镇江市2008年初中毕业升学考试数学试卷参考答案及评分标准
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27．（1） 1 ··································································（1 分，填 sin 30o 也得分）； 2
即点 Q 落在直线 y = x − 3 上的概率为 1 ． ·····················································（6 分） 3
21．（1）画角平分线，线段的垂直平分线． ························（3 分，仅画出 1 条得 2 分）
19．（1） x(x − 2) = 0 ．·············································································（3 分）
x1 = 0 ， x2 = 2 ． ··················································································（5 分）
（也可设 y = a(x −1)2 + k ）
（2） y = x2 − 2x − 3 = (x −1)2 − 4 ． ···························································（4 分）
函数的顶点坐标为 (1，− 4) ． ····································································（5 分）
24．（1） A(−4，0) ， B(0，2) ，
在 Rt△AOB 中， AB = OA2 + OB2 = 42 + 22 = 2 5 ．···························（2 分）
（2）由 ADH + DAH = 90o ， BAO + DAH = 90o ，
BAO = ADH ，又Q AOB = DHA = 90o ，
2
2
3 又 OC = 1，sin COB = CH = 2 = 3 ．
OC 1 2
COB = 60o，·····················································································（5 分）
BAC = 30o．
20．（1）用列表或画树状图的方法求点 Q 的坐标有 (1，−1) ， (1，− 2) ， (1，− 3) ， (2，−1) ，
(2，− 2) ， (2，− 3) ． ··························（4 分，列表或树状图正确得 2 分，点坐标 2 分）
（2）“点 Q 落在直线 y = x − 3 上”记为事件 A ，所以 P( A) = 2 = 1 ， 63
（3）5····································································································（6 分）
23．设该厂原来每天生产 x 顶帐篷，根据题意得： ··········································（1 分）
4 2 25
DH = 2 ， AH =1．
D(−5，2) ．···························································································（6 分）
25．（1）设反比例函数为 y = k (k 0) ．······················································（1 分） x
则 k = xy = mn = S矩形OATB = 10000 ， ···························································（2 分） y = 10000 ．························································································（3 分）
ቤተ መጻሕፍቲ ባይዱ
（2）原式 =
4
+ 1 ·······························································（1 分）
(x + 2)(x − 2) x + 2
=
4
+
x−2
·································································（2 分）
镇江市 2008 年初中毕业升学考试数学试卷
参考答案及评分标准
一、填空题：
1．3，3
2．1，6
3． 2a2 ， a
4． x2 + x − 2 ， (x +1)(x −1)
5． x = 1， x ≥ 2 6．3，3 7．65，35
8．4，12
9．1，1
10．45，2 11． 4
12． A
二、填空题：
13．B
（3）Q mn = 10000 ，在 Rt△TAO 中，TO = OA2 + AT 2 = m2 + n2
= (m − n)2 + 2mn = t2 + 20000 ． ···························································（6 分） 当 t = 0 时，TO 最小， 此时 m = n ，又 mn = 10000 ， m 0 ， n 0 ， m = n = 100 ，且10 100 1000 ． T (100，100) ．·······················································································（7 分）
26．（1）Q OC = OE ，E = OCE ·······················································（1 分） 又 OCE = DCE ，E = DCE ． OE ∥CD ． ························································································（2 分） 又 CD ⊥ AB ，AOE = BOE = 90o ．
作 OP ⊥ AC 于 P ，则 OP = 1 OA = 1 ． ······················································（6 分） 22
②3 ········································································································（7 分）
（2）由①，得 x 4 ； ··············································································（2 分） 由②，得 x ≥1 ． ·····················································································（4 分） 原不等式组的解集为1≤ x 4 ．······························································（5 分）
经检验： x = 1000 是原方程的根，且符合题意． ············································（5 分）
答：该厂原来每天生产 1000 顶帐篷． ···························································（6 分）
把点
(2，−
3)
，
(−1，0)
代入得
4a + 2b − 3 = a − b − 3 = 0.
−3，
··············································（2
分）
解方程组得
a b
= =
1， −2.
