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多項(xiàng)式四則運(yùn)算錯(cuò)誤類型的調(diào)查研究-資料下載頁(yè)

2025-06-24 03:57本頁(yè)面
  

【正文】 2-11X+9的和為12X2+X-3,求此多項(xiàng)式?ANS:10X2+12X-12 評(píng)量目的:瞭解學(xué)生對(duì)於加法逆運(yùn)算的文字題,所產(chǎn)生的錯(cuò)誤類型序號(hào)錯(cuò)誤類型錯(cuò)誤人數(shù)錯(cuò)誤比率15X2+6X-613214X2-10X+67310X2-10X+66(2)A為多項(xiàng)式,A-(X2-2X+6)=-9X2+5X-1,求多項(xiàng)式A?ANS:-8X2+3X+5評(píng)量目的:瞭解學(xué)生對(duì)於多項(xiàng)式減法逆運(yùn)算,所產(chǎn)生的錯(cuò)誤類型序號(hào)錯(cuò)誤類型錯(cuò)誤人數(shù)錯(cuò)誤比率1-10X2+7X-772-8X2+7X-74(3)A為多項(xiàng)式,-2X2+X+3減去A的差為6X2+X-3,求多項(xiàng)式A?ANS:-8X2+6 評(píng)量目的:瞭解學(xué)生對(duì)於多項(xiàng)式減法逆運(yùn)算的文字題,所產(chǎn)生的錯(cuò)誤類型序號(hào)錯(cuò)誤類型錯(cuò)誤人數(shù)錯(cuò)誤比率14X2+2X2428X2-615(4)A為多項(xiàng)式,(-3X2+X+7)-A=2X2+5X-8,求多項(xiàng)式A?ANS:-5X2-4X+15評(píng)量目的:瞭解學(xué)生對(duì)於多項(xiàng)式減法逆運(yùn)算,所產(chǎn)生的錯(cuò)誤類型序號(hào)錯(cuò)誤類型錯(cuò)誤人數(shù)錯(cuò)誤比率1-X2+6X-11525X2+4X-1573-5X2+6X-15(5)數(shù)學(xué)題「兩多項(xiàng)式A、B,B為-X2+9X-7試求A-B?」,某生因誤將「A-B」看成「A+B」,結(jié)果求出答案是「2X2+8X-1」,求A-B正確答案? ANS:-4X2-10X+13評(píng)量目的:瞭解學(xué)生對(duì)於加減混合運(yùn)算的文字題,所產(chǎn)生的錯(cuò)誤類型序號(hào)錯(cuò)誤類型錯(cuò)誤人數(shù)錯(cuò)誤比率1未完成 A=3X2-X+67(6)A、B為兩個(gè)多項(xiàng)式,A+B=2X2-3X+1,A-B=-2X2-X+5求A、 B?ANS:A=-2X+3 B=2X2-X-2評(píng)量目的:瞭解學(xué)生對(duì)於未知數(shù)A、B代表多項(xiàng)式的看法及聯(lián)立方程式的解法序號(hào)錯(cuò)誤類型錯(cuò)誤人數(shù)錯(cuò)誤比率1A=-4X+6 B=2X2+X-55(7)長(zhǎng)方形的面積為X2+3X+2,其長(zhǎng)為X+1,則其寬? ANS:X+2評(píng)量目的:瞭解學(xué)生對(duì)於多項(xiàng)式乘法逆運(yùn)算的文字題,所產(chǎn)生的錯(cuò)誤類型序號(hào)錯(cuò)誤類型錯(cuò)誤人數(shù)錯(cuò)誤比率1X3+3X2+2X1(8)一多項(xiàng)式除以-8X+5得商式為X+1,餘式為-2X+3,求多項(xiàng)式?ANS:-8X2-5X+8評(píng)量目的:瞭解學(xué)生對(duì)於多項(xiàng)式除法逆運(yùn)算的文字題,所產(chǎn)生的錯(cuò)誤類型序號(hào)錯(cuò)誤類型錯(cuò)誤人數(shù)錯(cuò)誤比率18X2-37X+2052-8X2-3X+54(9)A為多項(xiàng)式,(5X2-X-6)247。A=-X-1,求多項(xiàng)式A? ANS:-5X+6評(píng)量目的:瞭解學(xué)生對(duì)於多項(xiàng)式除法逆運(yùn)算,所產(chǎn)生的錯(cuò)誤類型序號(hào)錯(cuò)誤類型錯(cuò)誤人數(shù)錯(cuò)誤比率1-5X3-4X2+7X+612(10)X+1能整除X2-7X+K,求K之值? ANS:K=-8評(píng)量目的:瞭解學(xué)生對(duì)於多項(xiàng)式除法運(yùn)算的文字題,所產(chǎn)生的錯(cuò)誤類型序號(hào)錯(cuò)誤類型錯(cuò)誤人數(shù)錯(cuò)誤比率1K=817(11)A=3X+5,B=3X2+X+2,求3A-2B=? ANS:-6X2+7X+11評(píng)量目的:瞭解學(xué)生對(duì)於未知數(shù)A、B代表多項(xiàng)式的看法及四則運(yùn)算的解法序號(hào)錯(cuò)誤類型錯(cuò)誤人數(shù)錯(cuò)誤比率1-6X2+11X+1911(12)邊長(zhǎng)為X-1的正方體,其體積? ANS:X3-3X2+3X-1評(píng)量目