思而行試題答案期末高一

單項(xiàng)選擇題(每題2分,共10題)1.函數(shù)\(y=2x+1\)的斜率是(）A.1B.2C.-1D.-22.下列元素中,屬于主族元素的是()A.FeB.CuC.NaD.Zn3.不等式\(x-3>0\)的解集是()A.\(x<3\)B.\(x>3\)C.\(x\leq3\)D.\(x\geq3\)4.正弦函數(shù)\(y=\sinx\)的最小正周期是()A.\(\pi\)B.\(2\pi\)C.\(3\pi\)D.\(4\pi\)5.向量\(\overrightarrow{a}=(1,2)\),\(\overrightarrow=(3,4)\),則\(\overrightarrow{a}+\overrightarrow\)等于()A.\((4,6)\)B.\((2,2)\)C.\((-2,-2)\)D.\((3,6)\)6.直線\(y=x+1\)與\(y\)軸的交點(diǎn)坐標(biāo)是()A.\((0,1)\)B.\((1,0)\)C.\((0,-1)\)D.\((-1,0)\)7.若\(\cos\alpha=\frac{1}{2}\),且\(0<\alpha<\pi\),則\(\alpha\)等于()A.\(\frac{\pi}{6}\)B.\(\frac{\pi}{3}\)C.\(\frac{2\pi}{3}\)D.\(\frac{5\pi}{6}\)8.一個(gè)正方體的棱長(zhǎng)為\(2\),則它的表面積是()A.6B.8C.12D.249.數(shù)列\(zhòng)(1,3,5,7,\cdots\)的通項(xiàng)公式是()A.\(a_n=2n-1\)B.\(a_n=2n+1\)C.\(a_n=n^2\)D.\(a_n=n+1\)10.拋物線\(y=x^2\)的焦點(diǎn)坐標(biāo)是()A.\((0,\frac{1}{4})\)B.\((\frac{1}{4},0)\)C.\((0,-\frac{1}{4})\)D.\((-\frac{1}{4},0)\)多項(xiàng)選擇題(每題2分,共10題)1.以下屬于基本初等函數(shù)的有(）A.冪函數(shù)B.指數(shù)函數(shù)C.對(duì)數(shù)函數(shù)D.三角函數(shù)2.下列關(guān)于向量的說(shuō)法正確的是()A.向量有大小和方向B.零向量與任意向量平行C.向量的?？梢詾閈(0\)D.兩個(gè)向量相等則大小和方向都相同3.以下哪些是等差數(shù)列的性質(zhì)()A.\(a_{n+1}-a_n=d\)(\(d\)為常數(shù))B.\(a_n=a_1+(n-1)d\)C.若\(m+n=p+q\),則\(a_m+a_n=a_p+a_q\)D.\(S_n=\frac{n(a_1+a_n)}{2}\)4.關(guān)于直線方程\(Ax+By+C=0\)(\(A\)、\(B\)不同時(shí)為\(0\)),說(shuō)法正確的是()A.當(dāng)\(B=0\)時(shí),直線垂直于\(x\)軸B.當(dāng)\(A=0\)時(shí),直線垂直于\(y\)軸C.直線的斜率\(k=-\frac{A}{B}\)(\(B\neq0\))D.直線在\(y\)軸上的截距為\(-\frac{C}{B}\)(\(B\neq0\))5.下列函數(shù)中,是偶函數(shù)的有（）A.\(y=x^2\)B.\(y=\cosx\)C.\(y=|x|\)D.\(y=x^3\)6.關(guān)于\(\triangleABC\),根據(jù)正弦定理正確的有()A.\(\frac{a}{\sinA}=\frac{\sinB}\)B.\(\frac{a}{\sinA}=\frac{c}{\sinC}\)C.\(\frac{\sinB}=\frac{c}{\sinC}\)D.\(a\sinB=b\sinA\)7.以下哪些是直線的位置關(guān)系()A.平行B.相交C.異面D.重合8.下列運(yùn)算正確的是()A.