2013年龙岩市初中毕业、升学考试 下载本文

2013年龙岩市初中毕业、升学考试 参 考 答 案 及 评 分 标 准

数 学

说明:评分最小单位为1分,若学生解答与本参考答案不同,参照给分. 一、选择题(本大题共10题,每题4分,共40分)

题号 答案 1 A 2 C 3 D 4 D 5 B 6 C 7 A 8 C 9 B 10 B 二、填空题(本大题共7题,每题3分,共21分.注:答案不正确、不完整均不给分) 11.a(a?2)

12.9 13.8

14.3

15.70? 16.①④

a2?b2 17..

ab三、解答题(本大题共8题,共89分)

18.(10分,第(1)小题5分,第(2)小题5分)

(1)解:原式=2?1?(?1)?2?3 ····························································· 4分 = 2?3 ············································································· 5分 (2)解:方程两边同乘(2x+1),得 4=x+2x+1 ················································ 2分 3=3x

x=1 ························································································· 3分 检验:把x=1代入2x+1=3≠0 ······················································· 4分 ∴原分式方程的解为x=1. ···························································· 5分 19.(8分)解:原式=

x(2x?3)(2x?3)1?? ········································ 4分 2x?332x?3x= ·············································································· 6分 32当x=2时,原式=. ·································································· 8分

320.(10分)

(1)证明:(法一)如图:∵四边形ABCD是平行四边形

∴AD=BC,AD∥BC,∠3=∠4 ····················· 1分

∵∠1=∠3+∠5, ∠2=∠4+∠6 ························································ 2分 ∠1=∠2

∴∠5=∠6 ················································································· 3分 ∴△ADE≌△CBF ···································································· 5分 ∴AE=CF ················································································ 6分 (法二)如图:连接BD交AC于点O ··············· 1分 在平行四边形ABCD中

OA=OC,OB=OD ·································· 2分 ∵∠1=∠2,∠7=∠8

∴△BOF≌△DOE ······································································· 4分 ∴OE=OF ················································································ 5分 ∴OA-OE=OC-OF

即AE=CF. ················································································· 6分

(2) )证明:(法一)∵∠1=∠2,

∴DE∥BF ············································································· 7分

∵△ADE≌△CBF

∴DE=BF ·············································································· 9分 ∴四边形EBFD是平行四边形. ················································ 10分

(法二)∵OE=OF,OB=OD ······························································· 9分

∴四边形EBFD是平行四边形. ··············································· 10分

其他证法,请参照标准给分.

21.(10分,第(1)小题4分,第(2)小题3分,第(3)小题3分) (1) 0.11 , 540 ; (注:每空2分) (2)36?;

(3)9000. 22.(12分,每小题4分)

(1)6 ······························································································ 4分 (2)3?1··························································································· 8分 2(3)∵∠C=90?,BC=3,EC=1

BC=3 CE∴∠BEC=60? ······················································································ 9分 由翻折可知:∠DEA=45? ······································································· 10分 ∴?AEA??75?=?D?ED?? ····································································· 11分

∴tan∠BEC=∴l ?755?3 ································································· 12分 ?2??3?3601223.(12分,第(1)小题5分,第(2)小题7分)

解:(1)设需租赁甲、乙两种设备分别为x、y天. ········································ 1分

x?7y?80?12则依题意得 ? ··················································· 3分

10x?1y0?100??x?2解得 ? ·········································································· 4分

y?8?答:需租赁甲种设备2天、乙种设备8天. ··················································· 5分 (2)设租赁甲种设备a天、乙种设备(10-a)天,总费用为?元. ······················ 6分

依题意得

?a?5?10?a?7???12a?7(10?a)?80??10a?10(10?a)?100∴3≤a≤5. ∵a为整数,

∴a=3、4、5. ·················································································· 8分 方法一:

∴共有三种方案.

方案(1)甲3天、乙7天,总费用400×3+300×7=3300; ·············· 9分

[来源学科网ZXXK]

方案(2)甲4天、乙6天,总费用400×4+300×6=3400; ················· 10分 方案(3)甲5天、乙5天,总费用400×5+300×5=3500. ················ 11分 ∵3300<3400<3500 ∴方案(1)最省,最省费用为3300元. ····· 12分

方法二:

则?=400a+300(10-a)=100a+3000 ··········································· 10分 ∵100>0,

∴?随a的增大而增大.

∴当a=3时,?最小=3300. ······················································ 11分

答:共有3种租赁方案:①甲3天、乙7天;②甲4天、乙6天;③甲5天、乙5天.最少租赁费用3300元. ················································································ 12分

方法三:能用穷举法把各种方案枚举出来,并得出三种符合条件的方案,求出最省费用的,参照标准酌情给分.

24.(1)设F(x,y),(x>0,y>0) .

则OC=x, CF=y ···················································································· 1分

1∴S?OCF?xy?3. ··········································································· 2分

2∴xy=23.

∴k=23. ························································································ 3分 23∴反比例函数解析式为y=(x>0) . ············································· 4分

x(2)该圆与y轴相离. ·········································································· 5分

[来源学科网ZXXK]理由:过点E作EH⊥x轴,垂足为H,过点E作EG⊥y轴,垂足为G.

在△AOB中,OA=AB=4,∠AOB=∠ABO=∠A=60?. 设OH=m,则tan?AOB?∴EH=3m,OE=2m.

EH?3. OH