46. A property of arithmetic progression: Let nS be a series? The sum of the first n terms of na, A necessary and sufficient condition for na to be a arithmetic progression is that
bnanSn？ 2 (A and B are constants) The tolerance is 2a.
47. Do you know how to use the method of "dislocation subtraction" when summing series? (if nnnbac? , among them? Na is arithmetic progression? Nb equals
Contrast series, q? The sum of the first n terms of nc)
48. Did you notice 1 1Sa when using 1 nnnnssa to find the general formula of a series? have you finished? 49. Do you remember the summation of split terms? (e.g.
1
1
1) 1( 1nnnn。 )
Fourth, permutation and combination, binomial theorem
50. The basis for solving the problem of permutation and combination is: classification addition, step-by-step multiplication, orderly arrangement and disorderly combination.
5 1, and the rules for solving permutation and combination problems are: adjacent problem binding method; Interpolation method for non-adjacent problems: single-line method for multi-line problems; Positioning problem priority method;
Classification of multivariate problems; Ordered distribution problem method; Select a question first, and then return; At most, at least indirectly. Do you remember when the zoning method was used?
52. The formula of permutation number is: the formula of combination number is: the relationship between permutation number and combination number is: m.
n
mnCmP？ ! The property of combination number: m
North Carolina (USA)
=
mnn
C
multinational corporation
+
1
manganese
C
=m
North Carolina (USA)
1?
n
rrn
C
=n
2
1
12 1? rnrnrrrrrrCCCCC？
Binomial Theorem: nnnrrnrnnnnnnnnbCbaCbaCbaCaCba? 222 1 10) (general formula of binomial expansion: r.
rnrnrbaCT 1)2 10(nr，，，
Verb (abbreviation of verb) solid geometry
53. The proof of parallelism and verticality mainly uses the transformation of line-plane relationship: straight line//straight line? Line//surface? Face//face, line/line? ⊥ Surface line?
Facing the face of ⊥, the vertical vector is often used to prove.
54. What is the main method to make the plane angle of dihedral angle? (Definition method, three perpendicular lines method) Three perpendicular lines method: one plane, two perpendicular lines, three.
Draw a diagonal line and the projection will be visible.
55. The methods to solve dihedral angle mainly include: solving right triangle, cosine theorem, projective area method, normal vector 56, and what is the conventional method to find the distance from point to surface? (direct method, equal volume transformation method, normal vector method) 57. Do you still remember the three vertical theorems and their inverse theorems?
58. The solution of the spherical distance between two points on a sphere is mainly to find the angle of the center of the sphere, which is often associated with latitude and longitude. Do you remember longitude?
And what is the meaning of latitude? (Longitude is the face angle; Latitude is the angle between a line and a plane)
59. Remember the Euler formula of simple polyhedron? (V+F-E=2, where v is the number of vertices, e is the number of edges and f is the number of faces), there are two kinds of edges.
Algorithm, do you remember? (① Every face of a polyhedron is an N-polygon, then E=
2nF② If every vertex of a polyhedron has m edges, then E=2.
Average variation
) 6. Analytic geometry
60. When setting the linear equation, the slope of the straight line can generally be set to K. Have you noticed that when the straight line is perpendicular to the X axis, the slope K does not exist?
(For example, a straight line passes through a point?
23, 3, circled by 2522? The chord length of the yx tangent is 8. Find the equation of the straight line where this string lies. Pay attention to this problem and don't miss the solution of x+3=0. )
6 1, what is the coordinate formula of the bisector? (Starting point, midpoint, vernal equinox and? The value can be clearly stated)
Coordinate formula of fixed point of line segment
Let P(x, y), P 1(x 1, y 1), P2(x2, y2), and?
2 1PPPP？ , then
112121yyxxx midpoint coordinate formula
22
2 1
2 1 yyyxx
62.If), (), (), (3322 1 1yxCyxByxA,, △ What is the coordinate of the center of gravity g of △ABC?
Li zai, 332 132 1yyxxx
Did you notice 1 when solving the problem in fractions?
63. In analytic geometry, when studying the positional relationship between two straight lines, it is possible that these two straight lines overlap, which is generally mentioned in solid geometry.
Two straight lines can be understood as non-coincidence.
64. Several forms of linear equations: point oblique type, oblique truncated type, two-point type, truncated moment type, general type, and the limitations of various forms (such as points).
Tilting does not apply to straight lines with no slope)
65. For two non-overlapping straight lines 0:111cybxal, 0:2222CyBxAl, there are:
122
1 1
22 12 1//CACABABAll； 02 12 12 1bbaall。 66. The intercept of a straight line on the coordinate axis can be positive, negative or 0. 67, and the intercept of the straight line on the two coordinate axes is equal. The linear equation can be understood as follows
1? b
y
Ax, but don't forget that when a=0, the intercept of the straight line y=kx on both axes is 0 and the intercept is equal.
