成都外国语学校英语中考试试卷及答案
A
D
成都外国语学校2012—2013学年度下期期中考试
初一数学试卷
注意事项：
1、本试卷分第Ⅰ卷（选择题）和第Ⅱ（非选择题）两部分。
2、本堂考试120分钟，满分150分；
3、答题前，考试务必先将自己的姓名、学号填写在答题卡上，并用2B 铅笔填涂。
4、考试结束后，将答题卡交回。
A 卷（满分100分）
一、选择题（本大题共10小题，每小题3分，共30分）
每小题只有一个正确答案，请将正确答案的番号正确填涂在答题卡对应的位置上。 1．下列运算中，正确的是（ ）
A 、077=-ba ab
B 、3253
3-=+-x x C 、xy y x 532=+ D 、0)4(42
2
2
=-+y x y x
2．计算：(
)()2
3
224x
x -?-的结果是（ ）
A 、7
40x B 、740x - C 、7400x D 、7
256x - 3.下列多项式中不能用平方差公式计算的是（ ）
A 、()()22x y x y --+
B 、()()33
3
3m n m
n -+ C 、()()x y x y --- D 、()()2222a b b a -+
4．如果多项式2
9x mx -+是一个完全平方式，则m 的值为（ ）
A 、3±
B 、3
C 、6±
D 、6 5．一个角的余角是它补角的
1
3
，则这个角的度数为（ ） A 、60° B 、45° C 、30° D 、90°
6．小明要画一个有两边长分别为5cm 和11cm 的等腰三角形，则这个等腰三角形的周长是（ ） A 、21cm B 、27cm C 、21cm 和27cm D 、16cm
7．下列条件中，可得两直线互相垂直的是（ ）
① 对顶角的平分线； ② 邻补角的平分线； ③ 平行线中同位角的平分线； ④ 平行线中内错角的平分线； ⑤ 平行线中同旁内角的平分线
A 、①②
B 、③④
C 、①⑤
D 、②⑤
8．如图，已知△ABC ≌△DEF ，且AB ＝4，BC ＝5，AC ＝6，则DF 的长为（ ） A 、6 B 、5 C 、4 D 、不能确定 （8题图） 9．下列条件：①∠A ＋∠B ＝∠C ；②∠A ︰∠B ︰∠C ＝1︰2︰3；③90A B ∠=?-∠；④1
2
A B C ∠=∠=
∠；
⑤23A B C ∠=∠=∠，其中能确定△ABC 是直角三角形的条件有（ ） A 、2个 B 、3个 C 、4个 D 、5个 10．如图“直线AB ∥CD ，两相交直线EF 、GH 与AB 、CD 都相交，
则图中同旁内角共有（ ）对。
A 、4
B 、10
C 、12
D 、16
（10题图） 二、填空题（本大题共10小题，每小题2分，共16分）
A
11．计算：2
3(21)m m m ---+＝ 。 12．2013
2014
4433-??
??? ?
???
??
＝ 。
13．已知3=+b a ，1=ab ，则2
2b a +＝ 。
14．如图，锐角ΔABC 的角平分线交于三角形内一点O ，若∠BAC=50°，则∠BOC ＝ 。15．设c b a 、、是ΔABC 的三边，则||||a b c a b c ++---＝ 。
16．若代数式235x x ++的值为7，则代数式2
392x x +-的值是 。 （14题图）
17．已知∠α的两边与∠β的两边互相平行，若∠α＝50°，则∠β＝ 。
18．若0361212=+-
x x ，则x
12
=__________。
三、解答题：（本大题共54分） 19．计算（每小题5分，共20分）：
⑴ 2
201373-??
---+ ???
； ⑵ 33(2)(2)22x y x y +--+；
⑶22
11322x y xy xy xy ????
-+÷- ? ??
???
