F.2 MTH Question

問題翻譯~~
問題 1
在下面的圖中, 兩條線代表的方程式是 Ax -y = 1 及 x + y = B 相交於一點。
(a) 求A和B 的值。(4分)
(b) 求兩條線相交點的座標。(3分)
(c) 求陰影範圍的面積。(3分)

問題 2
當一顆石頭以每秒 u 米的初速被垂直向上拋, 方程式 h=ut - 5t² 代表了 t 秒後石頭的高度 h米。如初速是每秒20米, 求3秒後石頭的高度。

如果car:bus係75:50,最咪代表75架車:50架車?
答案：可以係
如果car:bus係75:50，即是
car 的數目：bus 的數目 = 75:50 = 3 : 2
所以 car 的數目可以是 3k, bus 的數目可以是 2k　 (而 k 是常數）
（75 及 50 只是其中１個可能性，而car 的數目可以例如是 150 , bus 的數目可以例如是 100, 只要 car 及 bus 的比是３：2 就可以了 ）


如有興趣, 以下是問題的答案:
Question 1
(a)
(1,0) is a point on the line Ax -y = 1, subsitute (1,0) into Ax-y =1
A(1) - 0 = 1
A= 1
(-3,0) is a point on the line x + y = B, substitute (-3,0) into x + y = B
(-3) + 0 = B
B = -3
therefore, A = 1 & B = -3

(b)
From (a), A = 1 & B = -3
the line Ax -y =1　becomes　x -y =1 ...................(1)
the line x+ y = B　becomes　x +y = -3 ...............(2)
(1) - (2)
(x -y) - (x+y) = 1- (-3)
-2y = 4
y = -2 ...............(3)
Substitute (3) into (1)
x - (-2) = 1
x = -1
therefore the coordinates of the point of intersection of the two lines is (-1, -2)

(c)
The shaded region is a triangle
Area of triangle = (1/2) x base x height
base is the distance between the points (1,0) & (-3,0) = 4
height is the y-coordinate of the point of intersection of the two lines = 2
therefore, the area of the shaded region
= (1/2)(4)(2)
= 4 square units

Question 2
h=ut - 5t²
the height of the stone after 3 seconds with initial speed is 20m/s
put u = 20, t =3
h = ut - 5t²
h = 20(3) - 5(3)²

h = 15
therefore, the height of stone after 3 seconds = 15 m