全国初中数学竞赛具体是怎么回事呢？ 全国初中数学竞赛问题。
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2\u3001\u4ee3\u6570\u5f0f
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3\u3001\u6052\u7b49\u5f0f\u4e0e\u6052\u7b49\u53d8\u5f62
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5\u3001\u51fd\u6570
y=|ax+b|,y=|ax2+bx+c|\u53ca y=ax2+bx+c\u7684\u56fe\u50cf\u548c\u6027\u8d28\u3002
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6\u3001\u903b\u8f91\u63a8\u7406\u95ee\u9898
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7\u3001\u51e0\u4f55
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2008\u5e74\u5168\u56fd\u521d\u4e2d\u6570\u5b66\u8054\u8d5b\u7b2c\u4e00\u8bd5\u8bd5\u9898\u53ca\u53c2\u8003\u7b54\u6848
\u4e00\u3001\u9009\u62e9\u9898\uff1a(\u672c\u9898\u6ee1\u520642\u5206\uff0c\u6bcf\u5c0f\u98987\u5206)
1.\u8bbea2+1=3a\uff0cb2+1=3b\uff0c\u4e14a\u2260b\uff0c\u5219\u4ee3\u6570\u5f0f+\u7684\u503c\u4e3a( )
A.5 B.7 C.9 D.11
2.\u5982\u56fe\uff0c\u8bbeAD\uff0cBE\uff0cCF\u4e3a\u25b3ABC\u7684\u4e09\u6761\u9ad8\uff0c\u82e5AB=6\uff0cBC=5\uff0cEF=3\uff0c\u5219\u7ebf\u6bb5BE\u7684\u957f\u4e3a( )
A. B.4 C. D.
3.\u4ece\u5206\u522b\u5199\u6709\u6570\u5b571\uff0c2\uff0c3\uff0c4\uff0c5\u76845\u5f20\u5361\u7247\u4e2d\u4efb\u610f\u53d6\u51fa\u4e24\u5f20\uff0c\u628a\u7b2c\u4e00\u5f20\u5361\u7247\u4e0a\u7684\u6570\u5b57\u4f5c\u4e3a\u5341\u4f4d\u6570\u5b57\uff0c\u7b2c\u4e8c\u5f20\u5361\u7247\u4e0a\u7684\u6570\u5b57\u4f5c\u4e3a\u4e2a\u4f4d\u6570\u5b57\uff0c\u7ec4\u6210\u4e00\u4e2a\u4e24\u4f4d\u6570\uff0c\u5219\u6240\u7ec4\u6210\u7684\u6570\u662f3\u7684\u500d\u6570\u7684\u6982\u7387\u662f( )
A. B. C. D.
4.\u5728\u25b3ABC\u4e2d\uff0c\u2220ABC=12\u00b0\uff0c\u2220ACB=132\u00b0\uff0cBM\u548cCN\u5206\u522b\u662f\u8fd9\u4e24\u4e2a\u89d2\u7684\u5916\u89d2\u5e73\u5206\u7ebf\uff0c\u4e14\u70b9M\uff0cN\u5206\u522b\u5728\u76f4\u7ebfAC\u548c\u76f4\u7ebfAB\u4e0a\uff0c\u5219( )
A.BM\uff1eCN B.BM=CN C.BM\uff1cCN D.BM\u548cCN\u7684\u5927\u5c0f\u5173\u7cfb\u4e0d\u786e\u5b9a
5.\u73b0\u6709\u4ef7\u683c\u76f8\u540c\u76845\u79cd\u4e0d\u540c\u5546\u54c1\uff0c\u4ece\u4eca\u5929\u5f00\u59cb\u6bcf\u5929\u5206\u522b\u964d\u4ef710\uff05\u621620\uff05\uff0c\u82e5\u5e72\u5929\u540e\uff0c\u8fd95\u79cd\u5546\u54c1\u7684\u4ef7\u683c\u4e92\u4e0d\u76f8\u540c\uff0c\u8bbe\u6700\u9ad8\u4ef7\u683c\u548c\u6700\u4f4e\u4ef7\u683c\u7684\u6bd4\u503c\u4e3ar\uff0c\u5219r\u7684\u6700\u5c0f\u503c\u4e3a( )
A.()3 B.()4 C.()5 D.
