New People's Education Edition Eighth Grade Mathematics Textbook Catalogue
Chapter 16 Quadratic Radicals
16. 1 quadratic radical
16.2 multiplication and division method of quadratic radical
Addition and subtraction of 16.3 quadratic radical
Mathematical activities
summary
Review questions 16
Chapter 17 Pythagorean Theorem
17. 1 Pythagorean theorem
Inverse Theorem of Pythagorean Theorem 17.2
Mathematical activities
summary
Review questions 17
Chapter 18 Parallelogram
18. 1 parallelogram
18.2 Special parallelogram
Mathematical activities
summary
Review questions 18
Chapter 19 Linear Functions
19. 1 function
19.2 linear function
14.3 project learning options
Mathematical activities
summary
Review questions 19
Chapter 20 Data Analysis
20. 1 data concentration trend
20.2 degree data fluctuation
20.3 Data Analysis in Physical Fitness Test of Project Learning
Mathematical activities
summary
Review question 20
Index of some Chinese and English words
People's education press eighth grade mathematics book 2 knowledge induction: quadrilateral
A quadrilateral with two sets of parallel opposite sides is called a parallelogram.
The nature of parallelogram: the opposite sides of parallelogram are equal; Diagonal angles of parallelogram are equal. Diagonal bisection of parallelogram.
Determination of parallelogram;
1. Two groups of quadrangles with equal opposite sides are parallelograms;
2. The quadrilateral whose diagonal lines bisect each other is a parallelogram;
3. Two groups of quadrangles with equal diagonal are parallelograms;
4. A set of quadrilaterals with parallel and equal opposite sides is a parallelogram.
The midline of the triangle is parallel to the third side of the triangle and equal to half of the third side.
The center line of the hypotenuse of a right triangle is equal to half of the hypotenuse.
The nature of the rectangle: all four corners of the rectangle are right angles; The diagonals of a rectangle are equally divided.
Rectangular judgment theorem;
1. A parallelogram with a right angle is called a rectangle.
2. Parallelograms with equal diagonals are rectangles.
A quadrilateral with three right angles is a rectangle.
The nature of the diamond: all four sides of the diamond are equal; The two diagonals of the diamond are perpendicular to each other, and each diagonal bisects a set of diagonals.
Judgement theorem of diamonds;
1. A set of parallelograms with equal adjacent sides is a diamond.
2. Parallelograms with diagonal lines perpendicular to each other are diamonds.
A quadrilateral with four equilateral sides is a diamond.
S diamond = 1/2? Ab(a and B are two diagonal lines)
The essence of a square: all four sides are equal and all four corners are right angles.
A square is both a rectangle and a diamond.
Square judgment theorem;
1. A rectangle with equal adjacent sides is a square.
Diamonds with right angles are squares.
A set of quadrangles with parallel opposite sides and another set of quadrangles with non-parallel opposite sides are called trapezoid.
The nature of isosceles trapezoid: the two angles on the same base of isosceles trapezoid are equal; The two diagonals of an isosceles trapezoid are equal.
Judgment theorem of isosceles trapezoid: two trapezoid with equal angles on the same base are isosceles trapezoid.
The center of gravity of the line segment is the midpoint of the line segment.
The center of gravity of a parallelogram is the intersection of its two diagonals.
The point of doubt when three center lines of a triangle meet is the center of gravity of the triangle.
A rectangle with an aspect ratio of (root number 5- 1)/2 (about 0.6 18) is called a golden rectangle.
Knowledge induction of the eighth grade mathematics volume II of People's Education Press: data analysis
1. Arithmetic average:
2. Weighted average: the calculation formula of weighted average.
Understanding of weight: It reflects the importance of a certain data in the whole data.
But in the form of ratio or percentage, the weighted average value is obtained by using the frequency distribution table.
3. Arrange a set of data in order from small to large (or from large to small). If the number of data is odd, the middle number is the median of this set of data; If the number of data is even, the average of the middle two data is the median of this set of data.
4. The data with the highest frequency in a set of data is the pattern of this set of data.
5. The difference between the maximum data and the minimum data in a set of data is called the range of this set of data.
6. The greater the variance, the greater the data fluctuation; The smaller the variance, the smaller the data fluctuation and the more stable it is.
Data collection and sorting steps: 1. Data collection II. Data arrangement 3. Data description 4. Data analysis. Investigation report writing. Communication.