68. The formula for the distance between two straight lines 0 1CByAx and 02CByAx is d = D = d=———————
69. Do you remember the direction vector of a straight line? What is the relationship between the direction vector of a straight line and its slope? When the direction vector of the straight line L is m=(x0, y0), the slope of the straight line K = —————; When the slope of a straight line is k, the direction vector m of the straight line is equal to —— 70, the formula of arrival angle and the formula of included angle ——, when to use it? 7 1. There are two ways to deal with the positional relationship between a straight line and a circle: (1) the distance from a point to a straight line; (2) The equation of a straight line and the equation of a circle are simultaneous and different.
Generally speaking, the former is simpler.
72. To deal with the positional relationship between circles, we can use the relationship between the center distance and radius of two circles.
73. In a circle, pay attention to the right triangle composed of radius, half chord length and chord center distance, and think more about the geometric properties of the circle. 74. When using conic to define and solve problems in a unified way, did you notice the order of numerator and denominator in the definition? The two definitions are often confused.
Sometimes it is very helpful for us to solve problems, and it may be more convenient to use the second definition for the focus chord problem. (formula of focal radius: ellipse: | pf1| = ————; | PF2 | =————； Hyperbola: | pf1| = ————; | pf2 | = —— (where F 1 is the left focus and f2 is the right focus.
Point); Parabola: |PF|=|x0|+
2
p
) 75. When solving a conic curve and a straight line at the same time, we should pay attention to the equation obtained after elimination: Is the coefficient of the quadratic term zero? discriminant
0? (Find the intersection point, chord length, midpoint, slope, symmetry, and existence problems are all in 0? Continue).
76. In an ellipse, the relationship between A, B and C is-; Eccentricity e = ———; The alignment equation is ————; The distance from the focus to the corresponding directrix is-twice.
In the curve, the relationship between a, b and c is-; Eccentricity e = ———; The alignment equation is ————; The distance from the focus to the corresponding directrix is-77, and the path is the shortest chord among all focus chord parabolas.
78. Do you know? The key to solving analytic geometry problems is to algebra the geometric conditions in the topic, especially some inconspicuous conditions, such as
Time plays a key role, such as: points on a curve, intersections, * * * lines, circles passing through a certain point with the diameter of a certain line segment, angles, verticality, parallelism, midpoints, bisectors of angles, midpoint chords and so on. Don't forget the parametric equations of circles and ellipses, sometimes it is very convenient to solve problems. The combination of numbers and shapes is an important way of thinking to solve several problems. Remember to draw and analyze!
79. Have you noticed? There is a difference between finding trajectory and finding trajectory equation. Don't forget to find the range when solving the trajectory equation!
80. When solving the application problem of linear programming, there are the following steps: first, find the constraints, make the feasible region and define the objective function.
The key is to find out the geometric meaning of the objective function, and pay attention to changing the coefficient of y in the linear equation to a positive value when finding the feasible region. Seek 2.
8 1, the condition that two vectors are parallel or * * * straight lines, they have two expressions, remember? Pay attention to it? Vector parallelism is necessary and sufficient.
Conditions. (Definition and coordinate representation) 82. Vector can solve the problems of included angle, distance, parallelism and verticality. Remember the following formula: |a|2.
=a a，
cosθ=
2
2222 12 12
12 1|
| | | yxyxyyxxbaba
83. Using vector parallelism or verticality to solve the problems of parallelism and verticality in analytic geometry can't discuss that the slope doesn't exist, so pay attention to it.
0? Ba is a necessary but not sufficient condition for vector Ba to form an obtuse angle with vector.
84. The operation of vectors should be different from the operation of real numbers: if a vector cannot be omitted on both sides, the multiplication of vectors will not satisfy the associative law, that is,
Cbacba) () (Remember that two vectors are inseparable.
85. Remember the geometric meaning of the basic theorem of vectors? Its essence is that any vector on the plane can use any straight line on the plane.
Do you know the meaning and solution of its coefficient?
86. The sum of the vectors formed by the end-to-end connection of closed figures is zero, which is a natural condition in the topic and should be paid attention to when applied.
In the quantity equation, the term can be shifted, squared on both sides, multiplied by a real number, modulus on both sides at the same time, multiplied by a vector on both sides, but not divided by a vector. 87. Cartesian coordinate operation of vectors
Let 32 132 1，，，BBBBAAAA。
And then what? 3322 1 1，，babababa？
babababa，3322 1 1
?
Raaaa
32 1,,
3322 1 1babababa？
2
three
222 1aaaaaa？
23
222 123
22
2
1
3322 1 1，cosb
Bachelor of business administration
aababababa
Rbabababa？
,,,//3322 1 1, 03322 1 1?
babababa
Let a =11,zyx, B=? 222，，zyx，
rule
OAOBAB？ 222，，zyx-？ 1 1 1，，zyx=？ 12 12 12，，zzyyxx？ 2 122 122 12 zzyyxxababab？
Eight. derivative
88, the geometric meaning of derivative is the slope of the tangent of the curve at this point, learn to define all kinds of deformation. 89. Derivatives of several important functions: ①0'
C, (c is a constant) ②Qnnxxnn
1
'
Four algorithms of derivative? '''
90. The monotonicity of a function can be proved or judged by using derivatives. Note that when f '(x)≥0 or f '(x)≤0, there is an equal sign.
