Current location - Training Enrollment Network - Mathematics courses - What are the knowledge points of Guangzhou senior one mathematics?
What are the knowledge points of Guangzhou senior one mathematics?
What I bring to you is the knowledge points of the first book of junior one mathematics, the basic knowledge points about the classification and formula of rational numbers, hoping to help students master the algorithm of rational numbers.

1. rational number:

(3) Note: among rational numbers, 1, 0 and-1 are three special numbers with their own characteristics; These three numbers divide the numbers on the number axis into four areas, and the numbers in these four areas also have their own characteristics;

(4) Natural numbers? 0 and positive integer; a & gt0 ? A is a positive number; a & lt0 ? A is a negative number;

a≥0? Is it a positive number or 0? A is negative; a≤ 0? Is it negative or 0? A is a non-positive number.

2. Number axis: The number axis is a straight line that defines the origin, positive direction and unit length.

3. The opposite number:

(1) There are only two numbers with different signs, and we say that one of them is opposite to the other; The antonym of 0 is still 0;

(2) Note: The inverse of a-b+c is-A+B-C; The inverse of a-b is b-a; The inverse of a+b is-a -a-b;;

(3) Is the sum of opposites 0? a+b=0? A and b are opposites.

4. Absolute value:

(1) The absolute value of a positive number is itself, the absolute value of 0 is 0, and the absolute value of a negative number is its inverse; Note: the absolute value means the distance between the point representing a number on the number axis and the origin;

5. Rational number ratio: (1) The greater the absolute value of a positive number, the greater the number; (2) Positive numbers are always greater than 0 and negative numbers are always less than 0; (3) Positive numbers are greater than all negative numbers; (4) The absolute values of two negative numbers are larger than the size, but smaller; (5) Of the two numbers on the number axis, the number on the right is always greater than the number on the left; (6) large number-decimal number >; 0, decimal-large number < 0.

6. Reciprocal: Two numbers whose product is 1 are reciprocal; Note: 0 has no reciprocal; If a≠0, the reciprocal is; The reciprocal itself is a number of 1; If ab= 1? A and b are reciprocal; If ab=- 1? A and b are negative reciprocal.

7. The 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.

8. 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).

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

10 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.

1 1 rational number multiplication algorithm;

(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.

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

13. Power Law of Rational Numbers:

(1) Any power of a positive number is a positive number;

(2) The odd power of a negative number is a negative number; Even the power of negative numbers is positive; Note: When n is positive odd number: (-a)n=-an or (a -b)n=-(b-a)n, when n is positive even number: (-a)n =an or (a-b) n = (b-a) n. 。

15. Scientific notation: Write numbers greater than 10 in the form of a× 10n, where a is a number with only one integer digit. This notation is called scientific notation.

16. Approximation precision: a divisor rounded to that bit, that is, the divisor is accurate to that bit.

17. Significant digits: All digits from the first non-zero digit on the left to the exact digit are called significant digits of this approximation.

18. Mixed algorithm: multiply first, multiply then divide, and finally add and subtract; Note: How to calculate simply and accurately is the most important principle of mathematical calculation.

19. special value method: it is a method of substituting numbers that meet the requirements of the topic into speculation to verify the establishment of the topic, but it cannot be used for proof.