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.
The second volume of the first day of junior high school mathematics knowledge points
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
Monomial division is to divide the coefficient and the same base separately as a factor of quotient. For the letter only contained in the division formula, it is used as the factor of quotient together with its index.
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.
Junior one mathematics knowledge points
One-dimensional linear equation
One-dimensional linear equation: an integral equation with only one unknown number, the degree of which is 1, and a one-dimensional linear equation with non-zero coefficient.
The standard form of one-dimensional linear equation: ax+b=0(x is unknown, a and b are known numbers, a≠0).
The simplest form of a linear equation with one variable: ax=b(x is unknown, a and b are known numbers, a≠0).
The general steps of solving a linear equation with one variable: sorting out the equation ... removing the denominator ... dismantling the bracket ... changing the terms ... merging similar terms ... converting the coefficient into 1 ... (testing the solution of the equation).
Common formulas for solving application problems with column equations;
(1) Travel problem: distance = speed time;
(2) Engineering problems: workload = work efficiency and working time;
(3) ratio: part = total ratio;
(4) Downstream problem: Downstream velocity = still water velocity+water velocity, and countercurrent velocity = still water velocity-water velocity;
(5) Commodity price: selling price = pricing discount 0. 1, profit = selling price-cost;
(6) Perimeter, area and volume: C circle =2πR, S circle =πR2, C rectangle =2(a+b), S rectangle =ab, C square =4a, S square =a2, S ring =π(R2-r2), V cuboid =abc, V cube =a3, V cylinder.
The related articles are summarized in the whole volume of junior one mathematics;
★ Induction of knowledge points in the first volume of junior high school mathematics.
★ Summarize the knowledge points in the first volume of junior high school mathematics.
★ Small induction of mathematics knowledge points in senior one.
★ Sort out and summarize the knowledge points of junior one mathematics.
★ Summary of knowledge points of the first-year mathematics people's education edition
★ Induction and learning methods of mathematics knowledge points in senior one.
★ Summary of mathematical knowledge points in the first volume of the first day of junior high school.
★ Summary of knowledge points in the first grade mathematics department edition
★ Summarize the knowledge points of seventh grade mathematics in junior high school.
★ The encyclopedia of mathematics knowledge points in grade seven.