Induction of the Essential Knowledge Points of Mathematics and Science in Senior Two 1
Derivative is an important basic concept in calculus. When the independent variable x of the function y=f(x) generates an increment δ x at the point x0, if there is a limit a in the ratio of the increment δ y of the function output value to the increment δ x of the independent variable when δ x tends to 0, then A is the derivative at x0, which is denoted as f'(x0) or df(x0)/dx.
Derivative is the local property of function. The derivative of a function at a certain point describes the rate of change of the function near that point. If the independent variables and values of the function are real numbers, then the derivative of the function at a certain point is the tangent slope of the curve represented by the function at that point. The essence of derivative is the local linear approximation of function through the concept of limit. For example, in kinematics, the derivative of the displacement of an object with respect to time is the instantaneous velocity of the object.
Not all functions have derivatives, and a function does not necessarily have derivatives at all points. If the derivative of a function exists at a certain point, it is said to be derivative at this point, otherwise it is called non-derivative. However, the differentiable function must be continuous; Discontinuous functions must be non-differentiable.
For differentiable function f(x), x? F'(x) is also a function called the derivative function of f(x). The process of finding the derivative of a known function at a certain point or its derivative function is called derivative. Derivative is essentially a process of finding the limit, and the four algorithms of derivative also come from the four algorithms of limit. Conversely, the known derivative function can also reverse the original function, that is, indefinite integral. The basic theorem of calculus shows that finding the original function is equivalent to integral. Derivation and integration are a pair of reciprocal operations, both of which are the most basic concepts in calculus.
Summary of the necessary knowledge points of mathematics and science in senior two II.
basic concept
Axiom 1: If two points on a straight line are in a plane, then all points on this straight line are in this plane.
Axiom 2: If two planes have a common point, then they have only one common straight line passing through this point.
Axiom 3: When three points that are not on a straight line intersect, there is one and only one plane.
Inference 1: Through a straight line and a point outside this straight line, there is one and only one plane.
Inference 2: Through two intersecting straight lines, there is one and only one plane.
Inference 3: Through two parallel straight lines, there is one and only one plane.
Axiom 4: Two lines parallel to the same line are parallel to each other.
Equiangular Theorem: If two sides of one angle are parallel and in the same direction as two sides of another angle, then the two angles are equal.
The positional relationship between two straight lines in space;
There are only three positional relationships between two straight lines in space: parallel, intersecting and nonplanar.
1, according to whether * * * surface can be divided into two categories:
(1)*** plane: parallel intersection.
(2) Different planes:
Definition of non-planar straight lines: two different straight lines on any plane are neither parallel nor intersecting.
Judgment theorem of out-of-plane straight line: use the straight line between a point in the plane and a point out of the plane, and the straight line in the plane that does not pass through this point is the out-of-plane straight line.
2, if from the perspective of the existence of public * * *, points can be divided into two categories:
(1) has only one thing in common-intersecting straight lines; (2) There is nothing in common-parallel or non-parallel.
Induction of necessary knowledge points of mathematics science in senior two 3.
1. Set, simple logic (14 class, 8) 1. Settings; 2. subset; 3. supplement; 4. Intersection; 5. Trade unions; 6. Logical connector; 7. Four propositions; 8. Necessary and sufficient conditions.
Second, the function (30 class hours, 12) 1. Mapping; 2. Function; 3. Monotonicity of the function; 4. Inverse function; 5. The relationship between function images of reciprocal function; 6. Extension of the concept of index; 7. Operation of rational exponential power; 8. Exponential function; 9. Logarithm; 10. Operational properties of logarithm; 1 1. logarithmic function. 12. An application example of the function.
III. Series (12 class hours, 5) 1. Series; 2. arithmetic progression and its general formula; 3. arithmetic progression's first N terms and formulas; 4. Geometric series and its topping formula; 5. The first n terms and formulas of geometric series.
Fourth, the promotion of the concept of trigonometric function (46 class hours 17) 1. Angle; 2. Curvature system; 3. Trigonometric function at any angle; 4. The trigonometric function line in the unit circle; 5. Basic relations of trigonometric functions with the same angle; 6. Inductive formulas of sine and cosine. Sine, cosine and tangent of sum and difference of two angles; 8. Sine, cosine and tangent of double angles; 9. Images and properties of sine function and cosine function; 10. Periodic function; The parity of 1 1. function; 12. Image of the function; 13. Images and properties of tangent function; 14. Find the angle with the known trigonometric function value; 15. Sine theorem; 16 cosine theorem; 17 example of oblique triangle solution.
5. Plane vector (12 class hours, 8) 1. Vector 2. Addition and subtraction of vectors 3. Product of real number and vector; 4. Coordinate representation of plane vector; 5. The demarcation point of the line segment; 6. The product of plane vectors; 7. The distance between two points on the plane; 8. Translation.
6. Inequality (22 class hours, 5) 1. Inequality; 2. Basic properties of inequality; 3. Proof of inequality; 4. Solving inequality; 5. Inequalities with absolute values.
VII. Equation of Line and Circle (22 class hours, 12) 1. Angle and slope of straight line; 2. Point-oblique and two-point linear equations; 3. General formula of linear equation; 4. Conditions for two straight lines to be parallel and vertical; 5. Angle of intersection of two straight lines; 6. Distance from point to straight line; 7. The plane area is expressed by binary linear inequality; 8. Simple linear programming problem. 9. Concepts of curves and equations; 10. The curve equation is listed by known conditions; Standard equation and general equation of 1 1. circle; 12. The parametric equation of the circle.
Eight, conic (18 class hours, 7) 1 ellipse and its standard equation; 2. Simple geometric properties of ellipse; 3. Parametric equation of ellipse; 4. Hyperbola and its standard equation; 5. Simple geometric properties of hyperbola; 6. Parabola and its standard equation; 7. Simple geometric properties of parabola.
