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人民教育出版社新編的高級中学課本代数第一册,在今年秋季开始,將在全国各地使用。这本書是根据中学数学教学大綱(修訂草案)編写的,供高中一年級代数教学之用。这本書主要取材於苏联A.Ⅱ.吉西略夫所編的十年制中学代数課本第二册和Ⅱ.A.拉尼切夫所編的十年制中学代数習題彙編第二集,在不少的地方引用了(?)法捷耶夫和(?)索明斯基合編的代数学下册中的材料。但是在处理教材的时候,力求适合我国的情况。这本書一共分为四章。第一章講冪和方根,第二章講二次方程和可以化成二次方程的方程,第三章講函数和它的圖象,第四章講二元二次方程組。第一章冪和方根分为四节。第Ⅰ节講乘方。这一节的大部分教材是学生在初中代数里学过的,因此基本上是复習的性質,主要是复習乘方的定义和冪的运算法則,替学習下一节方根做好准备。这一节中一个新的內容是把二項式平方的公式推广到多項式平方,这样在下一节复習开平方的一般方法的时候,遇到有必要就可以根据这个公式来进行論証。
The first volume of the new high school textbooks for algebra in the People’s Education Press will be used throughout the country beginning this fall. This book is based on the middle school mathematics syllabus (revised draft) for the use of algebra teaching in the first grade of high school. This book is mainly based on the second volume of the 10-year secondary school algebra textbook series compiled by the Soviet Union A.II.Gysylloff and the second episode of the 10-year secondary school algebra problem compilation compiled by II.A. Lanichev. Quite a few places cite materials in the second volume of the algebra, compiled by (?) Fadeyev and (?) Sominski. However, when dealing with teaching materials, we strive to be suitable for our country. This book is divided into four chapters. The first chapter deals with the power and square roots. The second chapter deals with the quadratic equations and equations that can be converted into quadratic equations. The third chapter deals with functions and its images. The fourth chapter deals with binary quadratic equations. The first chapter of the power and square root is divided into four sections. Section I speaks of power. Most of the textbooks in this section were learned by students in junior high school algebra, and therefore are basically the nature of review. They mainly review the definition of power and the algorithm of exponentiation to prepare for learning the next one. A new part of this section is to generalize the binomial squared formula to the polynomial square, so that when we review the general method of square-opening in the next section, it can be demonstrated based on this formula if necessary.