Main knowledge points of junior one mathematics:

Basic knowledge of algebra

1. Algebraic expression: the expression of the number of connections, and the letters indicating this number with the operation symbol "+-×℉ ..." are called algebraic expressions. Note: There are certain restrictions on using letters to represent numbers. First, the number obtained by letters should ensure that its formula is meaningful; second, the number obtained by letters should also make it meaningful in real life or production; A single number or letter is also algebraic.

2. Several important algebraic expressions: (m and n represent integers)

(1) The square difference between A and B is: A2-B2; The square of the difference between a and b is: (a-b) 2;

(2) If a, b and c are positive integers, the two-digit integer is 10a+b and the three-digit integer is10a+10b+c;

(3) If both m and n are integers, the quotient m is divided by 5, and the remainder n is 5m+n; Even number is 2n, and odd number is 2n+1; Three consecutive integers are: n- 1, n, n+1;

(4) If b>0, positive number is: a2+b, negative number is: -a2-b, non-negative number is: a2, and non-positive number is: -a2.

rational number

Any number that can be written in q/p form (p, q is an integer, p≠0) is a rational number. Positive integers, 0 and negative integers are collectively referred to as integers; Positive and negative scores are collectively called scores; Integers and fractions are collectively called rational numbers. Note: 0 is neither positive nor negative; -a is not necessarily negative, and +a is not necessarily positive; P is not a rational number;

Rational number addition rule:

(1) Add two numbers with the same symbol, take the same symbol, and add the absolute values;

(2) Add two numbers with different symbols, take the symbol with larger absolute value, and subtract the one with smaller absolute value from the one with larger absolute value;

(3) Adding a number to 0 still gets this number.

Arithmetic of rational number addition;

The commutative law of (1) addition: a+b = b+a; (2) The associative law of addition: (a+b)+c=a+(b+c).

Rational number subtraction rule: subtracting a number is equal to adding the reciprocal of this number; That is, a-b=a+(-b).

Rational number multiplication rule:

(1) Multiply two numbers, the same sign is positive, the different sign is negative, and the absolute value is multiplied;

(2) Multiply any number by zero to get zero;

(3) When several numbers are multiplied, one factor is zero and the product is zero; Each factor is not zero, and the sign of the product is determined by the number of negative factors.

Arithmetic of rational number multiplication;

(1) The commutative law of multiplication: ab = ba(2) The associative law of multiplication: (AB) C = A (BC);

(3) Distribution law of multiplication: a(b+c)=ab+ac.

Rational number division rule: dividing by a number is equal to multiplying the reciprocal of this number; Note: Zero cannot be divisible.

Addition and subtraction of algebraic expressions

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.

Single item's coefficient and number: the non-zero digital factor in a single item is called the single item's digital coefficient, which is simply called the single item's coefficient; When the coefficient is not zero, the sum of all the letter indexes in a single item is called the degree of the item.

Polynomial: The sum of several monomials is called polynomial.

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 degree term is called the degree of polynomial; Note: (If A, B, C, P and Q are constants) ax2+bx+c and x2+px+q are two common quadratic trinomials.

Algebraic expression: An algebraic expression without division or with division but without letters is called an algebraic expression.

One-dimensional linear equation

One-dimensional linear equation: an integral equation with only one unknown number, the degree of which is 1, and a one-dimensional linear equation with non-zero coefficient.

The standard form of one-dimensional linear equation: ax+b=0(x is unknown, a and b are known numbers, a≠0).

The simplest form of a linear equation with one variable: ax=b(x is unknown, a and b are known numbers, a≠0).

The general steps of solving a linear equation with one variable: sorting out the equation ... removing the denominator ... dismantling the bracket ... changing the terms ... merging similar terms ... converting the coefficient into 1 ... (testing the solution of the equation).

Common formulas for solving application problems with column equations;

(1) Travel problem: distance = speed time;

(2) Engineering problems: workload = work efficiency and working time;

(3) ratio: part = total ratio;

(4) Downstream problem: Downstream velocity = still water velocity+water velocity, and countercurrent velocity = still water velocity-water velocity;

(5) Commodity price: selling price = pricing discount 0. 1, profit = selling price-cost;

(6) Perimeter, area and volume: C circle =2πR, S circle =πR2, C rectangle =2(a+b), S rectangle =ab, C square =4a, S square =a2, S ring =π(R2-r2), V cuboid =abc, V cube =a3, V cylinder.