Mathematics Summary of Volume 2 of Grade 2, Grade 2
The first chapter scores
The numerator and denominator of 1 fraction and their basic properties are multiplied (or divided) by an algebraic expression that is not equal to zero at the same time, but the fraction remains unchanged.
Fractional operation of 2
(1) The law of multiplication, division and multiplication of fractions: Fractions are multiplied by fractions, the product of molecules is the numerator of the product, and the product of denominator is the denominator of the product. Law of division: a fraction is divided by a fraction, and the numerator and denominator of division are multiplied by the divisor in turn.
(2) Law of fractional addition and subtraction: fractional addition and subtraction with the same denominator, and numerator addition and subtraction with the same denominator; Fractions with different denominators are added and subtracted, first divided by fractions with the same denominator, and then added and subtracted.
Addition, subtraction, multiplication and division of exponential powers of three integers
4- Fractional Equation and Its Solution
Chapter II Inverse Proportional Function
Expressions, images and properties of 1 inverse proportional function
Image: hyperbola
Expression: y=k/x(k is not 0)
Nature: the increase and decrease of the two branches are the same;
2 the application of inverse proportional function in practical problems
Chapter III Pythagorean Theorem
Pythagorean Theorem of 1: The sum of squares of two right angles of a right triangle is equal to the square of the hypotenuse.
2 Pythagorean Theorem Inverse Theorem: If the sum of squares of two sides in a triangle is equal to the square of the third side, then the triangle is a right triangle.
The fourth chapter quadrilateral
1 parallelogram
Attribute: equilateral; Diagonally equal; Divide diagonally.
Judgment: two groups of quadrangles with equal opposite sides are parallelograms;
Two groups of quadrangles with equal diagonal are parallelograms;
Quadrilaterals whose diagonals bisect each other are parallelograms;
A set of quadrilaterals with parallel and equal opposite sides is a parallelogram.
Inference: The midline of a triangle is parallel to the third side and equal to half of the third side.
Special parallelogram: rectangle, diamond and square.
(1) rectangle
Properties: All four corners of a rectangle are right angles;
Diagonal lines of rectangles are equal;
A rectangle has all the characteristics of a parallelogram.
Judgment: a parallelogram with a right angle is a rectangle; Parallelograms with equal diagonals are rectangles;
Inference: The midline of the hypotenuse of a right triangle is equal to half of the hypotenuse.
(2) The nature of the diamond: all four sides of the diamond are equal; Diagonal lines of the rhombus are perpendicular to each other, and each diagonal line bisects a set of diagonal lines; A diamond has all the characteristics of a parallelogram.
Judgment: A set of parallelograms with equal adjacent sides is a diamond; Parallelograms with diagonal lines perpendicular to each other are rhombic; A quadrilateral with four equilateral sides is a diamond.
(3) Square: It is both a special rectangle and a special diamond, so it has all the properties of a rectangle and a diamond.
Trapezoid: right-angled trapezoid and isosceles trapezoid.
Isosceles trapezoid: two angles on the same bottom of isosceles trapezoid are equal; The two diagonals of isosceles trapezoid are equal; A trapezoid with two equal angles on the same base is an isosceles trapezoid.
Chapter V Data Analysis
Weighted mean, median, mode, range, variance
Mathematics knowledge necessary for the second day of junior high school
Position and coordinates
1, determine the location
In a plane, two data are usually needed to determine the position of an object.
2. Plane Cartesian coordinate system and related concepts
① Plane rectangular coordinate system
In a plane, two mutually perpendicular axes with a common origin form a plane rectangular coordinate system. Among them, the horizontal axis is called X axis or horizontal axis, and the right direction is the positive direction; The vertical axis is called Y axis or vertical axis, and the orientation is positive; The x-axis and y-axis are collectively referred to as coordinate axes. Their common origin o is called the origin of rectangular coordinate system; The plane on which the rectangular coordinate system is established is called the coordinate plane.
② Axis and quadrant
In order to describe the position of a point in the coordinate plane conveniently, the coordinate plane is divided into four parts, namely the first quadrant, the second quadrant, the third quadrant and the fourth quadrant.
Note: The points on the X axis and Y axis (points on the coordinate axis) do not belong to any quadrant.
(3) the concept of point coordinates
For any point P on the plane, the intersection point P is perpendicular to the X-axis and Y-axis respectively, and the numbers A and B corresponding to the vertical feet on the X-axis and Y-axis are respectively called the abscissa and ordinate of the point P, and the ordered number pair (A, B) is called the coordinate of the point P. ..
The coordinates of points are represented by (a, b), and the order is abscissa before, ordinate after, and there is a ","in the middle. The positions of horizontal and vertical coordinates cannot be reversed. The coordinates of points on the plane are ordered real number pairs, and (a, b) and (b, a) are the coordinates of two different points.
