蘇州初三數(shù)學(xué)試題和答案

一、單項(xiàng)選擇題(每題2分,共10題)1.一元二次方程\(x^2-3x=0\)的解是()A.\(x=3\)B.\(x=0\)C.\(x_1=0\),\(x_2=3\)D.\(x=-3\)2.拋物線\(y=(x-2)^2+3\)的頂點(diǎn)坐標(biāo)是(）A.\((2,3)\)B.\((-2,3)\)C.\((2,-3)\)D.\((-2,-3)\)3.在\(Rt\triangleABC\)中,\(\angleC=90^{\circ}\),\(\sinA=\frac{3}{5}\),則\(\cosB\)的值為()A.\(\frac{3}{5}\)B.\(\frac{4}{5}\)C.\(\frac{3}{4}\)D.\(\frac{4}{3}\)4.一個(gè)圓錐的底面半徑為\(3\),母線長(zhǎng)為\(5\),則圓錐的側(cè)面積是()A.\(15\pi\)B.\(30\pi\)C.\(24\pi\)D.\(36\pi\)5.已知\(\odotO\)的半徑為\(5\),點(diǎn)\(P\)到圓心\(O\)的距離為\(4\),則點(diǎn)\(P\)與\(\odotO\)的位置關(guān)系是()A.點(diǎn)\(P\)在圓內(nèi)B.點(diǎn)\(P\)在圓上C.點(diǎn)\(P\)在圓外D.無(wú)法確定6.若關(guān)于\(x\)的一元二次方程\(x^2+2x+k=0\)有兩個(gè)不相等的實(shí)數(shù)根,則\(k\)的取值范圍是()A.\(k\lt1\)B.\(k\gt1\)C.\(k=1\)D.\(k\leq1\)7.反比例函數(shù)\(y=\frac{k}{x}\)(\(k\neq0\))的圖象經(jīng)過(guò)點(diǎn)\((-2,3)\),則\(k\)的值為()A.\(6\)B.\(-6\)C.\(\frac{3}{2}\)D.\(-\frac{3}{2}\)8.若二次函數(shù)\(y=ax^2+bx+c\)(\(a\neq0\))的圖象開(kāi)口向下,且對(duì)稱軸在\(y\)軸右側(cè),則\(a\),\(b\),\(c\)的符號(hào)為()A.\(a\lt0\),\(b\gt0\),\(c\gt0\)B.\(a\lt0\),\(b\lt0\),\(c\gt0\)C.\(a\lt0\),\(b\gt0\),\(c\)不確定D.\(a\lt0\),\(b\lt0\),\(c\)不確定9.已知\(\triangleABC\)與\(\triangleDEF\)相似,且相似比為\(2:3\),則\(\triangleABC\)與\(\triangleDEF\)的面積比為（）A.\(2:3\)B.\(4:9\)C.\(\sqrt{2}:\sqrt{3}\)D.\(3:2\)10.如圖,在\(\triangleABC\)中,\(DE\parallelBC\),\(AD=2\),\(DB=3\),則\(\frac{DE}{BC}\)的值為()A.\(\frac{2}{3}\)B.\(\frac{2}{5}\)C.\(\frac{3}{5}\)D.\(\frac{4}{5}\)二、多項(xiàng)選擇題(每題2分,共10題)1.下列圖形中,是中心對(duì)稱圖形的有（）A.平行四邊形B.矩形C.菱形D.正方形2.以下關(guān)于二次函數(shù)\(y=ax^2+bx+c\)(\(a\neq0\))的說(shuō)法正確的有()A.當(dāng)\(a\gt0\)時(shí),函數(shù)圖象開(kāi)口向上B.對(duì)稱軸為直線\(x=-\frac{2a}\)C.頂點(diǎn)坐標(biāo)為\((-\frac{2a},\frac{4ac-b^2}{4a})\)D.當(dāng)\(b=0\)時(shí),對(duì)稱軸是\(y\)軸3.已知\(\odotO\)的半徑為\(r\),圓心\(O\)到直線\(l\)的距離為\(d\),直線\(l\)與\(\odotO\)有公共點(diǎn),則\(d\)與\(r\)的關(guān)系可能是（）A.\(d\ltr\)B.\(d=r\)C.\(d\gtr\)D.\(d\leqr\)4.下列函數(shù)中,\(y\)隨\(x\)的增大而增大的有()A.\(y=2x-1\)B.\(y=-\frac{1}{2}x+3\)C.\(y=x^2\)(\(x\geq0\))D.\(y=\frac{3}{x}\)(\(x\lt0\))5.若關(guān)于\(x\)的方程\((m-1)x^2+2x-1=0\)是一元二次方程,則\(m\)的值可能是（）A.\(0\)B.\(1\)C.\(2\)D.\(3\)6.