浙江高考數(shù)學(xué)答案及試題

單項選擇題(每題2分,共10題)1.若集合\(A=\{1,2\}\),\(B=\{2,3\}\),則\(A\cupB=\)（）A.\(\{1\}\)B.\(\{2\}\)C.\(\{1,2,3\}\)D.\(\varnothing\)2.已知\(i\)是虛數(shù)單位,若\(z=1+i\),則\(z\cdot\overline{z}=\)()A.\(0\)B.\(1\)C.\(2\)D.\(4\)3.直線\(y=2x+1\)的斜率為()A.\(1\)B.\(2\)C.\(-2\)D.\(\frac{1}{2}\)4.函數(shù)\(y=\log_{2}x\)的定義域是()A.\((0,+\infty)\)B.\([0,+\infty)\)C.\((-\infty,0)\)D.\((-\infty,+\infty)\)5.已知等差數(shù)列\(zhòng)(\{a_n\}\)中,\(a_1=1\),\(a_3=5\),則公差\(d=\)()A.\(1\)B.\(2\)C.\(3\)D.\(4\)6.若\(\sin\alpha=\frac{1}{2}\),且\(\alpha\)是第一象限角,則\(\cos\alpha=\)()A.\(\frac{\sqrt{3}}{2}\)B.\(-\frac{\sqrt{3}}{2}\)C.\(\frac{1}{2}\)D.\(-\frac{1}{2}\)7.拋物線\(y^2=4x\)的焦點坐標是()A.\((0,1)\)B.\((0,-1)\)C.\((1,0)\)D.\((-1,0)\)8.已知向量\(\overrightarrow{a}=(1,2)\),\(\overrightarrow=(-1,1)\),則\(\overrightarrow{a}\cdot\overrightarrow=\)()A.\(1\)B.\(-1\)C.\(3\)D.\(-3\)9.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.\(\frac{\pi}{4}\)10.若實數(shù)\(x\),\(y\)滿足約束條件\(\begin{cases}x+y\geq1\\x-y\leq1\\y\leq1\end{cases}\),則\(z=3x-y\)的最大值為()A.\(1\)B.\(2\)C.\(3\)D.\(4\)多項選擇題(每題2分,共10題)1.以下哪些是基本初等函數(shù)(）A.冪函數(shù)B.指數(shù)函數(shù)C.對數(shù)函數(shù)D.三角函數(shù)2.下列命題正確的是()A.平行于同一直線的兩條直線平行B.垂直于同一直線的兩條直線平行C.平行于同一平面的兩條直線平行D.垂直于同一平面的兩條直線平行3.已知函數(shù)\(f(x)\)是偶函數(shù),且在\((0,+\infty)\)上單調(diào)遞減,則\(f(x)\)可能是()A.\(f(x)=x^{-2}\)B.\(f(x)=\cosx\)C.\(f(x)=e^{-x}\)D.\(f(x)=\ln|x|\)4.等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項和為\(S_n\),若\(a_3=5\),\(a_5=9\),則()A.\(a_1=1\)B.\(d=2\)C.\(S_7=49\)D.\(a_8=17\)5.對于函數(shù)\(y=\cosx\),以下說法正確的是()A.周期是\(2\pi\)B.最大值為\(1\)C.是偶函數(shù)D.圖象關(guān)于\(y\)軸對稱6.已知直線\(l_1:ax+y+1=0\),\(l_2:x+ay+1=0\),若\(l_1\parallell_2\),則\(a\)的值為()A.\(1\)B.\(-1\)C.\(0\)D.\(2\)7.下列式子中,值為\(\frac{\sqrt{3}}{2}\)的是()A.\(\sin60^{\circ}\)B.\(\cos30^{\circ}\)C.\(\tan60^{\circ}\)D.\(\sin120^{\circ}\)8.橢圓\(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0)\)的性質(zhì)有()A.長軸長為\(2a\)B.短軸長為\(2b\)C.離心率\(e=\frac{c}{a}\)(\(c^2=a^2-b^2\))D.焦點在\(x\)軸上9.已知函數(shù)\(y=f(x)\),\(y=g(x)\)的圖象關(guān)于\(x\)軸對稱,則（）A.\(f(x)=-g(x)\)B.\(f(-x)=-g(-x)\)C.\(f(x)+g(x)=0\)D.\(f(0)=-g(0)\)10.已知\(a\),\(b\)為正實數(shù),且\(a+b=1\),則()A.\(ab\leq\frac{1}{4}\)B.