\(a^m\cdota^n=a^{m+n}\)B.\((a^m)^n=a^{mn}\)C.\((ab)^n=a^nb^n\)D.\(a^m\diva^n=a^{m-n}\)(\(a\neq0\))9.關(guān)于橢圓的標(biāo)準(zhǔn)方程\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)（\(a>b>0\)),說(shuō)法正確的是（)A.焦點(diǎn)在\(x\)軸上B.\(c^2=a^2-b^2\)(\(c\)為半焦距）C.長(zhǎng)軸長(zhǎng)為\(2a\)D.短軸長(zhǎng)為\(2b\)10.以下哪些是立體幾何中的基本元素()A.點(diǎn)B.線C.面D.體判斷題(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\((-\infty,0)\)上單調(diào)遞增。()3.若\(a>b\),則\(a^2>b^2\)。（)4.向量\(\overrightarrow{a}\)與\(-\overrightarrow{a}\)是相反向量。()5.等差數(shù)列的前\(n\)項(xiàng)和公式一定是關(guān)于\(n\)的二次函數(shù)。()6.直線\(y=2x+1\)與直線\(y=2x-1\)平行。()7.函數(shù)\(y=\sinx\)是奇函數(shù)。()8.若\(\alpha\)、\(\beta\)是異面直線,\(\beta\)、\(\gamma\)是異面直線,則\(\alpha\)、\(\gamma\)一定是異面直線。（)9.對(duì)數(shù)函數(shù)\(y=\log_ax\)(\(a>0\)且\(a\neq1\))的定義域是\((0,+\infty)\)。()10.圓\(x^2+y^2=r^2\)的圓心坐標(biāo)是\((0,0)\),半徑是\(r\)。（）簡(jiǎn)答題(每題5分,共4題)1.求函數(shù)\(y=\sqrt{x-1}\)的定義域。答:要使根式有意義,則根號(hào)下的數(shù)非負(fù),即\(x-1\geq0\),解得\(x\geq1\),定義域?yàn)閈([1,+\infty)\)。2.已知等差數(shù)列\(zhòng)(\{a_n\}\)中,\(a_1=1\),\(d=2\),求\(a_5\)。答：根據(jù)等差數(shù)列通項(xiàng)公式\(a_n=a_1+(n-1)d\),\(n=5\)時(shí),\(a_5=1+(5-1)×2=1+8=9\)。3.求直線\(2x+y-3=0\)的斜率。答:將直線方程\(2x+y-3=0\)化為斜截式\(y=-2x+3\),所以直線斜率\(k=-2\)。4.求\(\cos120^{\circ}\)的值。答:根據(jù)三角函數(shù)誘導(dǎo)公式\(\cos120^{\circ}=\cos(180^{\circ}-60^{\circ})=-\cos60^{\circ}=-\frac{1}{2}\)。討論題(每題5分,共4題)1.討論函數(shù)\(y=x^3\)的單調(diào)性。答:對(duì)\(y=x^3\)求導(dǎo)得\(y^\prime=3x^2\geq0\),當(dāng)且僅當(dāng)\(x=0\)時(shí)等號(hào)成立。所以\(y=x^3\)在\((-\infty,+\infty)\)上單調(diào)遞增。2.討論直線與圓的位置關(guān)系有哪些判斷方法。答:一是幾何法,通過(guò)比較圓心到直線的距離\(d\)與圓半徑\(r\)的大小,\(d>r\)相離,\(d=r\)相切,\(d<r\)相交;二是代數(shù)法,聯(lián)立直線與圓方程,看所得方程組解的個(gè)數(shù),無(wú)解相離,一組解相切,兩組解相交。3.討論如何根據(jù)三角函數(shù)圖象確定其解析式。答:先由圖象的最值確定\(A\)的值;再根據(jù)周期\(T\)求\(\omega\),\(T=\frac{2\pi}{\ome