【山東卷】.山東省青島市四區(qū)縣（膠州、平度、黃島、城陽）2024-2025學(xué)年高三上學(xué)期期中學(xué)業(yè)水平檢測考試（11.6-11.8）數(shù)學(xué)試卷答案

一、選擇題：本題共8小題，每小題5分，共40分。1-8：ADBBCCDA二、多項(xiàng)選擇題：本大題共3小題，每小題6分，共18分。9．AD10．BCD11．ACD三、填空題：本大題共3小題，每小題5分，共15分。12．g(x)=x（答案不唯一）13．202514．5，乙（第一空3分，第二空2分）四、解答題：本大題共5小題，共77分。解答應(yīng)寫出文字說明、證明過程或演算步驟。 解:（1）依題意， 即x=kπ+,k∈Z時(shí)，f(x)max=，··························································4分由g(x)在區(qū)間(0,)上單調(diào)遞增，解1）設(shè)等差數(shù)列{an}的公差為d（d≠0a2是a1和a4的等比中項(xiàng)，+d)2=9，····························································6分所以{bn+1-bn-10}是首項(xiàng)為-2，公比為2的等比數(shù)列，·········································9分n+1-bn-10=-2n，所以bn+1-bn=10-2n 13分24 n取最大值時(shí)n的值為4 即sinAcosC+3sinAsinCsinAcosCcosAsinCsinC=0··························3分因?yàn)锳是ΔABC的內(nèi)角，所以A=60o··································································6分所以·······························································8分所以·····································································10分)，sin2θ··················································································12分所以f(—)=0，且f(x)=aeax—1為增函數(shù)，······················································4分當(dāng)x<時(shí)，f(x)<0，f(x)在(∞,)單調(diào)遞減；當(dāng)x>時(shí)，f(x)>0，f(x)在(,+∞)單調(diào)遞增；af(x)在(—∞,)單調(diào)遞減，在(,+∞)單調(diào)遞增；所以f(0)=0>f(—)···················································································7分所以存在唯一x0∈(lna,)，使得f(x0)=綜上，當(dāng)0<a<1時(shí)，函數(shù)f(x)有兩個(gè)零點(diǎn)·····························································10分設(shè)曲線y=g(x)+kx+b與直線y=kx+b切點(diǎn)(x0,y0)，則{，0l2exex0x00l2exex0x0=0易證ex≥x+1，等號當(dāng)且僅當(dāng)x=0時(shí)成立；即···········································································6分定義f=數(shù)列記Q表示1,2,…,中任取m項(xiàng)構(gòu)成的單調(diào)遞增數(shù)列的全體，對于Q中的任意數(shù)列b1,b2,…,bm，因?yàn)閎k+1所以a1,a2,…,am單調(diào)遞增數(shù)列······································································1