How should I master the difficult knowledge points in junior high school mathematics in three years?

Mathematics learning: 1. Take the foundation as the foundation and master the basic knowledge;

2. Do a good job of sorting out knowledge points and important and difficult points;

3. Do a good job of mind mapping for each unit to ensure that you master book knowledge;

4. Verify mathematical formulas by hands, and obtain better results through practice than rote memorization;

5. Do more questions, not to brush the questions, but to see why the teacher is so questionable, what knowledge points you want to test, what knowledge points can be combined with the examination, etc.

In addition, pay attention to cultivating interest in mathematics learning.

Pay attention to important high-frequency test points and do it repeatedly.

Use the K12 artificial intelligence education system to detect and quickly measure the knowledge points you don't know.

What are you asking after you say it...

Knowledge point 1: The basic concept of one-dimensional quadratic equations.

Knowledge point 2: Cartesian coordinate system and the position of points.

Knowledge point 3: The value of the known independent variable is calculated as the value of the function.

Knowledge point 4: The concept and properties of basic functions.

Knowledge point 5: median and mode of data.

Knowledge point 6: Special trigonometric values.

Knowledge point 7: The basic properties of circles.

1 The circumferential angle of a semicircle or diameter is a right angle.

2 Any triangle must have an external circle.

3 In the same plane, the trajectory of a point whose distance to a fixed point is equal to the fixed length is a circle with the fixed point as the center and the fixed length as the radius.

4 In the same circle or in an equal circle, the arcs opposite the central angles of equal circles are equal.

5 The circumferential angle of the same arc is equal to half of the central angle of the circle.

6 The radius of the same circle or equal circle is equal.

7 After three points, you can make a circle.

8 Two arcs of equal length are equal arcs.

9 In the same circle or in an equal circle, the arcs of the central angles of the circle that are equal are equal.

10 The diameter of the bisector chord through the center of the circle is perpendicular to the chord.

Knowledge point 8: The positional relationship between a straight line and a circle.

1 When a straight line has a unique common point with a circle, it is called a tangent between a straight line and a circle.

2 The outer center of the circumscribed circle of the triangle is called the outer center of the triangle.

3 The chord chamfer angle is equal to the central angle of the arc being clamped.

4 The inner inscribed center of the triangle is called the inner part of the triangle.

5 A straight line perpendicular to the radius must be a tangent of a circle.

6 A straight line that passes the outer end of the radius and is perpendicular to the radius is a tangent of the circle.

7 A straight line perpendicular to the radius is a tangent of a circle.

The tangent of the 8 circle is perpendicular to the radius of the tangent point.

Knowledge point 9: The position relationship between circles and circles.

The difficulties in middle school mathematics are the Pythagorean theorem, circles, and the inner and outer angles of triangles.

1. The Pythagorean theorem.

The proof of the Pythagorean theorem is the beginning of the argument geometry; The Pythagorean theorem is the first theorem in history to link numbers with shapes, that is, it is the first theorem to link geometry with algebra; The Pythagorean theorem led to the discovery of irrational numbers, caused the first mathematical crisis, and greatly deepened people's understanding of numbers; The Pythagorean theorem is the first indefinite equation in history to give a complete solution, which led to Fermat's theorem.

The Pythagorean theorem is the basic theorem of Euclidean geometry and has great practical value This theorem is not only a glorious pearl in geometry, known as the "cornerstone of geometry", but also has a wide range of applications in higher mathematics and other scientific fields. On 15 May 1971, Nicaragua issued a set of stamps entitled "Ten Mathematical Formulas That Changed the Face of the World", chosen by renowned mathematicians, with the Pythagorean theorem being the first of them.

2. Circle. A circle refers to a closed curve formed by a moving point centered on a certain point and rotated around a certain length at a distance, and the standard equation is (x-a) +y-b) =r, where the point (a, b) is the center of the circle and r is the radius.

A circle is a geometric figure and an axisymmetric, center-symmetrical figure. At the same time, the circle is a "positive infinite polygon", and the more sides of the polygon, the closer its shape, circumference, and area are to the circle. Since "infinity" is a concept, there is no real circle in the world, only a conceptual figure.