There is a one-to-one correspondence between points on the plane and ordered real number pairs.
④ Coordinate characteristics of points at different positions.
First, the coordinate characteristics of points in each quadrant
Point P(x, y) is in the first quadrant → x >; 0，y & gt0
Point P(x, y) is in the second quadrant → X.
Point P(x, y) is in the third quadrant → X.
Point P(x, y) is in the fourth quadrant → x >; 0，y & lt0
B, the characteristics of the points on the coordinate axis
The point P(x, y) is on the x axis → y=0, and x is an arbitrary real number.
The point P(x, y) is on the y axis → x=0, and y is an arbitrary real number.
Point P(x, y) is on both X and Y axes → x and Y are zero at the same time, that is, the coordinate of point p is (0,0), that is, the origin.
C, the characteristics of the coordinates of the points on the bisector of the two axes.
Point P(x, y) is on the bisector of the first and third quadrants (straight line y=x) → x equals y.
Point P(x, y) is on the bisector of the second and fourth quadrants → x and Y are reciprocal.
D, parallel to the axis. Coordinate characteristics of points on a straight line.
The ordinate of each point on the straight line parallel to the X axis is the same.
The abscissa of each point on the straight line parallel to the Y axis is the same.
E. coordinate characteristics of points symmetrical about the x-axis, y-axis or origin.
The abscissa of point P and point P' is equal to the X axis, and the ordinate is opposite, that is, the symmetrical point of point P(x, y) relative to the X axis is P'(x, -y).
The axisymmetrical ordinate of point P and point P' with respect to Y is equal, and the abscissa is opposite, that is, the symmetrical point of point P(x, y) with respect to Y axis is P'(-x, y).
Point P and point P' are symmetrical about the origin, and the abscissa and ordinate are opposite, that is, the symmetrical point of point P(x, y) about the origin is P'(-x, -y).
F, the distance from point to coordinate axis and origin
Distance from point P(x, y) to coordinate axis and origin:
The distance from the point P(x, y) to the X axis is equal to? y？
The distance from the point P(x, y) to the y axis is equal to? x？
The distance from the point P(x, y) to the origin is equal to √x2+y2.
Mathematics knowledge in the second day of junior high school is often tested.
linear function
1, function
Generally speaking, there are two variables, X and Y, in a certain change process. If a value of X is given and a value of Y is determined accordingly, then we call Y a function of X, where X is the independent variable and Y is the dependent variable.
2, the independent variable value range
The whole set of values of independent variables that make a function meaningful is called the range of independent variables. Generally speaking, we should consider algebraic expression (taking all real numbers), fraction (denominator is not 0), quadratic root (root is not negative) and practical significance.
3. Three representations of functions and their advantages and disadvantages.
Relationship (analysis) method The functional relationship between two variables can sometimes be expressed by an equation containing these two variables and the symbols of digital operations. This representation is called relational (analytical) method.
The list method lists a series of values of the independent variable X and the corresponding values of the function Y in a table to represent the functional relationship. This representation is called list method.
The method of expressing functional relations with images is called image method.
4. The general steps of drawing an image with functional relation.
List: List gives some corresponding values of independent variables and functions.
Tracing point: trace the corresponding point on the coordinate plane with each pair of corresponding values in the table as coordinates.
Connection: according to the order of independent variables from small to large, connect the traced points with smooth curves.
5, proportional function and linear function
① The concepts of proportional function and linear function.
Generally speaking, if the relationship between two variables X and Y can be expressed as Y = KX+B (where K and B are constants and K is not equal to 0), then Y is said to be a linear function of X (where X is the independent variable and Y is the dependent variable).
Especially when the linear function y=kx+b=0 (k is constant and k is not equal to 0), it is called that y is the proportional function of x (2) the image of linear function:
The image of all linear functions is a straight line.
③ Main features of linear function and proportional function images.
The image with linear function y=kx+b is a straight line passing through point (0, b);
Related articles on mathematical knowledge points in the second volume of the second day of junior high school:
★ The arrangement of mathematics knowledge points in the second volume of the eighth grade
★ Knowledge point induction and mathematics learning methods in the second volume of junior two mathematics.
★ Summarize the mathematics knowledge points in the second volume of the eighth grade.
★ Sort out and summarize the knowledge points of Grade 2 mathematics.
★ Sort out and summarize the knowledge points of eighth grade mathematics.
★ Summary of eighth grade mathematics knowledge points
★ Review and arrangement of mathematics knowledge points in Grade Two.
★ Summary of Mathematics Knowledge Points in Senior Two.
★ The eighth grade focus of junior high school mathematics
★ The first volume of mathematics knowledge points induction of the second grade teaching edition.