Sorting out the knowledge points of mathematics in the first day of junior high school
One: the types of horns
Type of angle: the size of the angle has nothing to do with the length of the side; The size of an angle depends on the degree to which both sides of the angle are open. The bigger the opening, the bigger the angle. Conversely, the smaller the opening, the smaller the angle. In dynamic definition, it depends on the direction and angle of rotation. Angles can be divided into acute angle, right angle, obtuse angle, right angle, rounded corner, negative angle, positive angle, upper angle, lower angle and 0 angle, which are 10 respectively. An angle measuring system in degrees, minutes and seconds is called an angle system. In addition, there are secret system, arc system and so on.
Acute angle: An angle greater than 0 and less than 90 is called an acute angle.
Right angle: An angle equal to 90 is called a right angle.
Oblique angle: an angle greater than 90 and less than180 is called obtuse angle.
Boxer: An angle equal to 180 is called a boxer.
Excellent angle: more than180 and less than 360 is called excellent angle.
Bad angle: more than 0 and less than 180 is called bad angle, and acute angle, right angle and obtuse angle are all bad angles.
Fillet: An angle equal to 360 is called a fillet.
Negative angle: the angle formed by clockwise rotation is called negative angle.
Positive angle: the angle of counterclockwise rotation is positive angle.
Angle 0: An angle equal to zero.
Complementary angle and complementary angle: if the sum of two angles is 90, it is complementary angle; if the sum of two angles is180, it is complementary angle. The complementary angles of equal angles are equal, and the complementary angles of equal angles are equal.
Inverse vertex angle: When two straight lines intersect, there is only one common vertex, and both sides of the two corners are opposite extension lines. These two angles are called antipodal angles. Two straight lines intersect to form two pairs of vertex angles. The two opposite angles are equal.
The compulsory knowledge point of junior one mathematics: the solution of linear equations of one variable
General steps:
Step 1: Remove the denominator and multiply all the denominators by the least common multiple on both sides of the equation. Note: the numerator should be bracketed, and the item without denominator cannot be omitted.
Step 2: Remove the brackets, first remove the brackets, then remove the brackets, and finally remove the braces. Note: Do not omit the items in brackets. If there is a "-"in front of the bracket, everything in the bracket will change sign after deleting the bracket;
Step 3: Move the term, that is, move the term containing the unknown to one side of the equation and other terms to the other side. Note: the symbol of the item to be moved should be changed, the symbol of the item not to be moved should not be changed, and the item should not be omitted when moving;
Step 4: Merge similar terms and transform the equation into ax=b(a≠0). Note: when the coefficients are added, the letter part remains unchanged;
Step 5: Convert the coefficient into 1, divide both sides of the equation by the unknown coefficient A, and get the solution of the equation x={frac{b}{a}}(a≠0). Note: Do not reverse the position of numerator and denominator.
Two: Addition and subtraction of algebraic expressions
1. monomial: in algebraic expressions, if only multiplication (including power) operations are involved. Or algebraic expressions that contain division but do not contain letters in division are called monomials; The product of numbers or letters is called a monomial (a single number or letter is also a monomial).
2. Coefficient: The numerical factor in a single item is called the coefficient of this single item. The sum of the exponents of all letters is called the degree of this monomial. The zeroth power of any nonzero number is equal to 1.
3. Polynomial: The sum of several monomials is called polynomial.
4. Number and degree of polynomials: the number of monomials contained in a polynomial is the number of polynomial terms, and each monomial is called a polynomial term; In polynomial, the degree of the term with the highest degree is called the degree of polynomial.
5. Constant term: the term without letters is called constant term.
6. The arrangement of polynomials
(1) Arranging polynomials in descending alphabetical order is called arranging polynomials in descending alphabetical order.
(2) Arranging a polynomial according to the exponent of a letter from small to large is called arranging polynomials according to the ascending power of this letter.
7. Please note when arranging polynomials:
(1) Since a single item contains its preceding attribute symbol, the attribute symbol of each item should still be regarded as a part of the item and moved together.
(2) The arrangement of polynomials with two or more letters should pay attention to:
A. first of all, it must be arranged according to the index of which letter.
B. determine whether to arrange letters inward or outward.
(3) Algebraic expression:
Monomial and polynomial are collectively called algebraic expressions.
8. Polynomial addition:
Polynomial addition refers to the coefficient addition of polynomial similar terms (that is, merging similar terms).
