★前，，泉州市2021屆高中畢業班質量監測（三）參考答案與評析高三數學解答題17-19題部分四、解答題：本題共6共70分。解答應寫出文字說明，證明過程或演算步驟。110分）知列{a，{b足n n

a19，

a0a91 n

ba1．n n（1：{b比；n（2列()nlgb}前n和S．n n前方核．題】，

b a 1n1 n1 ··············································································1分b a1nn 1010a911 10n n （非零常數·····························2分a1 a1nn1 1又b110．故n}為首項b0比q0的等比．··················31 11（（）由可知bbqn110n···································································4分1nn以c)ngb)nlg10n)nn．··············································5分n n n2當n，S(1)3)[(n1)n]；··················7分n22n當n，S1)3)(n)]nn1．9分n2n故

2,n為偶數，n1S ·······················································n1n 2,.；（2）（知bn

bqn10n．············································（通項公式分）4分1以c)ngb(1)nl0n1nn．·······························（運分5分n nS1)2()2(n1))1n)n ①n1S1(122()3(n1))nn)n1 ②·········（方法分）6分n①得2S))2()nn)n1······························）7分n n(1) n(1)11) n1 ····················（等數求和式9分211(1(1)(1)n1n)n12(2n)(211(1S故11n)(1)n1．···················································（論）10分n 4 4 2S故112分）脫貧攻堅取得的全面勝利是中國共產黨領導全國人民造，村民通過懸崖峭壁間的藤條結成的“藤梯”往返村子，稱為脫長脫貧．的,B隊在崖底的P,Q兩點處分別測得APQ，BPQ，1 1APB，AQP，BQP，且PQs2 2（）用,s示AP1 2（）已知1，，90.0米51.，又經計算得AP250.0米，求AB．1 2：sin130.22，cos130.974，n30，cs30.625．

參【命題意圖】本小題以“懸崖村”的脫貧事件為背景，以修建鋼梯的測量為問題情境，考查正弦定理余創建．（1）如圖，在△APQ中正得APsin2

PQ ，····················3分 snπ1 22n 得APs；·······································································5分1 2（2在△BPQ根弦得BPsin2

PQ ，····························6分 snπ1 200BP2 200BP2s可得 n1800.225 ，·······································7分1 2又△ABP得AB2AP2BP22APPs············10分代入得A2400006502200200.654000，所以AB200米．·············································································12分112分）效于8年組織技術團隊進行發酵工藝改良的項目研究．2020，品取0值M，步有0，成的10．區 [2,) [1,0) [0,1) [1,2) [2,3) [3,4)間改良改良改良改良改良來源前 后 前 后 前個數 3 1 5 2 30

改良改良改良改良改良改良改良后 前 后 前 后 前 后26 31 34 24 15 7 2品用值M．2 002 00 2M[0,1)一等品

M[1,3)二等品

M[0,3)三等品合格 不合格（1）取2為X求X；（2）潤單值M關為, M[0,3, M,,現“長%則20步,M[0,3).至？【命題意圖】本小題主要考查條件概率、獨立性檢驗、數學期望等基礎知識；考查數據處理能力、應意等．試解】1有20，有5有5．······················································2分X,2．·························································································3分P(X0)5C52C20C

21；····································································4分381 1P(X)15C515；·····································································5分C2 81 120P(X2)15C52C20C

1．·····································································6分19故X：XP

0 1 221 15 138 38 19由樣本估計總體的思想···········································································7 分改良前成品醋利潤的數學期望53035)55；··············8分0 0 0使“改良后長20%，良至為251)2. ·····································9分假改良后20有，10 10 10則，改良后的一等品有