2025年高中知識(shí)考試題及答案

一、單項(xiàng)選擇題1.已知集合\(A=\{x|x^2-3x+2=0\}\)，\(B=\{x|0<x<6,x\inN\}\)，則滿足\(A\subseteqC\subseteqB\)的集合\(C\)的個(gè)數(shù)為（）A.4B.8C.7D.16答案：B2.函數(shù)\(y=\log_2(x^2-3x+2)\)的定義域?yàn)椋ǎ〢.\((1,2)\)B.\((-\infty,1)\cup(2,+\infty)\)C.\((-\infty,1]\cup[2,+\infty)\)D.\([1,2]\)答案：B3.已知\(\sin\alpha=\frac{3}{5}\)，\(\alpha\in(\frac{\pi}{2},\pi)\)，則\(\tan\alpha\)的值為（）A.\(\frac{3}{4}\)B.\(-\frac{3}{4}\)C.\(\frac{4}{3}\)D.\(-\frac{4}{3}\)答案：B4.等差數(shù)列\(zhòng)(\{a_n\}\)中，\(a_3+a_5=10\)，\(a_7=9\)，則\(a_1\)的值為（）A.1B.2C.0D.-1答案：C5.過點(diǎn)\((1,2)\)且與直線\(2x-y+1=0\)平行的直線方程為（）A.\(2x-y=0\)B.\(2x-y-4=0\)C.\(x+2y-5=0\)D.\(x+2y-4=0\)答案：A6.已知向量\(\overrightarrow{a}=(1,2)\)，\(\overrightarrow=(-2,m)\)，若\(\overrightarrow{a}\parallel\overrightarrow\)，則\(m\)的值為（）A.4B.-4C.1D.-1答案：B7.函數(shù)\(y=2\sin(2x+\frac{\pi}{6})\)的最小正周期是（）A.\(\pi\)B.\(2\pi\)C.\(\frac{\pi}{2}\)D.\(\frac{\pi}{4}\)答案：A8.已知\(a=2^{0.3}\)，\(b=0.3^2\)，\(c=\log_20.3\)，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：A9.拋物線\(y^2=8x\)的焦點(diǎn)坐標(biāo)是（）A.\((2,0)\)B.\((0,2)\)C.\((4,0)\)D.\((0,4)\)答案：A10.已知函數(shù)\(f(x)\)是定義在\(R\)上的奇函數(shù)，當(dāng)\(x>0\)時(shí)，\(f(x)=x^2-2x\)，則\(f(-1)\)的值為（）A.-1B.1C.3D.-3答案：A二、多項(xiàng)選擇題1.下列函數(shù)中，在其定義域上是增函數(shù)的有（）A.\(y=2^x\)B.\(y=\log_2x\)C.\(y=x^3\)D.\(y=\frac{1}{x}\)答案：ABC2.已知直線\(l_1\)：\(A_1x+B_1y+C_1=0\)，\(l_2\)：\(A_2x+B_2y+C_2=0\)，則下列說法正確的有（）A.若\(l_1\parallell_2\)，則\(\frac{A_1}{A_2}=\frac{B_1}{B_2}\neq\frac{C_1}{C_2}\)B.若\(l_1\perpl_2\)，則\(A_1A_2+B_1B_2=0\)C.若\(l_1\)與\(l_2\)相交，則\(\frac{A_1}{A_2}\neq\frac{B_1}{B_2}\)D.若\(A_1=A_2\)，\(B_1=B_2\)，\(C_1=C_2\)，則\(l_1\)與\(l_2\)重合答案：ABCD3.已知\(\alpha\)，\(\beta\)是兩個(gè)不同的平面，\(m\)，\(n\)是兩條不同的直線，則下列說法正確的有（）A.若\(m\parallel\alpha\)，\(n\subset\alpha\)，則\(m\paralleln\)B.若\(m\perp\alpha\)，\(m\paralleln\)，\(n\subset\beta\)，則\(\alpha\perp\beta\)C.若\(\alpha\cap\beta=m\)，\(n\parallelm\)，\(n\not\subset\alpha\)，\(n\not\subset\beta\)，則\(n\parallel\alpha\)且\(n\parallel\beta\)D.若\(m\subset\alpha\)，\(n\subset\alpha\)，\(m\capn=P\)，\(m\parallel\beta\)，\(n\parallel\beta\)，則\(\alpha\parallel\beta\)答案：BCD4.已知數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和\(S_n=n^2\)，則下列說法正確的有（）A.\(a_1=1\)B.\(a_n=2n-1\)C.數(shù)列\(zhòng)(\{a_n\}\)是等差數(shù)列D.數(shù)列\(zhòng)(\{a_n\}\)是等比數(shù)列答案：ABC5.已知函數(shù)\(y=\sin(2x+\varphi)\)，\(|\varphi|<\frac{\pi}{2}\)的圖象經(jīng)過點(diǎn)\((0,\frac{\sqrt{3}}{2})\)，則下列說法正確的有（）A.\(\varphi=\frac{\pi}{3}\)B.函數(shù)\(y=\sin(2x+\varphi)\)在\((-\frac{\pi}{6},\frac{\pi}{6})\)上單調(diào)遞增C.函數(shù)\(y=\sin(2x+\varphi)\)的圖象關(guān)于點(diǎn)\((\frac{5\pi}{12},0)\)對(duì)稱D.函數(shù)\(y=\sin(2x+\varphi)\)的圖象可以由\(y=\sin2x\)的圖象向左平移\(\frac{\pi}{6}\)個(gè)單位得到答案：ABCD6.已知\(a\)，\(b\)為正實(shí)數(shù)，且\(a+b=1\)，則下列說法正確的有（）A.