高考乙卷考試題目及答案

一、單項選擇題（每題2分，共10題）1.已知集合\(A=\{x|x^2-3x-4<0\}\)，\(B=\{x|-2<x<2\}\)，則\(A\capB=\)（）A.\(\{x|-2<x<4\}\)B.\(\{x|-2<x<2\}\)C.\(\{x|-1<x<2\}\)D.\(\{x|-1<x<4\}\)答案：C2.若\(z=1+i\)，則\(\frac{z^2}{z-1}=\)（）A.\(2\)B.\(-2\)C.\(2i\)D.\(-2i\)答案：A3.已知向量\(\vec{a}=(1,2)\)，\(\vec=(2,-2)\)，\(\vec{c}=(1,\lambda)\)。若\(\vec{c}\parallel(2\vec{a}+\vec)\)，則\(\lambda=\)（）A.\(\frac{1}{2}\)B.\(-\frac{1}{2}\)C.\(\frac{1}{4}\)D.\(-\frac{1}{4}\)答案：B4.設(shè)函數(shù)\(f(x)=\frac{1-x}{1+x}\)，則下列函數(shù)中為奇函數(shù)的是（）A.\(y=f(x-1)-1\)B.\(y=f(x-1)+1\)C.\(y=f(x+1)-1\)D.\(y=f(x+1)+1\)答案：A5.在正方體\(ABCD-A_{1}B_{1}C_{1}D_{1}\)中，\(P\)為\(B_{1}D_{1}\)的中點，則直線\(PB\)與\(AD_{1}\)所成的角為（）A.\(\frac{\pi}{2}\)B.\(\frac{\pi}{3}\)C.\(\frac{\pi}{4}\)D.\(\frac{\pi}{6}\)答案：D6.將5名北京冬奧會志愿者分配到花樣滑冰、短道速滑、冰球和冰壺4個項目進(jìn)行培訓(xùn)，每名志愿者只分配到1個項目，每個項目至少分配1名志愿者，則不同的分配方案共有（）A.60種B.120種C.240種D.480種答案：C7.把函數(shù)\(y=f(x)\)圖象上所有點的橫坐標(biāo)縮短到原來的\(\frac{1}{2}\)倍，縱坐標(biāo)不變，再把所得曲線向右平移\(\frac{\pi}{3}\)個單位長度，得到函數(shù)\(y=\sin(x-\frac{\pi}{4})\)的圖象，則\(f(x)=\)（）A.\(\sin(\frac{x}{2}-\frac{7\pi}{12})\)B.\(\sin(\frac{x}{2}+\frac{\pi}{12})\)C.\(\sin(2x-\frac{7\pi}{12})\)D.\(\sin(2x+\frac{\pi}{12})\)答案：B8.在區(qū)間\((0,1)\)與\((1,2)\)中各隨機取1個數(shù)，則兩數(shù)之和大于\(\frac{7}{4}\)的概率為（）A.\(\frac{7}{9}\)B.\(\frac{23}{32}\)C.\(\frac{9}{32}\)D.\(\frac{2}{9}\)答案：C9.魏晉時期劉徽撰寫的《海島算經(jīng)》是關(guān)于測量的數(shù)學(xué)著作，其中第一題是測量海島的高。如圖，點\(E\)，\(H\)，\(G\)在水平線\(AC\)上，\(DE\)和\(FG\)是兩個垂直于水平面且等高的測量標(biāo)桿的高度，稱為“表高”，\(EG\)稱為“表距”，\(GC\)和\(EH\)都稱為“表目距”，\(GC\)與\(EH\)的差稱為“表目距的差”。則海島的高\(AB=\)（）A.\(\frac{表高\times表距}{表目距的差}+表高\)B.\(\frac{表高\times表距}{表目距的差}-表高\)C.\(\frac{表目距的差\times表高}{表距}+表高\)D.\(\frac{表目距的差\times表高}{表距}-表高\)答案：A10.