高一選拔考試題及答案

單項(xiàng)選擇題（每題2分，共10題）1.下列函數(shù)中，定義域?yàn)閈(R\)的是（）A.\(y=\sqrt{x}\)B.\(y=\frac{1}{x}\)C.\(y=x^2\)D.\(y=\sqrt{x-1}\)2.已知\(a=2^{0.3}\)，\(b=0.3^2\)，\(c=\log_{2}0.3\)，則（）A.\(a>b>c\)B.\(b>a>c\)C.\(c>a>b\)D.\(b>c>a\)3.若\(\sin\alpha=\frac{3}{5}\)，\(\alpha\)是第二象限角，則\(\cos\alpha=\)（）A.\(-\frac{4}{5}\)B.\(\frac{4}{5}\)C.\(-\frac{3}{5}\)D.\(\frac{3}{5}\)4.直線\(x+y-1=0\)的傾斜角為（）A.\(30^{\circ}\)B.\(45^{\circ}\)C.\(60^{\circ}\)D.\(135^{\circ}\)5.已知向量\(\vec{a}=(1,2)\)，\(\vec=(3,1)\)，則\(\vec{a}+\vec=\)（）A.\((4,3)\)B.\((3,4)\)C.\((1,3)\)D.\((2,4)\)6.函數(shù)\(y=\sin(2x+\frac{\pi}{3})\)的最小正周期是（）A.\(\pi\)B.\(2\pi\)C.\(\frac{\pi}{2}\)D.\(\frac{\pi}{4}\)7.若\(x^2+2x+y^2-6y+10=0\)成立，則\(x+y=\)（）A.\(2\)B.\(-2\)C.\(4\)D.\(-4\)8.已知\(A(1,2)\)，\(B(3,4)\)兩點(diǎn)，則線段\(AB\)的中點(diǎn)坐標(biāo)為（）A.\((2,3)\)B.\((3,2)\)C.\((4,1)\)D.\((1,4)\)9.不等式\(x^2-2x-3<0\)的解集是（）A.\((-1,3)\)B.\((-3,1)\)C.\((-\infty,-1)\cup(3,+\infty)\)D.\((-\infty,-3)\cup(1,+\infty)\)10.函數(shù)\(y=\log_{2}(x-1)\)的圖象恒過(guò)點(diǎn)（）A.\((0,1)\)B.\((1,0)\)C.\((2,0)\)D.\((0,2)\)多項(xiàng)選擇題（每題2分，共10題）1.以下哪些是奇函數(shù)（）A.\(y=x^3\)B.\(y=\sinx\)C.\(y=x^2+1\)D.\(y=\frac{1}{x}\)2.下列函數(shù)中單調(diào)遞增的是（）A.\(y=2^x\)B.\(y=\log_{2}x\)C.\(y=x^3\)D.\(y=-x\)3.與角\(-30^{\circ}\)終邊相同的角是（）A.\(330^{\circ}\)B.\(-390^{\circ}\)C.\(150^{\circ}\)D.\(630^{\circ}\)4.直線\(2x-y+1=0\)的斜率為（）A.\(2\)B.\(-2\)C.\(\frac{1}{2}\)D.\(-\frac{1}{2}\)5.已知向量\(\vec{a}=(2,3)\)，\(\vec=(-1,2)\)，則（）A.\(\vec{a}\cdot\vec=4\)B.\(2\vec{a}+\vec=(3,8)\)C.\(\vec{a}-\vec=(3,1)\)D.\(\vec{a}\)與\(\vec\)夾角的余弦值為\(\frac{4\sqrt{65}}{65}\)6.下列函數(shù)中，值域?yàn)閈([0,+\infty)\)的是（）A.\(y=x^2\)B.\(y=\sqrt{x}\)C.\(y=2^x\)D.\(y=\log_{2}x\)7.圓\((x-1)^2+(y+2)^2=4\)的圓心坐標(biāo)和半徑分別為（）A.\((1,-2)\)B.\((-1,2)\)C.\(2\)D.\(4\)8.若\(a>b>0\)，則（）A.\(a^2>b^2\)B.