Eight-grade mathematics knowledge points
data analysis
1, average
① Generally speaking, for n numbers x 1x2...xn, we take (x 1+x2+? +xn) is called the arithmetic average of the n numbers, and the average for short is recorded as.
② In practical problems, the "importance" of each data in a set of data may be different, so when calculating the average of this set of data, each data is often given a weight, which is called weighted average.
2. Median and mode
① Median: generally, n data are arranged in order of size, and the data in the middle position (or the average of the two data in the middle) is called the median of this group of data.
② The data with the highest frequency in a group of data is called the pattern of this group of data.
③ Average, median and mode are all statistics that describe the trend in data set.
(4) When calculating the average, all the data participate in the operation, which can make full use of the information provided by the data, so it is commonly used in real life, but it is easily influenced by extreme values.
⑤ Median has the advantage of simple calculation and little influence by extreme value, but it can't make full use of all data information.
⑥ When the number of repetitions of each data is roughly equal, the pattern often has no special meaning.
3. Analyze the concentration trend of data from the statistical chart.
4. Degree of data dispersion
① In real life, people not only pay attention to the concentration trend of data, but also pay attention to the degree of dispersion of data, that is, the degree of deviation from the concentration trend. The difference between the data in a set of data and the minimum data (called range) is a statistic that describes the degree of data dispersion.
② Mathematically, the dispersion degree of data can also be described by variance or standard deviation.
③ Variance is the average of the square of the difference between each data and the average.
(4) where x 1, the mean of x2 ... xn, s2 is the variance, and the standard deviation is the arithmetic square root of variance.
⑤ Generally speaking, the smaller the range, variance or standard deviation of a set of data, the more stable it is.
Senior two mathematics knowledge points
I. Polygons
1, polygon: A figure composed of many end-to-end line segments is called a polygon.
2. Polygon edge: The line segments that make up a polygon are called polygon edges.
3. Vertex of the polygon: The common * * * endpoint of each adjacent edge of the polygon is called the vertex of the polygon.
4. Diagonal line of polygon: The line segment connecting two non-adjacent vertices is called diagonal line of polygon.
5. The perimeter of a polygon: The sum of the lengths of each side of the polygon is called the perimeter of the polygon.
6. Convex polygon: Any side of the polygon extends in two directions. A polygon is called a convex polygon if all other sides of the polygon are adjacent to a straight line derived from an extension line.
Note: A polygon must have at least three sides, and the one with three sides is called a triangle. Those with four sides are called quadrilaterals; Things with several sides are called polygons. The polygons mentioned later refer to convex polygons unless otherwise specified.
7. Polygon angle: The angle formed by two adjacent sides of a polygon is called the inner angle of the polygon, which is simply called the angle of the polygon.
8. Exterior Angle of Polygon: The angle formed by the extension line opposite to one side of the corner of Polygon is called the exterior angle of Polygon.
Note: The outer angle of a polygon is the adjacent complementary angle between the inner angle and its common vertex.
9. Theorem of the sum of interior angles of polygons: the sum of interior angles of n sides is equal to (n-2) 180.
10, inference of the theorem of the sum of inner angles of polygons: the sum of outer angles of N-polygons is equal to 360.
Note: The sum of the outer angles of a polygon is a constant (independent of the number of sides), and it is simpler to solve related calculation problems by using it than by using the formula of the sum of the inner angles of a polygon and the diagonal formula. No matter which formula is used to solve the related calculation, it must be linked with solving the equation and master the calculation method.
Second, quadrilateral.
On the same plane, a figure with four line segments that are not on the same straight line connected end to end is called a quadrilateral.
Third, convex quadrilateral
If any side of a quadrilateral extends to both sides, if the other sides are on the same side of the extended line, such a quadrilateral is called a convex quadrilateral.
Fourth, diagonal line
In a quadrilateral, the line segment connecting two nonadjacent vertices is called the diagonal of the quadrilateral.
The instability of verb (verb's abbreviation) quadrilateral.
When the three sides of a triangle are determined, its shape and size are determined, which is the stability of the triangle. However, after the four sides of a quadrilateral are determined, its shape cannot be determined, which is the instability of the quadrilateral, which has a wide range of applications in production and life.
The theorem of sum of inner angles and the theorem of sum of outer angles of a hexagon.
Theorem of the sum of quadrilateral internal angles: the sum of quadrilateral internal angles is equal to 360.
