Junior and senior high school mathematics convergence knowledge points
1. Cubic sum and difference formula
This part is not mentioned in many junior high school textbooks, but its calculation formula is still in use after entering senior high school. For example:
(1) cubic sum formula: (a+b) (a 2-ab+b 2) = a 3+b 3;
(2) Cubic difference formula: (a-b) (A2+AB+B2) = A3-B3;
(3) The sum and square formula of three numbers: (a+b+c) 2 = a2+b2+c2+2ab+2bc+2ac;
(4) The formula of two numbers and cube: (a+b) 3 = a3+3a2b+3ab2+b3;
(5) The cubic formula of the difference between two numbers: (a-b) 3 = a 3-3a 2b+3ab 2-b 3.
2. Factorization
Cross multiplication junior high school does not need, nor does it need polynomial factorization more than three times. But in high school, many textbooks are used.
3. The numerator and denominator in the quadratic formula are rationalized.
Junior high school doesn't need this, but the rationalization of numerator and denominator is a common problem-solving skill of functions and inequalities in senior high school, especially the rationalization of numerator.
4. Quadratic function
The image and nature of quadratic function is the most important content in the connection between junior high school and senior high school. The growth point of quadratic function knowledge is in junior high school and the development point is in senior high school, which is an important content in the connection of junior high school and senior high school mathematics. Quadratic function, as a simple and basic function type, has been a key examination content in college entrance examination for many years and lasted for a long time.
5. The relationship between roots and coefficients (Vieta theorem)
In junior high school, we usually use factorization method, formula method and collocation method to solve the quadratic equation of numerical coefficient, but in senior high school, we no longer study, but this type of questions will appear in the college entrance examination, which requires students to have the following abilities:
(1) Understand the discriminant of the roots of a quadratic equation with one variable and use the discriminant to judge the roots;
(2) Grasp the relationship between roots and coefficients of a quadratic equation with one variable, and use it to find the algebraic expression of the sum and product of two roots (here? Symmetry? ), we can construct a quadratic equation with real numbers p and q as roots.
6. Symmetry and translation transformation of images
Junior high school only makes a brief introduction, and after teaching functions in senior high school, the image will go up and down; For left-right translation, the symmetry of two functions about origin, symmetry axis and given straight line must be mastered.
7. Functions, equations and inequalities with parameters
There is no requirement in junior high school textbooks, but only quantitative research, while senior high school regards this part as the key and difficult point. The comprehensive examination of equations, inequalities and functions often becomes a comprehensive question in the college entrance examination.
8. Many concepts in geometry (such as center of gravity, vertical center, outer center, inner center, etc.). ) and theorems (such as parallel line segment ratio theorem, projective theorem, circular power theorem, etc. Most of them are not learned by junior high school students, but are often involved in high school textbooks and often used directly to solve problems.
Difference of Mathematics Convergence between Junior High School and Senior High School
First, the sudden change of mathematical language in abstraction: students have always reflected that concepts such as set and mapping are difficult to understand and far from life, which seems to be very? Xuan? .
The second is the transition from thinking method to rational level: the abstraction of mathematical language puts forward higher requirements for thinking ability.
Third, the total amount of knowledge content has increased dramatically, and time is tight and it is difficult. In this way, students will inevitably not adapt to high school mathematics learning, which will affect the improvement of their grades.
Three Mistakes in Junior High School and Senior High School Mathematics Cohesion Teaching
One of the misunderstandings: the bridging course has taught a lot of new knowledge in senior one, and it has become a new course.
Myth 2: Bridging course teaches many junior high school competitions, and bridging course has become a competition training course.