2012DSE MATHS 2 MC QUESTIONS

Question

1) http://upload.lsforum.net/users/public/c3432Q32h192.gif

2) Let f(x) be a quadratic function. If the coordinates of the vertex of the graph of y=f(x) are (3,-4), which of the following must be true?
A. The roots of the equation f(x)=0 are integers.
B. The roots of the equation f(x)-3=0 are rational numbers.
C. The roots of the equation f(x)+4=0 are real numbers.
D. The roots of the equation f(x)+5=0 are nonreal numbers.


第1 and 2題答案是C及C,
請詳細列出步驟,THZ!=]

? · Accepted Answer

1) y = mnx

Taking log base 3 on both sides:

log3 y = log3 m + xlog3 n

From the graph, slope = (4 - 0)/(0 + 2) = 2 = log3 n

Hence n = 9

2) From the given, f(x) should be in form of:

f(x) = a(x - 3)2 - 4 where a is a non-zero constant

For (A):

f(x) = 0, x - 3 = 2/√a or -2/√a which may not be integer

For (B):

f(x) = 3, x - 3 = √7/√a or -√7/√a which may be irrational

For (C):

f(x) = 0, x = 3 which is real

For (D):

f(x) = -1, (x - 3)2 = -1/a which can be still positive if a is negative, i.e. x can still be real

So ans = C

2012DSE MATHS 2 MC QUESTIONS

1 個解答