七年級(jí)數(shù)學(xué)下冊(cè)專項(xiàng)綜合全練整式乘除試題北師大版

整式的乘除一、選擇題1.在0,2,(-3)0,-5這四個(gè)數(shù)中,最大的數(shù)是()A.0B.2C.(-3)0D.-5答案B∵(-3)0=1,∴在0,2,(-3)0,-5中最大的數(shù)為2.應(yīng)選B.-1)2.計(jì)算a·a的結(jié)果為(A.-1B.0C.1D.-a答案C-11-10應(yīng)選C.a·a=a=a=1,3.計(jì)算-3a23)×a的結(jié)果為(A.-3a5B.3a6C.-3a6D.3a5答案A232+35-3a×a=-3a=-3a.4.若(x+2)(x-1)=x2+mx+n,則m+n=()A.1B.2C.-1D.-2答案C(x+2)(x-1)=x2-x+2x-2=x2+x-2,m=1,n=-2,m+n=1+(-2)=-1.5.計(jì)算的結(jié)果是()A.-x3y6B.-x3y5C.-x3y5D.-x3y6答案D32336=·x·(y)=-xy.6.計(jì)算×=()答案B×=×==12005=1.7.以下計(jì)算錯(cuò)誤的選項(xiàng)是()A.a·a=a2B.2a+a=3aC.(a3253-14)=aD.a÷a=a答案C(a3)2=a3×2=a6.8.以下計(jì)算正確的選項(xiàng)是()A.3a-2a=1B.a2+a5=a7246D.(ab)33C.a·a=a=ab答案C3a-2a=a,a2與a5不是同類項(xiàng),不可以歸并,(ab)3=a3b3.故A,B,D均錯(cuò),應(yīng)選C.19.計(jì)算(-6x2-3x+5)的結(jié)果是()432432A.6x+3x-5xB.2x+x+xC.2x4+x3-x2D.-2x4-x3+x2答案C(-6x2-3x+5)=(-6x2)+·(-3x)+×5=2x4+x3-x2.10.計(jì)算結(jié)果為x2+7x-18的是()A.(x+2)(x-9)B.(x+3)(x-6)C.(x-2)(x+9)D.(x-3)(x+6)答案CA.(x+2)(x-9)=x2-9x+2x-18=x2-7x-18;B.(x+3)(x-6)=x2-6x+3x-18=x2-3x-18;C.(x-2)(x+9)=x2+9x-2x-18=x2+7x-18;D.(x-3)(x+6)=x2+6x-3x-18=x2+3x-18.應(yīng)選C.以下各式:(a-2b)(3a+b)=3a2-5ab-2b2;(2x+1)(2x-1)=4x2-x-1;(x+y)(x-y)=x2-y2;(x+2)(3x+6)=3x2+6x+12.此中正確的有()A.4個(gè)B.3個(gè)C.2個(gè)D.1個(gè)答案C①(a-2b)(3a+b)=3a2222+ab-6ab-2b=3a-5ab-2b,正確;②(2x+1)(2x-1)=4x2不正確;-1,2(x+y)(x-y)=x-y,正確;(x+2)(3x+6)=3x2+6x+6x+12=3x2+12x+12,不正確.應(yīng)選C.二、填空題12.若m,n知足m2+n2=25,mn=3,則(m-n)2=.答案19分析22222因此原式=25-2×3=19.(m-n)=m+n-2mn,由于m+n=25,mn=3,13.已知(x-1)(x+k)的睜開(kāi)式中不含x的一次項(xiàng),則k=.答案1分析(x-1)(x+k)=x2+(k-1)x-k,由題意得k-1=0,k=1.14.若|y-3|+(3x-2y)2=0,則(-yx)y=.答案-36分析由已知得y-3=0,且3x-2y=0,∴y=3,x=2.故(-yx)y=(-32)3=-36.15.察看以下各式:2(1)42-12=3×5;(2)52-22=3×7;(3)62-32=3×9;則第(n)(n是正整數(shù))個(gè)等式為.答案22(n+3)-n=3(2n+3)分析察看題中等式可知第(n)(n22是正整數(shù))個(gè)等式為(n+3)-n=3(2n+3).三、解答題16.計(jì)算:2×[5+(-2)3]-(-|--1分)4|÷2).(6分析2×[5+(-2)3]-(-|-4|÷2-1)=2×(5-8)-=-6-(-8)=2.mnm3n17.已知10=20,10=,求8÷2的值.分析由題意知10m÷10n=20÷=100,即10m-n=102,∴m-n=2,m3n3m3n3m-3n3(m-n)=(2m-n3233∴8÷2=2÷2=2=2)=(2)=4=64.化簡(jiǎn)求值:(1)(y-3x)(y+3x)-y(2x+y),此中x=1,y=-2;(2)(2x+1)(x-2)-(-3x+1)(-3x-1),此中x=-2.分析2222(1)原式=y-9x-2xy-y=-9x-2xy,2當(dāng)x=1,y=-2時(shí),原式=-9×1-2×1×(-2)=-9+4=-5.(2)原式=2x2-4x+x-2-(9x2-1)=2x2-3x-2-9x2+1=-7x2-3x-1,當(dāng)x=-2時(shí),原式=-7×(-2)2-3×(-2)-1=-28+6-1=-23.19.先化簡(jiǎn),再求值:[(5x+4y)2-(5x-4y)2-5x2y2]÷(-5x),此中x=1,y=-1.分析[(5x+4y)2-(5x-4y)2-5x2y2]÷(-5x)=[(25x2+40xy+16y2)-(25x2-40xy+16y2)-5x2y2]÷(-5x)=(25x2+40xy+16y2-25x2+40xy-16y2-5x2y2)÷(-5x)=(80xy-5x2y2)÷(-5x)=-16y+xy2.當(dāng)x=1,y=-1時(shí),原式=-16×(-1)+1×(-1)2=17.20.計(jì)算圖1-9-1中暗影部分的面積.圖1-9-1分析2222S暗影=b(a+2b)-π·b=ab+2b-b=ab-b.321.如圖1-9-2,墨墨的爸爸將一塊長(zhǎng)為分米、寬為5a5分米的長(zhǎng)方形鐵皮的四個(gè)角都剪去一個(gè)邊長(zhǎng)為a4分米的小正方形,而后沿虛線折成一個(gè)無(wú)蓋的盒子.用含a,b的整式表示盒子的表面面的面積;(2)若a=1,b=0.2,現(xiàn)往盒子的表面面上噴漆,每平方分米噴漆價(jià)錢為15元,求噴漆共需多少元.圖1-9-2分