mock paper MC

1.
The answer is : B. 4 / (n² - 4)

[1 / (n - 2)] - [1 / (2 + n)]
= [1 / (n - 2)] - [1 / (n + 2)]
= [(n + 2) / (n + 2)(n - 2)] - [(n - 2) / (n + 2)(n - 2)]
= [(n + 2) / (n² - 4)] - [(n - 2) / (n² - 4)]
= [(n + 2) - (n - 2)] / (n² - 4)
= [n + 2 - n + 2] / (n² - 4)
= 4 / (n² - 4)


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2.
The answer is : B. II only

I. false
(x + y)² = x² +2xy + y²
(x + y)² = x² +y² only when 2xy = 0

II. true
L.S. = 1 + 4x
R.S. = 3 - 2(1 - 2x) = 3 - 2 + 4x = 1 + 4x = L.S.

III. false
When x = 0, x² = 0


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3.
All of the four options are NOT the answer.

(1 + 3x) / (-2) > 7
-2[(1 + 3x) / (-2)] <-2(7)
1 + 3x < -14
3x < -15
x < -5
The least value of x is -∞.


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4.
The answer is : C. x + √3 y - 2√3 = 0

Slope of the line = tan(180° - 30°) = -tan30° = -1/√3
y -intercept of the line = 2

Equation of the line (slope-intercept form) :
y = (-1/√3)x + 2
-√3 y = x - 2√3
x + √3 y - 2√3 = 0


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5.
All of the four options are NOT the answer.

Periods of y = f(x), y = g(x) and y = h(x) are 2π, π and 2π respectively.
Only II must be true.

(The question may be "which of the following must be false" or"which of the following must NOT be true".)


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6.
The answer is : A. k = -3 and θ = -10°

y = cos x° has the minimum of -1 when x° = 180°
Then, y = cos (x° - 10°) has the minimum of -1 when x = 190
Then, y = 3 cos (x° - 10°) has the minimum of -3 when x = 190
Then, y = -3 cos (x° - 10°) has the maximum of 3 when x = 190
Compare y = k cos (x° + θ) andy = -3 cos (x° - 10°)

2015-01-03 16:40:58 補充：
In case of further questions, please open a new page.

2015-01-03 19:43:42 補充：
6.
Transform the curve y = cos x° to obtain the unknown curve y = k cos (x° + θ)

For the curve y = cos x°, there is a minimum of -1 at x = 180°.
For the unknown curve, there is a maximum of 3 at x = 190°.

Then, the unknown curve should be y = -3 cos (x° - 10°)

2015-01-03 19:44:09 補充：
"-10°" : a right shift of 10° (i.e. shift from 180° to 190°) of the curve y = cos x°
"-" : rotate the curve by 180° about the x-axis (i.e. minimum is changed to maximum)
"3" : the amplitude is multiplied by 3.