Knowledge points of liberal arts mathematics in college entrance examination
First, functions and derivatives
This paper mainly examines the related concepts such as set operation, function definition domain, range, analytical formula, limit, function continuity, derivative and so on.
Second, plane vector and trigonometric function, trigonometric transformation and their applications.
This part is the focus of the college entrance examination, but it is not difficult. It mainly contains some basic or intermediate problems.
Thirdly, sequence and its application.
This part is the key and difficult part of the college entrance examination, which mainly produces some comprehensive questions.
Fourth, inequality.
This paper mainly investigates the solution and proof of inequality, rarely alone, mainly through the size comparison in solving problems. It is the key and difficult point of the college entrance examination.
Fifth, probability statistics.
This part is related to our life and is an applied problem.
Sixth, the qualitative and quantitative analysis of spatial position relationship.
Mainly to prove parallelism or verticality, and to find the angle and distance. This paper mainly investigates the familiarity and application of the theorem.
Seventh, analytic geometry.
The college entrance examination is difficult and requires a large amount of calculation, which generally includes parameters.
Liberal arts mathematics Gao pin Kao bi branch
Part I: Choose and fill in the blanks.
Basic operations of the 1. set (including operations in the newly defined set, emphasizing the mutual dissimilarity of elements in the set);
2. Commonly used logical terms (sufficient and necessary conditions, full-name quantifiers and existential quantifiers);
3. Concepts and properties of functions (parity, symmetry, monotonicity, periodicity, maximum and minimum of range);
4. Function operation of power, finger and pair, image and attribute
5. The zero point of function, the migration and change of function and equation (usually using the method of anti-object and the idea of combining numbers and shapes);
6. The surface area and volume of three views of the space body and its reduced diagram;
7. The positional relationship of points, lines and surfaces in space, the calculation of spatial angle, and the related problems of circumscribed or inscribed spherical surface and polyhedron;
8. Determination of slope and inclination of straight line; The positional relationship between a straight line and a circle, and the application of the distance formula between a point and a line;
9. Preliminary algorithm (cognitive block diagram and its function, dealing with problems according to given information and relevant knowledge of geometric sequence);
10. Classical probability and geometric probability science: permutation and combination, binomial theorem, normal distribution, statistical cases, regression linear equations, independence test; Liberal arts: overall estimation, stem leaf diagram, frequency distribution histogram;
1 1. Triangle identity deformation (tangent chord, lifting force, auxiliary angle formula); Trigonometric evaluation, trigonometric function images and properties;
12. Vector product, coordinate operation and application of geometric meaning;
13. application of sine and cosine theorem and triangle solution;
14. the application of the properties of arithmetic and geometric series, and the ability to find its general term, number of terms and sum by using simple formulas;
15. Application of linear programming; The target function will be found;
16. Application of conic properties (especially eccentricity);
17. Geometric meaning and operation of derivative and simple solution of definite integral
18. The concept, four operations and geometric meaning of complex numbers;
19. Identification and application of abstract functions;
Part II: Solving Problems
Question 17: Intersection of vector and triangle, solution of triangle and practical application of sine and cosine theorem;
Question 18: (Text) Probability and Statistics (Combination of Probability and Statistics)
Probability distribution table of discrete random variables and its numerical characteristics;
Question 19: solid geometry
① The clamping plane is parallel and vertical; Faces are parallel and perpendicular to each other.
(2) Find the middle angle in space (especially the dihedral angle in science).
③ Find the space volume of distance (science: dynamic);
Question 20: Analytic geometry (paying attention to thinking ability and skills and reducing the amount of calculation)
① Find the curve trajectory equation (by definition or undetermined coefficient method)
(2) The relationship between straight line and conic curve (using point difference method and chord length formula flexibly)
③ The problem of finding the fixed point, fixed value, maximum value and parameter value;
Question 2 1: Comprehensive application of function and derivative
This is a typical test designed at the intersection of applied knowledge networks, and it is a final exam aimed at examining candidates' problem-solving ability and liberal arts mathematics quality.
Examiner: classified discussion ideas; The transformation, transformation and migration of ideas; The idea of whole substitution, division and combination
Three questions about the overall design;
① Find the undetermined coefficient and determine the monotonicity of the function by derivative discussion;
(2) Find the value of the parameter variable or the maximum value of the function;
(3) Exploring questions or proving inequalities.
Question 22: Choose one of the three options:
(1) geometric proof mainly examines the similarity of triangles and the tangent theorem of circles, proves proportionality, and finds angles and lengths; Using projective theorem to solve the problem of calculation and proof in a circle is a hot topic in college entrance examination over the years.
(2) Coordinate system and parametric equation mainly focus on two points: transforming parametric equation and polar coordinate equation into constant equation; Solve the basic quantity of curve with parameters and polar coordinate equation. This kind of questions, clear thinking, not difficult, grasp the foundation, do not do difficult problems.
(3) Selected lecture on inequality: the combination of absolute inequality and function. The design is as follows: ① Solving the inequality about X with parametric variables; (2) the value of parameter variables when solving inequalities; ③ Prove inequality (using the mean value theorem, scaling method, etc.). ).
20 18 liberal arts mathematics knowledge points in college entrance examination: summary of mathematics knowledge points in senior high school
Compulsory 1: 1, the concepts of set and function (this part of knowledge is abstract and difficult to understand) 2, basic elementary function (exponential function and logarithmic function) 3, the nature and application of function (abstract and difficult to understand).
