第=page11頁，共=sectionpages22頁高2024級高二上第一學(xué)月考試數(shù)學(xué)參考答案一．單選題題號12345678答案DABACBCC二．多選題題號91011答案ADADACD三．填空題12．13．1314．15．（1）解：記甲被公司錄取為事件A，乙被公司錄取為事件B，則，，···············································4分因為，故乙被該公司錄取的概率更大. ··············································6分（2）解：由（1）可知，，，····························10分故甲、乙兩人中僅有1人被該公司錄取的概率：················································11分.······································13分16．解：（1）在中，由正弦定理及得：，化簡可得：，································································4分由余弦定理得，又，所以·································7分（2）是的角平分線，則，········································9分由可得···························12分因為，，即有，故.···········································15分17．解：（1）由題意可得，解得，············2分由頻率分布直方圖可知的頻率為，而的頻率為，·····························3分所以第85百分位數(shù)在區(qū)間內(nèi)，設(shè)第85百分位數(shù)為，···································4分則，解得，所以第85百分位數(shù)為；·····························5分（2）由頻率分布直方圖可知年齡為，，的三組觀眾頻率之比為：，······6分所以按比例用分層隨機抽樣的方法抽取10人，則年齡在中的觀眾應(yīng)抽取4人；···············8分（3）由頻率分布直方圖可知的頻率為，的頻率為，··························9分所以，····················································12分.···································15分18．解：（1）因為直四棱柱中，底面，底面，所以.因為菱形，所以，平面，所以平面.······4分（2）設(shè)，連接，因為平面，所以，且，，所以是二面角的平面角.因為，，所以是正三角形，所以，.因為，在直角三角形中，所以二面角的正切值為.······················································10分（3）如圖，連接，，在直四棱柱中，，，所以四邊形是平行四邊形，所以，平面，平面，所以平面.同理，平面因為，，平面，所以平面平面，因為平面平面，平面平面，所以.·····················17分19．解：（1）因為，，所以，，所以，所以，解得.····························································5分（2）因為，，與的夾角為，所以，·······································7分由（1）知，，···················································8分所以.···········································10分（3）由（1）知，，所以.··························12分設(shè)與的夾角為，其中，··············································13分則，而，因為，所以，即，所以，所以.························15分因為，所以