y = x2 − 2x − 3．····················································（3 分）
12000 x
−
12000 3x
=
4
．
···············································································（3
分）
2
解方程得： x = 1000 ．··············································································（4 分）
(x + 2)(x − 2) (x + 2)(x − 2)
=
x+2
·······················································································（4 分）
(x + 2)(x − 2)
= 1 ．·······························································································（5 分） x−2
（2） △BOE ≌△BOF ≌△DOF ·············（4 分，只要 1 对即可），证明全等．（6 分）
22．（1）设 y = ax2 + bx − 3 ， ····································································（1 分）
x （2）设鲜花方阵的长为 m 米，则宽为 (250 − m) 米，由题意得：
m(250 − m) = 10000 ． ·············································································（4 分）
即： m2 − 250m +10000 = 0 ， 解得： m = 50 或 m = 200 ，满足题意． 此时火炬的坐标为 (50，200) 或 (200，50) ． ·················································（5 分）
E 为 ¼ ADB 的中点． ···············································································（3 分）
（2）①Q CD ⊥ AB ， AB 为 e O 的直径， CD = 3 ，
CH = 1 CD = 3 ． ·············································································（4 分）
△ADH ∽△BAO ． ·············································································（4 分） （3）Q△ADH ∽△BAO ，
DH = AH = AD ，即 DH = AH = 5 ，
AO BO BA
14．A
15．D
16．C
17．C
三、解答题：
18．（1）原式 =1− 2 + 2 ····················································（3 分，每对 1 个得 1 分）
= 1．·····································································································（5 分）
即点 Q 落在直线 y = x − 3 上的概率为 1 ． ·····················································（6 分） 3
21．（1）画角平分线，线段的垂直平分线． ························（3 分，仅画出 1 条得 2 分）
19．（1） x(x − 2) = 0 ．·············································································（3 分）
x1 = 0 ， x2 = 2 ． ··················································································（5 分）
（也可设 y = a(x −1)2 + k ）
（2） y = x2 − 2x − 3 = (x −1)2 − 4 ． ···························································（4 分）
函数的顶点坐标为 (1，− 4) ． ····································································（5 分）
24．（1） A(−4，0) ， B(0，2) ，
在 Rt△AOB 中， AB = OA2 + OB2 = 42 + 22 = 2 5 ．···························（2 分）
（2）由 ADH + DAH = 90o ， BAO + DAH = 90o ，
BAO = ADH ，又Q AOB = DHA = 90o ，
2
2
3 又 OC = 1，sin COB = CH = 2 = 3 ．
OC 1 2
COB = 60o，·····················································································（5 分）
BAC = 30o．
20．（1）用列表或画树状图的方法求点 Q 的坐标有 (1，−1) ， (1，− 2) ， (1，− 3) ， (2，−1) ，
(2，− 2) ， (2，− 3) ． ··························（4 分，列表或树状图正确得 2 分，点坐标 2 分）
（2）“点 Q 落在直线 y = x − 3 上”记为事件 A ，所以 P( A) = 2 = 1 ， 63
（3）5····································································································（6 分）
23．设该厂原来每天生产 x 顶帐篷，根据题意得： ··········································（1 分）
4 2 25
DH = 2 ， AH =1．
D(−5，2) ．···························································································（6 分）
25．（1）设反比例函数为 y = k (k 0) ．······················································（1 分） x
则 k = xy = mn = S矩形OATB = 10000 ， ···························································（2 分） y = 10000 ．························································································（3 分）
ቤተ መጻሕፍቲ ባይዱ
（2）原式 =
4
+ 1 ·······························································（1 分）
(x + 2)(x − 2) x + 2
=
4
+
x−2
·································································（2 分）
镇江市 2008 年初中毕业升学考试数学试卷
参考答案及评分标准
一、填空题：
1．3，3
2．1，6
3． 2a2 ， a
4． x2 + x − 2 ， (x +1)(x −1)
5． x = 1， x ≥ 2 6．3，3 7．65，35
8．4，12
9．1，1
10．45，2 11． 4
12． A
二、填空题：
13．B
（3）Q mn = 10000 ，在 Rt△TAO 中，TO = OA2 + AT 2 = m2 + n2
= (m − n)2 + 2mn = t2 + 20000 ． ···························································（6 分） 当 t = 0 时，TO 最小， 此时 m = n ，又 mn = 10000 ， m 0 ， n 0 ， m = n = 100 ，且10 100 1000 ． T (100，100) ．·······················································································（7 分）
26．（1）Q OC = OE ，E = OCE ·······················································（1 分） 又 OCE = DCE ，E = DCE ． OE ∥CD ． ························································································（2 分） 又 CD ⊥ AB ，AOE = BOE = 90o ．
作 OP ⊥ AC 于 P ，则 OP = 1 OA = 1 ． ······················································（6 分） 22
②3 ········································································································（7 分）
（2）由①，得 x 4 ； ··············································································（2 分） 由②，得 x ≥1 ． ·····················································································（4 分） 原不等式组的解集为1≤ x 4 ．······························································（5 分）
经检验： x = 1000 是原方程的根，且符合题意． ············································（5 分）
答：该厂原来每天生产 1000 顶帐篷． ···························································（6 分）
把点
(2，−
3)
，
(−1，0)
代入得
4a + 2b − 3 = a − b − 3 = 0.
−3，
··············································（2
分）
解方程组得
a b
= =
1， −2.
y = x2 − 2x − 3．····················································（3 分）
12000 x
−
12000 3x
=
4
．
···············································································（3
分）
2
解方程得： x = 1000 ．··············································································（4 分）
(x + 2)(x − 2) (x + 2)(x − 2)
=
x+2
·······················································································（4 分）
(x + 2)(x − 2)
= 1 ．·······························································································（5 分） x−2
（2） △BOE ≌△BOF ≌△DOF ·············（4 分，只要 1 对即可），证明全等．（6 分）
22．（1）设 y = ax2 + bx − 3 ， ····································································（1 分）
x （2）设鲜花方阵的长为 m 米，则宽为 (250 − m) 米，由题意得：
m(250 − m) = 10000 ． ·············································································（4 分）
即： m2 − 250m +10000 = 0 ， 解得： m = 50 或 m = 200 ，满足题意． 此时火炬的坐标为 (50，200) 或 (200，50) ． ·················································（5 分）
E 为 ¼ ADB 的中点． ···············································································（3 分）
（2）①Q CD ⊥ AB ， AB 为 e O 的直径， CD = 3 ，
CH = 1 CD = 3 ． ·············································································（4 分）
△ADH ∽△BAO ． ·············································································（4 分） （3）Q△ADH ∽△BAO ，
DH = AH = AD ，即 DH = AH = 5 ，
AO BO BA
14．A
15．D
16．C
17．C
三、解答题：
18．（1）原式 =1− 2 + 2 ····················································（3 分，每对 1 个得 1 分）
= 1．·····································································································（5 分）