成人高考入學試題和答案大全

一、單項選擇題(每題2分,共10題)1.函數(shù)\(y=\sqrt{x-1}\)的定義域是(）A.\(x\gt1\)B.\(x\geq1\)C.\(x\lt1\)D.\(x\leq1\)2.下列向量中與向量\(\vec{a}=(1,2)\)垂直的是()A.\((2,1)\)B.\((-2,1)\)C.\((1,-2)\)D.\((-1,2)\)3.直線\(y=2x+1\)的斜率是()A.\(\frac{1}{2}\)B.\(-\frac{1}{2}\)C.\(2\)D.\(-2\)4.\(\sin150^{\circ}\)的值為()A.\(\frac{1}{2}\)B.\(\frac{\sqrt{3}}{2}\)C.\(-\frac{1}{2}\)D.\(-\frac{\sqrt{3}}{2}\)5.不等式\(\vertx-1\vert\lt2\)的解集是()A.\((-1,3)\)B.\((-3,1)\)C.\((-\infty,-1)\cup(3,+\infty)\)D.\((-\infty,-3)\cup(1,+\infty)\)6.拋物線\(y^{2}=4x\)的焦點坐標是()A.\((0,1)\)B.\((1,0)\)C.\((0,-1)\)D.\((-1,0)\)7.已知\(a,b,c\)成等差數(shù)列,則\(2b=\)()A.\(a+c\)B.\(ac\)C.\(a-c\)D.\(\frac{a+c}{2}\)8.函數(shù)\(y=\cos2x\)的最小正周期是()A.\(\pi\)B.\(2\pi\)C.\(\frac{\pi}{2}\)D.\(4\pi\)9.若\(a\gtb\),則下列不等式成立的是()A.\(a^{2}\gtb^{2}\)B.\(\frac{1}{a}\lt\frac{1}\)C.\(a+c\gtb+c\)D.\(ac\gtbc\)10.已知集合\(A=\{1,2,3\}\),\(B=\{2,3,4\}\),則\(A\capB=\)()A.\(\{1,2,3,4\}\)B.\(\{2,3\}\)C.\(\{1,4\}\)D.\(\varnothing\)二、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.\(y=x^{3}\)2.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3.關于等差數(shù)列\(zhòng)(\{a_{n}\}\),正確的有()A.\(a_{n}=a_{1}+(n-1)d\)B.\(S_{n}=\frac{n(a_{1}+a_{n})}{2}\)C.\(a_{m}+a_{n}=a_{p}+a_{q}(m+n=p+q)\)D.公差\(d\)為常數(shù)4.下列三角函數(shù)值為正的有()A.\(\sin120^{\circ}\)B.\(\cos225^{\circ}\)C.\(\tan30^{\circ}\)D.\(\sin330^{\circ}\)5.已知向量\(\vec{m}=(x_{1},y_{1})\),\(\vec{n}=(x_{2},y_{2})\),則下列運算正確的有()A.\(\vec{m}+\vec{n}=(x_{1}+x_{2},y_{1}+y_{2})\)B.\(\vec{m}-\vec{n}=(x_{1}-x_{2},y_{1}-y_{2})\)C.\(\lambda\vec{m}=(\lambdax_{1},\lambday_{1})\)D.\(\vec{m}\cdot\vec{n}=x_{1}x_{2}+y_{1}y_{2}\)6.橢圓\(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a\gtb\gt0)\)的性質有()A.焦點在\(x\)軸B.長軸長為\(2a\)C.短軸長為\(2b\)D.離心率\(e=\frac{c}{a}(c^{2}=a^{2}-b^{2})\)7.不等式\(ax^{2}+bx+c\gt0\)(\(a\neq0\))的解集情況與()有關A.\(a\)的正負B.\(\Delta=b^{2}-4ac\)C.方程\(ax^{2}+bx+c=0\)的根D.函數(shù)\(y=ax^{2}+bx+c\)的圖象8.下列屬于基本初等函數(shù)的有()A.