高考數(shù)學(xué)易錯題集及答案1.函數(shù)\(y=\sqrt{x-1}\)的定義域是（）A.\(x\gt1\)B.\(x\geq1\)C.\(x\lt1\)D.\(x\leq1\)答案：B2.已知向量\(\vec{a}=(1,2)\)，\(\vec=(2,3)\)，若\(k\vec{a}+\vec\)與\(\vec{a}-\vec\)平行，則\(k\)的值為（）A.\(-1\)B.\(0\)C.\(1\)D.\(2\)答案：A3.拋物線\(y=2x^2\)的焦點坐標(biāo)是（）A.\((0,\frac{1}{2})\)B.\((0,\frac{1}{4})\)C.\((\frac{1}{2},0)\)D.\((\frac{1}{4},0)\)答案：B4.若\(\sin\alpha=\frac{3}{5}\)，\(\alpha\in(\frac{\pi}{2},\pi)\)，則\(\tan\alpha\)的值為（）A.\(\frac{3}{4}\)B.\(-\frac{3}{4}\)C.\(\frac{4}{3}\)D.\(-\frac{4}{3}\)答案：B5.設(shè)等差數(shù)列\(zhòng)(\{an\}\)的前\(n\)項和為\(Sn\)，若\(a2=3\)，\(a5=9\)，則\(S5\)等于（）A.\(15\)B.\(20\)C.\(25\)D.\(30\)答案：C6.函數(shù)\(y=\cos(2x+\frac{\pi}{3})\)的最小正周期是（）A.\(\pi\)B.\(2\pi\)C.\(\frac{\pi}{2}\)D.\(\frac{\pi}{4}\)答案：A7.已知直線\(l\)過點\((1,0)\)且傾斜角為\(\frac{\pi}{4}\)，則直線\(l\)的方程為（）A.\(x-y-1=0\)B.\(x+y-1=0\)C.\(x-y+1=0\)D.\(x+y+1=0\)答案：A8.若\(x\)，\(y\)滿足約束條件\(\begin{cases}x+y\geq1\\x-y\geq-1\\2x-y\leq2\end{cases}\)，則\(z=3x-y\)的最大值為（）A.\(-1\)B.\(1\)C.\(2\)D.\(3\)答案：D9.一個幾何體的三視圖如圖所示，則該幾何體的體積為（）（此處可插入簡單的三視圖圖形示意）A.\(12\)B.\(18\)C.\(24\)D.\(30\)答案：C10.已知函數(shù)\(f(x)=\begin{cases}2^x,x\geq0\\-x,x\lt0\end{cases}\)，若\(f(a)+f(1)=0\)，則實數(shù)\(a\)的值等于（）A.\(-3\)B.\(-1\)C.\(1\)D.\(3\)答案：A11.從\(1\)，\(2\)，\(3\)，\(4\)，\(5\)中任取\(2\)個不同的數(shù)，事件\(A\)為“取到的\(2\)個數(shù)之和為偶數(shù)”，事件\(B\)為“取到的\(2\)個數(shù)均為偶數(shù)”，則\(P(B|A)\)等于（）A.\(\frac{1}{8}\)B.\(\frac{1}{4}\)C.\(\frac{2}{5}\)D.\(\frac{1}{2}\)答案：B12.已知雙曲線\(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1(a\gt0,b\gt0)\)的一條漸近線方程為\(y=\frac{4}{3}x\)，則雙曲線的離心率為（）A.\(\frac{5}{3}\)B.\(\frac{4}{3}\)C.\(\frac{5}{4}\)D.\(\frac{3}{2}\)答案：A13.已知函數(shù)\(f(x)=x^3-3x^2+1\)，則在曲線\(y=f(x)\)的切線中，斜率最小的切線方程是（）A.\(y=-3x+1\)B.\(y=-3x+3\)C.\(y=-2x+1\)D.\(y=-2x+3\)答案：A14.已知\(a=\log23\)，\(b=\log34\)，\(c=\log45\)，則（）A.\(a\gtb\gtc\)B.\(b\gta\gtc\)C.\(c\gta\gtb\)D.\(a\gtc\gtb\)答案：A15.若函數(shù)\(f(x)=x^2-2ax+a^2-4\)在區(qū)間\([a-2,a^2](a\gt0)\)上的值域為\([-4,0]\)，則實數(shù)\(a\)的取值范圍是（）A.\([0,2]\)B.\([1,2]\)C.\([1,3]\)D.\([2,3]\)答案：B16.已知\(\triangleABC\)的內(nèi)角\(A\)，\(B\)，\(C\)的對邊分別為\(a\)，\(b\)，\(c\)，若\(a=\frac{\sqrt{5}}{2}b\)，\(A=2B\)，則\(\cosB\)等于（）A.\(\frac{\sqrt{5}}{3}\)B.\(\frac{\sqrt{5}}{4}\)C.\(\frac{\sqrt{5}}{5}\)D.\(\frac{\sqrt{5}}{6}\)答案：B17.已知圓\(C\)：\((x-1)^2+(y-2)^2=25\)，直線\(l\)：\((2m+1)x+(m+1)y-7m-4=0(m\inR)\)，則直線\(l\)與圓\(C\)的位置關(guān)系是（）A.相離B.相切C.相交D.不確定答案：C18.已知數(shù)列\(zhòng)(\{an\}\)滿足\(a{n+1}=\frac{1}{1-an}\)，若\(a1=\frac{1}{2}\)，則\(a{2019}\)等于（）A.\(\frac{1}{2}\)B.