9 1、f？ (x0)=0 is the necessary and sufficient condition for the function f(x) to take the extreme value at x0, and the necessary and sufficient condition for f(x) to take the extreme value at x0 is
What? 92. Steps to seek the maximum value of derivative: (1) Seek the derivative? Brandy specification
'
(2) Find the equation? The root nxxx of xf'=0,,, 2 1
(3) Calculate extreme value and endpoint function value.
(4) Determine the maximum and minimum values according to the above values.
93. The method of finding the extreme value of a function: first find the domain, then find the derivative, find the boundary point of the domain, and find the extreme value according to monotonicity. Informing function
This condition is equivalent to giving two conditions: ① the derivative value of the function at this point is zero, and ② the value of the function at this point is fixed. Nine, probability statistics
94. Solution of the probability of an event: Convert the required event into equal probability of possible events (knowledge of common permutation and combination), and turn to.
Turn it into the probability that one of several mutually exclusive events occurs, and turn it into the probability that independent events occur at the same time with the probability of opposing events. This probability is regarded as the probability that an event happens exactly k times in n experiments, but we should pay attention to the use conditions of the formula. (1) if events a and b are mutually exclusive events, then P(A+B)=P(A)+P(B) (2) if events a and b are independent events, then P (A B) = P (A) P (B) (3) (3) if events a and b are.
APAp？ 1
(4) If the probability of an event in an experiment is p, then it happens exactly k times in n independent repeated experiments.
Rate:
k
Neck; neck
knnppCKP 1
95. Sampling methods mainly include: simple random sampling (drawing lots, random sample table method) is often used when the population is small, and its main feature is to extract one by one from the population; Systematic sampling is often used when the total number is large, and its main feature is that it is evenly divided into several parts.
Take only one from each part; The main characteristics of stratified sampling and stratified proportional sampling are mainly used for people with obvious differences. The same feature of them is that the probability of each individual being drawn is equal.
96. The method of estimating samples according to the population is to take the frequency of samples as the probability of the population. X. Methods and skills to solve problems
97. Overall test-taking strategy: easy first, then difficult. Generally, first do multiple-choice questions, then fill in the blanks, and finally do big questions. Multiple choice questions strive to ensure speed and accuracy.
Leave time for the big questions later, but accuracy is the premise. For the fill-in-the-blank problem, it seems that there is no idea or the calculation is too complicated to give up. For big questions, try not to leave blank, and it is possible to score by transforming the conditions in the questions into algebra. Learn to give up in the exam, get rid of the endless entanglement of a topic and create a good psychological environment for yourself. This is an important guarantee for the success of the exam. 98. What's the special way to answer multiple-choice questions?
(Forward deduction method, estimation method, special case method, feature analysis method, intuitive selection method, reverse deduction method, combination of numbers and shapes, etc.). 99. What should I pay attention to when answering the fill-in-the-blank questions? (specialization, diagram, equivalent deformation) 100. What are the most basic requirements when solving application problems?
10 1. Examine the questions, find the key words in the questions, set the unknowns, list the function relations, substitute the initial conditions, indicate the units, and learn to answer questions.
Skip the grading technique, the first question will not, and the second question will. If you use the first question, you can directly use the conclusion of the first question. You should learn to relate it with the language of "from the known", "from the meaning of the problem" and "from the knowledge of plane geometry". Once you want to come, you can write "supplementary proof" at the back.
Skills of Mathematics College Entrance Examination
In the math exam, candidates need to pay special attention to many places. Mastering all kinds of problem-solving skills in the exam can help you catch the dragon gate at the last minute. Precautions for the exam:
1. Five minutes before the exam is very important.
In the exam, we should make full use of the 5 minutes before the exam. After the papers are handed out, you can browse the topics. When preparing for work (fill in name, test number, etc. ) After the completion, you can turn to the answer at the back, read it through, and be aware of it.
2. Treat each topic differently.
The examination questions are divided into three types: easy, medium and difficult, and the score ratio is about 3: 5: 2. In the exam, everyone should treat it separately according to their own situation.
(1) When doing easy questions, try to finish them all at once, and don't leave blank. This kind of questions will be scored 100%. (2) When doing intermediate questions, you should calm down and try your best to get points, and at least complete 80%. (3) When doing difficult problems, people usually feel at a loss. At this time, we must do: ① Read more questions and carefully examine them. ② Have a simple feeling about the draft.
③ Don't give up easily. Many students regard it as a difficult problem and a big problem. Without much consideration, they completely surrendered. Most of the answers are small steps, and many small problems can be solved by students. Therefore, candidates should take every question seriously.
3. Time allocation should be reasonable.
(1) The exam is mainly about grabbing time on multiple-choice questions.
⑵ Check the questions while doing them to fully ensure the correctness of each question. Don't waste too much time on the later inspection with the idea of "re-inspection after completion".
(3) Go back and check your progress 30 minutes before handing in the paper. Pay attention to filling and reading cards in time.