Induction of basic knowledge points of mathematics in grade one of junior high school
The addition rule of 1 rational number
(1) Add two numbers with the same sign, take the same sign, and add the absolute values.
⑵ Add two numbers with different symbols with unequal absolute values, take the sign of the addend with larger absolute value, and subtract the number with smaller absolute value from the number with larger absolute value. Two opposite numbers add up to 0.
(3) When a number is added to 0, the number is still obtained.
When two numbers are added, the positions of the addend are exchanged and the sum is unchanged.
Additive commutative law: A+B = B+A.
Add three numbers, first add the first two numbers, or add the last two numbers first, and the sum remains the same.
Additive associative law: (a+b)+c = a+(b+c)
2 rational number multiplication rule
Multiply two numbers, the same sign is positive, the different sign is negative, and then multiply by the absolute value.
Any number multiplied by 0 is 0.
Two numbers whose product is 1 are reciprocal.
Multiply several numbers that are not 0. When the number of negative factors is even, the product is positive. When the number of negative factors is odd, the product is negative.
When two numbers are multiplied, the exchange factor and the product are in the same position.
ab=ba:
Multiply three numbers, first multiply the first two numbers, or multiply the last two numbers first, and the products are equal.
(ab)c=a(bc):
Multiplying a number by the sum of two numbers is equivalent to multiplying this number by these two numbers respectively, and then adding the products.
a(b+c)=ab+ac:
Writing specification for multiplication of numbers and letters;
(1) Multiplies a number with a letter, omitting the multiplication sign or using "".
(2) Numbers multiplied by letters. When the coefficient is 1 or-1, 1 should be omitted.
(3) The band score is multiplied by letters, and the band score becomes a false score.
If any rational number is represented by the letter X, the product of 2 and x is 2x, and the product of 3 and x is 3x, then the formula 2x+3x is the sum of 2x and 3x, 2x and 3x are the terms of this formula, and 2 and 3 are the coefficients of these two terms respectively.
Generally speaking, when combining formulas with the same letter factor, it is only necessary to combine their coefficients, and the obtained results are used as coefficients, and then multiplied by the letter factor, that is,
ax+bx=(a+b)x:
In the above formula, X is the letter factor, and A and B are the coefficients of ax and bx respectively.
Support removal rules:
There is a "+"before the brackets. Remove brackets and the "+"in front of brackets, and nothing in brackets will change its sign.
There is a "-"before the brackets. Remove brackets and the "-"sign in front of brackets, and change all the symbols in brackets.
The factors outside brackets are positive numbers, and the symbols of the items in the formula after removing brackets are the same as those of the corresponding items in the original brackets; The factor outside the bracket is negative, and the sign of each item in the formula after the bracket is opposite to that of the corresponding item in the original bracket.
3 One-dimensional linear equation
1, from formula to equation
An equation is an equation with unknowns.
All equations contain only one unknown (element) X, and the exponent of the unknown X is 1 (degree). Such an equation is called a linear equation with one variable. Solving the equation is to find the value of the unknown quantity that makes the left and right sides of the equation equal, and this value is the solution of the equation.
Properties of the equation: 1. Add (or subtract) the same number (or formula) on both sides of the equation and the result is still the same. 2. Both sides of the equation are multiplied by the same number, or divided by the same number that is not 0, and the results are still equal.
2. Starting from the ancient algebra books-On the linear equation of one variable;
Moving the sign of the term on one side of the equation to the other side is called moving the term.
4 triangle
1, the line segment related to the triangle
Triangles are stable.
2. Angle related to triangle
The sum of the internal angles of a triangle is equal to 180 degrees.
The outer angle of a triangle is equal to the sum of two non-adjacent inner angles.
The outer angle of a triangle is greater than any inner angle that is not adjacent to it.
3. The sum of polygons and their internal angles
Is the sum of the internal angles of the N-polygon equal to: (n-2)? 180 degrees.
The sum of the outer angles of a polygon is equal to 360 degrees.
5 reciprocal
(1) The concept of antipodal: Only two numbers with different symbols are called antipodal.
(2) The meaning of opposites: Grasp that opposites appear in pairs and cannot exist alone. From the number axis, except 0, they are two mutually opposite numbers, both on both sides of the origin, and the distance from the origin is equal.
(3) Simplification of multiple symbols: No matter the number of "+",the odd number of "﹣" is negative and the even number of "﹣" is positive.
(4) Summary of conventional methods: The way to find the reciprocal of a number is to add "﹣" in front of this number. For example, the reciprocal of A is ﹣a, and the reciprocal of m+n is ﹣(m+n). At this time, m+n is a whole. When you put a minus sign before an integer, use parentheses.