Sorting out and summarizing the basic knowledge of junior high school mathematics

Mathematics is a science about how to think, that is, it teaches us how to analyze and solve the relationship between quantity and quantity, the relationship between points and lines in space, and the relationship between lines. The following brings you some basic knowledge about junior high school, hoping to help you.

Summary of Junior High School Mathematics Basic Knowledge 1

The case of the root of a linear equation with one variable

△=b2-4ac

When △ > 0, a quadratic equation with one variable has two unequal real roots;

When △=0, the unary quadratic equation has two identical real roots;

When △ < 0, the quadratic equation of one variable has no real root.

Basic knowledge of junior high school mathematics II

Properties of parallelogram:

(1) Two groups of parallelograms with parallel opposite sides are called parallelograms.

(2) The line segment connected by two nonadjacent vertices of a parallelogram is called its diagonal.

③ The opposite sides/diagonals of parallelogram are equal.

(4) The diagonal of the parallelogram is equally divided.

Diamond: ① A group of parallelograms with equal adjacent sides is a diamond.

(2) The four sides of the collar are equal, and the two diagonal lines are equally divided vertically, and each diagonal line is equally divided into a set of diagonal lines.

③ Judgment conditions: define a parallelogram with vertical diagonal and a quadrilateral with equal sides.

Rectangular and square:

(1) There is a right-angled parallelogram called a rectangle.

② The diagonals of a rectangle are equal, and all four corners are right angles.

③ Parallelograms with equal diagonals are rectangles.

④ A square has all the properties of parallelogram, rectangle and diamond.

⑤ A set of rectangles with equal adjacent sides is a square.

Polygon:

① The sum of the internal angles of the N-polygon is equal to (N-2) 180 degrees.

(2) The angle formed by one side of the inner corner of a polygon and the extension line opposite to the other side is called the outer corner of the polygon. Take an outer angle of the polygon at each vertex, and their sum is called the sum of the inner angles of the polygon (both equal to 360 degrees).

Average: for n numbers X 1, x2...xn, we call it the arithmetic average of (x1+x2+...+xn)/n, and write it as x.

Weighted average: the importance of each data in a set of data may be different, so when calculating the average value of this set of data, each data is often given a weight, which is the weighted average.

Sorting out and summarizing the basic knowledge of junior high school mathematics III

Commonly used mathematical formulas

Formula classification formula expression

Multiplication and factorization a2-b2=(a+b)(a-b)

a3+b3=(a+b)(a2-ab+b2)

a3-b3=(a-b(a2+ab+b2)

Solution of quadratic equation in one variable -b+√(b2-4ac)/2a

-b-√(b2-4ac)/2a

The relationship between root and coefficient x1+x2 =-b/a.

X 1-X2=c/a note: Vieta theorem.

The sum of the first n terms of some series

1+2+3+4+5+6+7+8+9+…+n = n(n+ 1)/2

1+3+5+7+9+ 1 1+ 13+ 15+…+(2n- 1)= N2

2+4+6+8+ 10+ 12+ 14+…+(2n)= n(n+ 1)

12+22+32+42+52+62+72+82+…+N2 = n(n+ 1)(2n+ 1)/6

13+23+33+43+53+63+…n3 = N2(n+ 1)2/4

1-2+2-3+3-4+4-5+5-6+6-7+…+n(n+ 1)= n(n+ 1)(n+2)/3

Sine theorem a/sinA=b/sinB=c/sinC=2R.

Note: where r represents the radius of the circumscribed circle of the triangle.

Cosine theorem b2=a2+c2-2accosB

Note: Angle B is the included angle between side A and side C..

Sorting out and summarizing the basic knowledge of junior high school mathematics 4

Rational number size comparison:

Comparison of 1. rational numbers

The number axis can be used to compare the sizes of rational numbers, and their order is from left to right, that is, from big to small (the number on the right of two rational numbers represented on the number axis is always greater than the number on the left); You can also use the nature of numbers to compare the sizes of two numbers with different symbols and 0, and use absolute values to compare the sizes of two negative numbers.

2. The rational number size comparison law:

① Positive numbers are all greater than 0;

② Negative numbers are all less than 0;

③ Positive numbers are greater than all negative numbers;

(4) Two negative numbers, the greater the absolute value, the smaller it is.

Three methods of comparing rational numbers;

1. Rule comparison: all positive numbers are greater than 0, all negative numbers are less than 0, and all positive numbers are greater than all negative numbers. Two negative numbers are bigger, but the absolute value is bigger.

2. Number axis comparison: the number represented by the right point on the number axis is greater than that represented by the left point.

3. Compare the differences:

If a-b > 0, then a & gtb；;

If a-b

If a-b = 0, then a-b = 0 b.

Summarize the relevant articles about the basic knowledge of junior high school mathematics;

★ Summarize the basic knowledge points of junior high school mathematics.

★ Summary of basic knowledge points of junior high school mathematics

★ Arrangement of junior high school mathematics knowledge points:

★ Summary of junior high school mathematics knowledge points

★ Arrangement of junior high school mathematics knowledge points

★ Summary of junior high school mathematics knowledge points