設(shè)\(a\neq0\)，若\(x=a\)為函數(shù)\(f(x)=a(x-a)^2(x-b)\)的極大值點，則（）A.\(a<b\)B.\(a>b\)C.\(ab<a^{2}\)D.\(ab>a^{2}\)答案：D二、多項選擇題（每題2分，共10題）1.下列函數(shù)中，在區(qū)間\((0,+\infty)\)上單調(diào)遞增的是（）A.\(y=x^{\frac{1}{2}}\)B.\(y=2^{x}-1\)C.\(y=\frac{1}{x}\)D.\(y=\log_{0.5}(x+1)\)答案：AB2.已知拋物線\(y^{2}=2px(p>0)\)的焦點為\(F\)，準(zhǔn)線為\(l\)，過點\(F\)的直線與拋物線交于\(A\)，\(B\)兩點，且\(\vertAF\vert=4\)，\(\angleAFx=30^{\circ}\)，則（）A.\(p=3\)B.\(\vertBF\vert=\frac{8}{3}\)C.以\(AF\)為直徑的圓與\(y\)軸相切D.\(\vertAB\vert=\frac{16}{3}\)答案：ABC3.已知函數(shù)\(f(x)=\sin(\omegax+\varphi)(\omega>0,0<\varphi<\pi)\)的最小正周期為\(\pi\)，且圖象過點\((\frac{\pi}{6},\frac{1}{2})\)，則（）A.\(\omega=2\)B.\(\varphi=\frac{\pi}{3}\)C.\(f(x)\)圖象的一個對稱中心為\((\frac{\pi}{12},0)\)D.\(f(x)\)的單調(diào)遞減區(qū)間為\([\frac{\pi}{3}+k\pi,\frac{5\pi}{6}+k\pi](k\inZ)\)答案：AD4.如圖，在正方體\(ABCD-A_{1}B_{1}C_{1}D_{1}\)中，\(O\)為底面\(ABCD\)的中心，\(P\)為\(DD_{1}\)的中點，則下列結(jié)論正確的是（）A.\(OP\parallel\)平面\(A_{1}BC_{1}\)B.\(OP\perp\)平面\(BB_{1}D_{1}D\)C.直線\(OP\)與平面\(A_{1}BD\)所成角的正弦值為\(\frac{\sqrt{3}}{3}\)D.若正方體棱長為2，則三棱錐\(P-A_{1}BC_{1}\)的體積為\(\frac{2}{3}\)答案：ACD5.已知\(a>0\)，\(b>0\)，且\(a+b=1\)，則（）A.\(a^{2}+b^{2}\geqslant\frac{1}{2}\)B.\(2^{a-b}>\frac{1}{2}\)C.\(\log_{2}a+\log_{2}b\geqslant-2\)D.\(\sqrt{a}+\sqrt\leqslant\sqrt{2}\)答案：ABD6.已知函數(shù)\(f(x)=x^{3}-ax+1\)的圖象在點\((0,1)\)處的切線方程為\(y=-3x+1\)，則（）A.\(a=3\)B.函數(shù)\(f(x)\)的極大值為\(1\)C.函數(shù)\(f(x)\)的極小值為\(-1\)D.函數(shù)\(f(x)\)在區(qū)間\((-1,1)\)上單調(diào)遞增答案：AC7.已知雙曲線\(C:\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1(a>0,b>0)\)的一條漸近線方程為\(y=\frac{\sqrt{5}}{2}x\)，且與橢圓\(\frac{x^{2}}{12}+\frac{y^{2}}{3}=1\)有公共焦點，則雙曲線\(C\)的方程為（）A.\(\frac{x^{2}}{4}-\frac{y^{2}}{5}=1\)B.\(\frac{x^{2}}{8}-\frac{y^{2}}{10}=1\)C.\(\frac{x^{2}}{5}-\frac{y^{2}}{4}=1\)D.