北師大版高中高三上冊數(shù)學(xué)期末試卷后附答案

一、填空題1.函數(shù)\(y=\log_2(x-1)\)的定義域是______。2.已知向量\(\overrightarrow{a}=(1,2)\)，\(\overrightarrow=(x,1)\)，若\(\overrightarrow{a}\)與\(\overrightarrow\)共線，則\(x=\)______。3.等差數(shù)列\(zhòng)(\{a_n\}\)中，\(a_3=5\)，\(a_7=13\)，則\(a_{10}=\)______。4.若\(\sin\alpha=\frac{3}{5}\)，\(\alpha\in(\frac{\pi}{2},\pi)\)，則\(\cos\alpha=\)______。5.直線\(2x-y+3=0\)的斜率是______。6.拋物線\(y^2=8x\)的焦點坐標(biāo)是______。7.已知\(f(x)\)是奇函數(shù)，當(dāng)\(x\gt0\)時，\(f(x)=x^2-2x\)，則當(dāng)\(x\lt0\)時，\(f(x)=\)______。8.若\(\tan\theta=2\)，則\(\frac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}=\)______。9.函數(shù)\(y=\sin(2x+\frac{\pi}{3})\)的最小正周期是______。10.已知\(x,y\)滿足約束條件\(\begin{cases}x+y\geq1\\x-y\geq-1\\2x-y\leq2\end{cases}\)，則目標(biāo)函數(shù)\(z=3x+y\)的最大值是______。二、單項選擇題1.設(shè)集合\(A=\{x|x^2-3x+2=0\}\)，\(B=\{x|x^2-mx+2=0\}\)，若\(B\subseteqA\)，則實數(shù)\(m\)的取值范圍是（）A.\(\{3\}\)B.\(\{-2\sqrt{2},2\sqrt{2}\}\cup\{3\}\)C.\(\{-2\sqrt{2},2\sqrt{2}\}\)D.\(\{-2\sqrt{2},2\sqrt{2},3\}\)2.函數(shù)\(y=\frac{1}{x-1}\)的圖象是（）A.一條直線B.雙曲線C.拋物線D.橢圓3.下列函數(shù)中，在\((0,+\infty)\)上為增函數(shù)的是（）A.\(y=\sinx\)B.\(y=x^3-x\)C.\(y=x^{\frac{1}{2}}\)D.\(y=\frac{1}{x}\)4.已知\(a,b\)是兩條不同的直線，\(\alpha,\beta\)是兩個不同的平面，若\(a\perp\alpha\)，\(b\perp\beta\)，\(a\parallelb\)，則（）A.\(\alpha\parallel\beta\)B.\(\alpha\perp\beta\)C.\(\alpha\)與\(\beta\)相交但不垂直D.以上都有可能5.已知等比數(shù)列\(zhòng)(\{a_n\}\)的公比\(q=2\)，且\(a_1+a_3=5\)，則\(a_2+a_4\)的值為（）A.10B.15C.20D.256.若直線\(l_1:ax+2y+6=0\)與直線\(l_2:x+(a-1)y+a^2-1=0\)平行，則\(a\)的值為（）A.2B.-1C.2或-1D.-2或17.已知\(\alpha\in(0,\frac{\pi}{2})\)，\(\sin\alpha=\frac{3}{5}\)，則\(\tan2\alpha=\)（）A.\(\frac{24}{7}\)B.\(\frac{7}{24}\)C.\(-\frac{24}{7}\)D.\(-\frac{7}{24}\)8.已知點\(P(x,y)\)在圓\(x^2+y^2=1\)上，則\(\sqrt{(x-1)^2+(y-1)^2}\)的最大值為（）A.\(\sqrt{2}+1\)B.\(\sqrt{2}-1\)C.1D.29.函數(shù)\(y=\log_{\frac{1}{2}}(x^2-2x)\)的單調(diào)遞增區(qū)間是（）A.\((-\infty,0)\)B.\((-\infty,1)\)C.\((1,+\infty)\)D.\((2,+\infty)\)10.已知\(f(x)\)是定義在\(R\)上的偶函數(shù)，且在\((-\infty,0]\)上單調(diào)遞減，若\(f(\log_2a)\gtf(1)\)，則實數(shù)\(a\)的取值范圍是（）A.\((\frac{1}{2},2)\)B.\((0,\frac{1}{2})\cup(2,+\infty)\)C.\((\frac{1}{2},+\infty)\)D.\((2,+\infty)\)三、多項選擇題1.下列說法正確的是（）A.若\(a\gtb\)，則\(ac^2\gtbc^2\)B.若\(a\gtb\)，\(c\gtd\)，則\(a+c\gtb+d\)C.若\(a\gtb\)，\(c\gtd\)，則\(ac\gtbd\)D.若\(a\gtb\gt0\)，\(c\lt0\)，則\(\frac{c}{a}\gt\frac{c}\)2.已知函數(shù)\(y=f(x)\)的圖象關(guān)于直線\(x=1\)對稱，且在\((1,+\infty)\)上單調(diào)遞增，設(shè)\(a=f(-\frac{1}{2})\)，\(b=f(2)\)，\(c=f(3)\)，則\(a,b,c\)的大小關(guān)系可能是（）A.\(a\ltb\ltc\)B.\(b\lta\ltc\)C.\(c\ltb\lta\)D.\(c\lta\ltb\)3.已知向量\(\overrightarrow{a}=(1,2)\)，\(\overrightarrow=(x,1)\)，則以下結(jié)論正確的是（）A.若\(\overrightarrow{a}\parallel\overrightarrow\)，則\(x=\frac{1}{2}\)B.若\(\overrightarrow{a}\perp\overrightarrow\)，則\(x=-2\)C.