； ⑷ 22(32)(32)(32)(32)x y x y x y x y +--++- ；
20．解方程：()()()2
12215x x x +--+= （5分）
21．若多项式2
2x px ++和多项式2
2x x q -+相乘的积中不含3
x 和x 项，求p q +的值。（5分）
22．已知如图，AB ＝AD ，AC ＝AE ，∠BAD ＝∠CAE 。 求证：BC ＝DE 。 （8分）
（22题图）
23．如图，AD 、AE 分别是△ABC 的角平分线和高，且∠B ＝46°、∠C ＝84°，
求∠EAD 的度数。（8分）
（23题图）
12
A'
B
E
D
A 4E A 3A 2A 1
C
D
A n 24．如图，把△ABC 纸片沿DE 折叠，点A 落在四边形BCDE 的内部。 （8分） ⑴写出图中一对全等的三角形，并写出它们的所有对应角；（2分）
⑵设∠AED 的度数为x ，∠ADE 的度数为y ，那么∠1，∠2的度数分是多少？（2分） （用含有x 或y 的代数式表示） ⑶∠A 与∠1＋∠2之间有一种数量关系始终保持不变，请找出这个规律，并证明。（4分）
B 卷（满分50分）
一、填空题（每小题4分，共24分）
25．若2
2
9)12(4y xy m x +--是一个完全平方式，则m ＝__________。
26．三角形的两边分别为9和4，且周长为偶数，则第三边的长可能是 。 27．已知0101162
2
2
2
=++++xy y x y x ，则
11
_____x y
+=。 28．若△ABC 的三边长分别为a b c 、、，且a b c 、、满足等式(
)()2
222
3a b c a b c ++=++，则该三角
形是 三角形。
29．如下图，在△1ABA 中∠B ＝20°，1AB A B =，在1A B 上取一点C ，延长1AA 到2A ，使得12A A ＝1A C ；在2A C 上取一点D ，延长12A A 到3A ，使得232A A A D =；……，按此做法进行下去，∠n A 的度数为 。 30．如下图，在3×3的正方形网格中标出了∠1和∠2，则∠1＋∠2＝ 。
（5题图） （6题图）
二、解答题（本大题共26分，其中31、32题各8分，33题10分）
31．（8分）如图，AB=AD ，BC=DE ，∠1=∠2。求证：（1）AC=AE ；（2）∠CAE=∠CDE 。
④
③
③④③
④④③B B B B 32．（8分）已知：a b 、满足(
)()2
2
521842a b b ---÷=，()()9327b
a
a b =÷。
⑴ 求2
2
a b +的值；
⑵ 根据前面计算的结果，请计算下式的值：
()()()()()()()()
111220102011ab ab ab ab
a b a b a b a b a b a b a b a b +++++-++++++++++++L L
33．（10分）如图，直线AC ∥BD ，连结AB ，直线AC 、BD 及线段AB 把平面分成①②③④四个部分，规定：线上各点不属于任何部分。当动点P 落在某个部分时，连结PA 、PB ，构成与∠PAC 、∠APB 、 ∠PBD 三个角。（提示：有公共端点的两条重合的射线所组成的角是0°角。） ⑴ 当动点P 落在第①部分时，判断∠APB 、∠PAC 、∠PBD 的关系，并证明；（3分）
⑵ 当动点P 落在第②部分时，⑴中结论还是否成立？若成立请证明。若不成立，请写出正确的结论。（不需证明） （3分）
⑶ 当动点P 在第③部分时，请全面探究∠PAC 、∠APB 、∠PBD 之间的关系，并写出动点P 的具体位置和相应结论。并选择其一种结论加以证明。 （4分）
2
2013739913172-??---+ ???=--+=-L L L L L L L 分分
2
22233(2)(2)22
323294624x y x y x y x y y +--+??=-- ???=-+-L L L L L L L L 分分22
11322621x y xy xy xy x y ????-+÷- ? ?????=-+-()()
22
22222222222222
(32)(32)(32)(32)949124912439491249124192441x y x y x y x y x y x xy y x xy y x y x xy y x xy y x xy y +--++-=--+++-+=----+-+=--L L L L L 分分分成都外国语学校2012—2013学年度下期期中考试 初一数学试题参考答案及评分标准（仅作参考）
一、选择题
1、A
2、D
3、A
4、C
5、B
6、B
7、D
8、A
9、C 10、B
二、填空题
11）3
2
363m m m +- 12）
3
4
13）7 14）115° 15）2a 16）4 17）50°或130° 18）2
三、解答题：（本大题共54分） 19．计算（每小题5分，共20分）： ⑴ ⑵
⑶ ⑷
20．解：22
21415x x x ++-+= …………2分
210x = …………2分
5x = …………1分
21．解：∵()()()()()22
4322
222242x px x
x q x p x p q x pq x q ++-+=+-+-+++-+……2分
又∵不含3
x 和x 项
∴20
40p pq -=??-=?