\(\frac{1}{a}<\frac{1}\)C.\(\lga>\lgb\)D.\(a+b>2\sqrt{ab}\)9.函數(shù)\(y=\sin^2x\)的化簡(jiǎn)結(jié)果可以是（）A.\(\frac{1-\cos2x}{2}\)B.\(\frac{1+\cos2x}{2}\)C.\(-\frac{\cos2x-1}{2}\)D.\(-\frac{\cos2x+1}{2}\)10.已知點(diǎn)\(P(x,y)\)在圓\(x^2+y^2=1\)上，則\(x+y\)的取值范圍是（）A.\([-\sqrt{2},\sqrt{2}]\)B.\([-2,2]\)C.\((-\infty,-\sqrt{2}]\cup[\sqrt{2},+\infty)\)D.\((-\infty,-2]\cup[2,+\infty)\)判斷題（每題2分，共10題）1.函數(shù)\(y=\frac{1}{\sqrt{x-1}}\)的定義域是\((-\infty,1)\)。（）2.若\(\sin\alpha=\cos\alpha\)，則\(\alpha=45^{\circ}\)。（）3.向量\(\vec{a}=(1,2)\)，\(\vec=(2,1)\)，則\(\vec{a}=\vec\)。（）4.直線\(x=1\)的斜率不存在。（）5.函數(shù)\(y=\log_{a}x\)（\(a>0\)且\(a\neq1\)）在\((0,+\infty)\)上單調(diào)遞增。（）6.圓\(x^2+y^2=1\)與直線\(y=x\)相切。（）//7.若\(a\)，\(b\)，\(c\)成等差數(shù)列，則\(2b=a+c\)。（//）8.函數(shù)\(y=\cos(x+\frac{\pi}{2})\)是偶函數(shù)。（）9.不等式\(x^2-4x+3\geq0\)的解集是\((-\infty,1]\cup[3,+\infty)\)。（）10.若\(A\)，\(B\)，\(C\)三點(diǎn)共線，則\(\overrightarrow{AB}\)與\(\overrightarrow{AC}\)共線。（）簡(jiǎn)答題（總4題，每題5分）1.求函數(shù)\(y=2x+1\)在\([1,2]\)上的值域。答案：當(dāng)\(x=1\)時(shí)，\(y=3\)；當(dāng)\(x=2\)時(shí)，\(y=5\)，值域?yàn)閈([3,5]\)。2.已知\(\sin\alpha=\frac{1}{3}\)，\(\alpha\)為銳角，求\(\cos\alpha\)。答案：因?yàn)閈(\alpha\)為銳角，\(\cos\alpha=\sqrt{1-(\frac{1}{3})^2}=\frac{2\sqrt{2}}{3}\)。3.求過(guò)點(diǎn)\((1,2)\)且斜率為\(3\)的直線方程。答案：由點(diǎn)斜式得\(y-2=3(x-1)\)，即\(3x-y-1=0\)。4.已知圓的方程為\(x^2+y^2-4x+?=0\)，求圓心坐標(biāo)和半徑。答案：配方得\((x-2)^2+y^2=3\)，圓心\((2,0)\)，半徑\(\sqrt{3}\)。討論題（總4題，每題5分）1.討論函數(shù)\(y=x^2\)的單調(diào)性。答案：在\((-\infty,0)\)單調(diào)遞減，在\((0,+\infty)\)單調(diào)遞增。2.如何判斷直線與圓的位置關(guān)系？答案：比較圓心到直線距離與半徑大小，距離小于半徑相交，等于半徑相切，大于半徑相離。3.說(shuō)說(shuō)對(duì)數(shù)函數(shù)的性質(zhì)。答案：\(a>1\)時(shí)在\((0,+\infty)\)單調(diào)遞增，\(0<a<1\)時(shí)在\((0,+\infty)\)單調(diào)遞減，圖象過(guò)\((1,0)\)。4.討論向量平行的條件。答案：若\(\vec{a}=(x_1,y_1)\)，\(\vec=(x_2,y_2)\)，則\(\vec{a}\para