Qing asked in 科學及數學數學 · 7 years ago

# maths 6條MOCK MC

Update:

34:不明為何let 2012^2012=10^n,是否計這類數如:2012^50也是let=10^n,5^2012也let=10^n?

5C2 ways for choosing 2 horizontal lines.

5C2 ways for choosing 2 vertical lines.

Rating
• 7 years ago

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 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。