Summarize the knowledge points of high school mathematics.
1, the finite set with n elements has 2n subsets * *, 2n non-empty subsets and 2n- 1 non-empty proper subset.
2. In a set, Cu(A∩B)=(CuA)U(CuB), and the complement of intersection is equal to the sum of complement.
Cu(AUB)=(CuA)∩(CuB), and the complement of the union is equal to the complement.
3、ax2+bx+c & lt； The solution set of 0 is x(0
+c & gt； The solution set of 0 is x, cx2+bx+a >; The solution set of 0 is > x or x; The solution set of 0 is->; X or x 0) move y = f (x) to the left or right by one unit;
(2) vertical translation: y = f (x) b (b >; 0) image, which can be obtained by moving y=f(x) up or down by b units;
(3) Symmetry: If F (X+M) = F (X-M) exists for all x in the defined domain, then the image of y=f(x) is symmetrical about the straight line x=m; Y=f(x) The symmetric function about (a, b) is y! =2b—f(2a—x)。
(4), study plan; Folding: ①y=|f(x)| is an image with the X axis as the symmetry axis, and the part where y=f(x) is located below the X axis is folded above the X axis. ②y=f(|x|) is an image obtained by folding the image of y=f(x) on the left side of the y axis to the right side of the y axis.
(5) Relevant conclusions: ① If f (a+x) = f (b-x) is true when x is all real numbers, then the image of y=f(x) is about
X= symmetry. ② The images of function y=f(a+x) and function y = f (b-x) are symmetrical about the straight line x=.
15, arithmetic progression, an = a1+(n-1) d = am+(n-m) d; sn=n=na 1+
16, if n+m=p+q, then am+an = AP+AQ;
Sk, s2k-k and s3k-2k form a arithmetic progression with a tolerance of k2d. Ann is arithmetic progression, if AP = Q and AQ = P, then AP+Q = 0；; If sp = q and sq = p, then sp+q =-(p+q); If sk, sn, sn-k and sn = (sk+sn+sn-k)/2k are known; If an is arithmetic progression, let the sum of the first n terms be sn=an2+bn (note: there is no constant term), and solve A and B with the idea of equation. In arithmetic progression, if the item with the foot code arithmetic progression is taken out to form a series, the new series is still arithmetic progression.
17, geometric series, an=a 1? qn- 1=am？ Qn-m, if n+m=p+q, am? an=ap？ AQ； sn=na 1(q= 1)，
sn=，(q≠ 1)； If q≠ 1, then there is =q, if q ≠- 1, = q;
SK, S2K-K and S3K-2K are also geometric series. A 1+a2+a3, a2+a3+a4, a3+a4+a5 also form geometric series. In geometric progression, if the item with the foot code arithmetic progression is taken out to form a series, the new series is still geometric progression. Crack formula:
=—,=? (—), recurrence forms of commonly used series: superposition, superposition, multiplication,
18, arc length formula: l=|α|? r .
S fans =? lr=？ |α|r2=？ ; When the perimeter of the sector is constant (L),
Its area is, and its central angle is 2 radians.
19、Sina(α+β)= sinαcosβ+cosαsinβ； Sina(α—β)= sinαcosβ—cosαsinβ；
cos(α+β)= cosαcosβ—sinαsinβ； cos(α—β)=cosαcosβ+sinαsinβ
Required knowledge points of mathematics in college entrance examination
1. sequence &; Solving triangle
The knowledge points of series and trigonometric solution are in an either-or state when solving the first problem. In recent years, the characteristic is that the first problem of the big problem takes turns to solve the triangle for two years. The first question of 20 14 and 20 15 is investigated in series, and the first question of 20 16 is investigated in trigonometric solution, so it is estimated that 20 16.
Series mainly examines the definition of series, the properties of arithmetic progression and geometric progression, the general formula of series and the sum of series.
Solving triangles in solving problems mainly focuses on the application of sine and cosine theorems in solving triangles.
2. Solid geometry
The college entrance examination examines a solid geometry problem in the second or third position of solving problems, mainly examining the proof of parallelism and verticality between spatial straight lines and planes, and finding dihedral angles. The problem is relatively stable, and the second problem needs to establish a reasonable spatial rectangular coordinate system and calculate it correctly.
3. Possibility
The college entrance examination examines a probability question in the second or third position of the answer, mainly examining classical probability, geometric probability, binomial distribution, hypergeometric distribution, regression analysis and statistics. In recent years, probability questions are examined from different angles every year, which is a long problem for students. Understand the meaning of the question correctly.
4. Analytic geometry
The college entrance examination examines an analytic geometry problem in the position of the 20 th question. This paper mainly examines the definition and properties of conic curve, trajectory equation problem, parameter problem, fixed point fixed value problem and range problem, and solves the problem through coordinate operation of points.
5. derivative creatures
The college entrance examination examines a derivative question at the position of 2 1 question. In this paper, we mainly study the tangent, monotonicity, maximum, zero and inequality proof of functions with parameters. The problems with parameters are generally difficult and must be done at last.
Choose to do the problem
This year, the selected lecture on geometric proof in the college entrance examination was deleted, and there are only two selected lectures, one is coordinate system and parameter equation, and the other is inequality selected lecture. The problem of coordinate system and parameter equation mainly examines the geometric meaning of polar coordinate equation, parameter equation and linear parameter equation of curve and the application of the maximum value of range; Inequality multiple-choice questions mainly investigate the simplification of absolute inequality, the range of parameters and the proof of inequality.
Summary of high school mathematics knowledge points
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; The 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! The number of senior high school students tested x the outline of the national preliminary examination competition is completely in accordance with 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 in the preliminary examination. 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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