二九年山东省青岛市初级中学学业水平考试数学试题及答案(3)

∴抛物线开口向下． 在对称轴x?6左侧y随x的增大而增大． 由题意x?5，所以在4月份出售这种水产品每千克的利润最大．································· 9分 最大利润??18(4?6)?11?10212（元）． ··································································10分 23．（本小满分10分） 解：把一个正方形分割成11个小正方形： ············································································· 2分 图⑥ 把一个正三角形分割成4个小正三角形： ············································································· 3分 图a 把一个正三角形分割成6个小正三角形： ········································································· 5分 图b 把一个正三角形分割成9个、10个和11个小正三角形： 图c 图d 图e ················································· 8分 把一个正三角形分割成n（n≥9）个小正三角形的分割方法：通过“基本分割法1”、“基本分割法2”或其组合，把一个正三角形分割成9个、10个和11个小正三角形，再在此基础上每使用1次“基本分割法1”，就可增加3个小正三角形，从而把一个正三角形分割成12个、13个、14个小正三角形，依次类推，即可把一个正三角形分割成n（n≥9）个小正三角形． ··················································································································10分 24．（本小题满分12分） 解：（1）∵PE∥AB ∴DEDAt6?DPDB． A P B E Q N F D M C 而DE?t，DP?10?t， ∴?10?t10， ∴t?154． (s)，PE∥AB． ························ 2分 ∴当t?154 第 11 页 共 13 页 （2）∵EF平行且等于CD， ∴四边形CDEF是平行四边形． ∴?DEQ??C，?DQE??BDC． ∵BC?BD?10， ∴?DEQ??C??DQE??BDC． ∴△DEQ∽△BCD． ∴t10DEBC??EQCD． EQ425． t． ∴EQ?过B作BM⊥CD，交CD于M，过P作PN⊥EF，交EF于N． BM?10?2?22100?4?96?46． ∵ED?DQ?BP?t， ∴PQ?10?2t． 又△PNQ∽△BMD， PQBD?PNBM， PN10?2t10?46， t??PN?46?1?? 5??1212t?46246?t?46?1????t?t． ································ 6分 55?255?12?4?46?86． S△PEQ?EQ?PN?12?2（3）S△BCD?若S△PEQ?46252252?CD?BM?S△BCD， 则有?t?465t?225?86， 解得t1?1，t2?4． ····································································································· 9分 第 12 页 共 13 页 （4）在△PDE和△FBP中， ??PD?BF?10?t，??△PDE≌△FBP ?PDE??FBP，??DE?BP?t，∴S五边形PFCDE?S△PDE?S四边形PFCD ?S△FBP?S四边形PFCD ?S△BCD?86． ∴在运动过程中，五边形PFCDE的面积不变． ··························································12分 第 13 页 共 13 页