在\(Rt\triangleABC\)中,\(\angleC=90^{\circ}\),\(\cosA=\frac{4}{5}\),則下列說(shuō)法正確的是()A.\(\sinA=\frac{3}{5}\)B.\(\tanA=\frac{3}{4}\)C.\(a:b:c=3:4:5\)D.\(b:c=4:5\)7.下列命題正確的有()A.所有的等腰三角形都相似B.所有的等邊三角形都相似C.所有的直角三角形都相似D.有一個(gè)角是\(100^{\circ}\)的兩個(gè)等腰三角形相似8.二次函數(shù)\(y=x^2-2x-3\)的圖象與\(x\)軸的交點(diǎn)坐標(biāo)為()A.\((-1,0)\)B.\((3,0)\)C.\((1,0)\)D.\((-3,0)\)9.已知點(diǎn)\(A(x_1,y_1)\),\(B(x_2,y_2)\)在反比例函數(shù)\(y=\frac{6}{x}\)的圖象上,若\(x_1\ltx_2\lt0\),則\(y_1\)與\(y_2\)的大小關(guān)系是()A.\(y_1\lty_2\)B.\(y_1\gty_2\)C.\(y_1=y_2\)D.無(wú)法確定10.一個(gè)幾何體的三視圖如圖所示,則這個(gè)幾何體可能是()A.三棱柱B.四棱柱C.圓柱D.圓錐三、判斷題(每題2分,共10題)1.方程\(x^2=1\)的解是\(x=1\)。()2.二次函數(shù)\(y=x^2\)的圖象開(kāi)口向上。()3.直徑是圓中最長(zhǎng)的弦。()4.若\(\sinA=\frac{1}{2}\),則\(\angleA=30^{\circ}\)。（)5.兩個(gè)相似三角形的周長(zhǎng)比等于相似比。()6.反比例函數(shù)\(y=\frac{k}{x}\)(\(k\neq0\))的圖象是一條直線。()7.一元二次方程\(ax^2+bx+c=0\)（\(a\neq0\)),當(dāng)\(b^2-4ac\lt0\)時(shí),方程有兩個(gè)不相等的實(shí)數(shù)根。（)8.三角形的外心是三角形三條角平分線的交點(diǎn)。()9.若點(diǎn)\(A(2,m)\)在反比例函數(shù)\(y=\frac{6}{x}\)的圖象上,則\(m=3\)。(）10.拋物線\(y=2(x-1)^2+3\)可由拋物線\(y=2x^2\)向右平移\(1\)個(gè)單位,再向上平移\(3\)個(gè)單位得到。（）四、簡(jiǎn)答題(每題5分,共4題)1.解方程:\(x^2-4x+3=0\)。-答案:分解因式得\((x-1)(x-3)=0\),則\(x-1=0\)或\(x-3=0\),解得\(x_1=1\),\(x_2=3\)。2.已知二次函數(shù)\(y=x^2-2x-1\),求其頂點(diǎn)坐標(biāo)。-答案:將函數(shù)配方為\(y=(x-1)^2-2\),所以頂點(diǎn)坐標(biāo)為\((1,-2)\)。3.在\(Rt\triangleABC\)中,\(\angleC=90^{\circ}\),\(a=3\),\(b=4\),求\(\sinA\)的值。-答案:由勾股定理得\(c=\sqrt{a^2+b^2}=5\),則\(\sinA=\frac{a}{c}=\frac{3}{5}\)。4.已知\(\odotO\)的半徑為\(5\),弦\(AB=8\),求圓心\(O\)到弦\(AB\)的距離。-答案：過(guò)\(O\)作\(OC\perpAB\)于\(C\),則\(AC=\frac{1}{2}AB=4\)。在\(Rt\triangleAOC\)中,\(OC=\sqrt{OA^2-AC^2}=\sqrt{25-16}=3\)。五、討論題(每題5分,共4題)1.討論一元二次方程\(ax^2+bx+c=0\)(\(a\neq0\))根的情況與\(b^2-4ac\)的關(guān)系。-答案：當(dāng)\(b^2-4ac\gt0\),方程有兩個(gè)不相等的實(shí)數(shù)根；當(dāng)\(b^2-4ac=0\),方程有兩個(gè)相等的實(shí)數(shù)根；當(dāng)\(b^2-4ac\lt0\),方程沒(méi)有實(shí)數(shù)根。2.說(shuō)說(shuō)二次函數(shù)\(y=ax^2+bx+c\)(\(a\neq0\))的圖象性質(zhì)與\(a\)、\(b\)、\(c\)的關(guān)系。-答案：\(a\)決定開(kāi)口方向,\(a\gt0\)開(kāi)口向上,\(a\lt0\)開(kāi)口向下；\(b\)與\(a\)共同決定對(duì)稱軸位置；\(c\)是拋物線與\(y\)軸交點(diǎn)的縱坐標(biāo)。3.討論相似三角形的