Junior high school mathematics book 1 unit 1 knowledge 1
Chapter 1 Rational Numbers
(1) positive and negative numbers 1. Positive number: a number greater than 0. 2. Negative number: a number less than 0.
3.0 neither positive nor negative.
4. Positive numbers are greater than 0, negative numbers are less than 0, and positive numbers are greater than negative numbers.
(2) Rational number 1. Rational number: a number consisting of integers and fractions. Include positive integer, 0, negative integer, positive fraction and negative fraction. Can be written as the ratio of two integers. Irrational numbers cannot be written as the ratio of two integers. It is written in decimal form, and the numbers after the decimal point are infinite. Such as: π)2. Integer: positive integer, 0, negative integer, collectively referred to as integer. 3. Score: positive score and negative score.
(3) Axis 1. Number axis: Numbers are represented by points on a straight line, which is called number axis. Draw a straight line and take any point on the straight line to represent the number 0. This zero point is called the origin, which specifies that the right or upward direction of the straight line is positive; Select the appropriate length as the unit length, so as to take points on the number axis. ) 2. Three elements of the number axis: origin, positive direction and unit length. 3. Antiquities: Only two numbers with different symbols are called reciprocal. The antonym of 0 is still 0. 4. Absolute value: the absolute value of a positive number is itself, and the absolute value of a negative number is its inverse; The absolute value of 0 is 0, two negative numbers, the larger absolute value is smaller.
Addition and subtraction of rational numbers
1. Sign first, then calculate the absolute value. 2. Addition algorithm: the same sign is added, and the absolute value is added. For the addition of different symbols, take the sign of the addend with large absolute value, and subtract the sign with small absolute value from the sign with large absolute value. Two opposite numbers add up to 0. Add and subtract a number with 0, and you still get this number. 3. additive commutative law: a+b=b+a is added, the position of the addend is exchanged, and the sum is unchanged. 4. The law of addition and association: (a+b)+c=a+(b+c) three numbers are added, the first two numbers are added first, or the last two numbers are added first, and the sum is unchanged.
5.a-b=a+(-b) Subtracting a number is equal to adding the reciprocal of this number.
(5) rational number multiplication (first determine the sign of the product, and then determine the size of the product)
1. The same symbol is positive, different symbols are negative, and the absolute values are multiplied. Any number multiplied by 0 is 0.
2. Two numbers whose product is 1 are reciprocal. 3. Multiplicative commutative law: ab=ba
4. The law of multiplicative association: (ab)c=a(bc)5. Multiplication and distribution law: a(b+c)=ab+ac.
(6) rational number division
1. First divide and multiply, then sign, and finally find the result.
2. dividing by a number that is not equal to 0 is equal to multiplying the reciprocal of this number.
3. Divide two numbers, the same sign is positive and the different sign is negative, and divide by the absolute value. Divide 0 by any number that is not equal to 0, and you will get 0.
(7) Stand aside
1. The operation of finding the product of n identical factors is called power. Write one. The result of multiplication is called power, a is called base, and n is called exponent. )
2. The odd power of a negative number is negative and the even power of a negative number is positive; Any positive integer power of 0 is 0.
3. Multiplication with the same base, constant base and exponential addition.
4. Divided by the same base, the base is constant, minus the exponent.
(8) Mixed operations of addition, subtraction, multiplication and division of rational numbers.
1. Multiply first, then multiply and divide, and finally add and subtract.
2. Operate at the same level, from left to right.
3. If there are brackets, do the operation in brackets first, and then follow the brackets, brackets and braces in turn.
(9) Scientific notation, divisor and significant figures.
Junior one mathematics book 1 unit 1 knowledge 2
Chapter II Algebraic Expressions
(1) algebraic expression 1. Algebraic expression: monomials and polynomials are collectively called algebraic expressions.
2. Monomial: The formula consisting of the product of numbers and letters is called monomial. A single number or letter is also a monomial.