若\(\overrightarrow{a}\)與\(\overrightarrow\)的夾角為銳角，則\(x\gt-2\)D.若\(\overrightarrow{a}\)與\(\overrightarrow\)的夾角為鈍角，則\(x\lt-2\)4.已知等比數(shù)列\(zhòng)(\{a_n\}\)的公比\(q\gt0\)，且\(a_1=1\)，\(4a_3=a_2a_4\)，則（）A.\(q=2\)B.數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項和\(S_n=2^n-1\)C.數(shù)列\(zhòng)(\{na_n\}\)的前\(n\)項和\(T_n=(n-1)2^n+1\)D.數(shù)列\(zhòng)(\{\frac{1}{a_n}\}\)是公差為\(2\)的等差數(shù)列5.已知函數(shù)\(f(x)=\sin(\omegax+\varphi)(\omega\gt0,|\varphi|\lt\frac{\pi}{2})\)的部分圖象如圖所示，則（）A.\(\omega=2\)B.\(\varphi=\frac{\pi}{6}\)C.\(f(x)\)的單調(diào)遞增區(qū)間是\([k\pi-\frac{\pi}{3},k\pi+\frac{\pi}{6}],k\inZ\)D.\(f(x)\)的圖象關(guān)于直線\(x=\frac{\pi}{6}\)對稱6.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（）A.直線\(l\)恒過定點\((3,1)\)B.直線\(l\)與圓\(C\)相交C.直線\(l\)被圓\(C\)截得的弦長最長時，\(m=-\frac{3}{4}\)D.直線\(l\)被圓\(C\)截得的弦長最短時，\(m=-\frac{3}{4}\)7.已知\(x,y\)滿足約束條件\(\begin{cases}x+y\geq2\\x-y\leq2\\y\leq2\end{cases}\)，則（）A.目標(biāo)函數(shù)\(z=x+2y\)的最小值為\(2\)B.目標(biāo)函數(shù)\(z=x+2y\)的最大值為\(6\)C.目標(biāo)函數(shù)\(z=x^2+y^2\)的最小值為\(2\)D.目標(biāo)函數(shù)\(z=x^2+y^2\)的最大值為\(8\)8.已知函數(shù)\(f(x)=x^3-3x^2+1\)，則（）A.函數(shù)\(f(x)\)有三個不同的零點B.函數(shù)\(f(x)\)在\(x=0\)處取得極大值C.函數(shù)\(f(x)\)在\(x=2\)處取得極小值D.函數(shù)\(f(x)\)的圖象關(guān)于點\((1,-1)\)對稱9.已知雙曲線\(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1(a\gt0,b\gt0)\)的左、右焦點分別為\(F_1,F_2\)，過\(F_1\)且垂直于\(x\)軸的直線與雙曲線交于\(A,B\)兩點，若\(\triangleABF_2\)的面積為\(2b^2\)，則該雙曲線的離心率為（）A.\(\sqrt{2}\)B.\(\sqrt{3}\)C.\(\frac{\sqrt{6}}{2}\)D.\(\frac{\sqrt{10}}{2}\)10.已知函數(shù)\(y=f(x)\)是定義在\(R\)上的周期為\(2\)的奇函數(shù)，當(dāng)\(0\ltx\lt1\)時，\(f(x)=4^x\)，則（）A.\(f(-\frac{5}{2})=-2\)B.\(f(\frac{7}{2})=2\)C.\(f(x)\)在\([-1,1]\)上有\(zhòng)(3\)個零點D.\(f(x)\)在\([-1,1]\)上的值域為\([-2,2]\)四、判斷題1.若\(A\capB=\varnothing\)，則\(A=\varnothing\)或\(B=\varnothing\)。（）2.函數(shù)\(y=\frac{1}{x}\)在定義域內(nèi)是減函數(shù)。（）3.若\(\overrightarrow{a}\cdot\overrightarrow=0\)，則\(\overrightarrow{a}=\overrightarrow{0}\)或\(\overrightarrow=\overrightarrow{0}\)。（）4.等比數(shù)列\(zhòng)(\{a_n\}\)中，若\(a_1\lt0\)，\(q\gt0\)，則數(shù)列\(zhòng)(\{a_n\}\)單調(diào)遞減。（）5.函數(shù)\(y=\sinx\)與\(y=\cosx\)的圖象有無數(shù)個交點。（）6.直線\(Ax+By+C=0\)與圓\(x^2+y^2=r^2\)相切的充要條件是\(C^2=(A^2+B^2)r^2\)。（）7.若\(f(x)\)是偶函數(shù)，則\(f(|x|)=f(x)\)。（）8.若\(\tan\alpha=1\)，則\(\alpha=\frac{\pi}{4}\)。（）9.已知\(x,y\)滿足約束條件\(\begin{cases}x+y\geq1\\x-y\geq-1\\2x-y\leq2\end{cases}\)，則目標(biāo)函數(shù)\(z=x-2y\)的最小值是\(-2\)。（）10.若函數(shù)\(y=f(x)\)在區(qū)間\((a,b)\)內(nèi)有零點，則\(f(a)\cdotf(b)\lt0\)。（）五、簡答題1.已知集合\(A=\{x|x^2-3x+2=0\}\)，\(B=\{x|x^2-ax+a-1=0\}\)，若\(A\cupB=A\)，求實數(shù)\(a\)的值。2.已知等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項和為\(S_n\)，\(a_3=5\)，\(S_6=36\)，求數(shù)列\(zhòng)(\{a_n\}\)的通項公式。3.已知函數(shù)\(f(x)=\sin(2x+\frac{\pi}{3})\)，求\(f(x)\)在區(qū)間\([0,\frac{\pi