2020年2月2日 星期日

104學年度臺北市聯合轉學考-高中升高三-數學科詳解


臺北市高級中等學校 104 學年度聯合轉學考招生考試
升高三數學科試題
一、單選題


:(x+1)216y29=1{a=4b=3(3,0),(5,0):x29+y24{a=3b=2(3,0),(3,0)(3,0)(B)


(2+3t)3(12t)+4(1+at)=39t+4at=0t(9+4a)=0a=9/4(D)



(A)×:{[1000][1234]=[1200][1000][1299]=[1200][1234][1299](B)×:ABBA(A+B)(AB)=A2AB+BAB2A2B2(C):I(B+C)=IB+IC=B+C=BI+CI=(B+C)I(D)×:(B)AB=BA(A+B)2A2+2AB+B2(E)×:(AB)1=B1A1(C)


¯AB¯AC=sinCsinB=125cosC4/5=3cosC=3×513=1513(A)



{tanθ<0sinθ<0{cosθ>0sinθ<0tan2θ=sin2θcos2θ=2sinθcosθ2cos2θ1<0(E)




¯AP¯BP=dist(A,L)dist(B,L)=1+435/|1103|5=2/14=1/7(D)


{u=(2,1)a=(1,2)b=(2,1)c=(1,2)d=(1,2)e=(2,1){ua=2+2<0ub=221<0uc=22<0ud=22>0cosθd=ud|u||d|=2215ue=221>0cosθe=ue|u||e|=22115cosθe>cosθdθd>θeθe(E)


E:2xy2z1=0n=(2,1,2)A(1,0,1)EL1:(2t+1,t,2t+1)E2(2t+1)(t)2(2t+1)1=0t=1/9L1AEA(11/9,1/9,7/9)B(2,2,3)EL2:(2t+2,t+2,2t+3)E2(2t+2)(t+2)2(2t+3)1=0t=5/9BEB(28/9,13/9,17/9)¯AB=(17/9)2+(14/9)2+(10/9)2=3659=65/3(E)



{L1:x12=y1a=z14L2:x+11=y32=z73{L1:(2s+1,as+1,4s+1)L2:(t1,2t+3,3t+7){2s+1=t1as+1=2t+34s+1=3t+7{s=6t=10a=(2t+2)/sa=18/(6)=3(A)


a:b:c=sinA:sinB:sinC=4:5:6{a=4kb=5kc=6kcosC=a2+b2c22ab=16k2+25k236k240k2=18(D)



x2+y28x6y+21=0(x4)2+(y3)2=4{C(4,3)r=2Y{26213452611+2×3+1=8Y(D)


{x0y02x+y64x+7y28{O(0,0)A(0,4)B(7/5,16/5)C(3,0)f(x,y)=3x2y+1{f(O)=1f(A)7f(B)=4/5f(C)=1010(C)


PxyPOQ(B)





OAB{a=OA=(1,2)b=OB=(2,3)s+t=1OC=ta+sbC¯AB;|OC|¯OC¯AB;{OAB=12||1223||=1/2¯AB=22ׯOC÷2=1/2¯OC=2/2(B)

二、多重選擇題



(A)×:(AB)1=B1A1(B)×:AB=BCA=BCB1(C):(AB)1=B1A1(AB)1B1A1(D)×:AB=3Idet(AB)=det(3A)det(A)×det(B)=3×det(A)det(B)=3(E):ABA1=IABA1A=IAAB=AA1AB=A1AB=I(CE)


(A):32+5272=3449<03(B)×:52+6272=6149>0(C)×:5+6<13(D):102+242272=676729<0(E):652+7821392=1030919321<0(ADE)






(A)×:PQ//(3,4)(3,4)(3,4),(3,4)(3,4)0(B)×:¯PQ=2×dist(P,L)=2×|3s4t|5(C)×:Q=(t,s)P,QR=(t+s2,s+t2)3×s+t24×s+t20RL(D):AL¯PQLQL¯POLRL//L¯PO¯PR=¯PA¯AQ=11PRR=(s,t)(E):OLOP+OQ=L(OP+OQ)PQ(DE)




{△=|12a11b351|=15a+6b3a2+5b=8a+11b1z=|12111235c|=c5+1232c+10=14c(A):8a11b1⇒△≠0(B)×:(C)×:(0)c14(D)×:8a11b=1=0(E):=0z0c14(AE)


滿¯AP=¯AQA¯PQ¯PQ3(3)42=31/3(D)1/3(ABCE)




解題僅供參考

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