6.\u5df2\u77e5\u5b9e\u6570x\uff0cy\u6ee1\u8db3(x-)(y-)=2008\uff0c\u52193x2-2y2+3x-3y-2007\u7684\u503c\u4e3a( )
A.-2008 B.2008 C.-1 D.1
\u4e8c\u3001\u586b\u7a7a\u9898\uff1a(\u672c\u9898\u6ee1\u520628\u5206\uff0c\u6bcf\u5c0f\u98987\u5206)
1.\u8bbea =\uff0c\u5219=_____________.
2.\u5982\u56fe\uff0c\u6b63\u65b9\u5f62ABCD\u7684\u8fb9\u957f\u4e3a1\uff0cM\uff0cN\u4e3aBD\u6240\u5728\u76f4\u7ebf\u4e0a\u7684\u4e24\u70b9\uff0c\u4e14AM=\uff0c\u2220MAN=135\u00b0\uff0c\u5219\u56db\u8fb9\u5f62AMCN\u7684\u9762\u79ef\u4e3a_______________.
3.\u5df2\u77e5\u4e8c\u6b21\u51fd\u6570y=x2+ax+b\u7684\u56fe\u8c61\u4e0ex\u8f74\u7684\u4e24\u4e2a\u4ea4\u70b9\u7684\u6a2a\u5750\u6807\u5206\u522b\u4e3am\uff0cn\uff0c\u4e14|m|+|n|\u22641.\u8bbe\u6ee1\u8db3\u4e0a\u8ff0\u8981\u6c42\u7684b\u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\u5206\u522b\u4e3ap\uff0cq\uff0c\u5219|p|+|q|=___________.
4.\u4f9d\u6b21\u5c06\u6b63\u6574\u65701\uff0c2\uff0c3\uff0c\u2026\u7684\u5e73\u65b9\u6570\u6392\u6210\u4e00\u4e32\uff1a149162536496481100121144\u2026\uff0c\u6392\u5728\u7b2c1\u4e2a\u4f4d\u7f6e\u7684\u6570\u5b57\u662f1\uff0c\u6392\u5728\u7b2c5\u4e2a\u4f4d\u7f6e\u7684\u6570\u5b57\u662f6\uff0c\u6392\u5728\u7b2c10\u4e2a\u4f4d\u7f6e\u7684\u6570\u5b57\u662f4\uff0c\u6392\u5728\u7b2c2008\u4e2a\u4f4d\u7f6e\u7684\u6570\u5b57\u662f _________.
\u7b54\u6848
\u4e00\u30011.B 2.D 3.C 4.B 5.B 6.D
\u4e8c\u30011.- 2 2. 3. 4.1
\u89e3\u7b54\uff1a\u4e00\u30011.\u7531\u9898\u8bbe\u6761\u4ef6\u53ef\u77e5a2-3a+1=0\uff0cb2-3b+1=0\uff0c\u4e14a\u2260b\uff0c
\u6240\u4ee5a\uff0cb\u662f\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0bx2-3x+1=0\u7684\u4e24\u6839\uff0c\u6545a+b=3\uff0cab=1.
\u56e0\u6b64+====7.
2.\u56e0\u4e3aAD\uff0cBE\uff0cCF\u4e3a\u25b3ABC\u7684\u4e09\u6761\u9ad8\uff0c\u6613\u77e5B\uff0cC\uff0cE\uff0cF\u56db\u70b9\u5171\u5706\uff0c
\u4e8e\u662f\u25b3AEF\u223d\u25b3ABC\uff0c\u6545==\uff0c\u5373cos\u2220BAC=\uff0c\u6240\u4ee5sin\u2220BAC=.
