Summary of Mathematics Knowledge Points in Volume II of Grade One of Beijing Normal University Edition
1. 1 positive and negative numbers
A number preceded by a minus sign "-"is called a negative number.
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 number
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 rationalnumber.
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 reciprocal 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 number 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 number 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. mì
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 called radix and n is called 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.
Mathematics knowledge points in the second volume of the seventh grade
Probability; possibility
I. Events:
1. Events are divided into inevitable events, impossible events and uncertain events.
2. Inevitable events: events that will definitely happen in advance. In other words, the event must happen every time, and it is impossible not to happen, that is, what may happen is 100% (or 1).
3. Impossible events: events that will definitely not happen in advance. In other words, there is no chance at all, that is, the possibility of occurrence is zero.
4. Uncertain event: it is impossible to determine whether it will happen in advance, that is, the event may or may not happen, that is, the probability of occurrence is between 0 and 1.
Second, equal possibility: refers to the equal possibility of several events.
1. probability: it is a quantity that reflects the possibility of an event. It is a proportional number, generally expressed by p, and P(A)= the number of possible outcomes of event A/all possible outcomes.
2. The probability of the inevitable event is 1, and it is recorded as p (inevitable event) =1;
3. The probability of an impossible event is 0, and it is recorded as p (impossible event) = 0;
4. The probability of uncertain events is between 0 and 1, and it is recorded as 0.
Third, geometric probability.
1, the probability of the occurrence of event A is equal to the area of the possible result of this event A (expressed by SA) divided by the area of the graph of all possible results (expressed by S total), so the geometric probability formula can be expressed as P(A)=SA/S total, because the probability of the occurrence of events in each unit area is the same.
2. Find the geometric probability:
(1) Firstly, analyze the relationship between the area occupied by events and the total area;
(2) Then calculate the area of each part;
(3) Finally, the geometric probability is obtained by substituting into the formula.
Review method of mathematics in grade one of junior high school
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.
Coefficient and times of single item: the non-zero numerical factor in single item is called the numerical coefficient of single item, referred to as the coefficient of single item for short; 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.
Summarize and sort out the relevant articles about the knowledge points of junior one mathematics;
★ 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 points of seventh grade mathematics in junior high school.
★ High school mathematics knowledge points induction.
★ Induction and learning methods of mathematics knowledge points in senior one.
★ Small induction of mathematics knowledge points in senior one.
★ What are the key knowledge points of junior high school mathematics?
★ arrangement of key knowledge in the first volume of junior one mathematics
★ Arrangement of Mathematics Knowledge Points in Senior One.
★ Summarize the knowledge points of junior high school mathematics.