解得：22p q ==、 …………2分
∴ 4p q += …………1分 22．证明：∵∠BAD ＝∠CAE
∴∠BAD ＋∠BAE ＝∠CAE ＋∠BAE ，即∠DAE ＝∠BAC …………3分
在△ADE 和△ABC 中 AD AB
DAE BAC AE AC =??
∠=∠??=?
∴△ADE ≌△ABC …………4分
∴BC ＝DE ………… 1分
23．解： 在△ABC 中，∵∠B ＝46°、∠C ＝84°
∴()180468450BAC ∠=?-?+?=? ………………2分 ∵AD 平分∠BAC ∴1
252
BAD BAC ∠=
∠=?…………2分 ∴∠ADE ＝∠BAD ＋∠B ＝46°＋25°＝71° …………2分 ∵AE ⊥BC ∴∠AED ＝90° ………………1分 在Rt △AED 中，∠EAD ＝90°－71°＝19° ………………1分
24．解：⑴△AED ≌'A ED ；∠AED ＝∠'A ED 、∠EDA ＝∠'EDA 、∠A ＝∠'A 。（2分）
⑵ 11802x ∠=-，21802y ∠=- （2分） ⑶ ()1
122
A ∠=
∠+∠ （2分） 理由如下： ∵11802x ∠=-，21802y ∠=-
∴()1
180122
x y +=?-
∠+∠ ………… 1分 ∴∠A ＝180°－（x y +）＝()1
122
∠+∠ ………… 1分
B 卷（满分50分）
一、填空题（每小题4分，共24分）
25．131122-或。 26．7或9或11。 27．0。 28．等边。 29．1
1802n -???? ?
??
。 30．45°。
二、解答题（本大题共26分，其中31、32题各8分，33题10分） 31．证明：⑴∵∠ADC 是△ABD 的外角
∴∠ADC ＝∠B ＋∠1
∵∠1＝∠2 ∴∠ADE ＝∠B …………2分
在△ABC 和△ADE 中 AB AD B ADE BC DE =??
∠=∠??=?
∴△ABC ≌△ADE ∴ AC=AE ………………2分
⑵ ∵△ABC ≌△ADE ∴∠C ＝∠E …………1分
∵∠CAE ＝180°－∠E －∠3，∠CDE ＝180°－∠C －∠4 …………2分 ∴∠CAE ＝∠CDE ………………1分
B 32．解：由题意可得：2a b +=、3ab =- ………………3分 ⑴ ()()2
2
2
2
222310a b a b ab +=+-=-?-= …………1分
⑵ 原式＝1111111120102011ab a b a b a b a b a b a b ??
?-+-+-
?+-++++++++??
L ……2分
＝()()
1120121201112011ab ab a b a b a b a b ??
?-=
?
+-+++-++?? ………… 1分 ＝2012
671
-
…………1分
33．⑴关系是：∠APB ＝∠PAC ＋∠PBD …………1分
证明如下：过点P 作PF ∥AC 。∵AC ∥BD ∴PF ∥BD ∥AC
∴∠APF ＝∠PAC 、∠PBD ＝∠FPB …………1分
∴∠APB ＝∠APF ＋∠FPB ＝∠PAC ＋∠PBD …………1分
⑵当动点P 落在第②部分时，∠APB ＝∠PAC ＋∠PBD 不成立。 ……1分
正确的结论是：∠APB ＝360°－（∠PAC ＋∠PBD ）或∠APB ＋∠PAC ＋∠PBD ＝360°……2分
⑶ 根据学生答题情况酌情给分
情况①，当P 在如图①的位置时，有∠APB ＝∠PAC －∠PBD
证明如下：∵AC ∥BD ∴∠1＝∠PBD
∵∠PAC 是△PAE 的外角， ∴∠PAC ＝∠APB ＋∠1 即∠APB ＝∠PAC －∠PBD
图①
情况②，当P 在如图②的位置时，有∠APB ＝∠PBD －∠PAC
证明如下：∵AC ∥BD ∴∠2＝∠PBD
∵∠PFC 是△PAF 的外角， ∴∠PFC ＝∠APB ＋∠PAC 即∠APB ＝∠PBD －∠PAC
图②
成都外国语学校初七年级上学期期末考试英语试题
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