3. The inner and outer angles of the triangle burn.

The outer dust segment of the triangle is the angle of one side of the triangle and the opposite extension of the other side. The sum of the three outer angles of the triangle is 360°. The triangle has two equal outer angles at each vertex, so each triangle has six outer angles.

One of the outer angles of a triangle is greater than any of the interior angles that are not adjacent to it, and one of the outer angles of the triangle is equal to the sum of the two interior angles that are not adjacent.

In mathematics, the sum of the inner angles of a triangle is 180°, and the sum of the inner angles of a quadrilateral (polygon) is 360°. And so on, add an edge, and the sum of the internal angles is 180°. The internal angles and the formula are:

n 2) The number of internal angles of a 180° regular polygon is: (n 2) 180° n, e.g. the sum of the inner angles of a triangle is the sum of the three angles inside a triangle, and one inner angle is any one of the corners.

The geometric maximum-value problem refers to finding the maximum or minimum value of a certain quantity (such as line segment length, angle size, figure area, etc.) in a plane geometry under certain conditions. In the high school entrance examination, it is often in the form of fill-in-the-blank choice and solution questions, and the difficulty level is mostly difficult and finale. It is important to master the basic method of finding the geometric maximum:

1) Special position and extreme position method: first consider the special position or extreme position, determine the specific data of the maximum value, and then carry out the reasoning and proof under general circumstances (2) Geometric theorem (axiom) method: apply the properties and theorems of unequal quantities in geometry.

Common geometric properties are: the shortest line segment between two points; The point to straight perpendicular segment is the shortest; The sum of the two sides of the triangle is greater than the third side; The hypotenuse is larger than the right-angled edge (3) Combination of numbers and shapes: Analyze the algebraic relationship of the changing elements of the problem, construct quadratic functions, etc.

Algebraic maximums problems generally appear in the form of application problems, and the common question type is to find a scheme with the lowest cost, the least consumption, the highest output value, and the greatest profit. As one of the compulsory questions in the high school entrance examination in various places, the difficulty is mainly mid-range, which is a must for all students. The key point of solving this kind of problem is to reasonably establish a function model, on the basis of understanding the meaning of the problem, reasonably set the unknown quantity, analyze the equivalent relationship of the problem, list the analytic formula or equation of the function, solve it, discuss the meaning of the result and answer "Answer:

Do the ending. Pay special attention to the fact that if the listed equation is a fractional equation, you need to check the root increase!

The specific sample question types are as follows:

The key knowledge points of mathematics in the three years of junior high school are summarized as follows:

1. The relevant concepts of positive numbers and negative numbers: (1) Positive numbers: 0 numbers are called positive numbers; Negative: A number of 0 is called a negative number; 0 is neither positive nor negative; (2) Positive and negative numbers are opposites of the table.

2. Imitation of filial piety and classification of rational numbers.

3. Related number axis: (1) The three elements of the number axis: origin, forward direction, and unit length.

The number line is a straight line. (2) All rational numbers can be expressed by the points on the number line, but the points on the number line are not necessarily rational numbers. (3) On the number axis, the number on the right is always the number on the left; The point of the table positive number is to the right of the origin, and the point of the table negative number is to the left of the origin.

4. The absolute value of any number is negative. The most positive integer is 1, and the most negative integer is -1.

5. Comparison of the absolute value of profit: the comparison of two positive numbers: the number of the absolute value; The two negative numbers are compared: first calculate their absolute values, and the absolute values are inverse.

6. Addition of rational numbers:

1) The sum of two numbers with the same symbol: the sign of sum and the sign of two plus numbers, and the absolute value of sum is equal to the sum of the absolute values of two plus numbers; (2) the addition of two numbers with opposite signs: when the absolute value of two additions is not equal, the sign of the sum of the eggplant is the same as the sign of the addition of the absolute value, and the absolute value of the sum is equal to the absolute value of the addition minus the absolute value of the addition; When the absolute value of the two additions is equal, the two additions are opposite to each other, and the sum is zero; (3) If you add the number to zero, you will still get this number.

Commutative property of addition: a+b=b+a; Associative law of addition: (a+b)+c=a+(b+c).

7. Rational number subtraction: subtracting the number is equal to adding the opposite number of the number.