MC questions for points

Q40




圖片參考：https://s.yimg.com/rk/HA00981853/o/726259189.png


∵ M is the centroid of ΔABC
∴ AM:MN = 2:1
AM = (√3)(2/3) = (2√3)/3


圖片參考：https://s.yimg.com/rk/HA00981853/o/1821453340.png


In ΔAMD,
DM² = 2²-[(2√3)/3]²
DM ≈ 1.632993

So, volume
=(1/3)( (1/2)(2)(2)sin60° ) (1.632993)
≈0.943cm³



Q41

In ΔBFG,
∠EFB = 90°-35°-35° = 20°

In ΔBEF,
cos20° = BF/EF
EF = BF/cos20°

tan20° = BE/BF
BE= BFtan20°

In ΔADE,
tan(Ans.) = AE/AD
= (AG+GE)/(AG+GE+BE)
= (BF+EF)/(BF+EF+BE)
= (BF+BF/cos20°)/(BF+BF/cos20°+BFtan20°)
= (1+cos20°)/(1+cos20°+tan20°)
Ans.≈ 40°



Q42

圖片參考：https://s.yimg.com/rk/HA00981853/o/522214932.png

In ΔCDE,
sinα = 1/CD
CD = 1/sinα


∵ABCD is a rhombus
∴AB=BC=CD=AD

Area of ΔABD
= (1/2)(AB)(AD)sinα
= (1/2)(1/sinα)²sinα
= (1/2)(1/sinα)

Area of ABCD
=2*Area of ΔABD
=1/sinα



Q44

圖片參考：https://s.yimg.com/rk/HA00981853/o/1618042395.png


lower score -μ/
圖片參考：https://s.yimg.com/lo/api/res/1.2/Nk0ktwMwQFNXbhokJXCgmQ--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/http://upload.wikimedia.org/math/9/d/4/9d43cb8bbcb702e9d5943de477f099e2.png
= -1
lower score = μ-
圖片參考：https://s.yimg.com/lo/api/res/1.2/Nk0ktwMwQFNXbhokJXCgmQ--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/http://upload.wikimedia.org/math/9/d/4/9d43cb8bbcb702e9d5943de477f099e2.png


upper score -μ/
圖片參考：https://s.yimg.com/lo/api/res/1.2/Nk0ktwMwQFNXbhokJXCgmQ--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/http://upload.wikimedia.org/math/9/d/4/9d43cb8bbcb702e9d5943de477f099e2.png
= 2
upper score =μ+2
圖片參考：https://s.yimg.com/lo/api/res/1.2/Nk0ktwMwQFNXbhokJXCgmQ--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/http://upload.wikimedia.org/math/9/d/4/9d43cb8bbcb702e9d5943de477f099e2.png


So, the range is the yellow area in the above figure

Number of students
= 60000*(95/2+68/2)%
= 48900


2015-04-12 03:05:47 補充：
~更多/更快的方法請參考意見欄~

2015-04-12 03:11:52 補充：
Q40 這裏有條公式:
http://mathseasy.hk/articles/tetrahedron/
記到就記, 記唔到用其他方法都可以.