[數學]93年台中女中數學科教甄考題
由 J+W 於 星期四 四月 20, 2006 6:40 pm
#ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl#1.相異三質數,積為和的29倍,求此三數? #ed_op#BR#ed_cl##ed_op#BR#ed_cl#2.L上兩點A(0,1,2)、B(1,1,3),點P在xy平面上,若P到x軸的距離等於P到L的距離, P的軌跡方程式? #ed_op#BR#ed_cl##ed_op#BR#ed_cl#3.(1)1,2,3,...,9876,共有幾個0? #ed_op#BR#ed_cl#(2)1,2,3,...,9876,有0的數共有幾個? #ed_op#BR#ed_cl##ed_op#BR#ed_cl#4.有一圓,半徑為5,圓上三點A,B,C,AB=AC=8,在劣弧BC及AB、AC上分別取三點 D、E、F,△DEF為正三角形,且BE=CF,求△DEF邊長? #ed_op#BR#ed_cl##ed_op#BR#ed_cl#5.曲線1:√3(x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#-y#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#)=2xy、曲線2:x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#-y#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#=c(c>0),P為其交點,L1、L2分別 #ed_op#BR#ed_cl#為過P之切線,(1)L1與L2夾角為?(2)曲線1為何種圖形?(說明理由) #ed_op#BR#ed_cl##ed_op#BR#ed_cl#6.F為拋物線:y#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#=4x之焦點,AB為一焦弦,ABC為正三角形,C在準線上, #ed_op#BR#ed_cl#求AF/BF=?(AF、BF為線段長) #ed_op#BR#ed_cl##ed_op#BR#ed_cl#7.Z為C,│Z│=1,求│Z#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#-Z+2│之最小值與最大值? #ed_op#BR#ed_cl##ed_op#BR#ed_cl#8.三角形ABC中,內角成等差,公差X,且csc2A、csc2B、csc2C也成等差, #ed_op#BR#ed_cl#求sinX? #ed_op#BR#ed_cl# 2003 2003#ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl#9.令a >0,k=1,2,3,...,2003,且西格馬 a =1,試證西格馬 1/1-a >2004 #ed_op#BR#ed_cl# k k=1 k k=1 #ed_op#BR#ed_cl##ed_op#/DIV#ed_cl##ed_op#/SPAN#ed_cl#