\(\frac{1}{a}+\frac{1}\geq4\)C.\(a^{2}+b^{2}\geq\frac{1}{2}\)D.\(\sqrt{a}+\sqrt\leq\sqrt{2}\)判斷題(每題2分,共10題)1.空集是任何集合的子集。()2.函數(shù)\(y=x^2\)在\(R\)上是單調(diào)遞增函數(shù)。()3.若\(a>b\),則\(a^2>b^2\)。（)4.直線\(x=1\)的斜率不存在。()5.若\(\sin\alpha=\sin\beta\),則\(\alpha=\beta\)。（)6.等比數(shù)列的公比可以為\(0\)。()7.向量\(\overrightarrow{a}=(1,0)\)與向量\(\overrightarrow=(0,1)\)垂直。()8.雙曲線\(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\)的漸近線方程是\(y=\pm\frac{a}x\)。()9.若函數(shù)\(y=f(x)\)滿足\(f(x+T)=f(x)\)(\(T\neq0\)）,則\(T\)是函數(shù)\(f(x)\)的周期。(）10.已知\(A\),\(B\)為兩個事件,若\(P(AB)=P(A)P(B)\),則\(A\),\(B\)相互獨立。（）簡答題(每題5分,共4題)1.求函數(shù)\(y=2x^2-4x+3\)的對稱軸和頂點坐標。-答案:對于二次函數(shù)\(y=ax^2+bx+c\),對稱軸為\(x=-\frac{2a}\)。此函數(shù)\(a=2\),\(b=-4\),對稱軸\(x=1\)。把\(x=1\)代入得\(y=1\),頂點坐標為\((1,1)\)。2.已知\(\tan\alpha=2\),求\(\frac{\sin\alpha+\cos\alpha}{\sin\alpha-\cos\alpha}\)的值。-答案：將\(\frac{\sin\alpha+\cos\alpha}{\sin\alpha-\cos\alpha}\)分子分母同時除以\(\cos\alpha\)得\(\frac{\tan\alpha+1}{\tan\alpha-1}\),把\(\tan\alpha=2\)代入,得\(\frac{2+1}{2-1}=3\)。3.求過點\((1,2)\)且與直線\(2x-y+1=0\)平行的直線方程。-答案:兩直線平行斜率相等,已知直線斜率為\(2\)。設(shè)所求直線方程為\(y-2=2(x-1)\),整理得\(2x-y=0\)。4.已知數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項和\(S_n=n^2\),求\(a_n\)。-答案：當(dāng)\(n=1\)時,\(a_1=S_1=1\)；當(dāng)\(n\geq2\)時,\(a_n=S_n-S_{n-1}=n^2-(n-1)^2=2n-1\)。\(n=1\)時也滿足,所以\(a_n=2n-1\)。討論題(每題5分,共4題)1.討論函數(shù)\(y=\frac{1}{x}\)在\((0,+\infty)\)和\((-\infty,0)\)上的單調(diào)性。-答案:在\((0,+\infty)\)上,任取\(x_1<x_2\),\(f(x_1)-f(x_2)=\frac{1}{x_1}-\frac{1}{x_2}=\frac{x_2-x_1}{x_1x_2}>0\),所以\(y=\frac{1}{x}\)在\((0,+\infty)\)上單調(diào)遞減;同理在\((-\infty,0)\)上也單調(diào)遞減。2.如何判斷直線與圓的位置關(guān)系,有哪些方法?-答案：一是代數(shù)法,聯(lián)立直線與圓方程,消元得一元二次方程,根據(jù)判別式判斷。二是幾何法,計算圓心到直線的距離\(d\),與半徑\(r\)比較,\(d>r\)相離,\(d=r\)相切,\(d<r\)相交。3.說說等差數(shù)列和等比數(shù)列在通項公式和求和公式上的聯(lián)系與區(qū)別。-答案:聯(lián)系:都是數(shù)列重要類型。區(qū)別:等差數(shù)列通項\(a_n=a_1+(n-1)d\),求和\(S_n=\frac{n(a_1+a_n)}{2}\);等比數(shù)列通項\(a_n=a_1q^{n-1}\),求和\(S_n=\begin{cases}na_1(q=1)\\\frac{a_1(1-q^n)}{1-q}(q\neq1)\end{cases}\)。4.討論函數(shù)\(y=\sinx\)與\(y=\cosx\)圖象的關(guān)系。-答案:\(y=\sinx\)圖象向左平移\(\frac{\pi}{2}\)個單位可得\(y=\cosx\)圖象。二者周期都是\(2\pi\),\(y=\sinx\)圖象關(guān)于點\((k\pi,0)\)對稱,\(y=\cos