数学参考答案第1页（共4页）2024届南宁市初中毕业班适应性测试数学参考答案一、选择题（本大题共12小题，每小题3分，共36分）题号123456789101112答案ABACABDACBDC二、填空题（本大题共6小题，每小题2分，共12分）13．x(x-5)；14．x≥3；15．31；16．（0，6）；17．25；18．2nm．三、解答题（本大题共72分）19．（本题满分6分）解：原式＝）（19+2，·····························3分＝-9+2，·····································4分＝-7．········································6分20．（本题满分6分）解：原式＝22222babbaba，·············2分＝aba42．································4分当a＝2，b＝-41时，原式＝）（412422，·····················5分＝4-2＝2．··········································6分21．（本题满分10分）（1）如图所示，CE即为所求；·····················5分（2）证明： 在Rt△ABC中，∠ACB=90°，∠A=40°，∴∠B=90°-40°=50°．··················6分又点D为AB中点，∴CD=BD．·······························7分∴∠B=∠DCB=50°．·················8分 CE平分∠BCD，∴∠BCE=21∠BCD=25°．···········9分∴∠AEC=∠B+∠BCE=75°．········10分（第21题图）{#{QQABAYCUggAoAIJAARhCQQ2QCAMQkBEACAoGhFAEIAAByAFABAA=}#}数学参考答案第2页（共4页）22．（本题满分10分）（1）m＝40，a＝12，n%＝40%；·················3分（2）他的说法是错误的．····························4分理由如下： 在参加测试的40名学生测试成绩中，排在最中间的两个分数都是85，∴中位数为8528585．·····················6分 84＜85，∴有一半以上的同学成绩超过了84分．···7分∴小邕的说法是错误的．（3）解：500×(40%+30%)＝350（人）············9分答：估计本年级中食品安全意识良好的学生人数为350人．····················10分23．（本题满分10分）（1）证明： AB∥DE，∴∠B＝∠E．······································1分又BF＝CE，∴BF+FC＝CE+FC，即BC=EF．·············2分在△ABC和△DEF中ABDEBEBCEF，·····································3分∴△ABC≌△DEF（SAS）．···················4分（2）解：连接AD交FC于点O， △ABC≌△DEF，∴AC＝DF，∠ACB＝∠DFE．················5分∴AC∥DF．∴四边形ACDF是平行四边形．又AF＝FD，∴四边形ACDF是菱形．·······················6分∴AD⊥CF，OF＝OC＝12FC＝2．在Rt△ACO中∴2222(13)23AOACOC，··7分∴AD＝2AO＝6．··································8分∴S四边形ACDF=11641222FCAD．·····10分（第23题图）{#{QQABAYCUggAoAIJAARhCQQ2QCAMQkBEACAoGhFAEIAAByAFABAA=}#}数学参考答案第3页（共4页）24．（本题满分10分）（1）解：设团购群1《儒林外史》和《简爱》的单价分别是x元、y元；············1分由题意得：288342201223yxyx，·····3分解得3248yx．···························5分答：团购群1《儒林外史》和《简爱》的单价分别是48元、32元．············6分（2）解：团购群1：（元））（8407.0153248，·······················...