襄阳市襄州区2018-2019学年度上学期期末学业质量调研测试八年级数学试题(扫描版附答案)(8P版

襄州区2018—2019学年度上学期期末学业质量调研测试八年级

数 学 参 考 答 案

一、 选择题（每小题3分，共30分）

二、 填空题（每小题3分，共18分）

11. 34--ab ； 12. 2≠x ； 13.-4； 14. 50； 15.34°; 16.11. 三、解答题（共72分） 17.（每小题3分，共12分本） （1）因式分解

①解：原式=﹣3（x 2﹣2xy +y 2）………………1分

=﹣3（x ﹣y ）2；………………3分

②解：原式=[4（a +b ）+5（a-b ）][4（a+b ）﹣5（a-b ）]…………2分

=（9a-b ）（9b-a ）．………………3分

（2）化简：

①解：原式=a 2﹣2a +3a ﹣6﹣a 2+a ………………2分

=2a ﹣6．………………3分

②解：原式=4x 2﹣2xy ﹣4x 2+4xy ﹣y 2………………2分

=2xy ﹣y 2；………………3分

18. （本题6分）解：原式=

2

)3()

1(121--?---x x x x x ………………2分 =

2

)

3()

1(13--?--x x x x x ………………3分 =

3

-x x

………………4分 ∵03,01≠-≠-x x ，∴3,1≠≠x x ,

∴x 只能取2， ………………5分 把2=x 代入

3

-x x

=-2. ………………6分 19. （本题6分）

解：（1）四边形A ′B ′C ′D ′如图所示；………………2分

（2）BC AB S /四边形＝5×2﹣×2×2﹣×1×1﹣×1×3，…………4分

＝10﹣2﹣﹣，……………5分 ＝10﹣4＝6．………………6分

20.(本题6分）

解：（1）（a +b ）2﹣4ab =（a ﹣b ）2 ．…………3分 （2）由（1）得（x ﹣y ）2=（x +y ）2﹣4xy ．………4分

∵x +y =6，xy =5，∴（x ﹣y ）2=36﹣20=16，………………5分 ∴x ﹣y =±4．………………6分

21.（本题7分）

解：问题1：造桥选址．

如图，作点A 关于直线l 的对称点A ′，连接BA ′交直线l 于C ，连接AC ，

此时AC+BC 的值最小．…………2分

理由：两点之间线段最短．……………3分 问题2：测量河宽

如图2中，在Rt △CEE 和Rt △GFE 中，

，

∴△CDE ≌△GFE ，………………4分 ∴CD=FG=20米，………………5分 答：河道的宽度为20米．………………6分

22.（本题6分）解：（1）等式两边都乘以同一个整式，等式仍然成立；………………2分

（2）解法错误，………………3分

没有考虑x ﹣3≠0，即﹣m +6﹣3≠0，………………4分

解得：m ≠3，………………5分

所以正确的结果是m ＜6且m ≠3．………………6分

23.（本题8分）（没有检验，扣1分）

解：（1）设小王用自驾车方式上班平均每小时行驶x 千米，则：

x

x 27

739227?=+，………………2分

解得x =27………………3分

经检验x =27是原方程的解，且符合题意．∴x =27………………4分

答：小王用自驾车方式上班平均每小时行驶27千米；………………5分 （2）设步行速度是y 千米/时，依题意得：

3

492276276=+?-+y ………………6分 解得6=y ………………7分

经检验，y =6是所列方程的解，且符合题意． ∴6=y

答：他步行的速度是6千米/时．………………8分

24.(本题10分)

证明：（1）如图1，延长AC 交BN 于点F ，

∵AC =BC ，∴∠CAB =∠CBA ，………………1分 又∵AB ⊥AM ，∴∠BAM =90°， 又∵AM ∥BN ，∴∠BAM +∠ABN =180°， ∴∠ABN =90°，

∴∠BAF +∠AFB =90°，∠ABC +∠CBF =90°， ∴∠CBF =∠AFB ，………………2分 ∴BC =CF ，

∴AC =FC ，………………3分

又∵AM ∥BN ，∴∠DAF =∠AFB ， 在△ADC 和△FEC 中，

，

∴△ADC ≌△FEC （ASA ），………………4分

∴DC =EC ；………………5分

（2）AD +DC =BE

理由：如图2，在EB 上截取EH =EC ，连CH ，

∵AC =BC ，∠ABC =60°，∴△ABC 为等边三角形，……………6分 ∵∠DEB =60°，∴△CHE 是等边三角形，………………7分 ∴∠CHE =60°，∠HCE =60°，∴∠BHC =120°， ∵AM ∥BN ，∴∠ADC +∠BEC =180°， ∴∠ADC =120°，∴∠DAC +∠DCA =60°，

又∵∠DCA +∠ACB +∠BCH +∠HCE =180°， ∴∠DCA +∠BCH =60°，∴∠DAC =∠BCH ， 在△DAC 与△HCB 中，

，

∴△DAC ≌△HCB （AAS ），∴AD =CH ，DC =BH ，…………9分

又∵CH =CE =HE ，

∴BE =BH +HE =DC +AD ．………………10分

25.（本题11分）

解：（1）OE=5； …………2分

（2）如图，∵OE ＝OA ，OB ⊥AE ，

∴BA=BE,∴∠BAO ＝∠BEO ，…………3分

∵∠CEF ＝∠AEB ， ∴∠CEF ＝∠BAO ，

∴∠CEO ＝∠DAO …………4分 在△ADO 与△ECO 中，

∠CEO ＝∠DAO ，OA=OE,∠COE ＝∠AOD ∴△ADO ≌△ECO （ASA ）；…………5分

（2）设运动的时间为t 秒，当PO ＝QO 时，易证△OPM ≌△OQN.…………6分 （i ）当点P 、Q 分别在y 轴、x 轴上时PO ＝QO 得：

5﹣t ＝12﹣3t ，解得t ＝2

7（秒），…………7分

（ii ）当点P 、Q 都在y 轴上时PO ＝QO 得：

5﹣t ＝3t ﹣12，解得t ＝

417

（秒），…………8分 （iii ）当点P 在x 轴上，Q 在y 轴上时，

若二者都没有提前停止，则PO ＝QO 得：

t ﹣5＝3t ﹣12，解得t ＝2

7（秒）不合题意；………9分

当点Q 运动到点E 提前停止时，

有t ﹣5＝5，解得t ＝10（秒），…………10分

综上所述：当两动点运动时间为2

7

、

4

17

、10秒时，△OPM 与△OQN 全等.…………11分

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