\(ab\leq\frac{1}{4}\)B.\(\frac{1}{a}+\frac{1}\geq4\)C.\(a^2+b^2\geq\frac{1}{2}\)D.\(\sqrt{a}+\sqrt\leq\sqrt{2}\)答案：ABCD7.已知雙曲線\(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\)（\(a>0\)，\(b>0\)）的離心率\(e=\frac{\sqrt{5}}{2}\)，則雙曲線的漸近線方程為（）A.\(y=\pm\frac{1}{2}x\)B.\(y=\pm2x\)C.\(y=\pm\frac{\sqrt{5}}{2}x\)D.\(y=\pm\frac{2\sqrt{5}}{5}x\)答案：AB8.已知函數(shù)\(f(x)=x^3-3x^2+2\)，則下列說法正確的有（）A.函數(shù)\(f(x)\)有兩個(gè)極值點(diǎn)B.函數(shù)\(f(x)\)在\((-\infty,0)\)上單調(diào)遞增C.函數(shù)\(f(x)\)在\((1,+\infty)\)上單調(diào)遞減D.函數(shù)\(f(x)\)的極大值為\(2\)，極小值為\(-2\)答案：ABD9.已知向量\(\overrightarrow{a}=(1,1)\)，\(\overrightarrow=(2,k)\)，若\((\overrightarrow{a}+\overrightarrow)\perp\overrightarrow{a}\)，則下列說法正確的有（）A.\(k=-3\)B.\(|\overrightarrow|=\sqrt{13}\)C.向量\(\overrightarrow{a}\)與\(\overrightarrow\)的夾角為\(135^{\circ}\)D.向量\(\overrightarrow{a}\)在\(\overrightarrow\)上的投影為\(-\frac{\sqrt{2}}{2}\)答案：ABC10.已知\(f(x)\)是定義在\(R\)上的偶函數(shù)，且在\([0,+\infty)\)上單調(diào)遞減，則（）A.\(f(-2)>f(1)>f(3)\)B.\(f(1)>f(-2)>f(3)\)C.\(f(3)>f(-2)>f(1)\)D.\(f(3)<f(-2)<f(1)\)答案：AD三、判斷題1.若\(a>b\)，則\(ac^2>bc^2\)。（）答案：錯(cuò)誤2.函數(shù)\(y=\sinx\)的圖象與函數(shù)\(y=\cosx\)的圖象的對(duì)稱軸相同。（）答案：錯(cuò)誤3.若直線\(l\)與平面\(\alpha\)內(nèi)的無數(shù)條直線垂直，則\(l\perp\alpha\)。（）答案：錯(cuò)誤4.數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和\(S_n=2^n-1\)，則數(shù)列\(zhòng)(\{a_n\}\)是等比數(shù)列。（）答案：正確5.若\(z=a+bi\)（\(a\)，\(b\inR\)），則\(z\)為純虛數(shù)的充要條件是\(a=0\)。（）答案：錯(cuò)誤6.橢圓\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)（\(a>b>0\)）的離心率\(e=\frac{c}{a}\)，其中\(zhòng)(c^2=a^2-b^2\)。（）答案：正確7.函數(shù)\(y=\log_a(x+1)\)（\(a>0\)且\(a\neq1\)）的圖象恒過定點(diǎn)\((0,0)\)。（）答案：正確8.若\(\overrightarrow{a}\cdot\overrightarrow=0\)，則\(\overrightarrow{a}=\overrightarrow{0}\)或\(\overrightarrow=\overrightarrow{0}\)。（）答案：錯(cuò)誤9.對(duì)于函數(shù)\(y=f(x)\)，若\(f(x+1)=f(1-x)\)，則函數(shù)\(y=f(x)\)的圖象關(guān)于直線\(x=1\)對(duì)稱。（）答案：正確10.若\(f(x)\)是奇函數(shù)，且\(f(x)\)在\(x=0\)處有定義，則\(f(0)=0\)。（）答案：正確四、簡(jiǎn)答題1.求函數(shù)\(y=\sin^2x+\sqrt{3}\sinx\cosx\)的最小正周期及單調(diào)遞增區(qū)間。答案：先化簡(jiǎn)函數(shù)，\(y=\sin^2x+\sqrt{3}\sinx\cosx=\frac{1-\cos2x}{2}+\frac{\sqrt{3}}{2}\sin2x=\sin(2x-\frac{\pi}{6})+\frac{1}{2}\)。最小正周期\(T=\frac{2\pi}{2}=\pi\)。令\(2k\pi-\frac{\pi}{2}\leq2x-\frac{\pi}{6}\leq2k\pi+\frac{\pi}{2}\)，\(k\inZ\)，解得\(k\pi-\frac{\pi}{6}\leqx\leqk\pi+\frac{\pi}{3}\)，\(k\inZ\)，所以單調(diào)遞增區(qū)間是\([k\pi-\frac{\pi}{6},k\pi+\frac{\pi}{3}]\)，\(k\inZ\)。2.已知等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和為\(S_n\)，\(a_3=5\)，\(S_6=36\)，求數(shù)列\(zhòng)(\{a_n\}\)的通項(xiàng)公式及前\(n\)項(xiàng)和\(S_n\)。答案：設(shè)等差數(shù)列\(zhòng)(\{a_n\}\)的公差為\(d\)，首項(xiàng)為\(a_1\)。由\(a_3=5\)得\(a_1+2d=5\)，由\(S_6=36\)得\(6a_1+\frac{6\times5}{2}d=36\)，即\(6a_1+15d=36\)。聯(lián)立方程解得\(a_1=1\)，\(d=