Key knowledge points of mathematics in the first volume of senior one: 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. Such as: π)
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.
Absolute value (1) Definition of absolute value: The absolute value of a number A is the distance between the point representing the number A on the number axis and the origin. The absolute value of the number a is recorded as |a|. (2) The absolute value of a positive number is itself; The absolute value of a negative number is its number; The absolute value of 0 is 0. ? a(a？ 0)? | One |? 0(a？ 0)a(a？ 0)? Is it getting bigger or bigger? a(a？ 0)|a|？ a(a？ 0)-3-2- 10 123(3) The nature of absolute value: ① Besides 0, there are two numbers whose absolute values are positive and the directions are opposite; ② The absolute values of two opposite numbers (except 0) are equal; That is |a|=|b|, then a+b=0③ The absolute value of any number is always non-negative, that is |a|≥0④ For any rational number A, there is |a|=|-a|5. Comparing the sizes of two negative numbers, the larger absolute value is smaller. The steps of comparing the sizes of two negative numbers are as follows: ① First, find the absolute values of two negative numbers; ② Compare two absolute values; ③ Make a correct judgment according to "two negative numbers, the larger absolute value is smaller".
The above is a summary of the key knowledge points of mathematics in the first volume of Grade One, and I hope it will help you. Please continue to pay attention to this site for more information about the senior high school entrance examination!