9. Similar items: items with the same letters and times are called similar items.
10. Merge similar items: similar items in polynomials can be merged, which is called merging similar items. The rule of merging similar items is: the coefficients of similar items are added, and the obtained results are used as coefficients, and the index of letters remains unchanged.
Junior one mathematics knowledge points
Chapter 1 Rational Numbers
1. 1 positive and negative numbers
A number with a negative sign "-"in front of a number that is not 0 is called a negative number.
It has the opposite meaning to negative number, that is, I learned that numbers other than 0 are called positive numbers (sometimes "+"is added before positive numbers as needed).
1.2 rational number
Positive integers, 0 and negative integers are collectively called integers, and positive and negative fractions are collectively called fractions.
Integers and fractions are collectively called rational numbers.
Numbers are usually represented by points on a straight line, which is called the number axis.
Three elements of number axis: origin, positive direction and unit length.
Take any point on a straight line to represent the number 0, and this point is called the origin.
Numbers with only two different signs are called opposites. (Example: the reciprocal of 2 is-2; The reciprocal of 0 is 0)
The distance between the point representing the number A on the number axis and the origin is called the absolute value of the number A, and it is recorded as |a|.
The absolute value of a positive number is itself; The absolute value of a negative number is its reciprocal; The absolute value of 0 is 0. Two negative numbers, the larger one has the smaller absolute value.
Addition and subtraction of rational number 1.3
Rational number addition rule:
1. Add two numbers with the same sign, take the same sign, and then add the absolute values.
2. Add two different symbols with different absolute values, take the symbol of the addend with larger absolute value, and subtract the one with smaller absolute value from the one with larger absolute value. Two opposite numbers add up to 0.
When a number is added with 0, it still gets this number.
Rule of rational number subtraction: subtracting a number is equal to adding the reciprocal of this number.
Multiplication and division of rational number 1.4
Rational number multiplication rule: two numbers are multiplied, the same sign is positive, the different sign is negative, and the absolute value is multiplied. Any number multiplied by 0 is 0.
Two numbers whose product is 1 are reciprocal.
Rational number division rule: dividing by a number that is not equal to 0 is equal to multiplying the reciprocal of this number.
Divide two numbers, the same sign is positive, the different sign is negative, and divide by the absolute value. Divide 0 by any number that is not equal to 0 to get 0. mì
The operation of finding the product of n identical factors is called power, and the result of power is called power. In the n power of a, a is the base and n is the exponent.
The odd power of a negative number is negative and the even power of a negative number is positive. Any power of a positive number is a positive number, and any power of 0 is 0.
Scientific counting method is used to express numbers greater than 10 as the n power of a× 10.
From the first non-zero digit to the last digit on the left of a number, all digits are valid digits of this number.
Chapter II One-variable Linear Equation
2. 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.
2.2 Starting from the Ancient Algebra Books-Discussion on the Linear Equation of One Variable (1)
Moving the sign of the term on one side of the equation to the other side is called moving the term.
The third chapter is the preliminary understanding of graphics.
3. 1 color graphics
Geometry is also called solid for short. What surrounds the body is the surface.
3.2 Lines, rays and line segments
Axiom of line segment: Of all the connecting lines between two points, the line segment is the shortest (the line segment between two points is the shortest).
The length of the line segment connecting two points is called the distance between these two points.
3.3 Angle measurement
1 degree =60 minutes 1 minute =60 seconds 1 fillet =360 degrees 1 flat angle = 180 degrees.
3.4 Angle comparison and operation
If the sum of two angles is equal to 90 degrees (right angle), they are said to be complementary angles, that is, each angle is the complementary angle of another angle.
If the sum of two angles is equal to 180 degrees (flat angle), it is said that the two angles are complementary, that is, each angle is the complement of the other angle.
The complementary angles of equal angles (same angles) are equal.
The complementary angles of equal angles (same angles) are equal.
Chapter 4-6 Arrangement of Mathematics Knowledge Points in the First Day of Junior High School
Chapter IV Data Collection and Arrangement
Collecting, sorting, describing and analyzing data is the basic process of data processing.
Chapter V Intersecting Lines and Parallel Lines
5. 1 intersection line
The vertical angles are equal.
One and only one straight line is perpendicular to the known straight line.
Of all the line segments connecting a point outside the straight line with a point on the straight line, the vertical line segment is the shortest (in short, the vertical line segment is the shortest).
5.2 parallel lines
After a point outside the straight line, there is one and only one straight line parallel to this straight line.
If both lines are parallel to the third line, then the two lines are also parallel to each other.
