The first day of junior high school is a good time to lay a foundation of knowledge, in order to help students lay a better foundation of learning. The following is a summary of the first-grade mathematics knowledge points I compiled for your reference only. Welcome to reading. Summing up Chapter 65438 of Grade One Mathematics +0-3 Chapter I Rational Numbers 1. 1 Positive and Negative Numbers The numbers with the negative sign "-"before them are called negative numbers. 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 numbers 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 antonym 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 numbers 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 numbers 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. 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 2 One-variable linear equation 2. 1 From formula to equation, it 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 discussion of the ancient mathematical book-the one-dimensional linear equation (1), it is called moving the sign of an item on one side of the equation to the other side. Chapter III Preliminary Understanding of Graphics 3. 1 Color Graphics Geometry is also called Stereo. What surrounds the body is the surface. 3.2 axiom of straight line, ray and line segment: of all the connecting lines between two points, the line segment is short (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 Comparison and calculation of angles If the sum of two angles is equal to 90 degrees (right angle), they are called. 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. Summary of Mathematics Knowledge Points in Senior One Chapter 4-6 Chapter 4 Data Collection and Arrangement Collecting, arranging, describing and analyzing data is the basic process of data processing. Chapter V Intersections and parallel lines 5. 1 Intersections have equal vertical angles. 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 pass through a point outside the straight line, and one and only one straight line is parallel to this straight line. If both lines are parallel to the third line, then the two lines are also parallel to each other. Condition of parallel lines: two lines are cut by a third 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 the congruent angles are equal. 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 Planar Cartesian Coordinate System 6. 1 Planar Cartesian coordinate system contains two numbers to represent a certain position, where the two numbers each represent a different meaning. We call this number pair consisting of two numbers A and B in sequence an ordered pair. Summary of Mathematics Knowledge Points in Senior One 7- 10 Chapter VII Triangle 7. 1 Triangle related to triangle has stability. 7.2 The sum of the triangle internal angles related to the 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 The sum of the polygon and its internal angles and the internal angles of n sides is equal to: (n-2)? The sum of the external angles of the polygon with 180 degrees is equal to 360 degrees. Chapter 8 Binary linear equations 8. 1 Binary linear equations contain two unknowns (x and y), and the exponents of the unknowns are both 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 The idea of eliminating the number of unknowns from more to less and solving them one by one is called elimination thought. Chapter 9 Inequalities and Inequality Groups 9. 1 Inequality The formula that uses less than sign or greater than sign to express the relationship between size is called inequality. 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 inequality, and the direction of 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 is composed of two linear inequalities. Chapter 10 Square Root of Real Numbers 10. 1 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 exponent of the root. 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, and 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 infinite acyclic decimal number is also called irrational number. Rational numbers and irrational numbers are collectively called real numbers. Expanding reading: how to lay a good foundation for junior one mathematics? First, seriously explore concepts and formulas Many students pay insufficient attention to concepts and formulas, and their understanding of concepts only stays on the surface of words. For example, in the concept of algebra, many students ignore that "a single letter or number is also algebra"; Moreover, concepts and formulas are blindly memorized, lacking the connection with practical topics. The teacher's advice is: be more careful (observe special cases), go deeper (know the common test sites in the topic), and be more skilled (no matter what it looks like, we can apply it freely). Second, summarize similar types of problems. Only when you can sum up the problems, classify the problems you have done, know what types of problems you can solve, master what common problem-solving methods and what types of problems you can't do, can you really master the tricks of this subject and truly "let it change, I won't move." If this problem is not solved well, after entering the second and third grades, students will find that some students do problems every day, but their grades will fall instead of rising. The teacher's suggestion is that "summary" is the best way to do fewer and fewer problems. Third, collect your typical mistakes and solve the problems you can't solve. The most difficult thing for students is their own mistakes and difficulties. But this is precisely the problem that needs to be solved most. There are two important purposes for students to do problems: First, to practice the knowledge and skills they have learned in practical problems. The other is to find out your own shortcomings and make up for them. The teacher's suggestion is: doing problems is like digging gold mines. Every wrong question is a gold mine. Only by digging and refining can we gain something. Fourth, actively ask and discuss questions you don't understand, and actively ask others for advice when you find problems you don't understand. This is a very common truth. But this is what many students can't do. There may be two reasons: first, insufficient attention has been paid to this issue; Second, I'm sorry, I'm afraid of asking teachers to be trained and asking students to be looked down upon by them. The teacher's suggestion is that "diligence" is the foundation and "thirst for knowledge" is the key. Fifth, pay attention to the cultivation of actual combat (examination) experience. Examination itself is a science. Some students usually get good grades. Teachers ask questions in class, and they can do anything. I can also do problems after class. But when it comes to the exam, the results are not ideal. There are two main reasons for this: first, the test mentality is not bad, and it is easy to be nervous; Second, the examination time is tight and it can never be completed within the specified time. The teacher's suggestion is: treat "homework" as an exam and "exam" as homework.