2009年湖南省湘西州中考数学试题及参考答案

找家教、下试题，上易学网 http://www.estudy100.net 打造华南地区最好的家教、试题平台 所以原方程的解是：??x?3 ···························································································· 5分

y??1? 19．（本题6分）

证明：∵DE∥BC，∴DE∥FC，∴∠AED＝∠C ······························································ 3分

又∵EF∥AB，∴EF∥AD，∴∠A＝∠FEC ······························································· 5分 ∴△ADE∽△EFC ·································································································· 6分

20．（本题6分） 解：（1）总人数＝275?55%?500人 ······························································· 3分

（2）教师中专科学历的人数＝500?10%?50人 ··················································· 4分 作图： ···················································································································· 6分

人数300275250200150 100 50 0步行自行车 研究生 中师 私家车 专科 公交车 本科 其它 其它 学历结构 交通工具 21．（本题6分）

解（1）因为y的值随x的增大而减小，所以k＞0 ························································· 2分 （2）设A（x0，y0）

则由已知，应有｜x0y0｜＝6 ················································································ 4分 即｜k｜＝6 而k＞０

所以k＝6． ············································································································ 6分 22．（本题6分）

AC 解（1）如图，在Rt△ABC中，＝sin30° ··································································· 2分

BC ∴ BC＝

注：第(2)问虽然没明确指出专科人数为50，但只要作图准确就可得6分． 5＝10米 ···································································· 3分 ?sin3022 （2）收绳8秒后，绳子BC缩短了4米，只有6米， ··············································· 4分 这时，船到河岸的距离为6?5?36?25?11米． ·········································· 6分 23．（本题8分）

解：2000张80元的门票收入为2000×80＝160000元； ··················································· 2分 1800张200元的门票收入为1800×200＝360000元；··················································· 4分 1200000－160000－360000＝680000元， ······································································ 5分 故400元的门票至少要卖出：680000÷400＝1700张． 答：400元的门票最少要卖出1700张． ······································································ 8分

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找家教、下试题，上易学网 http://www.estudy100.net 打造华南地区最好的家教、试题平台 24．（本题10分）

解（1）图1中，∵AD＝DF，∠B＝45°，从而DF＝DB，∴AD＝DB， ∴AD∶AB＝1∶2 ·················································································· 2分 图2中，∵PM＝MN，∠B＝45°，从而PM＝MB，∴MN＝MB， ∴MN＝MB＝NC，

∴AP∶AB＝PQ∶BC＝MN∶BC＝1∶3 ···································································· 4分

12?1? （2）图1中，S１＝?a??a ····················································································· 6分

4?2?又PQ∶BC=AP∶AB=1∶3，

2?2?22??a2 ·∴PQ=·············································································· 8分 a，∴S２＝?a?3?39??从而S1+S2=?21182?12?2172??a?a 又S=a2?a 4936236??∴S1+S2＜S ····························································································································· 10分

25．（本题20分） 解（1）直线y?kx沿y轴向上平移3个单位后，过两点B，C

从而可设直线BC的方程为y?kx?3 ·················································································· 2分 令x?0，得C（0，3） ········································································································· 3分 又B（3，0）在直线上， ∴0?3k?3 ∴k??1 ································································································································· 5分 （2）由（1），直线BC的方程为y??x?3········································································ 7分 又抛物线y?x?bx?c过点B，C

2?b??4?c?3∴? ??c?39?3b?c?0??∴抛物线方程为y?x?4x?3 ·························································································· 10分 （3）由（2），令x?4x?3?0

22，x2?3 ·得x1?1·················································································································· 12分

即A（1，0），B（3，0），而C（0，3）

1（3-1）·3=3平方单位 ······························································· 15分 2 （4）由（2），D（2，?1），设对称轴与x轴交于点F，与BC交于E，可得E（2，1），

∴△ABC的面积S△ABC=连结AE．

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找家教、下试题，上易学网 http://www.estudy100.net 打造华南地区最好的家教、试题平台 ∵AF?FB?FE?1

∴AE⊥CE，且AE=2，CE=22 （或先作垂线AE⊥BC，再计算也可） 在Rt△AFP与Rt△AEC中， ∵∠ACE=∠APE（已知） ∴AFPFAE?CE 即1PF2=22 ∴PF?2 ··········································································· 18分 ∴点P的坐标为（2，2）或（2，?2） ···························· 20分 （x轴上、下方各一个） （注：只有一个点扣1分）

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