Compulsory courses include: function, trigonometric function, probability, algorithm, solid geometry.
Elective courses include: conic section, permutation and combination, probability.
There are: inequalities, matrices, polar coordinates, parametric equations.
Review some knowledge points of high school mathematics
Chapter 1 Set and Simple Logic
1, all subsets of a set containing n elements.
Chapter II Functions
1, exponent: operation:
2. Logarithm: ① There is no logarithm between negative numbers and zero, ②, the logarithm of 1 is equal to 0:,
③ The logarithm of the base number is equal to 1:,
④ Logarithm of product:, Logarithm of quotient:,
Logarithm of power:; ,
Bottom changing formula:
3. Exponential logarithmic function
Function image definition domain
Range increases interval decreases interval.
Chapter III Sequence of Numbers
1, sum of the first n items of the sequence:
The relationship between the sum of the first n terms of the sequence and the general term;
2. arithmetic progression: (1), definition:
(2) General formula:
(3) Sum of the first n items: 1.
(after finishing, it is a quadratic function about the constant term of n)
(4) Arithmetic average: three numbers are arithmetic: a-d, a, a+d.
3. Geometric series:
(1), definition: ().
(2) General formula:
(3) the sum of the first n items:
(4) such as ratio:
Chapter IV Trigonometric Functions
1, radian system: (1), radian 1 radian =;
Arc length formula: (is the radian number of the angle)
2, trigonometric function (1), definition:
3. Trigonometric function value of special angle
Angle of
radian
4. The basic relationship of trigonometric functions with the same angle:
5. Inductive formula: (parity is unchanged, the symbol looks at the quadrant) Sine is positive; Cosine right is positive; The tangent 13 is positive.
Formula 2: Formula 3: Formula 4: Formula 5:
6. Sine, cosine and tangent of sum and difference of two angles
：
：
：
：
：
：
7. Auxiliary angle formula:
8. Double angle formula: (1)
：
：
：
(2) Simplified formula: (mostly used to study properties)
9, trigonometric function:
Function image definition domain
Range Periodic Parity Increasing Interval Decreasing Interval
Function definition domain value domain amplitude periodic frequency phase initial phase image
10, triangle solution: (1), triangle area formula:
(2) Sine theorem:
(3) Cosine theorem:
Looking for an angle:
Chapter 5, Plane Vector
1, coordinate operation: (1) is set, then
Product of number and vector: λ, product of quantity:
(2) Let the coordinates of point A and point B be (x 1, y 1) and (x2, y2) respectively.
Then. (End minus Start)
;
Modulus of vector ||: =;
(3) Product of the number of plane vectors:,
Attention:,,
(4), the angle of vector, then
,
2. Important conclusion: (1), two vectors are parallel:
(Coordinate representation)
(2), two non-zero vectors are perpendicular = (coordinate representation),
(3) If p is divided into directed line segments, let P(x, y), P 1(x 1, y 1), P2(x2, y2),
Midpoint coordinate formula:
Chapter VI: Inequality
1, average inequality: (1), ()
(2)、a & gt0，b & gt0; Or positive, negative, three-phase and so on.
2. The method of solving exponential inequality and logarithmic inequality: the same base method, the true number of logarithm is greater than 0;
Chapter 7: Equations of Lines and Circles
1, dip angle:,;
Two points are on a straight line with a slope of
2. Linear equation: (1), point inclination:; ② Oblique type:;
(3) general formula: (A and B are not 0 at the same time) slope,
3. The positional relationship between two straight lines
(1), parallel:
Vertical:
(2), the distance formula from the point to the straight line (the straight line equation must be converted into a general formula)
6. Equation of circle:
(1), the standard equation of a circle with center and radius.
(2) General equation of circle
(Formula:)
When represents a circle with a center and a radius of;
Chapter 8: conic curve 1, elliptic standard equation: half focal length: eccentricity range.
2. Hyperbolic standard equation: half focal length
Eccentricity range
3. Parabolic definition: eccentricity:
Standard equation and symmetry axis equation of parabola;
Chapter 9 Solid Geometry
1. Diagonal mapping method: 2. Formula of surface area and volume of cylinder, cone, platform and sphere: 3. Characteristics of aircraft:
4. The plane representation and drawing:
5. Axiom 1, 2, 3 and mathematical symbol language 6. The positional relationship between two straight lines in space and the definition and range of angles formed by straight lines in different planes;
Axiom 4 and Equiangular Theorem: 7. The positional relationship and mathematical symbol representation between straight lines and planes in space: 8. The positional relationship between planes and mathematical symbol representation: 9. Determination of parallelism between straight line and plane and its mathematical symbol representation: 10. Determination of plane parallelism and its mathematical symbol representation: 1 1. The essence and mathematical symbol representation of parallelism between straight line and plane;
12. The property of plane parallel to plane and its mathematical symbol representation: 13. Determination of perpendicularity between straight line and plane and its mathematical symbol representation;
14. Definition and range of the angle formed by a straight line and a plane:
15. The plane is perpendicular to the plane:
Definition of dihedral angle and plane angle of dihedral angle
16. Determination of plane perpendicular to plane and mathematical symbol expression: 17. Properties of straight line perpendicular to plane and mathematical symbolic language;
18. The Nature of Plane Perpendicular to Plane and Mathematical Symbol Language;
There are also program block diagrams, full-name quantifiers and existential quantifiers.