Mathematicians also study pure mathematics, that is, mathematics itself, without aiming at any practical application. Although a lot of work begins with learning pure mathematics, it may find a suitable application later. The following is a summary of the mathematical knowledge points I have compiled, and you are welcome to refer to it!

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

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