Compulsory 2: 1, solid geometry (1), proof: vertical (multi-plane vertical), parallel (2), solution: mainly included angle, including line plane angle and plane angle.
This part of knowledge is the difficulty of senior one students, such as: an angle is actually an acute angle, but what is shown in the picture is an obtuse angle, etc., which requires students to have a strong three-dimensional sense. This part of the knowledge college entrance examination accounts for 22-27 points.
2. Linear equation: it is not a separate proposition in the college entrance examination, but it is easy to combine with conic curve.
3, the circle equation:
Compulsory course 3: 1, preliminary algorithm: required content of college entrance examination, 5 points (choose or fill in the blanks) 2, statistics: 3, probability: required content of college entrance examination, science accounted for 15 in 2009, liberal arts mathematics accounted for 5 points.
Compulsory 4: 1, trigonometric function: (image, nature, high school, emphasis and difficulty) must be tested: 15-20, often mixed with other functions.
2. Plane vector: NMET is not a separate proposition, but it can be easily combined with trigonometric functions and conic curves. In 2009, science accounted for 5 points, and liberal arts accounted for 13 points.
Compulsory course 5: 1, triangle solution: (sine, cosine theorem, trigonometric identity transformation) In the college entrance examination, science accounts for about 22 points, and mathematics accounts for about 13 points. 2. Sequence: required for the college entrance examination, 17-22. 3. Inequality: (Linear programming is easy to understand in class, but it is more complicated to do the problem. Inequality is not a separate proposition, but is generally combined with function to find the maximum value and solution set.
Summary of knowledge points of liberal arts mathematics in college entrance examination
Multiplication and factorization
a2-b2=(a+b)(a-b)
a3+b3=(a+b)(a2-ab+b2)
a3-b3=(a-b)(a2+ab+b2)
Triangle inequality
|a+b|≤|a|+|b|
|a-b|≤|a|+|b|
| a |≤b & lt； = & gt-b≤a≤b
|a-b|≥|a|-|b|-|a|≤a≤|a|
Solution of quadratic equation in one variable
-b+√(B2-4ac)/2a-b-b+√(B2-4ac)/2a
Relationship between root and coefficient
X1+x2 =-b/ax1_ _ x2 = c/a note: Vieta's theorem.
discriminant
B2-4a=0 Note: This equation has two equal real roots.
B2-4ac >0 Note: The equation has real roots.
B2-4ac & lt； 0 Note: The equation has multiple yokes.
formulas of trigonometric functions
Two-angle sum formula
sin(A+B)=sinAcosB+cosAsinB
sin(A-B)=sinAcosB-sinBcosA
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)=cosAcosB+sinAsinB
tan(A+B)=(tanA+tanB)/( 1-tanA tanB)
tan(A-B)=(tanA-tanB)/( 1+tanA tanB)
ctg(A+B)=(ctgActgB- 1)/(ctg B+ctgA)
ctg(A-B)=(ctgActgB+ 1)/(ctg b-ctgA)
Double angle formula
tan2A=2tanA/( 1-tan2A)
ctg2A=(ctg2A- 1)/2ctga
cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a
half-angle formula
sin(A/2)=√(( 1-cosA)/2)
sin(A/2)=-√(( 1-cosA)/2)
cos(A/2)=√(( 1+cosA)/2)
cos(A/2)=-√(( 1+cosA)/2)
tan(A/2)=√(( 1-cosA)/(( 1+cosA))
tan(A/2)=-√(( 1-cosA)/(( 1+cosA))
ctg(A/2)=√(( 1+cosA)/(( 1-cosA))
ctg(A/2)=-√(( 1+cosA)/(( 1-cosA))
Sum-difference product formula
2sinAcosB=sin(A+B)+sin(A-B)
2cosAsinB=sin(A+B)-sin(A-B)
2cosAcosB=cos(A+B)-sin(A-B)
-2sinAsinB=cos(A+B)-cos(A-B)
sinA+sinB = 2 sin((A+B)/2)cos((A-B)/2
cosA+cosB = 2cos((A+B)/2)sin((A-B)/2)
tanA+tanB=sin(A+B)/cosAcosB
tanA-tanB=sin(A-B)/cosAcosB
ctgA+ctgBsin(A+B)/sinAsinB
-ctgA+ctgBsin(A+B)/sinAsinB
The first n terms and formulas of some series
1+2+3+4+5+6+7+8+9+…+n = n(n+ 1)/2
1+3+5+7+9+ 1 1+ 13+ 15+…+(2n- 1)= N2
2+4+6+8+ 10+ 12+ 14+…+(2n)= n(n+ 1)
12+22+32+42+52+62+72+82+…+N2 = n(n+ 1)(2n+ 1)/6
13+23+33+43+53+63+…n3 = N2(n+ 1)2/4
1 _ _ 2+2 _ _ 3+3 _ _ 4+4 _ _ 5+5 _ _ 6+6 _ _ 7+…+n(n+ 1)= n(n+ 1)(n+2)/3
Sine theorem: a/sinA=b/sinB=c/sinC=2R
Note: where r represents the radius of the circumscribed circle of the triangle.
Cosine theorem: b2=a2+c2-2accosB
Note: Angle B is the included angle between side A and side C..
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