Eight-grade mathematics knowledge points
Collection, collation and description of data
I. Knowledge framework
Two. The concept of knowledge
1. Comprehensive survey: The survey method for all the subjects is called comprehensive survey.
2. Sampling survey: The survey method of investigating some data and estimating the whole according to some data is called sampling survey.
3. Population: All the investigated objects are called population.
4. Individuals: Each survey object that constitutes the population is called an individual.
5. Sample: All the extracted individuals constitute a sample.
6. Sample size: The number of individuals in a sample is called sample size.
7. Frequency: Generally speaking, the number of times the data falls into different groups is called the frequency of that group.
8. Frequency: The ratio of frequency to total data is frequency.
9. Number of groups and distance between groups: When counting data, the data is divided into several groups according to a certain range, and the number of groups is called the number of groups, and the difference between the two ends of each group is called the distance between groups.
The induction of mathematics knowledge points in the last semester of Grade One and Grade Two.
Exploration of quadrilateral properties
Definition: If two straight lines are parallel to each other, the distance between any two points on one straight line and the other straight line is equal, which is called the distance between parallel lines.
Parallelogram: Two sets of quadrangles with parallel opposite sides. The opposite sides are equal, the diagonal lines are equal, and the diagonal lines are equally divided. Two groups of parallelograms with parallel opposite sides are parallelograms, two groups of parallelograms with equal opposite sides are parallelograms, and one group of parallelograms with parallel and equal opposite sides are parallelograms.
Diamond: A group of parallelograms with equal adjacent sides (the nature of parallelograms). Four sides are equal, two diagonal lines are perpendicular to each other, and each diagonal line bisects a set of diagonal lines. A set of parallelograms with equal adjacent sides is a rhombus, a parallelogram with vertical diagonal is a rhombus, and a quadrilateral with equal four sides is a rhombus.
Rectangle: A parallelogram with a right angle (the nature of a parallelogram). Diagonal lines are equal and all four corners are right angles. A parallelogram with right angles is a rectangle, and a parallelogram with equal diagonal lines is a rectangle.
Square: A group of rectangles with equal adjacent sides. A square has all the properties of parallelogram, rhombus and rectangle. A set of rectangles with equal adjacent sides is a square, and a diamond with right angles is a square.
Trapezoid: a quadrilateral with parallel opposite sides and non-parallel opposite sides. A quadrilateral whose opposite sides are parallel and whose opposite sides are not parallel is a trapezoid. Isosceles trapezoid: A trapezoid with two equal waists. The two internal angles on the same base are equal and the diagonal lines are equal. A trapezoid with two equal waists is an isosceles trapezoid, and a trapezoid with two equal inner angles on the same base is an isosceles trapezoid.
Right trapezoid: A trapezoid with a vertical waist and bottom. The trapezoid with vertical waist bottom is a right-angled trapezoid.
Polygon: On a plane, a closed figure composed of several line segments that are not on the same line is called a polygon. The sum of the internal angles of an N-polygon is equal to (n-2)× 180.
The angle formed by the extension line with one side of the inner angle of a polygon opposite to the other side is called the outer angle of this polygon. The sum of the outer angles of a polygon is equal to 360 degrees. Triangles, quadrilaterals and hexagons can be densely laid.
Definition: On the plane, a figure rotates around a point 180. If the figures before and after rotation overlap, then this figure is called a central symmetric figure, and this point is called its symmetric center.
The line segments connected by each pair of corresponding points on the central symmetric figure are equally divided by the symmetric center.
Mathematics learning methods and skills
Remember what you should remember, remember what you should recite, and don't think you understand.
Some students think that mathematics is not like English, history and geography. Words, dates, and place names are required. Mathematics depends on wisdom, skill and reasoning. I said you were only half right. Mathematics is also inseparable from memory.
Therefore, mathematical definitions, rules, formulas, theorems, etc. Must recite, some can recite, catchy. For example, the familiar "Three Formulas of Algebraic Multiplication", I think some of you here can recite it, while others can't. Here, I want to remind the students who can't recite these three formulas. If they can't recite it, it will cause great trouble for future study, because these three formulas will be widely used in future study, especially the factorization of senior two, in which three very important factorization formulas are all derived from these three multiplication formulas, and they are deformations in opposite directions.
Remember the definitions, rules, formulas and theorems of mathematics, and remember those that you don't understand for the time being, and deepen your understanding on the basis of memory and application to solve problems. For example, mathematical definitions, rules, formulas and theorems are just like axes, saws, Mo Dou and planers in the hands of carpenters. Without these tools, carpenters can't make furniture. With these tools, coupled with skilled craftsmanship and wisdom, you can make all kinds of exquisite furniture. Similarly, if you can't remember the definition, rules, formulas and theorems of mathematics, it is difficult to solve mathematical problems. And remember these, plus certain methods, skills and agile thinking, you can be handy in solving mathematical problems, even solving mathematical problems.
1, the idea of "equation"
Mathematics studies the spatial form and quantitative relationship of things. The most important quantitative relationship in junior high school is equality, followed by inequality. The most common equivalence relation is "equation". For example, uniform motion, distance, speed and time are equivalent, and a related equation can be established: speed and time = distance. In this equation, there are generally known quantities and unknown quantities. An equation containing unknown quantities like this is an "equation", and the process of finding the unknown quantities through the known quantities in the equation is to solve the equation.
Energy conservation in physics, chemical equilibrium formula in chemistry, and a large number of practical applications in reality all need to establish equations and get results by solving them. Therefore, students must learn how to solve one-dimensional linear equations and two-dimensional linear equations, and then learn other forms of equations.
The so-called "equation" idea means that for mathematical problems, especially the complex relationship between unknown quantities and known quantities encountered in reality, we are good at constructing relevant equations from the viewpoint of "equation" and then solving them.
2. The idea of "combination of numbers and shapes"
In the world, "number" and "shape" are everywhere. Everything, except its qualitative aspect, has only two attributes: shape and size, which are left for mathematics to study. There are two branches of junior high school mathematics-algebra and geometry. Algebra studies "number" and geometry studies "shape". It is a trend to learn algebra by means of "shape" and geometry by means of "number". The more you learn, the more inseparable you are from "number" and "shape". In senior high school, a course called "Analytic Geometry" appeared, which used algebra to study geometric problems.
Summary of knowledge points in the second volume of eighth grade mathematics;
★ The arrangement of mathematics knowledge points in the second volume of the eighth grade
★ Summarize the 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.
★ Mathematics knowledge points in the second volume of the eighth grade
★ Sorting out the knowledge points in the second volume of eighth grade mathematics.
★ Summary of knowledge points in the second volume of Mathematics in the second day of junior high school.
★ Summary of knowledge points in the second volume of Mathematics in the second day of junior high school
★ Summary of the knowledge points that must be tested in mathematics in the second volume of the second day of junior high school
★ Sort out and summarize the knowledge points of eighth grade mathematics.