Induction of mathematical knowledge points in the last semester of senior two.
Position and coordinates
1, determine the location
In a plane, two data are usually needed to determine the position of an object.
2. Plane rectangular coordinate system
Meaning: In a plane, two mutually perpendicular axes with a common origin form a plane rectangular coordinate system.
(2) Usually, the two number axes are placed in horizontal and vertical positions respectively, and the right and upward directions are the positive directions of the two number axes respectively. The horizontal axis is called X axis or horizontal axis, and the vertical axis is called Y axis and vertical axis, both of which are collectively called coordinate axes, and their common origin O is called the origin of rectangular coordinate system.
③ Establish a plane rectangular coordinate system, and the points on the plane can be represented by a set of ordered real number pairs.
(4) In the plane rectangular coordinate system, two coordinate axes divide the coordinate plane into four parts, the upper right part is called the first quadrant, and the other three parts are called the second quadrant, the third quadrant and the fourth quadrant counterclockwise, and the points on the coordinate axes are not in any quadrant.
⑤ In the rectangular coordinate system, for any point on the plane, there is an ordered real number pair (that is, the coordinates of the point) corresponding to it; On the contrary, for any ordered real number pair, there is a point on the plane corresponding to it.
3. Axisymmetry and coordinate changes
Regarding the coordinates of two points about the axis symmetry of X, the abscissa is the same, and the ordinate is opposite; With regard to the coordinates of two points symmetrical about the Y axis, the ordinate is the same, and the abscissa is opposite.
Eighth grade mathematics knowledge point book 1
1, the corresponding edge of congruent triangles is equal to the corresponding angle.
2. Angular Axiom (SAS) has two sides and two triangles with equal included angles.
3. Angle and Angle Axiom (ASA) has congruence of two triangles, which have two angles and their sides correspond to each other.
4. Inference (AAS) has two angles, and the opposite side of one angle corresponds to the congruence of two triangles.
5. The side-by-side axiom (SSS) has two triangles with equal sides.
6. Axiom of hypotenuse and right-angled edge (HL) Two right-angled triangles with hypotenuse and a right-angled edge are congruent.
7. Theorem 1 The distance between a point on the bisector of an angle and both sides of the angle is equal.
8. Theorem 2 The point where two sides of an angle are equidistant is on the bisector of this angle.
9. The bisector of an angle is the set of all points with equal distance to both sides of the angle.
10, the property theorem of isosceles triangle, the two base angles of isosceles triangle are equal (that is, equilateral angles)
1 1, it is inferred that the bisector of the vertices of 1 isosceles triangle bisects the base and is perpendicular to the base.
12. The bisector of the top angle, the median line on the bottom edge and the height on the bottom edge of the isosceles triangle coincide with each other.
13, inference 3 All angles of an equilateral triangle are equal, and each angle is equal to 60.
14, the judgment theorem of isosceles triangle If a triangle has two equal angles, then the opposite sides of the two angles are also equal (equal angles and equal sides).
15, inference 1 A triangle with three equal angles is an equilateral triangle.
16, inference 2 An isosceles triangle with an angle equal to 60 is an equilateral triangle.
17. In a right-angled triangle, if an acute angle is equal to 30, the right-angled side it faces is equal to half of the hypotenuse.
18. The midline of the hypotenuse of a right triangle is equal to half of the hypotenuse.
19, it is proved that the distance between the point on the middle vertical line of a line segment and the two endpoints of the line segment is equal.
20. The inverse theorem and the point where the two endpoints of a line segment are equidistant are on the vertical line of this line segment.
2 1, the middle vertical line of a line segment can be regarded as the set of all points with the same distance at both ends of the line segment.
22. Theorem 1 Two graphs symmetric about a straight line are conformal.
23. Theorem 2 If two figures are symmetrical about a straight line, then the symmetry axis is the perpendicular line connecting the corresponding points.
24. Theorem 3 Two graphs are symmetrical about a straight line. If their corresponding line segments or extension lines intersect, then the intersection point is on the axis of symmetry.
25. Inverse Theorem If the straight line connecting the corresponding points of two graphs is vertically bisected by the same straight line, then the two graphs are symmetrical about this straight line.
26. Pythagorean Theorem The sum of squares of two right angles A and B of a right triangle is equal to the square of the hypotenuse C, that is, A 2+B 2 = C 2.
27. The Inverse Theorem of Pythagorean Theorem If the three sides of a triangle are related A 2+B 2 = C 2, then the triangle is a right triangle.
28. Theorem The sum of the internal angles of a quadrilateral is equal to 360 degrees.
29. The sum of the external angles of the quadrilateral is equal to 360.
30. Theorem The sum of the interior angles of a polygon is equal to (n-2) × 180.
3 1, it is inferred that the sum of the external angles of any polygon is equal to 360.
32. parallelogram property theorem 1 parallelogram diagonal is equal
33. parallelogram property theorem 2 The opposite sides of a parallelogram are equal
Math learning method in grade two of junior high school
orderly
Mathematics is an interlocking subject, and any link will affect the whole learning process. Therefore, don't be greedy when studying. You should pass the exam chapter by chapter, and don't leave questions that you don't understand or understand deeply easily.
Emphasize understanding
Concepts, theorems and formulas should be memorized on the basis of understanding. Every time you learn a new theorem, try to do an example without looking at the answer to see if you can correctly apply the new theorem; If not, compare the answers to deepen the understanding of the theorem.
basic skill
You can't learn mathematics without training. Usually do more exercises with moderate difficulty. Of course, don't fall into the misunderstanding of dead drilling questions, be familiar with the questions of the college entrance examination, and be targeted in training.
Pay attention to mistakes
Booking the wrong book and collecting the wrong questions by yourself is often your weakness. When reviewing, this wrong book has become a valuable review material.
Mathematics learning is a step-by-step process, and it is unrealistic to dream of reaching the sky in one step. After reciting the contents of the book, carefully write the exercises at the back of the book. Some students may think that the exercises after the book are too simple to do. This idea is highly undesirable. The function of the exercises after the book is not only to help you remember the contents in the book, but also to help you standardize the writing format, make your problem-solving structure compact and tidy, make proper use of formulas and theorems, and reduce unnecessary marks in the exam.
The usual mathematical research:
○ 1 preview carefully before class. The purpose of preview is to listen to the teacher better. Through preview, the mastery level should reach 80%. Listen to the teacher answer these questions with questions that you don't understand in the preview. Preview can also improve the overall efficiency of attending classes. Specific preview method: finish the topics in the book and draw the knowledge points. The whole process lasts about 10.
○2 Let math class combine with practice. It's no use just listening in math class. When the teacher asks the students to do calculus on the blackboard, they should also practice on the draft paper. You must ask questions you don't understand, or you may not do it if you encounter similar problems in the exam. When listening to the teacher's lecture, you must concentrate on the details, otherwise, "the embankment of a thousand miles will collapse in the ant nest."
○3 Review in time after class. After finishing your homework, sort out what the teacher said that day, and you can do extracurricular problems for about 25 minutes. You can choose the extracurricular books that suit you according to your own needs. The content of the extracurricular problem is probably today's class.
The fourth unit test is to test your recent study. In fact, the score represents your past. The key is to sum up and learn from each exam so that you can do better in the mid-term and final exams. Teachers often take exams without notice and review them in time after class.
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