Summarize and sort out the knowledge points of mathematics in the first volume of Grade One.

Mathematics learning lies in practice, and being diligent in practice can help us open the logic of thinking. The following is a summary of the mathematics knowledge points in the first volume of Grade One, hoping to help you!

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. For example:? )

2. Integer: positive integer, 0, negative integer, collectively referred to as integer.

3. Score: positive score and negative score.

(3) Number 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. Multiplicative associative law: (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.

Chapter II Algebraic Expressions (1) Algebraic Expressions

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 the monomial, the numerical factor is called the coefficient of the monomial.

4。 Times: The sum of the indices of all the letters in a 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.

After combing the knowledge points, let's take a look at the related exercises. According to the situation of doing the problem, analyze what knowledge points you have not mastered.

1, from the number axis, 0 is ()

A, the smallest integer b, the largest negative number c, the smallest rational number d and the smallest nonnegative number.

2, the reciprocal of a number is less than itself, this number is ()

A, nonnegative B, positive C, 0D, negative

3. The highest temperatures in winter in three cities in China are-10℃, 1℃ and -7℃ respectively. Their correct arrangement from high to low is ().

a，- 10℃，-7℃， 1℃B，-7℃，- 10℃， 1℃C， 1℃，-7℃， 10℃D， 1℃，- 10℃，-7℃

4, the following statement is correct ()

A. Positive numbers and negative numbers are collectively called rational number B. Rational numbers refer to five types of C, including integer, fraction, positive rational number, negative rational number and 0. Rational numbers are either integers or fractions d, and integers include positive integers and negative integers.

5, if a and b are both rational numbers, a >；; 0, b<0, and | a | < |b|, the following statement is incorrect ().

A, if the numbers A and B are represented on the number axis, A is on the right side of the origin and B is on the left side of the origin.

B, because positive numbers are greater than all negative numbers, a> B.

C, if the numbers A and B are represented on the number axis, then the distance from the number A to the origin is smaller than the distance from the number A to the origin.

D on the number axis, the points representing a, |a| and b are a, b and |a| respectively from left to right.

6. In the following algebraic expressions: (1/2)ab, (a+b)/2, ab2+b+ 1, (3/x)+(2/y), x3+x2-3, there is () A.2 B.3 polynomial.

7. The polynomial -23m2-n2 is () A. Quadratic binomial B. Cubic binomial C. Quadratic binomial D. Quintic binomial.

8, the following statement is correct ()

A. The items of 3x2-2x+5 are 3x2, 2x, 5.

B.(3/x)-(3/y) and 2x2-2xy-5 are polynomials.

The degree of C polynomial -2x2+4xy is 3.

If the degree of a polynomial is 6, then only one term in this polynomial is 6.

9, the following statement is correct ()

A. the algebraic expression abc has no coefficients.

B (x/2)+(y/3)+(z/4) is not an algebraic expression.

C.-2 is not an algebraic expression