高一数学参考答案一、选择题：1－4：CBCC5－8：CCCB二、选择题：9．ACD10．ABD11．AD三、填空题：312．13．114．45四、解答题：本题共5小题，共77分．解答应写出文字说明、证明过程或演算步棸．53π15．(1)∵sinα＝－，α∈(π，)5225∴cosα＝－1－sin2α＝－···························································································2分5sinα1∴tanα＝＝·············································································································4分cosα22tanα4∴tan2α＝＝······································································································6分1－tan2α33ππ(2)∵α∈(π，)，β∈(，π)223π5π∴α＋β∈(，)·········································································································7分2212∴cos(α＋β)＝1－sin2(α＋β)＝······················································································9分13∴sinβ＝sin(α＋β－α)＝sin(α＋β)cosα－cos(α＋β)sinα··························································································11分52512525＝()×(－)－×(－)＝···············································································13分1351356516．(1)由频率直方图知(0.004＋0.022＋0.030＋0.028＋m＋0.004)×10＝1∴m＝0.012················································································································2分易知[40，50)，[50，60)，[60，70)，[70，80)，[80，90)，[90，100]相应的频率分别为0.04，0.22，0.30，0.28，0.12，0.04∴100名同学的平均成绩估计值为：0.04×45＋0.22×55＋0.30×65＋0.28×75＋0.12×85＋0.04×95＝68.4······································5分（2）①由(1)知A等级的频率为0.04，A等级的人数为100×0.04＝4人B等级的频率为(0.28＋0.12)＝0.4，B等级的人数为100×0.4＝40人C等级的频率为(0.04＋0.22＋0.30)＝0.56，C等级的人数为100×0.56＝56人40∴抽取25人中B等级中的人数为25×＝10人··························································9分4＋40＋56②用频率代替概率，所以抽取一次，B等级被抽中的概率为0.4··············································11分抽取三次都没有抽中B等级的概率＝(1－0.4)3＝0.216所以随机抽取3人至少有一人为B等级的概率＝1－0.216＝0.784·············································15分17．(1)∵AP⊥BC→→→∴AP是AC在AP方向上的投影向量····················································································2分→→→→∴AP·AC＝AP2＝|AP|2＝32∴AP＝42·······