F6 Math

21. Join AB, since arc BC : arc AD = 1 : 4, therefore
ㄥBAC : ㄥABD = 1 : 4 = 12° : 48°
ㄥAOD = 2*ㄥABD . . . . (ㄥ at center = twice ㄥ at circumference)
Therefore ㄥAOD = 96° (Ans : B)45. Let the data be a1, a2, ... an, mean = m
Therefore,
am = 18 . . . . . . . . . . (i)
au - al = 8 . . . . . . . . (ii)
[Σ(ai - m)^2]/n = 16 . . . (iii)
New data are 4(a1-3), 4(a2-3), ... 4(an-3)
Therefore new mean = 4(m-3)
New median
= 4(am - 3)
= 4(am) - 12
= 4(18) - 12 . . . . . . . .[from (i)]
= 60
New inter-quartile range
= 4(au - 3) - 4(al - 3)
= 4(au - al)
= 4(8) . . . . . . . . . . .[from (ii)]
= 32
New variance
= {Σ[4(ai-3) - 4(m-3)]^2}/n
= {Σ[4(ai - m)]^2}/n
= [Σ16(ai - m)^2]/n
= 16[Σ(ai - m)^2]/n
= 16(16) . . . . . . . . . [from (iii)]
= 256
(Ans : B)