Chapter 1: Entering the world of mathematics.
1, point to line, line to surface, surface to body.
2. Faces intersect to get lines, and lines intersect to get points.
3.n prism face: n+2 sides (edges): 3n vertex: 2n.
4. Definition of cross-section: Geometry is cut by plane, and the section is called cross-section.
5. The cross section of a cube can be triangular, quadrilateral, pentagonal or hexagonal.
6. The geometric cross section consists of the intersection line between the plane and the geometric surface.
7. In a prism, the intersection of any two adjacent faces is called an edge, and the intersection of two adjacent sides is called a side. All sides of a prism are equal in length.
8. The upper and lower layers of the prism have the same shape, and the sides are rectangular.
9. Polygon features: n-3 diagonals and n-2 triangles can be obtained from the same vertex.
10. Generally, we call the view from the front a front view, the view from the left a left view, and the view from above a top view.
1 1. The number of columns in the front view is the same as that in the top view.
12. The part between point A and point B on the circle is called an arc, and the figure consisting of an arc and two radii passing through the end point of this arc is called a sector. A circle can be divided into several sectors.
Chapter II Rational Numbers
1, 5,1.2 ... and so on are called positive numbers, and they are all greater than 0.
2. Numbers preceded by "-"are called negative numbers, such as-10, -3…
3,0 is neither positive nor negative.
4. Integer: positive integer, zero and negative integer.
5. Score: positive score and negative score.
6. Integers and fractions are collectively called rational numbers.
7. Draw a horizontal straight line, take a point on the straight line to represent 0 (called the origin), choose a certain length as the unit length, and specify the right direction on the straight line as the positive direction, and you will get the following axes. Three elements: origin, unit length and positive direction.
8. Any rational number can be represented by a point on the number axis.
9. If two numbers are only different in sign, then we call one of them the inverse of the other number, which is also called the inverse of each other. In particular, the reciprocal of 0 is 0.
10, two points in opposite directions, located on both sides of the origin, have the same distance from the origin.
1 1, the books represented by two points on the number axis are always bigger on the right than on the left.
12, positive number greater than 0, negative number less than 0, positive number greater than negative number.
13, absolute value definition:
Geometric definition: On the number axis, the distance between the point corresponding to a number and the origin is called the absolute value of the number.
Algebraic definition: 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.
14, two negative numbers are larger, and the larger absolute value is smaller.
15, rational number addition rule: add two numbers with the same sign, take the same sign, and add the absolute values.
Two numbers with different signs are added, and the sum is 0 when the absolute values are equal; When the absolute values are not equal, take the sign of the number with the larger absolute value and subtract the smaller absolute value from the larger absolute value.
Add a number to 0 and you still get the number.
Two numbers with opposite numbers add up to zero.
16, rational number addition step: ① first judge the symbol ② take the symbol ③ add (subtract) the absolute value.
17, commutative law of addition: a+b=b+a (note: A and B can be arbitrary rational numbers).
The associative law of addition: (a+b)+c=a+(b+c) Note: They are antonyms, integers, denominators and symbols.
18, rational number subtraction rule: subtracting a number is equal to adding the reciprocal of this number.
19. Subtraction steps: ① The minus sign becomes a plus sign; ② Subtraction becomes its inverse; ③ rational number addition calculation.
20. Subtraction can be converted into addition. The same symbol is positive, but different symbols are negative.
2 1. In addition, you can omit the brackets and the plus sign before them.
22. Add and subtract mixed operation steps: ① minus sign to plus sign ② additive commutative law sum associative law.
23. Rational number multiplication rule: two numbers are multiplied, the same sign is positive, the different sign is negative, and the absolute value is multiplied. Multiply any number by 0, and the product is still 0.
24. Two rational numbers whose product is 1 are reciprocal.
25. The sign of the product is determined by the number of negative factors. When there are odd negative factors, the sign of the product is negative, and when there are even negative factors, the sign of the product is positive.
26. Multiplicative commutative law: ab=ba
Law of multiplicative association: (a×b)×c=a×(b×c)
The distribution law of multiplication to addition: a×(b+c)=ab+ac.
