高中数学联赛模拟试题10套5

636nn31234n−2A1B2C3D42y=f(x)[a,b]c(a,b)f(c)A()()2fafb+B2abf+⎛⎞⎜⎟⎝⎠C()()()()()bcfacafbba−+−−D()()()cafafbfaba−−⎡−⎤⎣⎦−3abca+b+c=1a2+b2+c2=1Aa+b1Ba+b=1Ca+b1Dab422221xyab+=32e=30,2P⎛⎞⎜⎟⎝⎠74b=A116B18C14D125S={1,2,,2003}ASAAA32003CB2210011002CC+C2210011002AA+D32003A6ABCD−A1B1C1D1AC1AABADAA1AC1V1V2V3V4AV4V1+V2+V3BV4=V1+V2+V3CV4V1+V2+V3D954133sincossincoskααββ==k2{an}a1=8k(k,ak)x2+y2=102_____3P−ABCPA=PB=aPC=AB=BC=CA=babab_____4Az=4(cosθ+isinθ)B2CABCABOADD_____5200313kk=∑8_____6100_____20y2=2px(p0)lABABMyM20ABCD−A1B1C1D1ABCDMA1B1C1D1NANB1M1ANB1M2ANB1M20abc222888abcbaccababc+++++950ABCD2PCDQPABABPAPBABCDPPAPB1AB2BC2AQBQ5012211,2nnnaaaaa++==⎧⎨=+⎩n11(a1,a2)(a3,a4)(a2k-1,a2k)x2+xy−y2+1=02f(x)=xn+xn-1−anx−an-1g(x)=x2−x−1g(x)f(x)50A1,A2,,AnAn112nAAAA=∪∪∪2ijAA≠∅∩1ijnmA{1,2,,m}13A1,A2,,A13Ai(1i13)Aiabba98b1D2C3A4C5B6C1111,,122⎛⎤⎡⎞−−⎜⎟⎥⎢⎝⎦⎣⎠∪2173()23,1−4()221143xy−+=546117600222,02,,088,2,,222lllpMpplplppllpMp⎧⎛⎞⎪⎜⎟⎝⎠⎪⎨⎛⎞−−⎪≥−⎜⎟⎪⎜⎟⎝⎠⎩122arccos31PAPB2APB902AQBQ=1m=117