The induction of mathematics knowledge points in the second volume of the ninth grade
circle
★ Key points ① Important properties of the circle; (2) the positional relationship between straight lines and circles, and between circles; ③ Angle theorem related to circle; ④ Theorem of proportional line segment related to circle.
☆ Summary ☆
First, the basic properties of the circle
Definition of 1. circle (two kinds)
2. Related concepts: chord and diameter; Arc, equal arc, upper arc, lower arc, semicircle; Distance from chord to center; Equal circle, same circle, concentric circle.
3. "Three-point circle" theorem
4. Vertical Diameter Theorem and Its Inference
5. "Equivalence" theorem and its inference
6. Angle related to circle: (1) Definition of central angle (equivalence theorem)
(2) the definition of the angle of circle (the theorem of the angle of circle, the relationship with the angle of center)
⑶ Definition of chord angle (chord angle theorem)
Second, the positional relationship between a straight line and a circle
1. Properties of Tangents (Key Points)
2. Tangent (key point) judgment theorem
3. Tangent length theorem
Third, the position relationship between circles.
1. Five positional relationships and their judgments and properties: (emphasis: tangency)
2. The property theorem of the tangent (intersection line) connecting two circles.
3. Common tangent of two circles: (1) Definition (2) Property
Four, proportional line segment related to the circle
1. Intersecting chord theorem
2. Cutting line theorem
Verb (abbreviation for verb) and regular polygon
The inscribed and circumscribed polygons of 1. circle (triangle, quadrilateral)
2. The circumscribed circle, inscribed circle and properties of triangle.
3. The properties of circumscribed quadrangles and inscribed quadrangles of a circle
4. Regular polygon and its calculation
Central corner: review outline of junior high school mathematics
Half of the Inner Corner: Review Outline of Junior High School Mathematics (right)
(Solve Rt△OAM to find out the relevant elements, junior high school mathematics review outline, junior high school mathematics review outline, etc. )
Six, a set of calculation formulas
1. circumference formula
2. Formula of circular area
3. Sector area formula
4. Arc length formula
5. Calculation method of arch area
6. The side development diagram of cylinder and cone and related calculation.
Summary of mathematical knowledge points in the second volume of the third grade
First, acute angle trigonometric function
Sine equals the hypotenuse of the opposite side.
Cosine is equal to the ratio of adjacent side to hypotenuse.
The tangent is equal to the opposite side of the adjacent side.
Cotangent equals the comparison of adjacent edges.
Secant is equal to the hypotenuse than the adjacent edge.
Second, the calculation of trigonometric function
power series
c0+c 1x+c2x2+...+cnxn+...=∑cnxn(n=0..∞)
c0+c 1(x-a)+c2(x-a)2+...+cn(x-a)n+...=∑cn(x-a)n(n=0..∞)
Their terms are power functions of positive integer powers, where c0, c 1, c2, ... communication network (abbreviation of Communicating Net) ... and A are constants, and this series is called power series.
Taylor expansion (power series expansion method)
f(x)=f(a)+f'(a)/ 1！ . (x-a)+f''(a)/2！ . (x-a)2+...f(n)(a)/n！ . (x-a)n+ ...
Third, solve the right triangle
1. The two acute angles of a right triangle are complementary.
2. The three high intersections of a right triangle are at the same vertex.
3. Pythagorean theorem: the sum of squares of two right angles is equal to the square of hypotenuse.
Fourthly, measure the height with trigonometric function.
1, the application of solving right triangle
(1) Many related measurement problems in practical problems can be solved by solving right triangles.
For example, to measure the height and river width of an object that is difficult to measure directly, the key is to construct a right triangle. By measuring the degree of the angle and the length of the side, the required height or length of the object can be calculated.
(2) The general process of solving a right triangle is:
(1) abstract practical problems into mathematical problems (draw a plane figure, construct a right triangle, and transform it into solving right triangle problems).
(2) According to the known characteristics of the topic, choose the appropriate acute trigonometric function or angular relationship to solve the right triangle, get the answer to the mathematical problem, and then turn it into the answer to the actual problem.
Math learning skills in grade three
Attach importance to the construction of knowledge network-grasp the mathematical framework macroscopically
To learn how to build a knowledge network, mathematical concept is the starting point of building a knowledge network, and it is also the focus of the senior high school entrance examination mathematics [Weibo]. Therefore, we should master the concepts, classifications, definitions, properties and judgments of numbers, formulas, inequalities, equations, functions, trigonometric ratios, parallel lines, triangles, quadrangles and circles in algebra, and apply these concepts to solve some problems.
Attach importance to consolidating the dual foundation of mathematics-mastering micro-level knowledge and skills
To lay a solid foundation of mathematics in the review process, we should pay attention to the deepening of knowledge and strengthen the training of exercise groups-understanding mathematical thinking methods.
In addition to doing basic training questions and plane geometry once a day, you can also do some comprehensive questions to develop the habit of reflection after solving problems. Reflect on your own thinking process, knowledge points and problem-solving skills, the advantages and disadvantages of various solutions, and the vertical and horizontal relations of various methods. And summed up the mathematical thinking methods it used, grouped the topics with similar thinking methods into a group, and constantly refined and deepened them, so as to draw inferences from others. Gradually learn to observe, experiment, analyze, guess, induce, analogy, association and other ways of thinking, and actively find and ask questions.
Attach importance to the establishment of "case files"-to be foolproof
Prepare a "case card" for math study, write down the mistakes you usually make, find out the "reasons" and prescribe a "prescription". Take it out often and think about where the mistakes are, why they are wrong and how to correct them, so that when you enter the senior high school entrance examination, there will be no "cases" in your math. It is necessary to do a certain number of math exercises under the guidance of teachers, accumulate experience in solving problems, sum up ideas for solving problems, form ideas for solving problems, stimulate inspiration for solving problems, and master learning methods.
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