Definition: If A and B represent two algebraic expressions, and B contains letters, then this formula is called a fraction.

Second, the basic nature of the fraction: the numerator and denominator of the fraction are multiplied or divided by an algebraic expression that is not equal to 0, and the value of the fraction remains unchanged.

Third, the score calculation: the law of fractional multiplication: fractional multiplication, with the product of molecules as the numerator of the product and the product of denominator as the denominator.

Law of fractional division: a fraction is divided by a fraction, and the numerator and denominator of the divisor are in turn multiplied by the divisor.

Fractional power: Fractional power should provide power for numerator and denominator respectively.

4. Integer exponential power: (1) (2) scientific notation of smaller numbers;

5. Test method of fractional equation: bring the solution of the whole equation into the simplest common denominator. If the value of the simplest common denominator is not 0, the solution of the whole equation is the solution of the original fractional equation; Otherwise, this solution is not the solution of the original fractional equation. This solution is root increasing, and the original equation has no solution.

Chapter 17 Inverse proportional function

A function with the shape y= (k is constant, k≠0) is called an inverse proportional function;

Second, the image of inverse proportional function belongs to hyperbola;

Third, properties: when k>0, the two branches of hyperbola are located in the first quadrant and the third quadrant respectively, and the Y value of each quadrant decreases with the increase of X value;

When k < 0, the two branches of hyperbola are located in the second and fourth quadrants respectively, and the y value of each quadrant increases with the increase of x value.

Chapter 18 Pythagorean Theorem

1. Pythagorean Theorem: If the lengths of two right angles of a right triangle are A and B, and the length of the hypotenuse is C, then

Second, the inverse theorem of Pythagorean theorem: If the three sides of a triangle are A, B and C, then the triangle is a right triangle.

Third, a proposition that is proved to be correct is called a theorem.

Fourthly, we call two propositions with opposite topics and conclusions reciprocal propositions. If one of them is called the original proposition, then the other is called its inverse proposition. (Example: Pythagorean Theorem and Pythagorean Theorem Inverse Theorem)

Chapter 19 Quadrilateral

A, parallelogram:

1. Definition: A quadrilateral with two groups of opposite sides parallel to each other is called a parallelogram.

2. Nature: the opposite sides of the parallelogram are equal; The diagonals of parallelogram are equal; Diagonal bisection of parallelogram.

3. Judgment: (1) Two groups of quadrangles with equal opposite sides are parallelograms;

(2) Two groups of quadrangles with equal diagonals are parallelograms;

(3) The quadrilateral whose diagonals bisect each other is a parallelogram;

(4) A set of quadrilaterals with parallel and equal opposite sides is a parallelogram.

(5) A quadrilateral with two groups of opposite sides parallel to each other is called a parallelogram. (definition)

4. The midline of the triangle is parallel to the third side of the triangle, which is equal to half of the third side.

Second, the rectangle:

1. Definition: A parallelogram with a right angle is called a rectangle.

2. Nature: All four corners of a rectangle are right angles; The diagonals of a rectangle are equally divided.

3. Judgment: (1) A parallelogram with a right angle is called a rectangle. (definition)

(2) Parallelograms with equal diagonals are rectangles.

(3) A quadrilateral with three right angles is a rectangle.

4. The midline of hypotenuse of right triangle is equal to half of hypotenuse.

Third, diamonds:

1. Definition: A set of parallelograms with equal adjacent sides is a diamond.

2. Nature: All four sides of a diamond are equal; The two diagonals of the diamond are perpendicular to each other, and each diagonal bisects a set of diagonals.

3. Judgment: (1) A set of parallelograms with equal adjacent sides is a diamond. (definition)

(2) Parallelograms with diagonal lines perpendicular to each other are rhombic.

(3) A quadrilateral with four equilateral sides is a diamond.

4.S diamond = bottom × height S diamond = ab(a and B are two diagonal lines)

Fourth, the square:

1. Definition: A set of rectangles with equal adjacent sides is a square. Or a diamond with a right angle is a square.

2. Nature: all four sides are equal and all four corners are right angles; A square is both a rectangle and a diamond.

3. Judgment: (1) A rectangle with equal adjacent sides is a square.

(2) A diamond with a right angle is a square.

Five, trapezoidal:

1. Definition: A set of quadrangles with parallel opposite sides and another set of quadrangles with non-parallel opposite sides are called trapezoid.

2. Definition of isosceles trapezoid: An isosceles trapezoid is called an isosceles trapezoid.

Properties: the two angles on the same base of isosceles trapezoid are equal; The two diagonals of an isosceles trapezoid are equal.

Judgment: a trapezoid with two equal angles on the same base is an isosceles trapezoid; A trapezoid with equal diagonal lines is an isosceles trapezoid.

3. The trapezoid midline is parallel to the upper and lower bottom surfaces respectively and is equal to half of the sum of the upper and lower bottom surfaces.

Sixth, the center of gravity:

1, the center of gravity of the line segment is the midpoint of the line segment.

2. The center of gravity of parallelogram is the intersection of its two diagonals.

3. The doubt that the three midlines of the triangle meet is the center of gravity of the triangle.

Seven, mathematics activities (textbook 1 15 pages):

The angle proof method of 1, the origami uses more than 60, 30 and 15 (with emphasis on 30).

2. A rectangle with an aspect ratio (about 0.6 18) is called a golden rectangle.

Chapter 20 Data Analysis

I. Weighted average: calculation formula (textbook 125. )

Second, the median: arrange a set of data in the order from small to large (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.

Third, the mode: the data with the highest frequency in a group of data is the mode of this group of data.

4. Extreme extreme range: the difference between the maximum data and the minimum data in a set of data is called the extreme range of this set of data.

Verb (abbreviation for verb) differences:

1, calculation formula: (average representation)

2. Nature: The greater the variance, the greater the data fluctuation; The smaller the variance, the smaller the data fluctuation and the more stable it is.

Six, the steps of data collection and collation:

1. Collect data. Organization data 3. Description data 4. Analyze data 5. Write an investigation report.