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Alex 發問於 科學及數學數學 · 5 年前

mock paper MC

1/(n-2)-1/(2+n) =

A. 4/(4- n^2 )

B. 4/(n^2-4 )

C. 2n/(4- n^2 )

D. 2n/(n^2-4)

(Answer is B)

Which of the following is/ate identity/identities?

I. (x + y) 2 = x2 + y2

II. 1 + 4x = 3 – 2 ( 1 - 2x)

III. x2 > 0

A. I only

B. II only

C. I and II only

D. II and III only

(Why the answer is B instead of D)

If x is an integer and satisfies the inequality (1+3x)/(-2)> 7, then the least value of x is

A. 3.

B. 4.

C. 5.

D. 6.

(Answer is D)

In the figure, the equation of the straight line L is

https://www.flickr.com/photos/130230543@N06/155616...

A. √3 x - y + 2 = 0.

B. -√3 x + y - 2=0.

C. x + √3 y - 2√3 = 0.

D. x - √3 y + 2√3 = 0.

(By observing the slopes of answers, i got the right answer C but couldn't get the correct one by direct calculation)

Consider the functions y = f(x), y = g(x) and y= h(x), where f(x) = 2 cos x, g (x) = cos 2x and h (x) =cos (x + 2). Which of

the following must be true?

I. Periods of y = f(x) and y= g (x) are the same.

II. Periods of y = f(x) and y= h(x) are the same.

III. Period of y = g(x) is greater than that of y = h(x).

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

(Answer is B)

Let k be a constant and -90° < θ < 90°. If the figure shows the graph of y = k cos (xo + B), then

https://www.flickr.com/photos/130230543@N06/155593...

A. k = -3 and θ= - 10°

B. k= -3 and θ= 10°

C. k= 3 and θ= -10°

D. k= 3 and θ= 10°.

更新:

sorry I can't really understand the final question

can you explain a bit more?!

1 個解答

評分
  • 土扁
    Lv 7
    5 年前
    最愛解答

    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)

    ====

    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

    ====

    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 -∞.

    ====

    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

    ====

    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".)

    ====

    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.

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