25.(10分) 【阅读理解】
对于任意正实数a、b,∵(a-b)2≥0,∴a+b-2ab≥0,∴a+b≥2ab,只有当a=b时,等号成立. 【数学认识】
在a+b≥2ab(a、b均为正实数)中,若ab为定值k,则a+b≥2k,只有当a=b时,a+b有最小值2k. 【解决问题】
1
(1)若x>0时,x+ 有最小值为 ▲ ,此时x= ▲ ;
x
63
(2)如图1,已知点A在反比例函数y=(x>0)的图像上,点B在反比例函数y=-
xx
(x>0)的图像上,AB∥y轴,过点A作AD⊥y轴于点 D,过点B作BC⊥y轴于点C.求四边形ABCD周长的最小值.
y A D
x O
C B
(图1)
(3)学校准备在图书馆后面的场地上建一个面积为100平方米的长方形自行车棚.图
书馆的后墙只有5米长可以利用,其余部分由铁围栏建成,图2是小尧同学设计的图纸,设所需铁围栏L米,自行车棚长为x米.L是否存在最小值,如果存在,那么当x为何值时,L最小,最小为多少米?如果不存在,请说明理由. 5米 后墙 x米 (图2) 初二数学 第 6 页 共 18 页
答案
说明:本评分标准每题给出了一种或几种解法供参考,如果考生的解法与本解答不同,参照本评分标准的精神给分.
一、选择题(每小题2分,共计12分)
题号 答案
二、填空题(每小题2分,共计20分)
17. a≥1 8.红 9. 10.k>2 11.4
2
1
12. 8 13.10 14. x>2或-4<x<0 15.10 16.(,0)
2
三、解答题(本大题共9小题,共计68分) 17.(本题8分)
a2-1
解:(1)原式= ················································································ 1分
a+1
=
(a+1)(a-1)
··········································································· 3分
a+1
1 C 2 C 3 D 4 C 5 B 6 B = a-1 ···························································································· 4分 a+3+a-32a(2)原式=()÷2 ····························································· 5分
a+3a-9
2
2aa-9=× ··················································································· 6分
2aa+3
=
2a(a+3)(a-3)× ·········································································· 7分
2aa+3
=a-3 ····························································································· 8分
18.(本题6分)
(1)原式=3?????3分 (2)原式=?6?26?????3分
E D
M F 18cm2
12cm2
G C
19.(本题6分)
解:由题意可得:AE=18=32(cm),?????2分
DE=CG=12=23(cm),?????????4分
原来大正方形的面积为:(32+23)2=30+126?????6分
20.(本题8分)
A
H (第19题)
B
解:(1)400 ·························································································· 2分
初二数学 第 7 页 共 18 页
(2)图略 ····························································································· 4分 (3)108 ······························································································· 6分 (4)100 ······························································································· 8分 21.(本题8分)
(1)证明:∵在□ABCD中,
∴AD∥BC.∴∠DAE=∠AEB. ∵∠BAD的平分线交BC于点E,
∴∠DAE=∠BAE.
∴∠BAE=∠AEB.∴AB=BE.???????2分 同理AB=AF.∴AF=BE.
∴四边形ABEF是平行四边形. ···························································· 3分 ∵AB=BE.∴四边形ABEF是菱形. ···················································· 4分 (2)解法一:过点A作AH⊥BC于点H.
∵四边形ABEF是菱形,AE=6,BF=8,
∴AE⊥BF,OE=3,OB=4.∴BE=5. ··············································· 5分 1124∵S菱形ABEF=AE?BF=BE?AH,∴AH=×6×8÷5=. ························· 6分
225524
∴S□ABCD=BC?AH=(5+)×=36. ···················································· 8分
25解法二:∵四边形ABEF是菱形,AE=6,BF=8,
∴AE⊥BF,OE=3,OB=4.∴BE=5. ··············································· 5分 11
∵S菱形ABEF=AE?BF=×6×8=24, ···················································· 6分
225
∵CE=,BE=5,
2
33
∴S□ABCD=?S菱形ABEF =×24=36. ····················································· 8分
22
22.(本题8分)
(1)解:∵点B(a,5)在直线y=2x+3上,
∴2a+3=5,∴a=1. ········································································ 2分 k
∴B(1,5)在反比例函数y=的图像上,
x
5∴k=1×5=5.∴反比例函数的表达式为y=. ······································ 4分
x55
(2)(2,)或(-2,-). ···································································· 8分
2223.(本题8分)
解:(1)∵每天运量×天数=总运量,∴xy=3000,
3000
∴y=(x>0) ············································································· 2分
x
B H
E
(第22题)
C
A O F D
初二数学 第 8 页 共 18 页
(2)设原计划x天完成,根据题意得:
30003000(1﹣20%)=, ···································································· 4分 xx+1解得:x=4 ······················································································· 6分 经检验:x=4是原方程的根, ······························································ 8分
答:原计划4天完成.
24.(本题6分)
已知:如图,在□ABCD中,AC、BD交于点O,点E为AD的中点,连接EO交BC
于F.
求证:F是BC的中点.??????????2分 证明:∵在□ABCD中,AC、BD交于点O,
∴DO=BO.??????????????3分 ∵E为AD的中点,∴DE=EA.
∴OE为△ABD的中位线.
∴OE∥AB,即EF∥AB.????????4分
∵□ABCD,∴AE∥BF.∴四边形AEFB是平行四边形.∴BF=AE.
