maths mc X 2

38.

Reflecting in the y-axis means that (x, y) on the original curve will be changed to (-x, y).
Both (x,y) and (-x,y) have the same distance, equal to the absolute value of x (+x if x is positive or –x if x is negative), from the y-axis but on different sides of the y-axis.

Therefore, for (i), y=f(x) is changed to y=f(-x).

Translating 5 units downward means each point on the original curve is moved towards the negative direction of y. The y-coordinate of each point should minus 5.

For (ii), y=f(-x) – 5

The answer is D.

23.

Let O be the centre, i.e. OA=OB=OC=OD

Angle EBC + Angle ECB + Angle CEB = 180º (Angle sum of triangle)

Angle EBC + Angle ECB + 63º = 180º

Angle EBC + Angle ECB = 180º - 63º = 117º

Angle EBC = Angle EDA; Angle ECB = Angle EAD (Exterior angle equal to opposite interior angle, cyclic quadrilateral)

Therefore Angle EDA + Angle EAD = 117º

Angle COA = 2 ×Angle EDA; Angle BOD = 2 × Angle EAD (Angle at centre twice angle at circumference)

Angle COA + Angle BOD = 2 × 117º = 234º

Angle COA = Angle COB + Angle BOA; Angle BOD = Angle BOC + Angle COD

Angle COB + Angle BOA + Angle BOC + Angle COD = 234º

As BOD is a straight line, Angle BOA + Angle BOC + Angle COD = 180º

Angle COB + 180º = 234º, Angle COB = 234º - 180º = 54º

Length of Arc BC = π × 20 cm × 54º / 360º = 3π cm

Answer is C.

2007-04-17 17:58:47 補充：
雖然好似好多steps，但是只為求清楚的解釋罷了．兩題並不繁複，因為MC不用寫出steps，在腦裏想過以上的步驟便可以．

38) A
reflect ma, y1=-y,
y=f(x) => , -y1=f(x) => y1=-f(x)

move down 5 ma, y2=y1-5,
y2=-f(x)-5

where y2 is the new function, g(x) lor


23) C
draw point F at centre of the semi-circle.

2007-04-17 17:57:46 補充：
38) D is the correct answer. (睇錯題..唔係reflect along x-axis)y1=f(-x)y2=f(-x)-5=g(x)

2007-04-17 18:07:25 補充：
let

38 ans is D
refer process ii) the result must be A or D, since the function 5 units downwards, the final function should be -5.
refer process i) the function reflects at y-axis, threrfore the answer is D.
since if a quadratic function times (-1) the function should be reflects at x-axis.

39) ans is C