Chapter 1 Rational Numbers
1, numbers greater than 0 are positive numbers.
2. Rational number classification: positive rational number, 0, negative rational number.
3. Classification of rational numbers: integer (positive integer, 0, negative integer) and fraction (positive fraction, negative fraction).
4. Specify the origin and unit length, and the straight line in the positive direction is called the number axis.
5. Comparison of figures:
① Positive number is greater than 0, 0 is greater than negative number, and positive number is greater than negative number.
② When comparing two negative numbers, the larger absolute value is smaller.
6. Numbers with only two different symbols are called antonyms.
7. If a+b=0, A and B are reciprocal.
8. The distance from the point representing the number A to the origin is called the absolute value of the number A..
9. Three sentences of absolute value: 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.
10, calculation of rational number: calculate the symbol first, then calculate the value.
1 1, plus or minus: ① positive+② big-small ③ small-big =-(big-small) ④-☆-о =-(☆+о)
12. Multiplication and division: the same sign is positive and the different sign is negative.
13, power: represents the product of n identical factors.
14, the odd power of negative number is negative, and the even power of negative number is positive.
15, mixed operation: multiply first, then multiply and divide, and then add and subtract. The operation at the same level is from left to right, with parentheses first.
16, scientific counting method: use ax 10n to represent a number. (where a is an integer with only one digit)
17, all numbers are valid from the first non-zero number on the left.
Knowledge carding
1. number axis: three elements of number axis: origin, positive direction and unit length; There is a one-to-one correspondence between points on the number axis and real numbers.
2. the reciprocal of real number a is-a; If A and B are opposites, then a+b=0, and vice versa; Geometric meaning: on the number axis, two points representing the opposite number are located on both sides of the origin, and the distance to the origin is equal.
3. Reciprocal: If the product of two numbers is equal to 1, then these two numbers are reciprocal.
4. Absolute value: Algebraic meaning: the absolute value of a positive number is itself, the absolute value of a negative number is its opposite number, and the absolute value of 0 is 0;
Geometric meaning: the absolute value of a number is the distance from the point representing this number to the origin on the number axis.
5. Scientific symbol:, in which.
6. Real number comparison: compare the size according to the law; Use the number axis to compare sizes.
7. In the range of real numbers, addition, subtraction, multiplication, division and power operations can be performed, but the root operation may not work, for example, negative numbers can't even be opened. The operation basis of real numbers is rational number operation, and all the operation properties and laws of rational numbers are applicable to real number operation. It is the key to master the real number operation to correctly determine the symbol of the operation result and flexibly use the algorithm.
Summary of Basic Knowledge Points of Mathematics in Junior One (2)
Knowledge points of unary linear equation
Knowledge point 1: the concept of equality: an equation with an equal sign is called an equality.
Knowledge point 2: the concept of equation: an equation with unknown number is called an equation, and the equation must contain unknown number, and it must be an equation, and both are indispensable.
Note: algebraic expressions do not contain equal signs, equations are connected by equal signs, and must contain unknowns.
Knowledge point 3: The concept of linear equation of one variable: An equation with only one unknown number and the degree of the unknown number is 1 is called linear equation of one variable. Any form of linear equation can always be transformed into the form of ax=b(a≠0, A and B are known numbers). This form of equation is called the general formula of linear equation. Note a.