27. Division rule: ① Divide two rational numbers, the same sign is positive, the different sign is negative, and the absolute value is divided. Divide 0 by any number except 0 to get 0.
Note: 0 cannot be divided.
(2) Dividing by a number equals multiplying by its reciprocal.
28. This operation of finding the product of n identical factors A is called power, the result of power is called power, A is called base, and N is called exponent.
29. The zeroth power of any number is equal to 1.
30. Any number of positive numbers is positive; The odd power of a negative number is negative and the even power of a negative number is positive.
3 1, first calculate the power, then multiply and divide, and finally add and subtract. If there are brackets, count them first.
Chapter III Addition and subtraction of algebraic expressions
1, algebraic expression:
(1) Features: ① There are letters or rational numbers ② There must be operation symbols.
(2) Definition: Formulas that connect rational numbers or letters with operational symbols are called algebraic expressions.
Note: Numbers come before letters. A single number or letter is also algebraic.
2. Monomial: An algebraic expression consisting of the product of numbers and letters, in which the number factor is called its coefficient. (A single letter or number is also a monomial) (A monomial without a letter is called a constant term)
3. Polynomial: the sum of several monomials. In polynomials, each monomial is called its term. Every term of a polynomial is preceded by a symbol.
4, the number of monomials: the exponential sum of all letters.
Polynomial Degree: The highest degree of all the monomials it contains.
5. Items with the same letter and the same letter index are called similar items. Merging similar items into one item is called merging similar items. All constant terms belong to the same category.
6. When merging similar items, we add up the coefficients of similar items, and the indexes of letters and letters remain unchanged.
7. Rules for deleting brackets: there is a "+"in front of brackets. After the brackets and the preceding "+"are removed, the symbols of the items in the meta brackets remain unchanged;
There is a "-"before the brackets. After removing the brackets and the "-"sign in front of them, the symbols of the original brackets will change.
The fourth chapter is a preliminary understanding of graphics.
1, taut chords and crosswalk lines can be approximately regarded as line segments. A line segment has two endpoints.
A line segment extending infinitely in one direction forms a ray. A ray has an endpoint.
A straight line is formed by an infinite extension of a line segment in two directions. A straight line has no end.
There is only one straight line after two o'clock.
3. Axiom: Of all the connecting lines between two points, the line segment is the shortest.
The length of the line segment between two points is called the distance between these two points.
4. Comparative length method:
Compare on the same straight line.
② Measure the length of line segment AB and line segment CD with a scale, and then compare them.
5, the definition of angle:
The (1) angle consists of two rays with a common endpoint, and the common point of the two rays constitutes the vertex of the angle.
(2) Angle can also be regarded as the time for light to rotate around its endpoint.
6. Angle representation:
① Use three capital letters and "∞" symbol, and the letter representing the vertex must be written among the three letters.
(2) When the sum symbol "∞" is represented by capital letters and the vertex has only one angle.
(3) Use the number and the symbol "∞" to add an arc to the corner.
④ Use a Greek letter and the symbol "∞" to add an arc to the corner.
7.∠AOB and ∠DOB have a common vertex and a common edge, and the OD edge falls within ∠AOB, indicating that ∠DOB is less than ∠AOB, and it is recorded as ∠ DOB < ∠ AOB.
8. Draw a ray from the vertex of an angle and divide the angle into two equal angles. This ray is called the bisector of this angle.
9. The 1/60 of 1 is1,and it is recorded as "1'", that is, 1 = 60'.
1/60 of 1' is 1 sec, and it is recorded as "1",that is, 1' = 60 ".
10, parallelism axiom: after passing a point outside a straight line, there is one and only one straight line parallel to this straight line.
Inference: If both lines are parallel to the third line, then the two lines are parallel to each other.
1 1. If two lines intersect at right angles, they are perpendicular to each other.
The intersection of two vertical lines is called vertical foot.
12. At a point on the plane, there is only one straight line perpendicular to the known straight line.
Of all the line segments connecting the outer point and the point on the line, the vertical line segment is the shortest. The vertical line passing through point A is L, the vertical foot is point B, and the length of vertical line AB is called the distance from point A to line L.
Chapter V Data Collection and Representation
1, data collection
2. Data representation