初二下學(xué)期入學(xué)考試題目及答案

單項(xiàng)選擇題(每題2分,共20分)1.一次函數(shù)\(y=2x-3\)的圖象經(jīng)過的象限是(）A.一、二、三象限B.二、三、四象限C.一、三、四象限D(zhuǎn).一、二、四象限2.下列式子中,屬于最簡二次根式的是()A.\(\sqrt{9}\)B.\(\sqrt{7}\)C.\(\sqrt{20}\)D.\(\sqrt{\frac{1}{3}}\)3.菱形具有而平行四邊形不具有的性質(zhì)是()A.對角線互相平分B.鄰角互補(bǔ)C.每條對角線平分一組對角D.對角相等4.已知一組數(shù)據(jù)\(2\),\(3\),\(4\),\(x\),\(1\),\(4\),\(3\)有唯一的眾數(shù)\(4\),則這組數(shù)據(jù)的中位數(shù)是()A.\(2\)B.\(3\)C.\(4\)D.\(5\)5.下列計(jì)算正確的是()A.\(\sqrt{2}+\sqrt{3}=\sqrt{5}\)B.\(2+\sqrt{2}=2\sqrt{2}\)C.\(\sqrt{(-4)\times(-9)}=\sqrt{-4}\times\sqrt{-9}\)D.\(\sqrt{27}\div\sqrt{3}=3\)6.函數(shù)\(y=\frac{1}{\sqrt{x-2}}\)中,自變量\(x\)的取值范圍是()A.\(x\neq2\)B.\(x\gt2\)C.\(x\geqslant2\)D.\(x\leqslant2\)7.若平行四邊形的兩條對角線長為\(6\)和\(16\),則下列長度的線段可作為平行四邊形邊長的是()A.\(5\)B.\(8\)C.\(12\)D.\(16\)8.已知一次函數(shù)\(y=(m-1)x+m^2-1\)的圖象經(jīng)過原點(diǎn),則\(m\)的值為()A.\(1\)B.\(-1\)C.\(\pm1\)D.\(0\)9.已知四邊形\(ABCD\)是平行四邊形,下列結(jié)論中不正確的是()A.當(dāng)\(AB=BC\)時(shí),它是菱形B.當(dāng)\(AC\perpBD\)時(shí),它是菱形C.當(dāng)\(\angleABC=90^{\circ}\)時(shí),它是矩形D.當(dāng)\(AC=BD\)時(shí),它是正方形10.某單位若干名職工參加普法知識(shí)競賽,將成績制成如圖所示的扇形統(tǒng)計(jì)圖和條形統(tǒng)計(jì)圖,根據(jù)圖中提供的信息,這些職工成績的中位數(shù)和平均數(shù)分別是()A.\(94\)分,\(96\)分B.\(96\)分,\(96\)分C.\(94\)分,\(96.4\)分D.\(96\)分,\(96.4\)分多項(xiàng)選擇題(每題2分,共20分)1.下列關(guān)于一次函數(shù)\(y=kx+b\)(\(k\neq0\))的說法正確的有()A.當(dāng)\(k\gt0\),\(b\gt0\)時(shí),函數(shù)圖象經(jīng)過一、二、三象限B.當(dāng)\(k\gt0\),\(b\lt0\)時(shí),函數(shù)圖象經(jīng)過一、三、四象限C.當(dāng)\(k\lt0\),\(b\gt0\)時(shí),函數(shù)圖象經(jīng)過一、二、四象限D(zhuǎn).當(dāng)\(k\lt0\),\(b\lt0\)時(shí),函數(shù)圖象經(jīng)過二、三、四象限2.下列二次根式中,能與\(\sqrt{2}\)合并的有（）A.\(\sqrt{8}\)B.\(\sqrt{12}\)C.\(\sqrt{18}\)D.\(\sqrt{24}\)3.矩形具有而一般平行四邊形不具有的性質(zhì)有()A.對角線相等B.四個(gè)角都是直角C.對邊平行且相等D.對角線互相平分4.已知數(shù)據(jù)\(x_1\),\(x_2\),\(x_3\)的平均數(shù)是\(5\),則數(shù)據(jù)\(3x_1+2\),\(3x_2+2\),\(3x_3+2\)的平均數(shù)可能是()A.\(15\)B.\(17\)C.數(shù)據(jù)不足無法計(jì)算D.以上都不對5.下列計(jì)算正確的有()A.\((\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})=1\)B.\((2\sqrt{2}+3)(2\sqrt{2}-3)=-1\)C.\((\sqrt{5}+\sqrt{3})^2=8+2\sqrt{15}\)D.\((\sqrt{6}-\sqrt{2})^2=8-4\sqrt{3}\)6.函數(shù)\(y=\frac{\sqrt{x+1}}{x-1}\)中,自變量\(x\)的取值可能是()A.\(x\geqslant-1\)B.\(x\neq1\)C.\(x\gt-1\)且\(x\neq1\)D.\(x\geqslant-1\)且\(x\neq1\)7.下列四邊形中,對角線一定互相垂直的有()A.