2025年浙江數(shù)學(xué)理科真題及答案

一、單項(xiàng)選擇題1.已知集合\(A=\{x|x^2-5x+6=0\}\)，\(B=\{x|mx-1=0\}\)，若\(B\subseteqA\)，則實(shí)數(shù)\(m\)的值為（）A.\(\frac{1}{2}\)B.\(\frac{1}{3}\)C.\(\frac{1}{2}\)或\(\frac{1}{3}\)D.\(0\)或\(\frac{1}{2}\)或\(\frac{1}{3}\)答案：D2.復(fù)數(shù)\(z=\frac{2-i}{1+i}\)（\(i\)為虛數(shù)單位）的共軛復(fù)數(shù)\(\overline{z}\)在復(fù)平面內(nèi)對(duì)應(yīng)的點(diǎn)位于（）A.第一象限B.第二象限C.第三象限D(zhuǎn).第四象限答案：A3.已知\(\overrightarrow{a}=(1,2)\)，\(\overrightarrow=(x,-1)\)，且\(\overrightarrow{a}\perp(\overrightarrow{a}-\overrightarrow)\)，則實(shí)數(shù)\(x\)的值為（）A.\(-3\)B.\(3\)C.\(-\frac{1}{2}\)D.\(\frac{1}{2}\)答案：B4.函數(shù)\(f(x)=\sin(2x+\varphi)\left(|\varphi|\lt\frac{\pi}{2}\right)\)的圖象向左平移\(\frac{\pi}{6}\)個(gè)單位后關(guān)于原點(diǎn)對(duì)稱(chēng)，則函數(shù)\(f(x)\)在\(\left[0,\frac{\pi}{2}\right]\)上的最小值為（）A.\(-\frac{\sqrt{3}}{2}\)B.\(-\frac{1}{2}\)C.\(\frac{1}{2}\)D.\(\frac{\sqrt{3}}{2}\)答案：A5.已知雙曲線(xiàn)\(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1(a\gt0,b\gt0)\)的一條漸近線(xiàn)方程為\(y=\sqrt{3}x\)，且它的一個(gè)焦點(diǎn)在拋物線(xiàn)\(y^2=24x\)的準(zhǔn)線(xiàn)上，則雙曲線(xiàn)的方程為（）A.\(\frac{x^2}{9}-\frac{y^2}{27}=1\)B.\(\frac{x^2}{36}-\frac{y^2}{108}=1\)C.\(\frac{x^2}{108}-\frac{y^2}{36}=1\)D.\(\frac{x^2}{27}-\frac{y^2}{9}=1\)答案：A6.執(zhí)行如圖所示的程序框圖，若輸入\(n=10\)，則輸出的\(S=（）\)A.\(\frac{5}{11}\)B.\(\frac{10}{11}\)C.\(\frac{36}{55}\)D.\(\frac{72}{55}\)答案：A7.已知函數(shù)\(f(x)\)是定義在\(R\)上的奇函數(shù)，當(dāng)\(x\geq0\)時(shí)，\(f(x)=x(1+x)\)，則當(dāng)\(x\lt0\)時(shí)，\(f(x)\)的表達(dá)式為（）A.\(x(1+x)\)B.\(-x(1+x)\)C.\(x(1-x)\)D.\(-x(1-x)\)答案：C8.從\(1\)，\(2\)，\(3\)，\(4\)，\(5\)這\(5\)個(gè)數(shù)字中任取\(3\)個(gè)數(shù)字組成無(wú)重復(fù)數(shù)字的三位數(shù)，則這個(gè)三位數(shù)是偶數(shù)的概率為（）A.\(\frac{1}{5}\)B.\(\frac{2}{5}\)C.\(\frac{3}{5}\)D.\(\frac{4}{5}\)答案：B9.已知\(a\gt0\)，\(b\gt0\)，且\(a+b=1\)，則\(\frac{1}{a}+\frac{1}\)的最小值為（）A.\(2\)B.\(4\)C.\(6\)D.\(8\)答案：B10.已知函數(shù)\(f(x)=x^3-3x^2+2\)，若\(x\in[-1,2]\)，則函數(shù)\(f(x)\)的值域?yàn)椋ǎ〢.\([-2,2]\)B.\([-2,0]\)C.