山東成考預(yù)測題庫及答案

一、單項選擇題(每題2分,共10題)1.下列函數(shù)中,在其定義域內(nèi)既是奇函數(shù)又是增函數(shù)的是（）A.\(y=x^3\)B.\(y=-x^2\)C.\(y=\frac{1}{x}\)D.\(y=\sinx\)答案：A2.已知向量\(\vec{a}=(1,2)\),\(\vec=(2,3)\),則\(\vec{a}-\vec\)等于()A.\((-1,-1)\)B.\((1,1)\)C.\((-3,-5)\)D.\((3,5)\)答案：A3.不等式\(x^2-2x-3<0\)的解集是()A.\((-1,3)\)B.\((-3,1)\)C.\((-\infty,-1)\cup(3,+\infty)\)D.\((-\infty,-3)\cup(1,+\infty)\)答案：A4.函數(shù)\(y=\log_2(x+1)\)的定義域是()A.\((-1,+\infty)\)B.\([-1,+\infty)\)C.\((0,+\infty)\)D.\([0,+\infty)\)答案：A5.已知\(\sin\alpha=\frac{3}{5}\),且\(\alpha\)是第二象限角,則\(\cos\alpha\)等于()A.\(-\frac{4}{5}\)B.\(\frac{4}{5}\)C.\(-\frac{3}{5}\)D.\(\frac{3}{5}\)答案：A6.直線\(y=2x+3\)的斜率為()A.2B.3C.\(\frac{1}{2}\)D.\(-\frac{1}{2}\)答案：A7.圓\(x^2+y^2=4\)的圓心坐標是()A.\((0,0)\)B.\((1,1)\)C.\((2,2)\)D.\((-2,-2)\)答案：A8.已知等差數(shù)列\(zhòng)(\{a_n\}\)中,\(a_1=1\),\(a_3=5\),則公差\(d\)等于()A.1B.2C.3D.4答案：B9.函數(shù)\(y=\sqrt{x-1}\)的反函數(shù)是()A.\(y=x^2+1(x\geq0)\)B.\(y=x^2+1(x\geq1)\)C.\(y=x^2-1(x\geq0)\)D.\(y=x^2-1(x\geq1)\)答案：A10.已知\(a=2^{0.3}\),\(b=0.3^2\),\(c=\log_{2}0.3\),則\(a,b,c\)的大小關(guān)系是()A.\(a>b>c\)B.\(b>a>c\)C.\(c>a>b\)D.\(a>c>b\)答案：A二、多項選擇題(每題2分,共10題)1.下列函數(shù)中,是冪函數(shù)的有（）A.\(y=x^2\)B.\(y=2^x\)C.\(y=x^{\frac{1}{2}}\)D.\(y=\frac{1}{x}\)答案:ACD2.下列向量中,與向量\(\vec{a}=(1,0)\)垂直的有（）A.\(\vec=(0,1)\)B.\(\vec{c}=(-1,0)\)C.\(\vecz3jilz61osys=(0,-1)\)D.\(\vec{e}=(1,1)\)答案:AC3.下列不等式中,解集為\(R\)的有（）A.\(x^2+2x+1>0\)B.\(x^2-2x+1\geq0\)C.\(x^2+1>0\)D.\(x^2-1<0\)答案:BC4.下列函數(shù)中,是偶函數(shù)的有（）A.\(y=x^4\)B.\(y=\sinx\)C.\(y=\cosx\)D.\(y=2^x\)答案:AC5.已知等比數(shù)列\(zhòng)(\{a_n\}\)中,\(a_1=2\),公比\(q=2\),則（）A.\(a_2=4\)B.\(a_3=8\)C.\(a_4=16\)D.\(a_5=32\)答案:ABCD6.直線\(x+y-1=0\)的傾斜角為(）A.\(45^{\circ}\)B.\(135^{\circ}\)C.\(60^{\circ}\)D.\(120^{\circ}\)答案：B7.圓\((x-1)^2+(y-2)^2=9\)的半徑為()A.1B.2C.3D.4答案：C8.