廈門高三一模試題答案

單項選擇題(每題2分,共10題)1.函數(shù)\(y=2^x\)的定義域是()A.\((0,+∞)\)B.\([0,+∞)\)C.\((-∞,+∞)\)D.\((-∞,0)\)答案:C2.已知向量\(\vec{a}=(1,2)\),\(\vec=(-1,m)\),若\(\vec{a}\parallel\vec\),則\(m\)的值為()A.\(2\)B.\(-2\)C.\(\frac{1}{2}\)D.\(-\frac{1}{2}\)答案:B3.\(\sin30^{\circ}\)的值為()A.\(\frac{1}{2}\)B.\(\frac{\sqrt{2}}{2}\)C.\(\frac{\sqrt{3}}{2}\)D.\(1\)答案:A4.雙曲線\(\frac{x^{2}}{4}-\frac{y^{2}}{5}=1\)的漸近線方程為()A.\(y=\pm\frac{\sqrt{5}}{2}x\)B.\(y=\pm\frac{2}{\sqrt{5}}x\)C.\(y=\pm\frac{5}{4}x\)D.\(y=\pm\frac{4}{5}x\)答案:A5.若\(a\gtb\),則下列不等式一定成立的是()A.\(a^2\gtb^2\)B.\(\frac{1}{a}\lt\frac{1}\)C.\(a^3\gtb^3\)D.\(ac\gtbc\)答案:C6.已知等差數(shù)列\(zhòng)(\{a_{n}\}\)中,\(a_{3}=5\),\(a_{5}=9\),則\(a_{7}\)等于()A.\(11\)B.\(12\)C.\(13\)D.\(14\)答案:C7.函數(shù)\(f(x)=\log_{2}(x+1)\)的零點是()A.\(0\)B.\(1\)C.\(-1\)D.不存在答案:A8.曲線\(y=x^3\)在點\((1,1)\)處的切線斜率為()A.\(1\)B.\(2\)C.\(3\)D.\(4\)答案:C9.已知\(\cos\alpha=\frac{3}{5}\),\(\alpha\in(0,\frac{\pi}{2})\),則\(\sin\alpha\)的值為()A.\(\frac{4}{5}\)B.\(-\frac{4}{5}\)C.\(\frac{3}{4}\)D.\(\frac{\sqrt{7}}{4}\)答案:A10.已知集合\(A=\{1,2,3\}\),\(B=\{2,3,4\}\),則\(A\capB\)等于()A.\(\{1,2,3,4\}\)B.\(\{2,3\}\)C.\(\{1,2,3\}\)D.\(\{2,3,4\}\)答案:B多項選擇題(每題2分,共10題)1.下列函數(shù)中,是偶函數(shù)的有()A.\(y=x^2\)B.\(y=\cosx\)C.\(y=\sinx\)D.\(y=|x|\)答案:ABD2.以下哪些是直線的方程形式()A.點斜式B.斜截式C.兩點式D.截距式答案:ABCD3.已知\(a,b\gt0\),且\(a+b=1\),則下列說法正確的有()A.\(ab\leqslant\frac{1}{4}\)B.\(\frac{1}{a}+\frac{1}\geqslant4\)C.\(a^2+b^2\geqslant\frac{1}{2}\)D.\(\sqrt{a}+\sqrt\leqslant\sqrt{2}\)答案:ABCD4.一個正方體的棱長為\(a\),以下說法正確的是（）A.正方體表面積為\(6a^2\)B.正方體體積為\(a^3\)C.正方體的面對角線長為\(\sqrt{2}a\)D.正方體的體對角線長為\(\sqrt{3}a\)答案:ABCD5.以下哪些是橢圓的標準方程形式(焦點在\(x\)軸和\(y\)軸）(）A.\(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a\gtb\gt0)\)B.\(\frac{y^{2}}{a^{2}}+\frac{x^{2}}{b^{2}}=1(a\gtb\gt0)\)C.\(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1(a\gt0,b\gt0)\)D.\(\frac{y^{2}}{a^{2}}-\frac{x^{2}}{b^{2}}=1(a\gt0,b\gt0)\)答案:AB6.已知函數(shù)\(y=\sin(2x+\varphi)\),為了得到函數(shù)\(y=\sin2x\)的圖象,可將\(y=\sin(2x+\varphi)\)的圖象進行平移,以下說法正確的是()A.