∵□ABCD,∴ AD=BC.∴BF=CF,即F是BC的中点. ······················ 6分
25.(本题10分)
(1)2,1. ···························································································· 2分 63(2)解:设A(a,),则B(a,-),
aa
9
∴四边形ABCD周长=2(a+) ······························································ 4分
a≥2×2
9
a?=4×3=12 ······································································ 6分 a
200 ········································································ 8分 x
A E D O F C B (第20题)
(3)∵L=2x-5+≥22002x ?-5=35 ·········································································· 9分
x
200
当2x=,即x=10时,L最小. ····················································· 10分
x答:当x为10时,L最小,最小为35米.
初二数学 第 9 页 共 18 页
2017~2018学年度第二学期期末测试
八 年 级 数 学
注 意 事 项 考生在答题前请认真阅读本注意事项: 1.本试卷共6页,分两部分,:必做题(满分100分),附加题(满分20分)考试时间为120分钟. 2.答题前,请务必将自己的姓名、考试证号用0.5毫米黑色字迹的签字笔填写在答题卡上指定的位置. 3.答案必须按要求填涂、书写在答题卡上,在试卷、草稿纸上答题一律无效. 第一部分 必做题(满分100分)
一、选择题(本大题共10小题,每小题3分,共30分.在每小题给出的四个选项中,恰有一项是符合题目要求的,请将正确选项的字母代号填涂在答题卡相应位置上) .......1.下列实数中,为无理数的是【▲】
A.0.2
B.
1 2
C.2 D.?5
2.如图,一把矩形直尺沿直线断开并错位,点E、D、 B、F在同一条直线上,若∠ADE=128°,则∠DBC 的度数为【▲】 A.52° B.62°
C.72° D.128° (第2题)
3.已知点P(2a?1,1?a)在第一象限,则a的取值范围在数轴上表示正确的是【▲】
0 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1 A. B. C. D.
x5xx得到y??的图象,那么直线y?必须【▲】
333355 A.向左平移个单位 B.向右平移个单位
3355C.向上平移个单位 D.向下平移个单位
334.如果通过平移直线y?5.已知一组数据2,3,4,x,1,4,3有唯一的众数4,则这组数据的中位数分别是【▲】
A.3 B.3.5 C.4 D.4.5
6.某运动服经过两次降价,每件零售价由560元降为315元,已知两次降价的百分率相 同.设每次降价的百分率为x,则下面所列的方程中正确的是【▲】 A.560?1+x??315 C.560?1?2x??315
22B.560?1?x??315 D.5601+x2?315
B′
C
2??7.如图,在△ABC中,∠CAB=65°,将△ABC在平
面内绕点A旋转到△AB′C′的位置,使CC′∥AB, C′ 则旋转角的度数为【▲】 A.35° B.40°
A
初二数学 第 10 页 共 18 页
B
C.50° D.65° 8.已知0≤x≤
12
,那么函数y=-2x+8x-6的最大值是【▲】 2(第7题)
A.-10.5 B.2 C.-2.5 D.-6 9.小刚以400米/分的速度匀速骑车5分,在原地休息了6分,然后以500米/分的速度 骑回出发地.下列函数图象能表达这-过程的是【▲】
s(千米) v(千米/分) v(千米/分) s(千米)
0.50.420.50.451115(t分) OB
32O51115t(分) 51115t(分)
C AD
2
10.若二次函数y=ax+bx+c(a>0)图象与x轴的两交点坐标为(x1,0)、(x2,0),
O51115(t分) O且0<x1<x2,且图象上有一点M(x0,y0)在x轴下方,则下列判断错误的是【▲】
A.a(x0-x1)(x0-x2)>0 B.c>0 C.b2-4ac>0 D.x1<x0<x2 二、填空题(本大题共8小题,每小题3分,共18分.不需写出解答过程,请把答案直接
填写在答题卡相应位置上) .......11.函数y?1中自变量x的取值范围是 ▲ . x?312.在平面直角坐标系中,点A(-2,1)与点B关于原点对称,则点B的坐标为 ▲ . 13.甲、乙、丙、丁四位同学最近五次数学成绩统计如表,如果从这四位同学中,选出一位成绩较好且状态稳定的同学参加即将举行的中学生数学竞赛,那么应选 ▲ .
平均数 方差 甲 80 42 乙 85 42 丙 85 54 丁 80 59 14.如果x2-x-1=(x+1)0,那么x的值为 ▲ .
15.如图,经过点B(-2,0)的直线y=kx+b与直线y=4x+2相
交于点A(-1,-2),则不等式4x+2<kx+b<0的解集 为 ▲ .
16.如图,在等边△ABC内有一点D,AD=5,BD=6,CD=4,
将△ABD绕A点逆时针旋转,使AB与AC重合,点D旋 转至点E,过E点作EH⊥CD于H,则EH的长为 ▲ . 三、解答题(本大题共8小题,共52分.请在答题卡指定区
域内作答,解答时应写出文字说明、证明过程或演算步骤) 17.(本题8分)
初二数学 第 11 页 共 18 页
(第16题) (第15题)
百度搜索“77cn”或“免费范文网”即可找到本站免费阅读全部范文。收藏本站方便下次阅读,免费范文网,提供经典小说综合文库2017-2018学年苏科版八年级数学下册期末考试试卷及答案(精选2套(2)在线全文阅读。
相关推荐: