Summary of Mathematics Knowledge Points in Volume 2 of Grade One.
1, monomial: The product of numbers and letters is called monomial.
2. Polynomial: The sum of several monomials is called polynomial.
3. Algebraic expressions: monomials and polynomials are collectively referred to as algebraic expressions.
4. The number of monomials: The sum of the indices of all the letters in the monomials is called the number of monomials.
5. Degree of Polynomial: The degree of the degree term in a polynomial is the degree of this polynomial.
6. Complementary angle: The sum of two angles is 90 degrees, and these two angles are called complementary angles.
7. Complementary angle: The sum of two angles is 180 degrees, and these two angles are called complementary angles.
8. Relative vertex angles: two corners have a common vertex, and two sides of one corner are opposite to the extension lines of two sides of the other corner. These two angles are antipodal angles.
9. Common angle: In the "three-line octagon", the angles at the same position are common angles.
10, internal angle: in the "three-line octagon", the angle sandwiched between two straight lines is the internal angle.
1 1, ipsilateral inner angle: in "trilinear octagon", the angle on the same side of trilinear is ipsilateral inner angle.
12, significant number: an approximation, starting with the first number on the left that is not 0 and ending with the exact 1, all numbers are significant numbers.
13, probability: the probability of an event is the probability of this event.
14, triangle: A figure composed of three line segments that are not on the same line is called a triangle.
15, Angle bisector of triangle: In a triangle, the angle bisector of an inner angle intersects its opposite side, and the line segment between the intersection of the vertex and this angle is called the angle bisector of triangle.
16, triangle midline: the line segment connecting the vertex and the midpoint of the opposite side of the triangle is called the midline of the triangle.
17, congruent graphics: two graphics that can overlap are called congruent graphics.
18, variable: the number of changes is called variable.
19, independent variable: the variable is called the independent variable.
20. Dependent variable: The quantity that changes passively with the change of independent variables is called dependent variable.
2 1, axisymmetric figure: If a figure is folded along a straight line and the parts on both sides of the straight line can overlap each other, then this figure is called an axisymmetric figure.
22. Symmetry axis: A straight line folded in half in an axisymmetric figure is called symmetry axis.
Summary of Mathematics Knowledge Points in Volume II of Grade One of Beijing Normal University Edition
First, multiplication with the same base.
(m, n is an integer) is the most basic rule in power operation. When applying regular operations, the following points should be noted:
A) The prerequisite for using this rule is that when the bases of powers are the same and multiplied, the base a can be a specific number, letter, monomial or polynomial;
B) When the index is 1, don't mistake it for no index;
C) Don't confuse multiplication with addition of algebraic expressions. Multiplication, as long as the base is the same, the indexes can be added; For addition, not only the radix is the same, but also the exponent needs to be added;
Second, the power of power and the power of products.
Third, the division of power with the same base.
(1) The premise of applying the rule is that the cardinality is the same, and this rule can only be used if the cardinality is the same.
(2) Cardinality can be a specific number, or a monomial or polynomial.
(3) Exponential subtraction refers to subtracting the exponent of the divisor from the exponent of the divisor, and the difference is not negative.
Fourth, multiplication of algebraic expressions.
1, the concept of monomial: the algebraic expression composed of the product of numbers and letters is called monomial. A single number or letter is also a monomial. The numerical factor of a single item is called the coefficient of a single item, and the sum of all letter indexes is called the number of times of a single item.
For example, the coefficient of bca22- is 2-, the degree is 4, and the degree of a single nonzero number is 0.
2. Polynomial: The sum of several monomials is called polynomial. Each monomial in a polynomial is called a polynomial term, and the degree of the degree term is called the degree of the polynomial.
Five, the square difference formula
Expression: (a+b) (a-b) = a 2-b 2. The product of the sum of two numbers and the difference of two numbers is equal to the square of the difference of two numbers. This formula is called the square difference formula of multiplication.
Formula application
Can be used for some fractions whose denominator contains the root sign:
1/(3-4 root number 2) Simplification:
Six, the complete square formula
Common mistakes in the complete square formula are:
(1) missed a semester.
② Confusion formula
③ Symbol error in the operation result.
④ Variant application is difficult to master.
VII. Division of algebraic expressions
1, the division rule of monomial
In monomial division, the coefficient and the power of the same base number are separated as a factor of the quotient, and the letter only contained in the division formula, together with its exponent, is taken as a factor of the quotient.
Note: first determine the coefficient of the result (that is, coefficient division), and then divide it by the same base power. If only the letters in the division formula are included, it will be used as the factor of quotient together with its exponent.
Learning methods and skills of seventh grade mathematics
preview
For science study, preview is essential. In the preview, we should read the contents of the book, try our best to understand, mark the problems that cannot be solved, consult the teacher or listen to the class to solve them, and try our best to do exercises after the book to test the preview effect.
Second listening and speaking
This link is the most important, because the teacher concentrates the essence of knowledge in the classroom, and he should master the teacher's ideas and methods when listening to the math class. Write down the problem, sort it out after class and solve it. We must think positively in math class and do it according to the teacher's ideas.
review
Experience the examples in the teacher's class, organize your own thinking, think about your own ideas, what are the similarities and differences with the teacher's ideas, think about the test sites of each question, try to solve as many questions as possible, and make inferences.
Four assignments
Seriously finish the exercises left by the teacher, and appropriately select some extracurricular exercises as exercises, but don't blindly pursue digression and strange questions, let alone play "sea tactics".
Five summaries
This step is to better master what you have learned. After learning a piece of knowledge or doing a typical problem, you can sum up: summarize the mathematical knowledge of the topic; Summarize where you are stuck; Summarize how you are wrong, where you are wrong, where the "trap" of the topic is, and what you or others think.
How to choose and deal with exercises
There are countless problem sets in the market, most of which are copied from each other and full of loopholes, which makes students waste time and effort in the process of practice. I think the real problem of the calendar is an exercise, which is closely related to the exam outline and has moderate difficulty, so there will be no strange problems. At the same time, it also allows students to firmly grasp the direction of the exam and avoid detours.
Second, some students like "crowd tactics". They just do problems and never sum them up. They feel that the more they do, the higher their grades will be. This is one of the disadvantages of learning mathematics.
Remember: the problem is not much but the essence. It is essential to do exercises, but after each exercise, we should seriously reflect on what the test center of this exercise is, how many solutions there are, and which one is the simplest. We should repeatedly think about the wrong exercises, find out the reasons for the mistakes, and ensure that we can master this knowledge point.
Many students like to ask difficult questions outside the topic. But it ignores the understanding of definitions, concepts and formulas in books. As a result, mistakes in "basic questions" often appear in exams.
Therefore, in the usual math practice, we should deeply understand every knowledge point in the book and find out the possible test sites and traps. In the exam, we should make sure that the basic questions are all right, that the intermediate questions are not wasted, and that the high-scoring questions are fully attacked, even if they are wrong.
Summary of seventh grade mathematics knowledge points of Beijing Normal University Edition;
★ Review and summary of mathematics knowledge points in the second volume of the first day of Beijing Normal University Edition
★ Beijing Normal University Edition Seventh Grade Mathematics Outline Volume II
★ Beijing Normal University Edition Grade One Mathematics Book II Knowledge Points
★ Beijing Normal University Edition Seventh Grade Mathematics Outline
★ Beijing Normal University Edition Seventh Grade Volume II Mathematics Teaching Plan
★ Summary of Mathematics Knowledge Points below Grade 7 in Junior Middle School of Beijing Normal University
★ Guidance on learning methods in grade seven
★ Beijing Normal University Edition seventh grade mathematics knowledge points
★ Beijing Normal University Edition Seventh Grade Volume II Mathematics Review Outline
★ Beijing Normal University Edition seventh grade mathematics knowledge points