\([0,2]\)D.\([-1,2]\)答案：A二、多項(xiàng)選擇題1.下列說(shuō)法正確的是（）A.命題“\(\forallx\inR\)，\(x^2+x+1\gt0\)”的否定是“\(\existsx\inR\)，\(x^2+x+1\leq0\)”B.若\(a\gtb\)，則\(ac^2\gtbc^2\)C.已知\(a,b\inR\)，則“\(a\gtb\)”是“\(a^3\gtb^3\)”的充要條件D.若“\(p\landq\)”為假命題，則\(p\)，\(q\)均為假命題答案：AC2.已知函數(shù)\(f(x)=\cos(2x+\frac{\pi}{3})\)，則下列說(shuō)法正確的是（）A.函數(shù)\(f(x)\)的最小正周期為\(\pi\)B.函數(shù)\(f(x)\)在\(\left[0,\frac{\pi}{2}\right]\)上單調(diào)遞減C.函數(shù)\(f(x)\)的圖象關(guān)于點(diǎn)\((\frac{\pi}{12},0)\)對(duì)稱(chēng)D.函數(shù)\(f(x)\)的圖象可由\(y=\cos2x\)的圖象向左平移\(\frac{\pi}{3}\)個(gè)單位得到答案：AC3.已知直線(xiàn)\(l\)：\(y=kx+m\)與圓\(C\)：\((x-1)^2+(y-2)^2=25\)相交于\(A\)，\(B\)兩點(diǎn)，則下列說(shuō)法正確的是（）A.若\(|AB|=8\)，則圓心到直線(xiàn)\(l\)的距離為\(3\)B.若\(\angleACB=120^{\circ}\)，則圓心到直線(xiàn)\(l\)的距離為\(\frac{5}{2}\)C.若直線(xiàn)\(l\)過(guò)圓心\(C\)，則\(k+m=2\)D.若直線(xiàn)\(l\)與圓\(C\)相切，則\(k^2+m^2=25\)答案：ABC4.已知\(a,b,c\)分別為\(\triangleABC\)內(nèi)角\(A,B,C\)的對(duì)邊，且滿(mǎn)足\(a\sinA=b\sinB+c\sinC\)，則下列說(shuō)法正確的是（）A.\(\triangleABC\)一定是直角三角形B.\(\cosA=\frac{b^2+c^2-a^2}{2bc}\)C.若\(b=c\)，則\(A=\frac{\pi}{4}\)D.若\(A=\frac{\pi}{2}\)，則\(b^2+c^2=a^2\)答案：ABD5.已知函數(shù)\(f(x)=\begin{cases}x+1,x\leq0\\\lnx,x\gt0\end{cases}\)，則下列說(shuō)法正確的是（）A.\(f(f(\frac{1}{e}))=0\)B.方程\(f(x)=1\)有兩個(gè)不同的實(shí)數(shù)根C.函數(shù)\(y=f(x)\)的值域?yàn)閈(R\)D.函數(shù)\(y=f(x)\)在\((-\infty,0]\)上單調(diào)遞增，在\((0,+\infty)\)上單調(diào)遞減答案：ABC6.已知\(\overrightarrow{a},\overrightarrow\)是兩個(gè)非零向量，且\(|\overrightarrow{a}|=1\)，\(|\overrightarrow|=2\)，則下列說(shuō)法正確的是（）A.若\(|\overrightarrow{a}-\overrightarrow|=\sqrt{7}\)，則\(\overrightarrow{a}\)與\(\overrightarrow\)的夾角為\(120^{\circ}\)B.若\(\overrightarrow{a}\cdot\overrightarrow=1\)，則\(\overrightarrow{a}\)與\(\overrightarrow\)的夾角為\(60^{\circ}\)C.若\(\overrightarrow{a}\)與\(\overrightarrow\)共線(xiàn)，則\(|\overrightarrow{a}+\overrightarrow|=3\)D.若\(\overrightarrow{a}\perp\overrightarrow\)，則\(|\overrightarrow{a}+\overrightarrow|=\sqrt{5}\)答案：ABD7.已知\(a,b\inR\)，且\(a\gt0\)，\(b\gt0\)，則下列不等式一定成立的是（）A.