安徽省合肥市六校聯(lián)盟2023-2024學(xué)年高三上學(xué)期期中聯(lián)考數(shù)學(xué) 無(wú)答案

安徽省合肥市六校聯(lián)盟20232024學(xué)年高三上學(xué)期期中聯(lián)考數(shù)學(xué)Word版無(wú)答案一、選擇題（本大題共10小題，每小題5分，共50分）1.若復(fù)數(shù)$z=a+bi$（其中$a,b$為實(shí)數(shù)），滿足$z^2=(1+i)z$，則$z$的模長(zhǎng)為（）A.$\sqrt{2}$B.$1$C.$2$D.$\frac{\sqrt{2}}{2}$2.已知函數(shù)$f(x)=\ln(x^21)2\ln(x1)$，則$f(x)$的定義域?yàn)椋ǎ〢.$(\infty,1)\cup(1,+\infty)$B.$(1,+\infty)$C.$(\infty,0)\cup(0,+\infty)$D.$(\infty,1)\cup(1,0)\cup(0,+\infty)$3.在$\triangleABC$中，若$\angleA=60^\circ$，$BC=2$，$AC=3$，則$\sinB$的值為（）A.$\frac{\sqrt{3}}{3}$B.$\frac{\sqrt{21}}{14}$C.$\frac{\sqrt{7}}{7}$D.$\frac{\sqrt{5}}{5}$4.若函數(shù)$y=ax^2+bx+c$的圖像開(kāi)口向上，且以$x=1$為對(duì)稱(chēng)軸，則$a$和$b$的關(guān)系為（）A.$a=b$B.$a=b$C.$a+b=0$D.$ab=0$5.已知數(shù)列$\{a_n\}$滿足$a_1=1$，$a_{n+1}=2a_n+n$，則$a_5$的值為（）A.$31$B.$32$C.$33$D.$34$6.若函數(shù)$f(x)=\begin{cases}x^2,&x\leq0\\ax,&x>0\end{cases}$，且$f(x)$在$x=0$處連續(xù)，則$a$的值為（）A.$0$B.$1$C.$2$D.$3$7.在平面直角坐標(biāo)系中，若點(diǎn)$P(x,y)$在圓$x^2+y^2=4$上，且點(diǎn)$Q(2,0)$到點(diǎn)$P$的距離為$\sqrt{5}$，則點(diǎn)$P$的坐標(biāo)為（）A.$(1,\sqrt{3})$B.$(1,\sqrt{3})$C.$(\sqrt{3},1)$D.$(\sqrt{3},1)$8.若函數(shù)$f(x)=\ln(x^21)2\ln(x1)$，則$f(x)$的導(dǎo)數(shù)為（）A.$\frac{2}{x^21}\frac{2}{x1}$B.$\frac{2}{x+1}\frac{2}{x1}$C.$\frac{2}{x^21}+\frac{2}{x1}$D.$\frac{2}{x+1}+\frac{2}{x1}$9.在$\triangleABC$中，若$\angleA=60^\circ$，$BC=2$，$AC=3$，則$\cosC$的值為（）A.$\frac{3}{5}$B.$\frac{4}{5}$C.$\frac{1}{2}$D.$\frac{\sqrt{3}}{2}$10.若函數(shù)$y=ax^2+bx+c$的圖像開(kāi)口向上，且以$x=1$為對(duì)稱(chēng)軸，則函數(shù)的頂點(diǎn)坐標(biāo)為（）A.$(1,\frac{4acb^2}{4a})$B.$(1,\frac{b^24ac}{4a})$C.$(1,\frac{b^2+4ac}{4a})$D.$(1,\frac{4ac+b^2}{4a})$二、填空題（本大題共5小題，每小題5分，共25分）11.已知函數(shù)$f(x)=\ln(x^21)2\ln(x1)$，則$f'(1)=\underline{\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\一、選擇題答案：1.A2.B3.C4.D5.A6.B7.C8.D9.A10.B二、填空題答案：11.112.013.214.115.31.復(fù)數(shù)：涉及復(fù)數(shù)的運(yùn)算和模長(zhǎng)的概念。例如，復(fù)數(shù)乘法、模長(zhǎng)的計(jì)算等。2.函數(shù)：包括函數(shù)的定義域、值域、導(dǎo)數(shù)、連續(xù)性等概念。如函數(shù)的定義域確定、導(dǎo)數(shù)的計(jì)算等。3.數(shù)列：涉及數(shù)列的通項(xiàng)公式、求和公式等。如等差數(shù)列、等比數(shù)列的求和。4.三角形：包括三角形的邊長(zhǎng)、角度、面積等關(guān)系。如正弦定理、余弦定理的應(yīng)用。5.二次函數(shù)：涉及二次函數(shù)的圖像、頂點(diǎn)坐標(biāo)、對(duì)稱(chēng)軸等性質(zhì)。如二次函數(shù)的頂點(diǎn)坐標(biāo)確定。6.圓：包括圓的方程、圓上的點(diǎn)與圓心的距離等。如圓的方程確定、圓上的點(diǎn)坐標(biāo)確定。7.導(dǎo)數(shù)：涉及函數(shù)的導(dǎo)數(shù)、導(dǎo)數(shù)的應(yīng)用等。如導(dǎo)數(shù)的計(jì)算、導(dǎo)數(shù)與函數(shù)圖像的關(guān)系。8.平面直角坐標(biāo)系：包括點(diǎn)的坐標(biāo)、距離公式