正方形B.菱形C.矩形D.平行四邊形8.一次函數(shù)\(y=-2x+4\)的圖象與坐標(biāo)軸的交點(diǎn)坐標(biāo)可能是()A.\((0,4)\)B.\((2,0)\)C.\((0,-4)\)D.\((-2,0)\)9.若四邊形\(ABCD\)是平行四邊形,要使它成為矩形,可添加的條件有()A.\(AC=BD\)B.\(\angleABC=90^{\circ}\)C.\(AB=BC\)D.\(AC\perpBD\)10.一組數(shù)據(jù)\(1\),\(2\),\(3\),\(4\),\(5\)的方差和標(biāo)準(zhǔn)差可能是()A.方差\(2\)B.方差\(\sqrt{2}\)C.標(biāo)準(zhǔn)差\(2\)D.標(biāo)準(zhǔn)差\(\sqrt{2}\)判斷題(每題2分,共20分)1.二次根式\(\sqrt{-x^2-1}\)一定有意義。()2.一次函數(shù)\(y=-3x\)中,\(y\)隨\(x\)的增大而增大。（)3.菱形的對角線互相垂直且相等。()4.若\(\sqrt{(x-2)^2}=2-x\),則\(x\leqslant2\)。（)5.函數(shù)\(y=\frac{1}{x-3}\)的自變量\(x\)的取值范圍是\(x\neq3\)。()6.平行四邊形的四條邊都相等。()7.數(shù)據(jù)\(1\),\(2\),\(3\),\(4\),\(5\)的中位數(shù)是\(3\)。()8.當(dāng)\(k\gt0\)時(shí),一次函數(shù)\(y=kx+b\)(\(b\neq0\)）的圖象一定經(jīng)過第一、三象限。(）9.若一個(gè)四邊形的對角線互相平分且相等,則這個(gè)四邊形是矩形。（)10.計(jì)算\(\sqrt{12}\div\sqrt{3}=4\)。(）簡答題(每題5分,共20分)1.化簡:\(\sqrt{18}-\sqrt{8}+\sqrt{\frac{1}{2}}\)。2.已知一次函數(shù)\(y=kx+b\)的圖象經(jīng)過點(diǎn)\((-1,-5)\),且與正比例函數(shù)\(y=\frac{1}{2}x\)的圖象相交于點(diǎn)\((2,a)\),求\(k\),\(b\)的值。3.已知菱形的兩條對角線長分別為\(6\)和\(8\),求該菱形的周長和面積。4.某班\(10\)名學(xué)生的體育測試成績?nèi)缦拢▎挝唬悍郑篭(58\),\(60\),\(59\),\(52\),\(58\),\(55\),\(57\),\(58\),\(49\),\(57\),求這組數(shù)據(jù)的眾數(shù)和中位數(shù)。討論題(每題5分,共20分)1.討論一次函數(shù)\(y=kx+b\)(\(k\),\(b\)為常數(shù),\(k\neq0\))中\(zhòng)(k\),\(b\)的取值對函數(shù)圖象的影響。2.討論在四邊形中,從平行四邊形、矩形、菱形、正方形中任選兩種,分析它們之間的聯(lián)系與區(qū)別。3.討論二次根式在化簡和運(yùn)算時(shí)需要注意哪些問題。4.討論統(tǒng)計(jì)中的平均數(shù)、中位數(shù)和眾數(shù)在實(shí)際生活中的應(yīng)用。答案單項(xiàng)選擇題1.C2.B3.C4.B5.D6.B7.B8.B9.D10.D多項(xiàng)選擇題1.ABCD2.AC3.AB4.B5.ACD6.D7.AB8.AB9.AB10.AD判斷題1.×2.×3.×4.√5.√6.×7.√8.√9.√10.×簡答題1.原式\(=3\sqrt{2}-2\sqrt{2}+\frac{\sqrt{2}}{2}=\frac{3\sqrt{2}}{2}\)。2.把\((2,a)\)代入\(y=\frac{1}{2}x\),得\(a=1\)。把\((-1,-5)\),\((2,1)\)代入\(y=kx+b\),得\(\begin{cases}-k+b=-5\\2k+b=1\end{cases}\),解得\(\begin{cases}k=2\\b=-3\end{cases}\)。3.菱形面積\(S=\frac{1}{2}\times6\times8=24\)。對角線一半分別為\(3\)和\(4\),根據(jù)勾股定理邊長為\(\sqrt{3^{2}+4^{2}}=5\),周長\(C=4\times5=20\)。4.眾數(shù)是\(58\)分。將數(shù)據(jù)從小到大排列：\(49\),\(52\),\(55\),\(57\),\(57\),\(58\),\(58\),\(58\),\(59\),\(60\),中位數(shù)是\(\frac{57+58}{2}=57.5\)分。討論題1.\(k\)決定函數(shù)增減性,\(k\gt0\),\(y\)隨\(x\)增大而增大;\(k\lt0\),\(y\)隨\(x\)增大而減小。\(b\)決定圖象與\(y\)軸交點(diǎn),\(b\gt0\),交點(diǎn)在正半軸;\(b