\(-1\)C.\(2\)D.\(1\)答案：C19.已知函數(shù)\(y=f(x)\)的圖象關(guān)于直線\(x=1\)對稱，且當(dāng)\(x\gt1\)時，\(f(x)=\frac{1}{x-1}\)，則當(dāng)\(x\lt1\)時，\(f(x)\)的解析式為（）A.\(\frac{1}{x-1}\)B.\(\frac{1}{2-x}\)C.\(\frac{1}{x-2}\)D.\(-\frac{1}{x-2}\)答案：C20.已知\(f(x)\)是定義在\(R\)上的奇函數(shù)，當(dāng)\(x\geq0\)時，\(f(x)=x^2-2x\)，則當(dāng)\(x\lt0\)時，\(f(x)\)的表達(dá)式為（）A.\(y=-x^2-2x\)B.\(y=-x^2+2x\)C.\(y=x^2+2x\)D.\(y=x^2-2x\)答案：A1.下列函數(shù)中，既是偶函數(shù)又在\((0,+\infty)\)上單調(diào)遞增的是（）A.\(y=x^3\)B.\(y=|x|+1\)C.\(y=-x^2+1\)D.\(y=2^{|x|}\)答案：BD2.已知集合\(A=\{x|x^2-3x-4\lt0\}\)，\(B=\{x|x^2+4mx-5m^2\lt0\}\)，若\(A\subseteqB\)，則實數(shù)\(m\)的取值范圍是（）A.\(m\geq1\)B.\(m\leq-4\)C.\(-4\ltm\lt1\)D.\(m\gt1\)或\(m\lt-4\)答案：AB3.已知\(a\)，\(b\)為非零向量，則“\(\vec{a}\cdot\vec\gt0\)”是“\(\vec{a}\)與\(\vec\)夾角為銳角”的（）A.充分而不必要條件B.必要而不充分條件C.充分必要條件D.既不充分也不必要條件答案：B4.已知函數(shù)\(f(x)=\sin(\omegax+\varphi)(\omega\gt0,|\varphi|\lt\frac{\pi}{2})\)的圖象如圖所示，則（）（此處可插入函數(shù)圖象示意）A.\(\omega=2\)B.\(\varphi=\frac{\pi}{6}\)C.\(f(x)\)的最小正周期為\(\pi\)D.\(f(x)\)在區(qū)間\([-\frac{\pi}{3},\frac{\pi}{6}]\)上單調(diào)遞增答案：ABC5.已知數(shù)列\(zhòng)(\{an\}\)是等比數(shù)列，其前\(n\)項和為\(Sn\)，若\(a1=1\)，\(a5=8a2\)，則（）A.公比\(q=2\)B.\(S6=63\)C.\(an=2^{n-1}\)D.\(Sn=2^n-1\)答案：ACD6.已知函數(shù)\(f(x)=\begin{cases}x^2+1,x\geq0\\1,x\lt0\end{cases}\)，則滿足不等式\(f(1-x^2)\gtf(2x)\)的\(x\)的取值范圍是（）A.\((-1,\sqrt{2}-1)\)B.\((0,\sqrt{2}-1)\)C.\((-\sqrt{2}-1,\sqrt{2}-1)\)D.\((0,\sqrt{2}+1)\)答案：A7.已知橢圓\(C\)：\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a\gtb\gt0)\)的左、右焦點分別為\(F1\)，\(F2\)，點\(P\)在橢圓\(C\)上，若\(|PF1|=2|PF2|\)，\(\cos\anglePF2F1=\frac{1}{4}\)，則橢圓\(C\)的離心率為（）A.\(\frac{1}{3}\)B.\(\frac{1}{2}\)C.\(\frac{\sqrt{2}}{2}\)D.\(\frac{\sqrt{3}}{3}\)答案：B8.已知函數(shù)\(f(x)=x^3-3x\)，過點\(P(2,-6)\)作曲線\(y=f(x)\)的切線，則切線方程為（）A.\(y=-3x\)B.\(y=9x-24\)C.\(y=-24x+42\)D.\(y=3x-12\)答案：AB9.已知\(x\)，\(y\)滿足\(x^2+y^2=1\)，則\((1-xy)(1+xy)\)的取值范圍是（）A.\([\frac{3}{4},1]\)B.\([\frac{1}{2},1]\)C.\([\frac{3}{4},\frac{4}{3}]\)D.\([1,\frac{4}{3}]\)答案：C10.已知函數(shù)\(f(x)=\begin{cases}\log2x,x\gt0\\2^x,x\leq0\end{cases}\)，若\(f(a)=\frac{1}{2}\)，則\(a\)的值為（）A.\(-1\)B.\(\sqrt{2}\)C.\(-\sqrt{2}\)D.\(\frac{\sqrt{2}}{2}\)答案：AC1.若函數(shù)\(f(x)\)在區(qū)間\([a,b]\)上單調(diào)遞增，則\(f^\prime(x)\gt0\)在\([a,b]\)上恒成立。（）答案：×2.若\(a\)，\(b\)，\(c\)成等比數(shù)列，則\(b^2=ac\)。（）答案：√3.向量\(\vec{a}=(1,2)\)，\(\vec=(2,3)\)，則\(\vec{a}\cdot\vec=2+6=8\)。（）答案：√4.函數(shù)\(y=\sinx\)的圖象關(guān)于點\((\frac{\pi}{2},0)\)對稱。（）答案：√5.若\(A\)，\(B\)是兩個集合，則\(A\capB=A\)等價于\(A\subseteqB\)。（）答案：√6.若\(