\u5728Rt\u25b3ABE\u4e2d\uff0cBE=ABsin\u2220BAC=6\u00d7=.
3.\u80fd\u591f\u7ec4\u6210\u7684\u4e24\u4f4d\u6570\u670912\uff0c13\uff0c14\uff0c15\uff0c21\uff0c23\uff0c24\uff0c25\uff0c31\uff0c32\uff0c34\uff0c35\uff0c41\uff0c42\uff0c43\uff0c45\uff0c51\uff0c52\uff0c53\uff0c54\uff0c\u517120\u4e2a\uff0c\u5176\u4e2d\u662f3\u7684\u500d\u6570\u7684\u6570\u4e3a12\uff0c15\uff0c21\uff0c24\uff0c42\uff0c45\uff0c51\uff0c54\uff0c\u51718\u4e2a\uff0c\u6240\u4ee5\u6240\u7ec4\u6210\u7684\u6570\u662f3\u7684\u500d\u6570\u7684\u6982\u7387\u662f=.
4.\u2235\u2220ABC=12\u00b0\uff0cBM\u4e3a\u2220ABC\u7684\u5916\u89d2\u5e73\u5206\u7ebf\uff0c\u2234\u2220MBC =(180\u00b0-12\u00b0)=84\u00b0.
\u53c8\u2220BCM = 180\u00b0-\u2220ACB=180\u00b0-132\u00b0=48\u00b0\uff0c\u2234\u2220BCM=180\u00b0-84\u00b0-48\u00b0=48\u00b0.
\u2234BM=BC.\u53c8\u2220ACN=(180\u00b0-\u2220ACB)=(180\u00b0-132\u00b0)=24\u00b0\uff0c
\u2234\u2220BNC=180\u00b0-\u2220ABC-\u2220BCN= 180\u00b0-12\u00b0-(\u2220ACB+\u2220CAN)=12\u00b0=\u2220ABC.
\u2234CN=CB.\u56e0\u6b64\uff0cBM=BC=CN.
5.\u5bb9\u6613\u77e5\u9053\uff0c4\u5929\u4e4b\u540e\u5c31\u53ef\u4ee5\u51fa\u73b05\u79cd\u5546\u54c1\u7684\u4ef7\u683c\u4e92\u4e0d\u76f8\u540c\u7684\u60c5\u51b5.
\u8bbe5\u79cd\u5546\u54c1\u964d\u4ef7\u524d\u7684\u4ef7\u683c\u4e3aa\uff0c\u8fc7\u4e86n\u5929\uff0cn\u5929\u540e\u6bcf\u79cd\u5546\u54c1\u7684\u4ef7\u683c\u4e00\u5b9a\u53ef\u4ee5\u8868\u793a\u4e3aa\u00b7(1-10%)k \u00b7(1-20%)n-k=a\u00b7()k\u00b7()n-k\uff0c\u5176\u4e2dk\u4e3a\u81ea\u7136\u6570\uff0c\u4e140\u2264k \u2264n\uff0c\u8981\u4f7fr\u7684\u503c\u6700\u5c0f\uff0c\u4e94\u79cd\u5546\u54c1\u7684\u4ef7\u683c\u5e94\u8be5\u5206\u522b\u4e3a\uff1aa\u00b7()i\u00b7()n-i\uff0ca\u00b7()i+1\u00b7()n-i-1\uff0ca\u00b7()i+2\u00b7()n-i-2\uff0ca\u00b7()i+3\u00b7()n-i-3\uff0ca\u00b7()i+4\u00b7()n-i-4.
\u5176\u4e2di\u4e3a\u4e0d\u8d85\u8fc7n\u7684\u81ea\u7136\u6570\uff0c\u6240\u4ee5r\u7684\u6700\u5c0f\u503c\u4e3a=()4.
