初二數(shù)學經(jīng)典難題

1、2012年初二數(shù)學經(jīng)典難題一、解答題（共10小題，滿分100分）1已知：如圖，p是正方形abcd內(nèi)點，pad=pda=15求證：pbc是正三角形（初二）2已知：如圖，在四邊形abcd中，ad=bc，m、n分別是ab、cd的中點，ad、bc的延長線交mn于e、f求證：den=f3如圖，分別以abc的邊ac、bc為一邊，在abc外作正方形acde和cbfg，點p是ef的中點，求證：點p到ab的距離是ab的一半4設p是平行四邊形abcd內(nèi)部的一點，且pba=pda求證：pab=pcb5p為正方形abcd內(nèi)的一點，并且pa=a，pb=2a，pc=3a，求正方形的邊長6一個圓柱形容器的容積為v立方米，開

2、始用一根小水管向容器內(nèi)注水，水面高度達到容器高度一半后，改用一根口徑為小水管2倍的大水管注水向容器中注滿水的全過程共用時間t分求兩根水管各自注水的速度7如圖1，已知正比例函數(shù)和反比例函數(shù)的圖象都經(jīng)過點m（-2，-1），且p（-1，-2）為雙曲線上的一點，q為坐標平面上一動點，pa垂直于x軸，qb垂直于y軸，垂足分別是a、b（1）寫出正比例函數(shù)和反比例函數(shù)的關系式；（2）當點q在直線mo上運動時，直線mo上是否存在這樣的點q，使得obq與oap面積相等？如果存在，請求出點的坐標，如果不存在，請說明理由；（3）如圖2，當點q在第一象限中的雙曲線上運動時，作以op、oq為鄰邊的平行四邊形opcq，求

3、平行四邊形opcq周長的最小值8如圖，p是邊長為1的正方形abcd對角線ac上一動點（p與a、c不重合），點e在線段bc上，且pe=pb（1）求證：pe=pd；pepd；（2）設ap=x，pbe的面積為y求出y關于x的函數(shù)關系式，并寫出x的取值范圍；當x取何值時，y取得最大值，并求出這個最大值9如圖，直線y=k1x+b與反比例函數(shù)yk2x（x0）的圖象交于a（1，6），b（a，3）兩點（1）求k1、k2的值（2）直接寫出k1x+bk2x0時x的取值范圍；（3）如圖，等腰梯形obcd中，bcod，ob=cd，od邊在x軸上，過點c作ceod于點e，ce和反比例函數(shù)的圖象交于點p，當梯形obcd的

4、面積為12時，請判斷pc和pe的大小關系，并說明理由10如圖，已知直線y=12x與雙曲線ykx(k0)交于a，b兩點，且點a的橫坐標為4（1）求k的值；（2）若雙曲線ykx(k0)上一點c的縱坐標為8，求aoc的面積；（3）過原點o的另一條直線l交雙曲線ykx(k0)于p，q兩點（p點在第一象限），若由點a，b，p，q為頂點組成的四邊形面積為24，求點p的坐標c29c91afe4ced1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afedd1b6c87d1b6c8795ad9c91afe4c

5、ed1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af95ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9d1b6c8795ad9c91afe4ced1b6c8795a1afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afc91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6cd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c87

6、95ad9c91fe4ced1b6c8795ad29c91af8795ad9c91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c87d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af5d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afad9c91fe4ced1b6c8795ad29c91afb6c8795ad29c91afb6c

7、8795ad29c91afd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91affe4ced1b6c8795ad29c91afc8795ad9c91fe4ced1b6c8795ad29c91afd1b6c8795ad9c91afed1b6c8795ad9c91afe4ced1b6c8795ad91a

8、fe4ced1b6c8d1b6c8795ad9c91afe4ced1d91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afc91fe4ced1d1b6c871afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afc91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6cd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af8795a

9、d9c91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c87d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af5d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afad9c91fe4ced1b6c8795ad29c91afb6c8795ad29c91afb6c8795ad29c91afd1b6c8795ad9c91afe4ced1

10、b6c8795ad91afe4ced1b6d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8791afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afc91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6cd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af8795ad9c91fe4ced1d1b6c8795ad9c91af

11、e4ced1b6c8795ad91afe4ced1b6c87d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af5d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afad9c91fe4ced1b6c8795ad29c91afb6c8795ad29c91afb6c8795ad29c91afd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6d1b6c879

12、5ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91affe4ced1b6c8795ad29c91afc8795ad9c91fe4ced1b6c8795ad29c91afd1b6c8795ad9c91afed1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8d1b6c8795ad9c91afe4ced15ad9c91d1b6c8795ad9c91afe4ced1b

13、6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91affe4ced1b6c8795ad29c91afc8795ad9c91fe4ced1b6c8795ad29c91afd1b6c8795ad9c91afed1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8d1b6c8795ad9c91afe4ced195ad9c91afe4ced1b6c8795ad91afe4ced1b6cd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6

14、c8795ad29c91af8795ad9c91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c87d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af5d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afad9c91fe4ced1b6c8795ad29c91afb6c8795ad29c91afb6c8795ad29c91afd1b6

15、c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91affe4ced1b6c8795ad29c91afc8795ad9c91fe4ced1b6c8795ad29c91afd1b6c8795ad9c91afed1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8d1b6c8

16、795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af795ad9c91fe4ced1b6c8795add1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af29c91af4ced1b6c8795ad1b6c8795ad9c91afe4ced1b6c8795ad91afd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795

17、ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afd1b6c8795ad29c91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afd91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c9d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af1afd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afd1bd1b6c