Theorem of the sum of quadrilateral external angles: the sum of quadrilateral external angles is equal to 360.
Inference: theorem of polygon interior angle sum: the sum of n polygon interior angles is equal to180;
Theorem of the sum of external angles of polygons: the sum of external angles of any polygon is equal to 360.
Knowledge points of eighth grade mathematics text
1. Two straight lines that do not intersect in the same plane are called parallel lines, which can also be said to be parallel to each other. For example, 1, 1, the positional relationship between two straight lines in the same plane is (intersecting) and (parallel). When two straight lines intersect at right angles, they are said to be perpendicular to each other.
Parallelogram Rectangular rhombic square trapezoid isosceles trapezoid figure Two groups of quadrangles with parallel opposite sides. Define the parallelogram represented by "",for example: ABCD, the parallelogram ABCD is recorded as a plane with right angles, a group of parallelograms with equal adjacent sides are diamonds, and a group of parallelograms with equal adjacent sides are …
Chapter 18 Review of parallelogram knowledge points: characteristics of parallelogram and special parallelogram and their relationship 1. A rectangle is a special parallelogram, and its four internal angles are _ _ _ _ _. Diagonal line of the rectangle __2. The diamond is a special parallelogram, its four sides are _ _, and its two diagonals are flat …
Knowledge induction of special parallelogram and unary quadratic equation
diamond
1. Definition of rhombus: A group of parallelograms with equal adjacent sides is called a rhombus.
2. The nature of diamonds:
The properties of (1) rhombus are as follows: ① All properties of parallelogram; (2) all four sides are equal; ③ Diagonal lines are perpendicular to each other, and each diagonal line bisects a set of diagonal lines; (4) the diamond is the figure of symmetry axis, which has two symmetry axes, and these two symmetry axes are the straight lines where its two diagonals are located.
(2) rhombic area = bottom × height = half of diagonal product.
3. Diamond trial:
(1) is determined by definition (that is, a set of parallelograms with equal adjacent sides is a diamond).
(2) Parallelograms with diagonal lines perpendicular to each other are rhombic.
(3) A quadrilateral with four equilateral sides is a diamond.
To sum up, the common ideas for judging diamonds are:
There are four diamonds of equal sides.
Diamond quadrangle
parallel
A quadrilateral has a set of equilateral diamonds.
rectangle
1. Definition of rectangle: A parallelogram with a right angle is called a rectangle.
2. The properties of rectangle: (1) has all the properties of parallelogram; (2) All four corners of a rectangle are right angles;
(3) All four corners of a rectangle are equal.
4. The rectangle determination method:
(1) is determined by the definition (that is, a parallelogram with right angles is a rectangle);
(2) A quadrilateral with three right angles is a rectangle;
(3) Parallelograms with equal diagonals are rectangles.
To sum up, the common ideas for judging rectangles are:
square
1. Definition of a square: A group of parallelograms with equal adjacent sides and a right angle is called a square.
2. Properties of Square: Square has all the properties of parallelogram, rectangle and diamond.
(1) sides: four sides are equal, adjacent sides are vertical and opposite sides are parallel and equal.
1(2) Angle: All four angles are right angles.
(3) Diagonal lines: Diagonal lines are equal and bisected vertically, and each diagonal line bisects a set of diagonal lines.
3. The trial in the square
(1) According to the definition; (2) A rhombus with equal diagonals is a square;
(2) A diamond with a right angle is a square;
(3) A group of rectangles with equal adjacent sides are squares;
(4) A rectangle with diagonal lines perpendicular to each other is a square.
4. The relationship between special parallelograms
Rectangular and rhombic are special parallelograms, and square is a more special parallelogram, which is both rectangular and rhombic. The relationship between them is as follows:
5. The quadrilateral shape obtained by connecting the midpoints of the sides of the quadrilateral in turn:
(1) The quadrilateral obtained by connecting the midpoints of the sides of any quadrilateral in turn is a parallel deformation;
(2) The quadrangle obtained by sequentially connecting the midpoints of the sides of the quadrangle with equal diagonals is a rhombus;
(3) The quadrilateral obtained by connecting the midpoints of the sides of the quadrilateral with vertical diagonal lines in turn is a rectangle;
(4) The quadrangle obtained by connecting the midpoints of the sides of the quadrangle with vertical equal diagonal lines in turn is a square;
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