Summary and arrangement of mathematics knowledge points in college entrance examination 1
Test the knowledge points of mathematics: the sum formula of two angles
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)
cot(A+B)=(cotA cotB- 1)/(cot B+cotA)
cot(A-B)=(cotA cotB+ 1)/(cot b-cotA)
Double angle formula tan2A=2tanA/( 1-tan2A)
cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin 2
Sine theorem a/sinA=b/sinB=c/sinC=2R Note: where r represents the radius of the circumscribed circle of a triangle.
Cosine Theorem b2=a2+c2-2accosB Note: Angle B is the included angle between side A and side C..
The standard equation of a circle (x-a)2+(y-b)2=r2 Note: (A, B) is the center coordinate.
General equation of circle x2+y2+Dx+Ey+F=0 Note: D2+E2-4f > 0
Parabolic standard equation y2=2px y2=-2px x2=2py x2=-2py
Mathematics knowledge point of college entrance examination: tangent equation of circle
(1) known cycles.
① Given that the tangent point is on the circle and there is only one tangent line, use the vertical relation to find the slope.
② The tangent equation of a point outside the circle can be set as, and then k can be obtained by using the tangent condition. There must be two tangents at this time. Be careful not to miss the tangent parallel to the Y axis.
③ The tangent equation with a slope of k can be set as, and then using the tangent condition to find b, there must be two tangents.
(2) The tangent equation of a point on a known circle is
Mathematical knowledge points of college entrance examination: summary of common methods of line-line parallelism
(1) Definition: Two straight lines with no common point on the same plane are parallel straight lines.
(2) Axiom: Two lines parallel to the same line in space are parallel to each other.
(3) The method of judging the parallelism of straight lines in plane geometry.
(4) Properties of parallel lines and planes: If a straight line is parallel to a plane and the plane passing through this straight line intersects this plane, then this straight line is parallel to the intersection of two planes.
(5) Verticality of straight line and plane: If two straight lines are perpendicular to the same plane at the same time, they are parallel.
(6) Properties of parallel planes: If two parallel planes intersect with the third plane at the same time, their intersection lines are parallel.
Summary and arrangement of mathematics knowledge points in college entrance examination II
The essence of summarizing mathematical knowledge points in college entrance examination
1. The college entrance examination mathematics has nine chapters, such as function, sequence, trigonometric function, plane vector, inequality and solid geometry.
Mainly test function and derivative, because this is the core part of the whole high school stage, so this part also focuses on two aspects: the properties of linear function, including monotonicity and parity of function; The second is the solution of functions, focusing on quadratic functions and higher-order functions, fractional functions and their partial distribution, but this distribution also includes two analyses.
Second, plane vectors and trigonometric functions
This part of knowledge focuses on three aspects: subtraction and evaluation. First, it focuses on mastering formulas and five basic formulas. Second, master the images and properties of trigonometric functions, especially the properties of sine and cosine functions; Thirdly, it is not difficult to solve triangles with sine theorem and cosine theorem.
Summary essence of mathematics knowledge points in college entrance examination II
Third, the order
This series focuses on two aspects: a common term; One is summation.
Four, space vector and solid geometry
It focuses on two aspects: first, proof; One is calculation.
Probability and statistics of verb (verb)
Probability statistics mainly belongs to the category of mathematical application problems, and it needs to master several aspects: …… and other possible probabilities; ..... event; Probability of occurrence of independent events and independent repeated events.
Summary essence of mathematics knowledge points in college entrance examination III
Six, analytic geometry
This part of the content is easier said than done, and several types of problems need to be mastered. The first kind of positional relationship between straight line and curve needs to master its general method; Fixed point problems of the second kind; The third category is the chord length problem; The fourth category is symmetry; The fifth kind of key questions, which often feel thoughtful but have no clear answer, need to master better algorithms to improve the accuracy of doing the questions.
Seven, the finale
In the final preview review, students should also focus on the method of inequality calculation. Although it is very difficult, it is also forbidden to leave blank in the test paper. Usually do more finale questions, try to solve them when you can, and think when you can.
Knowledge points of the unary linear equation in college entrance examination mathematics: what is the unary linear equation?
From the point of view of plane analytic geometry, a straight line on a plane is a graph represented by a binary linear equation in a plane rectangular coordinate system. To require the intersection of two straight lines, we only need to solve these two binary linear equations simultaneously. When simultaneous equations have no solution, two straight lines are parallel. When there are infinite solutions, two straight lines coincide; When there is only one solution, two straight lines intersect at one point. The angle between the upward direction of a straight line and the positive direction of the X axis (called the inclination angle of the straight line) or the tangent of the angle (called the slope of the straight line) is often used to indicate the inclination degree of the straight line (for the X axis) on the plane. Slope can be used to judge whether two straight lines are parallel or perpendicular, and also to calculate their intersection angle. The coordinates of the intersection of the straight line on the coordinate axis and the coordinate axis are called the intercept of the straight line on the coordinate axis. The position of a straight line on a plane is completely determined by its slope and intercept. In space, when two planes intersect, the intersection line is a straight line. Therefore, in the spatial rectangular coordinate system, two three-dimensional first-order equations representing the plane are simultaneous as the equations of the straight line obtained by their intersection.
Summary and arrangement of mathematics knowledge points in college entrance examination 3
1, the structure of space solid geometry. Includes the structural features of prism, pyramid and frustum. Structural characteristics of cylindrical frustum and sphere.
2. How to find the area of cylinder lateral area, cone lateral area, frustum of a cone lateral area, regular prism lateral area, regular prism lateral area, regular prism lateral area and sphere?
3, column, cone, table, ball volume formula.
4. Three views and direct vision.
5. The judgment and nature of parallel lines and planes. The judging theorem of line and plane parallelism, the judging theorem of plane parallelism, the property theorem of line and plane parallelism, the property theorem of plane parallelism. Determination and properties of vertical line and vertical line plane. The judging theorem of vertical line and plane, the judging theorem of vertical plane; Property theorem of vertical line and plane, property theorem of vertical plane.
6. Statistics: estimate the population with samples. Use the frequency distribution of samples to estimate the frequency distribution of the population, and use the digital characteristics of samples to estimate the digital characteristics, variance and standard deviation of the population. Correlation between variables and linear relationship between two variables.
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