2333∴y?2?(t?). ············································································································ 1分
t2t23当y?1时，t?，
23?A(,1).
2设OA的解析式为y?kt. ∴1?k?∴k?3， 22， 323t(0?t?). ··················································································· 2分 32∴OA的解析式为y?注：不写自变量的取值范围不扣分.
（2）当t?0.25时，
0.25?23t1，即t1?. ··········································································································· 3分 3830.25?2，即t2?6. ············································································································· 4分
t2答：从这次药物释放开始，在小时?t?6小时内，学生在教室有危害. ····················· 5分
五、解答题（本题满分6分） 20．解：（1）图1中，实心球（男）所占的百分比为37.5%，统计表中填80． ··············· 2分 （2）27?． ···························································································································· 3分 （3）耐久跑的平均数是9，图略． ······················································································· 4分 （4）只要符合以上数据所反映的现象，且积极健康即可得分． ········································ 6分 六、解答题（共2道小题，21题5分，22题4分，共9分）
21．解：设招聘室内员工x人，则招聘室外员工(150?x)人． ········································· 1分 依题意，得150?x?2x． ···································································································· 2分 解之得x?50． ······················································································································ 3分 因为室内、室外两种员工每月的保底工资分别为600元和1000元， ?x?50时，此家政公司每月付的保底工资最少，
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38
所以，此家政公司每月付的保底工资为600?50?1000(150?50)?130000． ··············· 4分 答：此家政公司每月付的保底工资最少为130000元． ······················································· 5分
25． ······································································································ 2分 2（2）答案不唯一，两个图形面积均为12给1分，关于点O对称给1分． ······················· 4分
22．解：（1）1;七、解答题（本题满分7分）
23．解：（1）3.5. ·················································································································· 2分 （2）由题意，得2x2?1?(0.5?x)?0． ············································································ 4分
整理，得4x?2x?1?0， 解之，得x?2?1?5 ． ························································································· 5分 4∴当x?x0.5?x?1?5?1?5或x?时，?0．
12x44（3）x?8,y?2．????????????????????????????7分 八、解答题（本题满分7分）
24．解：（1）在图1中，∵直线AC交x轴于点C，
0)． ·∴点C?2,0?，即D(2，································································································ 1分
y过点B作BE?x轴于点E.
∵?OBD是等腰直角三角形，直角顶点为B， BA?OB?BD,?BDE?45?， 1?OE?ED?BE?OC?1,
2oEC(D)x 图1 ∴B(1,1)． ····························································································································· 2分 （2）∵直线AC交y轴于点A，
y23)． ∴A(0,3在图2中，过点O作OF?AC于点F. 在Rt△AOC中， tan?ACO?AFB'oCDxAO3?， OC3??ACO?30?， 图2 请点击查看更多内容：www.xuetongedu.com 第 9 页 共 12 页
??FOC?60?,OF?1．
在Rt△B?OD中，利用勾股定理，得OB??2， 在Rt△OB?F中， cos?B?OF?OF2， ?OB?2??B?OF?45?．
??B?OD?45?， ??DOF?90?，
??COD???30?． ·········································································································· 4分
（3）?抛物线y?mx2?3x过点B(1,1)，
?m??2，
················································································· 5分 ?抛物线的解析式为y??2x2?3x． ·设点B??a,b?，则a2?b2?(2)2?2． 又点B??a,b?在直线AC上，
?b??323， a?333232a?)?2， 33?a2?(??a?1?3（负值不符合题意，舍）， 23?1． ······················································································································· 6分 21?32代入抛物线的解析式y??2x?3x中， 2?b?将a?1?321?3??2?()?3?22
3?1?2?b.
∴点B?在过点B的抛物线y??2x?3x上． ····································································· 7分 九、解答题（本题满分8分）
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