的:瞭解學(xué)生對(duì)於多項(xiàng)式連乘積的文字題,所產(chǎn)生的錯(cuò)誤類型序號(hào)錯(cuò)誤類型錯(cuò)誤人數(shù)錯(cuò)誤比率1X2-2X+1242X3-1436(X-1)2=6X2-12X+64(13)鋼筆每枝3X2+2元,鉛筆每枝X2+5元,買5枝鋼筆7枝鉛筆共需幾元? ANS:22X2+45評(píng)量目的:瞭解學(xué)生對(duì)於代數(shù)式的文字題,所產(chǎn)生的錯(cuò)誤類型序號(hào)錯(cuò)誤類型錯(cuò)誤人數(shù)錯(cuò)誤比率1答案是數(shù)字4226X2+392(14)求斜線面積=? ANS:15X2-9X2X+16X3X-4評(píng)量目的:瞭解學(xué)生對(duì)於邊長(zhǎng)為多項(xiàng)式的圖形面積,所產(chǎn)生的錯(cuò)誤類型序號(hào)錯(cuò)誤類型錯(cuò)誤人數(shù)錯(cuò)誤比率115X-97(15)長(zhǎng)方形,求斜線的面積=?周長(zhǎng)=? 3X2 面積方面: ANS:3X+6評(píng)量目的:瞭解學(xué)生對(duì)於邊長(zhǎng)為多項(xiàng)式的圖形面積,所產(chǎn)生的錯(cuò)誤類型序號(hào)錯(cuò)誤類型錯(cuò)誤人數(shù)錯(cuò)誤比率16X11周長(zhǎng)方面: ANS:2X+10評(píng)量目的:瞭解學(xué)生對(duì)於邊長(zhǎng)為多項(xiàng)式的圖形周長(zhǎng),所產(chǎn)生的錯(cuò)誤類型序號(hào)錯(cuò)誤類型錯(cuò)誤人數(shù)錯(cuò)誤比率1X+5924X+665X-33(16)求圖形面積=?周長(zhǎng)=? X+29 2X-1面積方面: ANS:61X-18評(píng)量目的:瞭解學(xué)生對(duì)於邊長(zhǎng)為多項(xiàng)式的圖形面積,所產(chǎn)生的錯(cuò)誤類型序號(hào)錯(cuò)誤類型錯(cuò)誤人數(shù)錯(cuò)誤比率126X+36272X-126周長(zhǎng)方面: ANS:12X+22評(píng)量目的:瞭解學(xué)生對(duì)於邊長(zhǎng)為多項(xiàng)式的圖形周長(zhǎng),所產(chǎn)生的錯(cuò)誤類型序號(hào)錯(cuò)誤類型錯(cuò)誤人數(shù)錯(cuò)誤比率112X+2027214X+165A Study of Error Patterns in Polynomials Operation by Eighth Graders in Kaohsiung CityChengJen Kuo1 CheJen Hsieh21Kaohsiung Municipal HsaioKang School2Mei Ho Institute of TechnologyAbstractPolynomials operation serves as the foundation of algebraic operation. This study explores the errors patterns in polynomials operation and analyzes the causes for errors made by the eighth graders in Kaohsiung City as the basis for providing maximal benefits to teachers’(remedial)instruction, assessment, and future study. Subjects in this study include 58 mathematics teachers and 262 eighth graders in four junior high schools. Students are first surveyed for identifying their errors and asked for an unstructured interview to further explore the causes for study indicates that students are easiest to cause errors in the question of graph, the rate of space is highest in the question of character,and the cognizance of inverse operation of division is most hard. Students exhibit dominant errors in: definition, analogy, term move,and sign of aggregation.Key words: polynomials, error pattern
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