Rational number knowledge points in junior one mathematics
I. Knowledge framework
Two. The concept of knowledge
1. rational number:
(1) Any number that can be written in form 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; Not a rational number;
(2) Classification of rational numbers: ① ②
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) The sum of enantiomers is 0a+b=0a, and B is the enantiomer.
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;
(2) The absolute value can be expressed as: or; The problem of absolute value is often discussed in categories;
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; If ab= 1a and b are reciprocal; If ab=- 1a 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. 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.
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. 。
14. Definition of power:
(1) The operation of seeking common ground factor product is called power;
(2) In power, the same factor is called base, the number of the same factor is called exponent, and the result of power is called power;
15. scientific notation: write a number greater than 10 as a? 10n, where a is an integer with only one bit. 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.
Knowledge points of mathematics corner in the first day of junior high school.
Type of angle: the size of the angle has nothing to do with the length of the side; The size of an angle depends on the degree to which both sides of the angle are open. The bigger the opening, the bigger the angle. Conversely, the smaller the opening, the smaller the angle. In dynamic definition, it depends on the direction and angle of rotation. Angles can be divided into acute angle, right angle, obtuse angle, right angle, rounded corner, negative angle, positive angle, upper angle, lower angle and 0 angle, which are 10 respectively. An angle measuring system in degrees, minutes and seconds is called an angle system. In addition, there are secret system, arc system and so on.
Acute angle: greater than 0? Less than 90? This angle is called acute angle.
Right angle: equal to 90? This angle is called a right angle.
Oblique angle: greater than 90? And less than 180? This angle is called obtuse angle.
Boxer: equal to 180? This angle is called a right angle.
Excellent angle: greater than 180? Less than 360? This is called an actor.
Error angle: greater than 0? Less than 180? It is called a bad angle, and acute angle, right angle and obtuse angle are all bad angles.
Fillet: 360? Trumpets are called rounded corners.
Negative angle: the angle formed by clockwise rotation is called negative angle.
Positive angle: the angle of counterclockwise rotation is positive angle.
Angle 0: An angle equal to zero.
Complementary angle and complementary angle: the sum of the two angles is 90? So the two angles are complementary, and the sum of the two angles is 180? These two angles are complementary. The complementary angles of equal angles are equal, and the complementary angles of equal angles are equal.
Inverse vertex angle: When two straight lines intersect, there is only one common vertex, and both sides of the two corners are opposite extension lines. These two angles are called antipodal angles. Two straight lines intersect to form two pairs of vertex angles. The two opposite angles are equal.
There are also many kinds of angle relationships, such as internal dislocation angle, congruent angle and internal angle of the same side (in the three-line octagon, it is mainly used to judge parallelism)!
High school mathematics geometry figure classification knowledge points.
(1) solid geometry can be divided into the following categories:
The first category: cylinders;
Comprises a cylinder and a prism, wherein the prism can be divided into a straight prism and an oblique prism, and the prism can be divided into a triangular prism, a quadrangular prism and an N prism according to the number of sides of the bottom surface;
The volume of the prism is equal to the area of the bottom multiplied by the height, that is, V=SH,
The second category: cones;
Comprises a cone and a pyramid, wherein the pyramid is divided into a triangular pyramid, a quadrangular pyramid and an n-pyramid;
The pyramid volume is unified as V=SH/3,
The third category: sphere;
This classification contain only one geometric shape of a sphere,
Volume formula V=4? R3/3，
Other uncommon classifications: frustum of a cone, pyramid, spherical cap, etc. Rarely touched.
Most geometric figures are composed of these geometric figures.
(2) How to classify plane geometry?
A. circle
B Polygon: triangle (divided into general triangle, right triangle, isosceles triangle and equilateral triangle), quadrilateral (divided into irregular quadrilateral, figure and parallelogram, and parallelogram divided into rectangle, diamond and square), pentagon and hexagon.
Note: A square is both a rectangle and a diamond.
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