全一卷
1.设等差数列
满足
且
,
为其前
项之和,则
中最大的是( )
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A.![]() | B.![]() | C.![]() | D.![]() |
2.设复平面上单位圆内接正20边形的20个顶点所对应的复数依次为
,
,…,
。则复数
,
,…,
所对应的不同的点的个数是( )
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A.4 | B.5 | C.10 | D.20 |
3.如果甲的身高数或体重数至少有一项比乙大,则称甲不亚于乙,在100个小伙子中,如果某人不亚于其他99人,就称他为棒小伙子。那么,100个小伙子中的棒小伙子是最多可能有( )
A.1个 | B.2个 | C.50个 | D.100个 |
4.已知方程
在区间
上有两个不相等的实根。则
的取值范围是( )
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A.![]() | B.![]() |
C.![]() | D.以上都不是 |
5.
,
,
,
的大小关系是( )
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A.![]() |
B.![]() |
C.![]() |
D.![]() |
6.设
是正三棱锥
底面
的中心,过
的动平面与
的三条侧棱或其延长线的交点分别记为
,
,
.则和式
( )
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A.有最大值而无最小值 | B.有最小值而无最大值 |
C.既有最大值又有最小值,且二者不等 | D.是一个与平面![]() |
7.设
,
为一对共轭复数,若
且
为实数,则
________.
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8.一个球的内接圆锥的最大体积与这个球的体积之比为 .
9.用[x]表示不大于实数x的最大整数, 方程
的实根个数是__________ .
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10.直角坐标平面上,满足不等式组
的整点(即横、纵坐标均为整数的点)的个数是________.
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11.将一个四棱锥的每个顶点染上一种颜色,并使同一条棱的两端点异色,如果只有5种颜色可供使用,那么不同的染色方法的总数是________ .
12.设
,
是
的子集且满足条件;当
时,
,则
中元素的个数最多是________.
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13.给定曲线族
,
为参数,求该曲线族在直线
上所截得的弦长的最大值。
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14.求一切实数
,使得三次方程
的三个根均为自然数。
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15.如图,菱形
的内切圆
与各边分别切于
,
,
,
,在
与
上分别作
的切线交
于
,交
于
,交
于
,交
于
,求证:
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16.将平面上每个点都以红、蓝两色之一着色,证明:存在这样的两个相似三角形,它们的相似比为1995,并且每一个三角形的三个顶点同色。