管理类联考MBA、MPA、MPACC数学考试综合真题及答案

(2) C6CC= 36 < 62 天 3 2

111

21.档案馆在一个库房中按装了 n个烟火感应报警器,每个报警器遇到烟火成功报警的概率 均为 p,该库房遇烟火发出警报的概率达到 0.999 (1) n= 3, p = 0.9

(2) n= 2, p = 0.97

解:选 D,三个烟火独立

(1) P(A+ A+ A) = 1 ? P(A)= 1 ? 0.1= 0.999

3 3

(2) P(A+ A) = 1 ? P(A)= 1 ? 0.03= 0.9991

2

2

22.已知 a,b是实数,则 a ≤ 1 , b ≤ 1

(1) a+ b ≤ 1, (2) a? b ≤ 1, 解:

选 C

显然(1)和(2)单独不成立,联立,则

??(a+ b)2 ≤ 1 ① ?? a+ b ≤ 1

①+② ? a2 + b2 ≤ 1∴ a ≤ 1 , b ≤ 1 ? ? ?

2

??(a? b)≤ 1 ② ?? a? b ≤ 1

23.某单位年终共发了 100 万元奖金,奖金金额分别是一等奖 1.5 万元,二等奖 1 万元,三等

奖 0.5 万元,则该单位至少有 100 人 (1)得二等奖的人数最多 (2)得三等奖的人数最多 解:选 B

设一、二、三等奖的人数分别为 x, y 、 z则

?1.5x+ y+ 0.5z = 100

?(1) ? y≥ x ,任取 x= 30 , y = 50 , z = 10 ,不符合题意

?y≥ z ? ?1.5x+ y+ 0.5z = 100

100 ?? (1.5 + 1+ 0.5)z > 100 ? z > ,∴ z≥ 34 , (2) ? z≥ x

3 ?z≥ y

?

L = x+ y+ z,由于 z的系数最小,权重也最小, x的系数最大,权重也最大,所以

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z越小, L越小,令 z= 34 , y = 34 ,则 x=

98 302 x+ y+ z = 34 + 34 + = > 100

3 3

49 98 = , 1.5 3

24.设 x, y, z为非零实数,则 2x+ 3y? 4z = 1.

?x+ y? 2z

(1) 3x? 2y = 0

(2) 2y? z = 0

解:选 C

?

?2 x = y

显然单独不成立,联立则 ?

y = 3 ,则 x= 2 , y = 3 , z= 6 代入即可 3 ,不妨令

?z = 2y ?

25.设a1 = 1,a2 = k,an+1 = an ? an?1 (n≥ 2) .则 a100 + a101 + a102 = 2 . (1) k = 2.

(2)是小于 20 的正整数. 解:选 D (1)当 k = 2 时

a1 = 1, a2 = 2 , a3 = 1,a4 = 1,a5 = 0 , a6 = 1, a7 = 1, a8 = 0 ,?, a99 = 1,a, 100 = 1,a101 = 0

a102 = 1,∴ a100 + a101 + a102 = 2

(2) ①当 k = 1时

a1 = 1,a2 = 1,a3 = 0 , a4 = 1, a5 = 1, a6 = 0 ,?, a100 = 1,a101 = 1,a102 = 0 ,

∴ a100 + a101 + a102 = 2

②当 k = 2 时,同(1) ③当 k = 3 时

a1 = 1, a2 = 3 , a3 = 2 , a4 = 1,a5 = 1,a6 = 0 , a7 = 1,a8 = 1,a9 = 0 ,?,

a100 = 1,a101 = 1,a102 = 0 ,∴ a100 + a101 + a102 = 2

? ?

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⒆当 k = 19 时

a1 = 1, a2 = 19 , a3 = 18 , a4 = 1, a5 = 17 , a6 = 16 ,?, a28 = 1,a29 = 1,a30 = 0

?, a100 = 1,a101 = 1,a102 = 0 ,∴ a100 + a101 + a102 = 2

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