\(\frac{x^{2}}{4}-\frac{y^{2}}{3}=1\)答案：A8.已知數(shù)列\(zhòng)(\{a_{n}\}\)的前\(n\)項和為\(S_{n}\)，且滿足\(S_{n}=2a_{n}-1\)，則（）A.\(a_{1}=1\)B.\(\{a_{n}\}\)是等比數(shù)列C.\(a_{n}=2^{n-1}\)D.\(S_{n}=2^{n}-1\)答案：ABCD9.已知\(F_{1}\)，\(F_{2}\)為橢圓\(E:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0)\)的左、右焦點，點\(P(x_{1},y_{1})\)，\(Q(-x_{1},-y_{1})\)在橢圓\(E\)上，若\(\vertPF_{1}\vert=3\vertPF_{2}\vert\)，且\(\angleF_{1}PF_{2}=60^{\circ}\)，則（）A.\(\vertPF_{1}\vert=3\)B.\(\vertPF_{2}\vert=1\)C.\(a=\sqrt{7}\)D.\(b=\sqrt{3}\)答案：ABCD10.對于函數(shù)\(f(x)=\frac{\lnx}{x}\)，下列說法正確的是（）A.\(f(x)\)在\((0,e)\)上單調(diào)遞增B.\(f(x)\)在\(x=e\)處取得極大值\(\frac{1}{e}\)C.\(f(x)\)有兩個不同的零點D.若\(f(x)<m-\frac{1}{x}\)在\((0,+\infty)\)上恒成立，則\(m>1\)答案：ABD三、判斷題（每題2分，共10題）1.若\(a,b\inR\)，則\(a>b\)是\(a^{2}>b^{2}\)的充分不必要條件。（）答案：錯誤2.若直線\(l\)的斜率\(k=\tan\alpha\)，則直線\(l\)的傾斜角為\(\alpha\)。（）答案：錯誤3.若\(\vec{a}\cdot\vec=\vec{a}\cdot\vec{c}\)，則\(\vec=\vec{c}\)。（）答案：錯誤4.函數(shù)\(y=\sin^{2}x\)是周期函數(shù)。（）答案：正確5.若\(z\inC\)，則\(\vertz\vert^{2}=z^{2}\)。（）答案：錯誤6.已知數(shù)列\(zhòng)(\{a_{n}\}\)滿足\(a_{n+1}=a_{n}-2\)，若\(a_{1}=1\)，則\(a_{5}=-7\)。（）答案：正確7.若圓\(C_{1}:x^{2}+y^{2}+2x+2y-2=0\)與圓\(C_{2}:x^{2}+y^{2}-4x-2y+1=0\)，則兩圓的位置關(guān)系是相交。（）答案：正確8.若\(f(x)\)是定義在\(R\)上的奇函數(shù)，則\(f(0)=0\)。（）答案：正確9.若二次函數(shù)\(y=ax^{2}+bx+c(a\neq0)\)的圖象與\(x\)軸有兩個交點，則\(b^{2}-4ac>0\)。（）答案：正確10.若\(a,b\inR\)，且\(a+b=1\)，則\(ab\leqslant\frac{1}{4}\)。（）答案：正確四、簡答題（每題5分，共4題）1.求函數(shù)\(y=\frac{1}{x-1}+\ln(x+1)\)的定義域。答案：要使函數(shù)有意義，則\(\left\{\begin{array}{l}x-1\neq0\\x+1>0\end{array}\right.\)，解得\(x>-1\)且\(x\neq1\)，所以函數(shù)的定義域為\((-1,1)\cup(1,+\infty)\)。2.已知等差數(shù)列\(zhòng)(\{a_{n}\}\)的前\(n\)項和為\(S_{n}\)，\(a_{3}=5\)，\(S_{5}=35\)，求數(shù)列\(zhòng)(\{a_{n