1, rational number

Rational Numbers: ① Integer → Positive Integer /0/ Negative Integer

② Score → Positive/Negative Score

Number axis: ① Draw a horizontal straight line, take a point on the straight line to represent 0 (origin), select a certain length as the unit length, and specify the right direction on the straight line as the positive direction to get the number axis. ② Any rational number can be represented by a point on the number axis. (3) If two numbers differ only in sign, then we call one of them the inverse of the other number, and we also call these two numbers the inverse of each other. On the number axis, two points representing the opposite number are located on both sides of the origin, and the distance from the origin is equal. The number represented by two points on the number axis is always larger on the right than on the left. Positive numbers are greater than 0, negative numbers are less than 0, and positive numbers are greater than negative numbers.

Absolute value: ① On the number axis, the distance between the point corresponding to a number and the origin is called the absolute value of the number. (2) The absolute value of a positive number is itself, the absolute value of a negative number is its reciprocal, and the absolute value of 0 is 0. Comparing the sizes of two negative numbers, the absolute value is larger but smaller.

Operation of rational number:

Addition: ① Add the same sign, take the same sign, and add the absolute values. ② When the absolute values are equal, the sum of different symbols is 0; When the absolute values are not equal, take the sign of the number with the larger absolute value and subtract the smaller absolute value from the larger absolute value. (3) A number and 0 add up unchanged.

Subtraction: Subtracting a number equals adding the reciprocal of this number.

Multiplication: ① Multiplication of two numbers, positive sign of the same sign, negative sign of different sign, absolute value. ② Multiply any number by 0 to get 0. ③ Two rational numbers whose product is 1 are reciprocal.

Division: ① Dividing by a number equals multiplying the reciprocal of a number. ②0 is not divisible.

Power: the operation of finding the product of n identical factors A is called power, the result of power is called power, A is called base, and N is called degree.

Mixing order: multiply first, then multiply and divide, and finally add and subtract. If there are brackets, calculate first.

2. Real numbers

Irrational number: Infinitely circulating decimals are called irrational numbers.

Square root: 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. If the square of a number X is equal to A, then this number X is called the square root of A. (3) A positive number has two square roots /0 square root is 0/ negative number without square root. (4) Find the square root of a number, which is called the square root, where a is called the square root.

Cubic root: ① If the cube of a number X is equal to A, then this number X is called the cube root of A. ② The cube root of a positive number is positive, the cube root of 0 is 0, and the cube root of a negative number is negative. The operation of finding the cube root of a number is called square root, where a is called square root.

Real numbers: ① Real numbers are divided into rational numbers and irrational numbers. ② In the real number range, the meanings of reciprocal, reciprocal and absolute value are exactly the same as those of reciprocal, reciprocal and absolute value in the rational number range. ③ Every real number can be represented by a point on the number axis.

3. Algebraic expressions

Algebraic expression: A single number or letter is also an algebraic expression.

Merge similar items: ① Items with the same letters and the same letter index are called similar items. (2) Merging similar items into one item is called merging similar items. (3) When merging similar items, we add up the coefficients of similar items, and the indexes of letters and letters remain unchanged.

4. Algebraic expressions and fractions.

Algebraic expression: ① The algebraic expression of the product of numbers and letters is called monomial, the sum of several monomials is called polynomial, and monomials and polynomials are collectively called algebraic expressions. ② In a single item, the index sum of all letters is called the number of times of the item. ③ In a polynomial, the degree of the term with the highest degree is called the degree of this polynomial.

Algebraic expression operation: when adding and subtracting, if you encounter brackets, remove them first, and then merge similar items.

Power operation: AM+AN=A(M+N)

(AM)N=AMN

(A/B)N=AN/BN division.

Multiplication of algebraic expressions: ① Multiply the monomial with the monomial, respectively multiply their coefficients and the power of the same letter, and the remaining letters, together with their exponents, remain unchanged as the factors of the product. (2) Multiplying polynomial by monomial means multiplying each term of polynomial by monomial according to the distribution law, and then adding the products. (3) Polynomial multiplied by polynomial. Multiply each term of one polynomial by each term of another polynomial, and then add the products.

Function and circle are the key points, accounting for a large proportion.

Some knowledge such as probability accounts for a small part,

This has basically been the case over the years.