maths 6條MOCK MC

14)

(-k)³ + k(-k)² + 2k(-k) + 3 = k
2k(-k) + 3 = k
2k² + k - 3 = 0
(2k + 3)(k - 1) = 0
k = - 3/2 or k = 1
(C)


28)

If f(x) and g(x) intersect at more than 1 point , then
x² + ax + 1 = x² + bx + 1
(a - b)x = 0 more than 1 root , if and only if a - b = 0 so a = b.
P(a = b) = 6/6 * 1/6 = 1/6.
(B)


29)

Note that 9² + 40² = 41² therefore it is a right-angled △.
So K + G + 9*40/2 = E
K + G + 180 = E
(B)


42)

P(Koopa is ahead of Mario)

= P(Koopa is the 1st)
+ P(Koopa is the 2nd and ahead of Mario)
+ P(Koopa is the 3rd and ahead of Mario)
+ P(Koopa is the last and ahead of Mario)

= 1/4 + (1/4)(2/3) + (1/4)(1/3) + 0
= 1/2
(C)


34)

2012²º¹² = 10ⁿ
2012log2012 = n
6646.899488 = n
So 2012²º¹² have 6647 digits.
(C)


44)
5C2 ways for choosing 2 horizontal lines.
5C2 ways for choosing 2 vertical lines.
There are 5C2 * 5C2 = 100 rectangles can be choosed.
(D)


2013-03-03 20:48:16 補充：
34)

2012²º¹²
= 10^6646.899488
所以
10^6646 = 100...00(6646個0) < 2012²º¹² < 10^6647 = 100...00(6647個0)
肯定 2012²º¹² 是 6647 位數。

44)

4 x 4 正方由 5 橫 5 直所組成 ,
一矩形被唯一的某2橫及某2直所確定,反之亦然。

2013-03-03 20:50:42 補充：
5C2 即 5 條抽 2 條的方法數量 , 即 5 * 4 / 2 = 10。

For Q34, reference:
http://math.stackexchange.com/questions/169797/write-down-the-sum-of-sum-of-sum-of-digits-of-44444444