Conditions of parallel lines:
Two straight lines are cut by a third straight line. If congruent angles are equal, two straight lines are parallel.
Two straight lines are cut by a third straight line. If the internal angles are equal, two straight lines are parallel.
Two straight lines are cut by a third straight line. If they are complementary, then these two straight lines are parallel.
5.3 Properties of parallel lines
Two parallel lines are cut by a third straight line and have the same angle.
Two parallel lines are cut by a third line, and their inner angles are equal.
Two parallel lines intersect with the third straight line, which complement each other.
A statement that judges a thing is called a proposition.
Chapter VI Plane Cartesian Coordinate System
6. 1 plane rectangular coordinate system
A word containing two numbers represents a definite position, where the two numbers represent different meanings. We call this number pair consisting of two numbers A and B in sequence an ordered pair.
Chapter 7-10 Arrangement of Mathematics Knowledge Points in Grade One of Junior High School
Chapter VII Triangle
7. 1 Line segment related to triangle
Triangles are stable.
7.2 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.
7.3 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.
Chapter VIII Binary Linear Equations
8. 1 binary linear equations
An equation contains two unknowns (X and Y) whose exponents are 1. Equations like this are called binary linear equations.
Two binary linear equations are combined to form a system of linear equations with two unknowns.
The values of two unknowns that make the values on both sides of the binary linear equation equal are called the solutions of the binary linear equation.
The common * * * solution of two equations of binary linear equations is called the solution of binary linear equations.
8.2 elimination
The idea of solving the unknowns one by one from more to less is called elimination thought.
Chapter 9 Inequality and Unequal Groups
9. 1 inequality
Formulas that indicate the size relationship with less than sign or greater than sign are called inequalities.
The value of the unknown quantity that makes the inequality valid is called the solution of the inequality.
The value range of x that can make inequality hold is called the solution set of inequality, which is called the solution set for short.
An inequality whose unknown number is 1 is called a linear inequality of one variable.
The essence of inequality:
Add (or subtract) the same number (or formula) on both sides of the inequality, and the direction of the inequality remains unchanged.
Both sides of inequality multiply (or divide) the same positive number, and the direction of inequality remains unchanged.
When both sides of the inequality are multiplied (or divided) by the same negative number, the direction of the inequality changes.
The difference between any two sides in a triangle is less than the third side.
The sum of any two sides in a triangle is greater than the third side.
9.3 One-dimensional linear inequality system
When two linear inequalities are combined, a unitary linear inequality is formed.
Chapter 10 Real Numbers
10. 1 square root
If the square of a positive number X is equal to A, then this positive number X is called the arithmetic square root of A, and 2 is the root index.
The arithmetic square root of A is pronounced as "root number A", and A is called radix.
The arithmetic square root of 0 is 0.
If the square of a number is equal to a, then this number is called the square root or quadratic root of a.
The operation of finding the square root of a number is called square root.
10.2 cube root
If the cube of a number is equal to A, then this number is called the cube root or cube root of A. ..
The operation of finding the cube root of a number is called finding the cube root.
10.3 real number
Infinitely cyclic decimals are also called irrational numbers.
Rational numbers and irrational numbers are collectively called real numbers.
Mathematics learning method
1, form a good habit of learning mathematics. Establishing a good habit of learning mathematics will make you feel orderly and relaxed in your study. The good habits of high school mathematics should be: asking more questions, thinking hard, doing easily, summarizing again and paying attention to application. In the process of learning mathematics, students should translate the knowledge taught by teachers into their own unique language and keep it in their minds forever. Good habits of learning mathematics include self-study before class, paying attention to class, reviewing in time, working independently, solving problems, systematically summarizing and studying after class.
2. To understand and master the commonly used mathematical thinking methods in time and learn high school mathematics well requires us to master them from the height of mathematical thinking methods. Mathematics thoughts that should be mastered in middle school mathematics learning include: set and correspondence thoughts, classified discussion thoughts, combination of numbers and shapes, movement thoughts, transformation thoughts and transformation thoughts.
3. Gradually form a "self-centered" learning model. Mathematics is not taught by teachers, but obtained through positive thinking activities under the guidance of teachers. To learn mathematics, we must actively participate in the learning process, develop a scientific attitude of seeking truth from facts, and have the innovative spirit of independent thinking and bold exploration.
4. Take math notes, especially the different aspects of concept understanding and mathematical laws, as well as the extra-curricular knowledge developed by teachers in class. Write down the most valuable thinking methods or examples in this chapter, as well as your unsolved problems, so as to make up for them in the future.
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