6.\u2235(x-)(y-)=2008\uff0c
\u2234x-==y+\uff0cy-==x+.
\u7531\u4ee5\u4e0a\u4e24\u5f0f\u53ef\u5f97x=y\uff0c \u6240\u4ee5(x-)2=2008.\u89e3\u5f97x2=2008.
\u6240\u4ee53x2-2y2+3x-3y-2007=3x2-2x2+3x-3x-2007=x2-2007=1.
\u4e8c\u30011.\u2235a2=()2==1-a\uff0c\u2234a2+a=1.
\u2234\u539f\u5f0f=
===-=-(1+a+a2)=-(1+1)=-2.
2.\u8bbeBD\u4e2d\u70b9\u4e3aO\uff0c\u8fdeAO\uff0c\u5219AO\u22a5BD\uff0cAO=OB=\uff0cMO==\uff0c
\u2234MB=MO-OB=.\u53c8\u2220ABM=\u2220NDA=135\u00b0\uff0c
\u2220NAD=\u2220MAN-\u2220DAB-\u2220MAB=135\u00b0-90\u00b0-\u2220MAB=45\u00b0-\u2220MAB=\u2220AMB\uff0c
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.
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A. . B. . C. . D. .
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4\uff0e\u8bbe\u6b63\u65b9\u5f62ABCD\u7684\u4e2d\u5fc3\u4e3a\u70b9O\uff0c\u5728\u4ee5\u4e94\u4e2a\u70b9A\u3001B\u3001C\u3001D\u3001O\u4e3a\u9876\u70b9\u6240\u6784\u6210\u7684\u6240\u6709\u4e09\u89d2\u5f62\u4e2d\u4efb\u610f\u53d6\u51fa\u4e24\u4e2a\uff0c\u5b83\u4eec\u7684\u9762\u79ef\u76f8\u7b49\u7684\u6982\u7387\u4e3a \uff08 \uff09
A. . B. . C. . D. .
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\u56e0\u6b64\uff0c\u6240\u6c42\u7684\u6982\u7387\u4e3a .
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A. . B. . C. . D. .
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6\uff0e\u8bbe \u662f\u5927\u4e8e1909\u7684\u6b63\u6574\u6570\uff0c\u4f7f\u5f97 \u4e3a\u5b8c\u5168\u5e73\u65b9\u6570\u7684 \u7684\u4e2a\u6570\u662f \uff08 \uff09
A.3. B. 4. C. 5. D. 6.
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\u89e3\u5f97 .
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\u6240\u4ee5\u56db\u8fb9\u5f62DECF\u7684\u9762\u79ef\u4e3a .
3\uff0e\u5982\u679c\u5b9e\u6570 \u6ee1\u8db3\u6761\u4ef6 \uff0c \uff0c\u5219 ______.
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4\uff0e\u5df2\u77e5 \u662f\u6b63\u6574\u6570\uff0c\u4e14\u6ee1\u8db3 \u662f\u6574\u6570\uff0c\u5219\u8fd9\u6837\u7684\u6709\u5e8f\u6570\u5bf9 \u5171\u6709_____\u5bf9.
\u3010\u7b54\u3011 7.
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\u540c\u7406\u53ef\u5f97 \uff08\u5176\u4e2d \u4e3a\u6b63\u6574\u6570\uff09\uff0c\u5219 .
\u53c8 \uff0c\u6240\u4ee5 \uff0c\u6240\u4ee5 .
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\uff082\uff09 \u65f6\uff0c\u540c\u7406\u53ef\u6c42\u5f97 .
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\uff084\uff09 \u65f6\uff0c\u540c\u7406\u53ef\u6c42\u5f97 .
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\uff082\uff09\u5982\u679cAB\u6070\u597d\u4e3a\u2299P\u7684\u76f4\u5f84\u4e14 \uff0c\u6c42 \u548c \u7684\u503c.
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