平陰考試題型及答案高中

單項(xiàng)選擇題(每題2分,共10題)1.函數(shù)\(y=\sinx\)的最小正周期是(）A.\(2\pi\)B.\(\pi\)C.\(4\pi\)D.\(\frac{\pi}{2}\)2.等差數(shù)列\(zhòng)(\{a_n\}\)中,\(a_1=1\),\(a_3=5\),則公差\(d\)為()A.1B.2C.3D.43.下列函數(shù)中,是偶函數(shù)的是()A.\(y=x^3\)B.\(y=x+1\)C.\(y=x^2\)D.\(y=\frac{1}{x}\)4.\(\cos60^{\circ}\)的值是()A.\(\frac{1}{2}\)B.\(\frac{\sqrt{3}}{2}\)C.\(\frac{\sqrt{2}}{2}\)D.\(\frac{\sqrt{3}}{3}\)5.直線\(y=2x+1\)的斜率是()A.1B.2C.\(\frac{1}{2}\)D.-26.橢圓\(\frac{x^{2}}{9}+\frac{y^{2}}{4}=1\)的長軸長是()A.3B.4C.6D.87.若\(\vert\vec{a}\vert=3\),\(\vert\vec\vert=4\),且\(\vec{a}\)與\(\vec\)夾角為\(60^{\circ}\),則\(\vec{a}\cdot\vec\)等于()A.6B.\(6\sqrt{3}\)C.12D.\(12\sqrt{3}\)8.已知集合\(A=\{1,2,3\}\),\(B=\{2,3,4\}\),則\(A\capB\)等于()A.\(\{1,2\}\)B.\(\{2,3\}\)C.\(\{3,4\}\)D.\(\{1,4\}\)9.函數(shù)\(y=\log_2x\)的定義域是()A.\((0,+\infty)\)B.\([0,+\infty)\)C.\((-\infty,0)\)D.\((-\infty,+\infty)\)10.已知\(\sin\alpha=\frac{3}{5}\),\(\alpha\)是第二象限角,則\(\cos\alpha\)的值是()A.\(\frac{4}{5}\)B.\(-\frac{4}{5}\)C.\(\frac{3}{4}\)D.\(-\frac{3}{4}\)答案:1.A2.B3.C4.A5.B6.C7.A8.B9.A10.B多項(xiàng)選擇題(每題2分,共10題)1.以下哪些是高中數(shù)學(xué)中的基本初等函數(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.下列不等式中,正確的是()A.\(x^2+1\geq2x\)B.\(a+b\geq2\sqrt{ab}\)(\(a,b\gt0\)）C.\(x^2+y^2\geq2xy\)D.\(a^2+b^2\geq\frac{(a+b)^2}{2}\)3.直線的方程形式有()A.點(diǎn)斜式B.斜截式C.兩點(diǎn)式D.截距式4.關(guān)于數(shù)列,下列說法正確的是()A.等差數(shù)列通項(xiàng)公式是\(a_n=a_1+(n-1)d\)B.等比數(shù)列通項(xiàng)公式是\(a_n=a_1q^{n-1}\)C.等差數(shù)列前\(n\)項(xiàng)和公式\(S_n=\frac{n(a_1+a_n)}{2}\)D.等比數(shù)列前\(n\)項(xiàng)和公式\(S_n=\frac{a_1(1-q^n)}{1-q}\)(\(q\neq1\))5.以下哪些是向量的運(yùn)算(）A.加法B.減法C.數(shù)乘D.數(shù)量積6.已知圓的方程\((x-a)^2+(y-b)^2=r^2\),則()A.圓心坐標(biāo)為\((a,b)\)B.半徑為\(r\)C.當(dāng)\(r=0\)時(shí)表示一個(gè)點(diǎn)D.與\(x\)軸可能無交點(diǎn)7.下列函數(shù)中,在\((0,+\infty)\)上單調(diào)遞增的是()A.\(y=x^2\)B.\(y=2^x\)C.\(y=\log_2x\)D.\(y=\frac{1}{x}\)8.對于\(\triangleABC\),以下哪些是正弦定理的表述()A.\(\frac{a}{\sinA}=\frac{\sinB}=\frac{c}{\sinC}\)B.\(a\sinB=b\sinA\)C.\(b\sinC=c\sinB\)D.\(c\sinA=a\sinC\)9.以下哪些是導(dǎo)數(shù)的應(yīng)用()A.求函數(shù)的極值B.求函數(shù)的最值C.判斷函數(shù)的單調(diào)性D.求曲線的切線方程10.已知\(a\),\(b\)為實(shí)數(shù),且\(ab\gt0\),則下列不等式成立的是()A.\(\frac{a}+\frac{a}\geq2\)B.