\(a+b\geq2\sqrt{ab}\)B.\(\frac{a+b}{2}\geq\sqrt{ab}\)C.\(a^2+b^2\geq2ab\)D.\(\frac{a}+\frac{a}\geq2\)答案：ABCD8.已知函數(shù)\(f(x)\)是定義在\(R\)上的偶函數(shù)，且在\([0,+\infty)\)上單調(diào)遞減，則下列說(shuō)法正確的是（）A.\(f(-2)\gtf(1)\)B.\(f(-x)=f(x)\)C.若\(f(x)\gtf(1)\)，則\(|x|\lt1\)D.函數(shù)\(f(x)\)在\((-\infty,0]\)上單調(diào)遞增答案：ABCD9.已知\(x,y\)滿(mǎn)足約束條件\(\begin{cases}x+y\geq2\\x-y\leq2\\y\leq2\end{cases}\)，則下列說(shuō)法正確的是（）A.目標(biāo)函數(shù)\(z=x+2y\)的最大值為\(8\)B.目標(biāo)函數(shù)\(z=3x-y\)的最小值為\(-2\)C.目標(biāo)函數(shù)\(z=x^2+y^2\)的最小值為\(2\)D.目標(biāo)函數(shù)\(z=\frac{y}{x+1}\)的最大值為\(1\)答案：ABC10.已知數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和為\(S_n\)，且滿(mǎn)足\(S_n=2a_n-1\)，則下列說(shuō)法正確的是（）A.\(a_1=1\)B.\(a_n=2^{n-1}\)C.數(shù)列\(zhòng)(\{a_n\}\)是等比數(shù)列D.\(S_n=2^n-1\)答案：ABCD三、判斷題1.若\(a\gtb\)，則\(\frac{1}{a}\lt\frac{1}\)。（）答案：錯(cuò)誤2.函數(shù)\(y=\sinx\)的圖象的對(duì)稱(chēng)軸方程為\(x=k\pi+\frac{\pi}{2}(k\inZ)\)。（）答案：正確3.若直線(xiàn)\(l_1\)：\(A_1x+B_1y+C_1=0\)與直線(xiàn)\(l_2\)：\(A_2x+B_2y+C_2=0\)平行，則\(A_1B_2-A_2B_1=0\)且\(A_1C_2-A_2C_1\neq0\)。（）答案：正確4.若\(\overrightarrow{a}\cdot\overrightarrow=0\)，則\(\overrightarrow{a}\perp\overrightarrow\)。（）答案：錯(cuò)誤（當(dāng)\(\overrightarrow{a}=\overrightarrow{0}\)或\(\overrightarrow=\overrightarrow{0}\)時(shí)不成立）5.函數(shù)\(y=x^3\)在\(R\)上是單調(diào)遞增函數(shù)。（）答案：正確6.若\(p\)：\(x\gt1\)，\(q\)：\(x^2\gt1\)，則\(p\)是\(q\)的充分不必要條件。（）答案：正確7.已知橢圓\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a\gtb\gt0)\)的離心率\(e=\frac{c}{a}\)，其中\(zhòng)(c^2=a^2-b^2\)。（）答案：正確8.若\(a,b,c\)成等比數(shù)列，則\(b^2=ac\)。（）答案：正確9.函數(shù)\(y=\log_2x\)的定義域?yàn)閈((0,+\infty)\)。（）答案：正確10.若\(f(x)\)是定義在\(R\)上的奇函數(shù)，則\(f(0)=0\)。（）答案：正確四、簡(jiǎn)答題1.已知函數(shù)\(f(x)=\sin^2x+\sqrt{3}\sinx\cosx\)。求\(f(x)\)的最小正周期和單調(diào)遞增區(qū)間。答案：先化簡(jiǎn)\(f(x)=\frac{1-\cos2x}{2}+\frac{\sqrt{3}}{2}\sin2x=\sin(2x-\frac{\pi}{6})+\frac{1}{2}\)。根據(jù)正弦函數(shù)性質(zhì)，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-\f