3. Coefficient: In a single item, the numerical factor is called the coefficient of this single item.
4. Times: The sum of the indices of all the letters in the monomial is called the times of this monomial.
5. Polynomial: The sum of several monomials is called polynomial.
6. Term: Each monomial that constitutes a polynomial is called a polynomial term.
7. Constant term: the term without letters is called constant term.
8. Degree of Polynomial: In a polynomial, the degree of the term with the highest degree is called the degree of this polynomial.
9. Similar terms: In polynomials, terms with the same letters and the same index of the same letters are called similar terms.
10. Merging similar items: Merging similar items in polynomials into one item is called merging similar items.
(2) Algebraic expression addition and subtraction Algebraic expression addition and subtraction operation, if you encounter brackets, remove the brackets first, and then merge similar items.
1. bracket removal: Generally speaking, several algebraic expressions are added and subtracted. If there are brackets, remove them first, and then merge similar items. If the factor outside the brackets is positive, the symbols of the items in the original brackets are the same as the original symbols after the brackets are removed. If the factor outside the brackets is negative, the symbols of the items in the original brackets are opposite to those after the brackets are removed.
2. Merging similar items: Merging similar items in polynomials into one item is called merging similar items. After merging similar items, the coefficient of the obtained item is the sum of the coefficients of similar items before merging, and the letter part remains unchanged.
Junior high school mathematics learning methods
1. Combination of seeking advice and self-study.
In the process of learning, we should strive for the guidance and help of teachers, but we should not rely on them everywhere-teachers must take the initiative to study, explore and obtain, and seek the help of teachers and classmates on the basis of their own serious study and research.
2. Combination of learning and thinking
In the process of learning, we should carefully study the content of teaching materials, ask questions and trace back to the source. For every concept, formula and theorem, we should understand its context, cause and effect, internal relations, and mathematical ideas and methods involved in the derivation process. When solving problems, we should try our best to adopt different ways and methods, and overcome the rigid learning methods of books and machinery.
3. Combine learning with application and be diligent in practice.
In the process of learning, we should accurately grasp the essential meaning of abstract concepts and understand the evolution process of abstraction from actual model to theory. For theoretical knowledge, we should look for concrete examples in a wider scope, make them concrete, and try our best to apply theoretical knowledge and thinking methods to practice.
4. broaden your horizons, accept the appointment, and return to the appointment from Bo.
Textbooks are the main source of students' knowledge, but they are not the only source. In the process of learning, in addition to studying textbooks carefully, we should also read relevant extracurricular materials to expand our knowledge. At the same time, on the basis of extensive reading, do research seriously and master its knowledge structure.
5. There are both imitation and innovation.
Imitation is an indispensable learning method in mathematics learning, but it must not be copied mechanically. On the basis of digestion and understanding, use your brains and put forward your own opinions and opinions, instead of sticking to the existing framework and existing model.
6. Review in time to enhance memory.
The content of study in class must be digested on the same day, reviewed first, then practiced, and the review work must be carried out frequently. Every time you finish a unit, you should summarize and sort out the knowledge you have learned so as to make it systematic and profound.
The first volume of the first day of junior high school is related to the first unit of mathematics knowledge;
★ Induction of knowledge points in the first volume of junior high school mathematics.
★ Summary of mathematical knowledge points in the first volume of the first day of junior high school.
★ Summarize the knowledge of the first volume of seventh grade mathematics.
★ arrangement of key knowledge in the first volume of junior one mathematics
★ The third summary of mathematics knowledge points in the first volume of the seventh grade
★ Knowledge points in the first volume of first grade mathematics
★ Mind map of the first unit of mathematics in the first volume of senior one.
★ Summarize the knowledge points of mathematics in the first semester of senior one.
★ Summary of knowledge points in the first volume of seventh grade mathematics
★ Summary of knowledge points in the first chapter of the first volume of seventh grade mathematics