20242025學年全國初二上數(shù)學仁愛版期中試卷一、選擇題（每題3分，共15分）1.下列哪個選項是二次根式的定義？A.$\sqrt{a^2}=a$B.$\sqrt{ab}=\sqrt{a}\sqrt$C.$\sqrt[a]=b^{\frac{1}{a}}$D.$\sqrt[n]{a^n}=a$2.已知實數(shù)a滿足$a^22a3<0$，則a的取值范圍是？A.$a<1$或$a>3$B.$1<a<3$C.$a<3$或$a>1$D.$a<1$或$a>3$3.下列哪個選項是函數(shù)$y=2x^2+3x1$的頂點坐標？A.$(\frac{3}{4},\frac{17}{8})$B.$(\frac{3}{4},\frac{17}{8})$C.$(\frac{3}{4},\frac{17}{8})$D.$(\frac{3}{4},\frac{17}{8})$4.已知等腰三角形ABC，AB=AC，$\angleBAC=120^\circ$，則$\angleABC$的大小是？A.$30^\circ$B.$45^\circ$C.$60^\circ$D.$90^\circ$5.下列哪個選項是二次函數(shù)$y=ax^2+bx+c$的圖像？A.拋物線，開口向上B.拋物線，開口向下C.直線D.橢圓二、填空題（每題3分，共15分）1.已知實數(shù)x滿足$x^25x+6=0$，則$x+\frac{1}{x}=\underline{\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\一、選擇題答案：1.B2.B3.A4.C5.A二、填空題答案：1.2,32.(frac13,frac23),(frac23,frac13)3.5,64.2,35.(frac12,frac34),(frac34,frac12)三、解答題答案：1.(frac12,frac34)2.(frac34,frac12)3.(frac12,frac34)4.(frac34,frac12)5.(frac12,frac34)一、二次根式定義：sqrta2a性質：sqrtabsqrtasqrtb,sqrt[a]bbfrac1a,sqrt[n]ana應用：解二次方程，求二次函數(shù)的定義域和值域二、二次函數(shù)定義：yax2bxc圖像：拋物線，開口向上或向下性質：頂點坐標(fracba,frac4acb24a),對稱軸xfracba應用：求解最值，判斷圖像位置，求解方程和不等式三、等腰三角形定義：兩邊長度相等的三角形性質：兩個底角相等，頂角等于180circ減去兩個底角的和應用：求解角度，判斷三角形類型四、一次函數(shù)定義：ykxb圖像：直線性質：斜率k，截距b應用：求解方程和不等式，判斷圖像位置五、二次方程定義：ax2bxc0解法：因式分解，公式法，圖像法應用：求解方程，判斷方程的根的性質六、二次不等式定義：ax2bxc0解法：因式分解，公式法，圖像法應用：求解不等式，判斷不等式的解集七、函數(shù)的定義域和值域定義：函數(shù)中自變量的取值范圍和因變量的取值范圍求法：根據(jù)函數(shù)的性質和圖像，求解定義域和值域應用：求解方程和不等式