四川省瀘州市瀘縣瀘縣第五中學20232024學年高二上學期期中數學試卷一、選擇題（每題5分，共20分）1.若復數$z=a+bi$（其中$a,b$為實數），且$|z|=1$，則$z$的取值范圍是（）。A.$a^2+b^2=1$B.$a^2+b^2>1$C.$a^2+b^2<1$D.$a^2+b^2\neq1$2.設集合$A=\{x|x^25x+6=0\}$，集合$B=\{2,3,5\}$，則$A\capB$等于（）。A.$\{2\}$B.$\{3\}$C.$\{2,3\}$D.$\{2,3,5\}$3.函數$f(x)=\ln(x^21)$的定義域是（）。A.$(\infty,1)\cup(1,+\infty)$B.$(1,1)$C.$(\infty,1)\cup(1,+\infty)$D.$(\infty,0)\cup(0,+\infty)$4.已知等差數列$\{a_n\}$的前$n$項和為$S_n=3n^2+2n$，則$a_4$等于（）。A.14B.16C.18D.20二、填空題（每題5分，共20分）1.已知函數$f(x)=2x^23x+1$，則$f(1)+f(2)=\underline{\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\一、選擇題答案：1.B2.A3.C4.B二、填空題答案：1.82.53.14.0三、解答題答案：1.（1）由題意得，an3n22n，所以a1S1S2S1=322321=3，所以d=a2a1=S2S1S1=3222×321=3，所以an=a1+(n1)d=3+3(n1)=3n。所以an=3n。（2）由（1）知，an=3n，所以Sn=n(a1+an)/2=n(3+3n)/2=3n(n+1)/2。所以Sn=3n(n+1)/2。2.（1）由題意得，f(x)=2x23x+1，所以f'(x)=4x3。令f'(x)=0，得x=3/4。當x<3/4時，f'(x)<0；當x>3/4時，f'(x)>0。所以f(x)在x=3/4處取得極小值，即最小值。所以f(x)的最小值為f(3/4)=2(3/4)23(3/4)+1=1/8。（2）由題意得，f(x)=2x23x+1，所以f(x)=2(x)23(x)+1=2x2+3x+1。所以f(x)+f(x)=2x23x+1+2x2+3x+1=4x2+2。所以f(x)+f(x)=4x2+2。1.復數：掌握復數的定義、性質和運算規則。2.集合：理解集合的概念、運算和性質。3.函數：了解函數的定義、性質、圖像和運算。4.數列：熟悉等差數列和等比數列的定義、性質和運算。5.導數：理解導數的概念、性質和應