一、选择题:本题共8小题,每小题5分,40分。在每小题给出的四个选项中,第只有一项符合题目要求
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A . {x|﹣3<x<﹣2}
B . {x|﹣2<x<1}
C . {x|1<x<4}
D . {x|﹣3<x≤4}
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A . {﹣1,2,5,8}
B . {﹣1,2,5}
C . {2,5,8}
D . {2,5}
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A . 若a>b , 则ac>bc
B . 若a>b , c>d , 则a+c>b+d
C . 若a>b , c>d , 则ac>bd
D . 若a>b , 则a2>b2
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4.
(2023高三上·喀什模拟)
某文具店购进一批新型台灯,每盏的最低售价为15元,若每盏按最低售价销售,每天能卖出45盏,若每盏售价每提高1元,日销售量将减少3盏,为了使这批台灯每天获得600元以上的销售收入,则这批台灯的销售单价
x(单位:元)的取值范围是( )
A . (10,20)
B . [15,20)
C . (18,20)
D . [15,25)
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5.
(2023高三上·喀什模拟)
若一系列函数的解析式和值域相同,但定义域不相同,则称这些函数为“同值函数”.例如函数
y=
x2 ,
x∈[1,2]与函数
y=
x2 ,
x∈[﹣2,﹣1]即为“同值函数”,给出下面四个函数,其中能够被用来构造“同值函数”的是( )
A .
B . y=x3
C . y=log2x
D . y=|x﹣1|
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A . (﹣∞,3]
B . (1,+∞)
C . (1,3]
D . (﹣∞,1)∪[3,+∞)
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A . 30°
B . 45°
C . 60°
D . 135°
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8.
(2023高三上·喀什模拟)
已知点
M(3,5),在直线
l:
x﹣2
y+2=0和
y轴上各找一点
P和
Q , 则△
MPQ的周长的最小值为( )
二、多选题(本题共4小题,每题5分,共20分,每道题有多项符合题目要求。全部选对的得5分,选对但不全的得2分,有选错或不答的得0分。)
三、填空题(本题共4小题,每小题5分,共20分。)
四、解答题:(本题共6小题,共70分。其中17题10分,其余每题均12分。解答应写出必要的文字说明、方程式和重要演算步骤。只写出最后答案的不能得分。有数值计算的题,答案中必须明确写出数值和单位。)
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(1)
求方程组
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfenced+open%3D%22%7B%22+close%3D%22%22%3E%3Cmrow%3E%3Cmtable+columnalign%3D%22left%22%3E%3Cmtr%3E%3Cmtd%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmath%3E)
的解集;
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(1)
已知﹣1<x<4,2<y<3,求x﹣y的取值范围;
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(2)
比较(x﹣1)(x2+x+1)与(x+1)(x2﹣x+1)的大小,其中x∈R .
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(2)
判断
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ES%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ES%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ES%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmo%3E%E2%8B%AF%3C%2Fmo%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ES%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3En%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
与2的大小关系并证明你的结论.
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(2)
若
M ,
N是线段
BC上的动点,且|
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmover%3E%3Cmrow%3E%3Cmi%3EM%3C%2Fmi%3E%3Cmi%3EN%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmover%3E%3C%2Fmath%3E)
|=1,求
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmover%3E%3Cmrow%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmi%3EM%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmover%3E%3Cmo%3E%E2%8B%85%3C%2Fmo%3E%3Cmover%3E%3Cmrow%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmi%3EN%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%E2%86%92%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmover%3E%3C%2Fmath%3E)
的最小值.
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(2)
若
m=2,设
a+
bi(
a ,
b∈
R),试求
a+
b的值.