\(a+b\geq2\sqrt{ab}\)C.\(\frac{1}{a}+\frac{1}\geq\frac{2}{\sqrt{ab}}\)D.\(a^2+b^2\geq2ab\)答案:1.ABCD2.ACD3.ABCD4.ABCD5.ABCD6.ABCD7.ABC8.ABCD9.ABCD10.ACD判斷題(每題2分,共10題)1.空集是任何集合的子集。()2.若\(a\gtb\),則\(a^2\gtb^2\)。（)3.函數(shù)\(y=\tanx\)的定義域是\(x\neqk\pi+\frac{\pi}{2},k\inZ\)。()4.向量\(\vec{a}\)與\(\vec\)平行,則\(\vec{a}\)與\(\vec\)的方向相同。（)5.橢圓是軸對稱圖形也是中心對稱圖形。()6.若\(f(x)\)是奇函數(shù),則\(f(0)=0\)。()7.直線\(Ax+By+C=0\)(\(A\),\(B\)不同時(shí)為\(0\)）的斜率為\(-\frac{A}{B}\)。(）8.等比數(shù)列中,若\(m+n=p+q\),則\(a_m\cdota_n=a_p\cdota_q\)。（)9.函數(shù)\(y=a^x\)(\(a\gt0\)且\(a\neq1\))在\(R\)上單調(diào)遞增。()10.兩條異面直線所成角的范圍是\((0,\frac{\pi}{2}]\)。(）答案:1.√2.×3.√4.×5.√6.×7.×8.√9.×10.√簡答題(每題5分,共4題)1.求函數(shù)\(y=x^2-4x+3\)的對稱軸和頂點(diǎn)坐標(biāo)。答案:對于二次函數(shù)\(y=ax^2+bx+c\),對稱軸\(x=-\frac{2a}\),此函數(shù)\(a=1\),\(b=-4\),對稱軸\(x=2\)。把\(x=2\)代入函數(shù)得\(y=4-8+3=-1\),頂點(diǎn)坐標(biāo)為\((2,-1)\)。2.已知\(\sin\alpha=\frac{1}{2}\),且\(\alpha\)是第一象限角,求\(\cos\alpha\)和\(\tan\alpha\)的值。答案：根據(jù)\(\sin^2\alpha+\cos^2\alpha=1\),\(\cos\alpha=\sqrt{1-\sin^{2}\alpha}=\sqrt{1-(\frac{1}{2})^2}=\frac{\sqrt{3}}{2}\),\(\tan\alpha=\frac{\sin\alpha}{\cos\alpha}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{\sqrt{3}}{3}\)。3.求過點(diǎn)\((1,2)\)且斜率為\(3\)的直線方程。答案:根據(jù)直線點(diǎn)斜式方程\(y-y_1=k(x-x_1)\)(\(k\)為斜率,\((x_1,y_1)\)為直線上一點(diǎn)),已知\(k=3\),\((x_1,y_1)=(1,2)\),則直線方程為\(y-2=3(x-1)\),即\(y=3x-1\)。4.已知等差數(shù)列\(zhòng)(\{a_n\}\)中,\(a_1=1\),\(a_3=5\),求其前\(5\)項(xiàng)和\(S_5\)。答案：先求公差\(d\),\(a_3=a_1+2d\),即\(5=1+2d\),得\(d=2\)。再根據(jù)等差數(shù)列前\(n\)項(xiàng)和公式\(S_n=na_1+\frac{n(n-1)}{2}d\),\(S_5=5\times1+\frac{5\times4}{2}\times2=25\)。討論題(每題5分,共4題)1.討論函數(shù)\(y=\sinx\)與\(y=\cosx\)的性質(zhì)差異與聯(lián)系。答案:差異:\(y=\sinx\)對稱軸\(x=k\pi+\frac{\pi}{2}\),對稱中心\((k\pi,0)\);\(y=\cosx\)對稱軸\(x=k\pi\),對稱中心\((k\pi+\frac{\pi}{2},0)\),單調(diào)性區(qū)間也不同。聯(lián)系:周期都為\(2\pi\),值域都是\([-1,1]\),且\(\sin(x+\frac{\pi}{2})=\cosx\)。2.在解析幾何中,直線與圓的位置關(guān)系有哪些判斷方法?答案：一是幾何法,通過圓心到直線的距離\(d\)與圓半徑\(r\)比較,\(d\gtr\)相離,\(d=r\)相切,\(d\ltr\)相交；二是代數(shù)法,聯(lián)立直線與圓的方程,消元得一元二次方程,根據(jù)判別式\(\Delta\)判斷,\(\Delta\lt0\)相離,\(\Delta=0\)相切,\(\Delta\gt0\)相交。3.談?wù)勀銓Φ炔顢?shù)列和等比數(shù)列通項(xiàng)公式推