已知函數(shù)\(y=f(x)\)的定義域為\([0,1]\),則函數(shù)\(y=f(x+1)\)的定義域為()A.\([-1,0]\)B.\([0,1]\)C.\([1,2]\)D.\([-2,-1]\)答案：A9.下列函數(shù)中,在\((0,+\infty)\)上單調(diào)遞增的有()A.\(y=x^2\)B.\(y=\lnx\)C.\(y=2^x\)D.\(y=\frac{1}{x}\)答案:ABC10.已知\(\tan\alpha=2\),則\(\sin2\alpha\)等于（）A.\(\frac{4}{5}\)B.\(\frac{3}{5}\)C.\(\frac{2}{5}\)D.\(\frac{1}{5}\)答案：A三、判斷題(每題2分,共10題)1.函數(shù)\(y=\frac{1}{\sqrt{x}}\)的定義域是\((0,+\infty)\)。(）答案：√2.向量\(\vec{a}=(1,2)\)與向量\(\vec=(2,4)\)平行。()答案：√3.不等式\(x^2+3x+2>0\)的解集是\((-2,-1)\)。()答案：×4.函數(shù)\(y=\sin(x+\frac{\pi}{2})\)是偶函數(shù)。()答案：√5.等差數(shù)列\(zhòng)(\{a_n\}\)中,若\(a_1=1\),\(d=2\),則\(a_5=9\)。()答案：√6.直線\(2x-y+1=0\)與直線\(4x-2y+3=0\)平行。()答案：×7.圓\(x^2+y^2-2x-4y+3=0\)的圓心坐標是\((1,2)\)。()答案：×8.函數(shù)\(y=3^x\)的值域是\((0,+\infty)\)。()答案：√9.已知\(\cos\alpha=\frac{1}{2}\),則\(\alpha=\frac{\pi}{3}+2k\pi,k\inZ\)。()答案：×10.函數(shù)\(y=\log_{\frac{1}{2}}x\)在\((0,+\infty)\)上單調(diào)遞減。()答案：√四、簡答題(每題5分,共4題)1.求函數(shù)\(y=x^2-4x+3\)的對稱軸和頂點坐標。答案:對稱軸\(x=-\frac{2a}=2\),將\(x=2\)代入函數(shù)得\(y=4-8+3=-1\),頂點坐標為\((2,-1)\)。2.已知\(\sin\alpha=\frac{3}{5}\),\(\alpha\)是第二象限角,求\(\cos\alpha\)和\(\tan\alpha\)。答案：因為\(\alpha\)是第二象限角,所以\(\cos\alpha=-\sqrt{1-\sin^{2}\alpha}=-\frac{4}{5}\),\(\tan\alpha=\frac{\sin\alpha}{\cos\alpha}=-\frac{3}{4}\)。3.求過點\((1,2)\)且斜率為\(3\)的直線方程。答案:由點斜式可得\(y-2=3(x-1)\),整理得\(3x-y-1=0\)。4.已知等比數(shù)列\(zhòng)(\{a_n\}\)中,\(a_1=2\),\(a_4=16\),求公比\(q\)和通項公式\(a_n\)。答案：\(a_4=a_1q^3\),即\(16=2q^3\),解得\(q=2\),通項公式\(a_n=a_1q^{n-1}=2^n\)。五、討論題(每題5分,共4題)1.討論函數(shù)\(y=x^3\)的單調(diào)性。答案:對\(y=x^3\)求導(dǎo)得\(y^\prime=3x^2\geq0\),僅當(dāng)\(x=0\)時\(y^\prime=0\),所以\(y=x^3\)在\(R\)上單調(diào)遞增。2.討論向量平行的條件及應(yīng)用。答案:兩非零向量\(\vec{a}=(x_1,y_1)\),\(\vec=(x_2,y_2)\)平行的充要條件是\(x_1y_2-x_2y_1=0\)。可用于證明幾何圖形平行關(guān)系等,比如判斷兩直線方向向量是否平行來確定直線是否平行。3.討論不等式\(ax^2+bx+c>0\)(\(a\neq0\))的解集情況與哪些因素有關(guān)。答案：與\(a\)的正負有關(guān),