冪函數(shù)B.指數(shù)函數(shù)C.對數(shù)函數(shù)D.三角函數(shù)9.對于直線\(Ax+By+C=0\)(\(A,B\)不同時為\(0\)),說法正確的有()A.斜率\(k=-\frac{A}{B}(B\neq0)\)B.在\(y\)軸上截距為\(-\frac{C}{B}(B\neq0)\)C.與直線\(Bx-Ay+D=0\)垂直D.平行于直線\(Ax+By+D=0(D\neqC)\)10.已知\(a,b\inR\),則下列等式成立的有()A.\(a^{m}\cdota^{n}=a^{m+n}\)B.\((a^{m})^{n}=a^{mn}\)C.\((ab)^{n}=a^{n}b^{n}\)D.\(a^{0}=1(a\neq0)\)三、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)\(y=x^{3}\)在\(R\)上是增函數(shù)。()3.若\(a,b\)為實數(shù),\(a\gtb\),則\(a^{3}\gtb^{3}\)。()4.圓\(x^{2}+y^{2}=r^{2}\)的圓心是\((0,0)\),半徑是\(r\)。(）5.若向量\(\vec{a}\)與向量\(\vec\)平行,則\(\vec{a}\)與\(\vec\)的方向相同。（)6.數(shù)列\(zhòng)(1,2,4,8,\cdots\)是等差數(shù)列。()7.\(\cos(A+B)=\cosA+\cosB\)。()8.函數(shù)\(y=\lgx\)的定義域是\((0,+\infty)\)。()9.直線\(x=1\)的斜率不存在。()10.若\(x^{2}-3x+2=0\),則\(x=1\)或\(x=2\)。（）四、簡答題(每題5分,共4題)1.求函數(shù)\(y=\frac{1}{\sqrt{x-3}}\)的定義域。答案:要使函數(shù)有意義,則根號下的數(shù)大于\(0\),即\(x-3\gt0\),解得\(x\gt3\),所以定義域為\((3,+\infty)\)。2.已知等差數(shù)列\(zhòng)(\{a_{n}\}\)中,\(a_{1}=2\),\(d=3\),求\(a_{5}\)。答案：根據(jù)等差數(shù)列通項公式\(a_{n}=a_{1}+(n-1)d\),當\(n=5\),\(a_{1}=2\),\(d=3\)時,\(a_{5}=2+(5-1)\times3=2+12=14\)。3.求直線\(2x-y+3=0\)的斜率和在\(y\)軸上的截距。答案:將直線方程化為斜截式\(y=2x+3\),所以斜率\(k=2\),在\(y\)軸上的截距為\(3\)。4.計算\(\sin135^{\circ}\)的值。答案:\(\sin135^{\circ}=\sin(180^{\circ}-45^{\circ})\),根據(jù)誘導公式\(\sin(180^{\circ}-\alpha)=\sin\alpha\),所以\(\sin135^{\circ}=\sin45^{\circ}=\frac{\sqrt{2}}{2}\)。五、討論題(每題5分,共4題)1.討論函數(shù)\(y=x^{2}-2x+3\)的單調性。答案:對函數(shù)\(y=x^{2}-2x+3\)進行配方得\(y=(x-1)^{2}+2\)。其圖象開口向上,對稱軸為\(x=1\)。在\((-\infty,1)\)上函數(shù)單調遞減,在\((1,+\infty)\)上函數(shù)單調遞增。2.已知直線\(l_{1}\):\(y=k_{1}x+b_{1}\),\(l_{2}\):\(y=k_{2}x+b_{2}\),討論\(l_{1}\)與\(l_{2}\)的位置關系。答案：當\(k_{1}=k_{2}\)且\(b_{1}\neqb_{2}\)時,\(l_{1}\parallell_{2}\)；當\(k_{1}=k_{2}\)且\(b_{1}=b_{2}\)時,\(l_{1}\)與\(l_{2}\)重合；當\(k_{1}\neqk_{2}\)時,\(l_{1}\)與\(l_{2}\)相交,若\(k_{1}k_{2}=-1\),則\(l_{1}\perpl_{2}\)。3.討論橢圓和雙曲線在定義和性質上的異同。答案:相同點:都是圓錐曲線。不同點:定義上,橢圓是到兩定點距離之和為定值,雙曲線是到兩定點距離之