Nine, (b) What are straight lines, planes and simplicity (36 class hours, 28) 1. Plane and its basic properties; 2. Intuitive drawing of plane graphics; 3. Plane straight line; 4. Determination and nature of parallelism between straight line and plane: 5. Determination of perpendicularity between straight line and plane; 6. Three vertical theorems and their inverse theorems; 7. The positional relationship between two planes; 8. Space vector and its addition, subtraction, multiplication and division; 9. Coordinate representation of space vector; 10. the product of space vectors; 1 1. The direction vector of the straight line; 12. angles formed by straight lines on different planes; 13. Common perpendicular of straight lines on different planes; 14 straight line distance in different planes; 15. Verticality of straight line and plane; 16. The normal vector of the plane; 17. Distance from point to plane; 18. The angle formed by a straight line and a plane; 19. The projection of the vector on the plane; 20. The nature that the plane is parallel to the plane; 2 1. Distance between parallel planes; 22. dihedral angle and its plane angle; 23. Determination and nature of verticality of two planes; 24. Polyhedron; 25. Prism; 26. pyramids; 27. Regular polyhedron; 28. Ball.
X. permutation and combination and binomial theorem (18 class hours, 8) 1. Principles of classified counting and step-by-step counting. 2. Arrangement; 3. permutation number formula' 4. Combination; 5. Combination number formula; 6. Two properties of combinatorial numbers: 7. Binomial theorem; 8. The nature of binomial expansion.
XI。 Probability (12 class hours, 5) 1. Probability of random events; 2. The probability of this possible event; 3. mutually exclusive events has the probability of occurrence; 4. The probability of mutually independent events occurring simultaneously; 5. Independent repeated test. Elective 2 (24)
Twelve. Probability statistics (14 class hours, 6) 1. Distribution table of discrete random variables; 2. Expected value and variance of discrete random variables; 3. Sampling method; 4. Estimation of the overall distribution; 5. Normal distribution; 6. Linear regression.
Thirteen. Limit (12 class hours, 6) 1. Mathematical induction; 2. Examples of application of mathematical induction; 3. Limit of sequence; 4. Limit of function; 5. Four operations of limit; 6. Functional continuity.
XIV. Derivative (18 class hours, 8) 1. The concept of derivative; 2. Geometric meaning of derivative; 3. Derivatives of several common functions; 4. Derivative of sum, difference, product and quotient of two functions; 5. Derivative of composite function; 6. Basic derivative formula; 7. Using derivatives to study monotonicity and extremum of functions: the values and minimum values of eight functions.
Fifteen. Complex number (4 class hours, 4) 1. The concept of complex number; 2. Addition and subtraction of complex numbers; 3. Multiplication and division of complex numbers There are 130 knowledge points in high school mathematics. In the past, a test paper had to examine 90 knowledge points, and the coverage rate was about 70%, which was regarded as one of the criteria to measure the success of the test paper. This tradition has been broken in recent years, replaced by attaching importance to thinking, highlighting ability, and attaching importance to the examination of thinking methods and thinking ability. Now we are happier in math than our predecessors! ! I believe it will be helpful to your study. Wish you success! Try the outline of the national senior high school mathematics competition for the first time, completely according to the teaching requirements and contents stipulated in the full-time middle school mathematics syllabus, that is, the knowledge scope and methods stipulated in the college entrance examination, and the requirements for methods are slightly improved, among which probability and calculus are not tested for the first time. Test 1, basic requirements of plane geometry: master all the contents determined by the outline of junior high school mathematics competition. Supplementary requirements: area and area method. Several important theorems: Menelius Theorem, Seva Theorem, Ptolemy Theorem and siemsen Theorem. Several important extreme values: the point with the smallest sum of the distances to the three vertices of a triangle-fermat point. The center of gravity is the point where the sum of squares of the distances to the three vertices of a triangle is the smallest. The point of the distance product of three sides in a triangle is the center of gravity. Geometric inequality. Simple isoperimetric problem. Understand the following theorem: the area of a regular N-polygon in a group of N-polygons with a certain perimeter. The area of a circle in a simple closed curve set with a certain perimeter. In a group of N-sided polygons with a certain area, the perimeter of the regular N-sided polygon is the smallest. In a set of simple closed curves with a certain area, the circumference of a circle is the smallest. Motion in geometry: reflection, translation and rotation. Complex number method and vector method. Planar convex set, convex hull and their applications. The answer complements the second mathematical induction. Recursion, first and second order recursion, characteristic equation method. Function iteration, finding n iterations, simple function equation. N-element mean inequality, Cauchy inequality, rank inequality and their applications. Exponential form of complex number, Euler formula, Dimov theorem, unit root, application of unit root. Cyclic permutation, repeated permutation and combination, simple combinatorial identity. The number of roots of an unary n-degree equation (polynomial), the relationship between roots and coefficients, and the pairing theorem of imaginary roots of real coefficient equations. Simple elementary number theory problems should include infinite descent method, congruence, Euclid division, nonnegative minimum complete residue class, Gaussian function, Fermat's last theorem, Euler function, Sun Tzu's theorem, lattice points and their properties. 3, solid geometry polyhedron angle, the nature of polyhedron angle. Basic properties of trihedral angle and straight trihedral angle. Regular polyhedron, euler theorem. Proof method of volume. Sections, sections, and surface flat patterns will be made. 4. Normal formula of plane analytic geometric straight line, polar coordinate equation of straight line, straight line bundle and its application. The region represented by binary linear inequality. The area formula of triangle. Tangents and normals of conic curves. Power and root axis of a circle.
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