當\(\varphi=\frac{\pi}{2}\)時,向右平移\(\frac{\pi}{4}\)個單位B.當\(\varphi=\frac{\pi}{2}\)時,向左平移\(\frac{\pi}{4}\)個單位C.當\(\varphi=-\frac{\pi}{2}\)時,向右平移\(\frac{\pi}{4}\)個單位D.當\(\varphi=-\frac{\pi}{2}\)時,向左平移\(\frac{\pi}{4}\)個單位答案：AC7.以下哪些點在圓\(x^{2}+y^{2}=4\)上()A.\((0,2)\)B.\((2,0)\)C.\((\sqrt{2},\sqrt{2})\)D.\((-\sqrt{2},-\sqrt{2})\)答案:ABCD8.已知向量\(\vec{m}=(1,1)\),\(\vec{n}=(x,-1)\),若\(\vec{m}\perp\vec{n}\),則\(x\)的值可能為()A.\(1\)B.\(-1\)C.\(0\)D.\(2\)答案:A9.下列函數(shù)在其定義域上單調(diào)遞增的有()A.\(y=2^x\)B.\(y=x^3\)C.\(y=\lnx\)D.\(y=\sinx\)答案:ABC10.等差數(shù)列\(zhòng)(\{a_{n}\}\)的前\(n\)項和為\(S_{n}\),若\(a_{1}=1\),\(d=2\),則()A.\(a_{n}=2n-1\)B.\(S_{n}=n^2\)C.\(a_{5}=9\)D.\(S_{5}=25\)答案:ABCD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)\(y=\tanx\)的定義域是\(x\neqk\pi+\frac{\pi}{2},k\inZ\)。(√)3.若\(a\),\(b\)為實數(shù),且\(ab=0\),則\(a=0\)且\(b=0\)。（×)4.直線\(x+y+1=0\)的斜率為\(1\)。(×)5.拋物線\(y^2=2px(p\gt0)\)的焦點坐標為\((\frac{p}{2},0)\)。(√)6.若\(\sin\alpha=\sin\beta\),則\(\alpha=\beta\)。(×）7.兩個向量的數(shù)量積為\(0\),則這兩個向量一定垂直。（√)8.函數(shù)\(y=\cos^2x\)的最小正周期是\(\pi\)。(√)9.若\(a\gtb\gt0\),\(c\gtd\gt0\),則\(ac\gtbd\)。(√）10.等比數(shù)列\(zhòng)(\{a_{n}\}\)中,若\(a_{1}=1\),\(q=2\),則\(a_{3}=4\)。（√）簡答題(每題5分,共4題)1.求函數(shù)\(y=3x-1\)在\(x=2\)處的函數(shù)值。答案:將\(x=2\)代入\(y=3x-1\),得\(y=3×2-1=5\)。2.求圓\(x^{2}+y^{2}-4x=0\)的圓心坐標和半徑。答案:將圓方程化為標準式\((x-2)^{2}+y^{2}=4\),所以圓心坐標為\((2,0)\),半徑\(r=2\)。3.已知\(\tan\alpha=2\),求\(\frac{\sin\alpha}{\cos\alpha}\)的值。答案:因為\(\tan\alpha=\frac{\sin\alpha}{\cos\alpha}\),已知\(\tan\alpha=2\),所以\(\frac{\sin\alpha}{\cos\alpha}=2\)。4.已知等差數(shù)列\(zhòng)(\{a_{n}\}\)中,\(a_{1}=1\),\(d=3\),求\(a_{5}\)。答案：根據(jù)等差數(shù)列通項公式\(a_{n}=a_{1}+(n-1)d\),\(a_{5}=a_{1}+4d=1+4×3=13\)。討論題(每題5分,共4題)1.討論函數(shù)\(y=x^2\)與\(y=2^x\)在\((0,+∞)\)上的增長情況。答案:\(y=x^2\)是二次函數(shù),在\((0,+∞)\)上增長速度先慢后快;\(y=2^x\)是指數(shù)函數(shù),在\((0,+∞)\)上增長速度越來越快,且后期\(y=2^x\)比\(y=x^2\)增長更快。2.探討在解析幾何中,如何根據(jù)已知條件確定直線方程的形式。答案:若已知直線斜率和一點,用點斜式;已知斜率和縱截距,用斜截式;已知兩點,用兩點式;已知橫縱截距,用截距式。要根據(jù)所給條件的特點靈活選擇。3.分析在立體幾何中,證明線面垂直的常用方法。答案:常用方法有:若一條直線與一個平