The relationship between permutation number and combination number;
The connection and difference of permutation and combination;
From the definition of permutation and combination, we can know that both of them take m (m≤n, n, m∈N) elements from n different elements, which is the * * * similarity of permutation and combination. The difference between the two is that the arrangement is to arrange the extracted elements into a column in sequence, which is related to the order of the elements, while the combination only needs to extract the elements, regardless of the order. Only two arrangements with the same elements and the same order are the same arrangement, otherwise they will be different; For a combination, as long as the elements of two combinations are the same, no matter what the order of the elements is, it is the same combination, such as A, B and B, A is two different permutations, but it is the same combination.
The most basic solution to the scheduling application problem is:
(1) Direct method: taking elements as the object of investigation, first meeting the requirements of special elements and then considering general elements, which is called factor analysis method, or taking positions as the object of investigation, first meeting the requirements of special positions and then considering general positions, which is called position analysis method;
(2) Indirect method: Calculate the total number of permutations without considering additional conditions, and then subtract the number of permutations that do not meet the requirements.
2. Senior one mathematics compulsory three key knowledge induction 2
random digit
Generation of uniform random numbers;
We usually use uniform random numbers on [0, 1]. If the test result is any number in the interval [0, 1], and any real number is also possible, we can use a calculator to generate a uniform random number between 0 and 1 for random simulation. We often use stochastic simulation to calculate the area of irregular figures.
Uniform random function:
Uniform random function and can only generate uniform random numbers in the interval of [0, 1].
Generate a uniform random number in the interval [a, b]:
Generate a uniform random number in the interval [a, b]. If x is a uniform random number in [0, 1], then x(b-a)+a is a uniform random number in [a, b].
The idea of computer simulation experiment for generating uniform random numbers;
(1) Determine the number of random numbers to be generated according to the number of quantities that affect the results of random events, such as only one set of length and angle; Area type needs two sets of random numbers, and volume type needs three sets of random numbers;
(2) determining the range of random number generation according to the region corresponding to the whole population;
(3) Determine the relationship that random numbers should meet according to the occurrence conditions of event A. ..
3. High school mathematics compulsory three key knowledge induction three
Functional domain:
The function of the real number x that can make the function meaningful is called the domain of the function.
The main basis for finding the domain of function is:
The denominator of the (1) score is not equal to zero.
(2) The number of even roots is not less than zero.
(3) The truth value of the logarithmic formula must be greater than zero.
(4) The bases of exponential and logarithmic expressions must be greater than zero and not equal to 1.
(5) If the function is composed of some basic functions through four operations. Then, its domain is a function of x value, which makes all parts meaningful.
(6) The zero base of the index cannot be equal to zero.
(7) The definition domain of the function in the actual problem should also ensure that the actual problem is meaningful.
Method for judging the same function:
(1) the same expression (regardless of the letters representing the independent variables and function values)
(2) Domain consistency (two points must be met at the same time)
4. Summary of three key knowledge of compulsory mathematics in senior high school
Analytic expression of function
The analytical expression of (1) function is a representation of function. When the functional relationship between two variables is needed, the corresponding law between them and the definition domain of the function are needed.
(2) The main methods for finding analytic expressions of functions are:
1) matching method
2) undetermined coefficient method
3) Alternative methods
4) Parameter elimination method
5. Summary of Three Key Knowledge Required in Senior High School Mathematics Part 5
Surface area volume formula of space geometry;
1, cylinder: surface area: 2πRr+2πRh volume: πR2h(R is the radius of the upper and lower bottom circles of the cylinder, and h is the height of the cylinder).
2. Cone: surface area: πR2+πR[(h2+R2)] Volume: πR2h/3(r is the radius of the low circle of the cone, and H is its height.
3. Length of side A, S=6a2, V=a3.
4. Cuboid a- length, b- width, c- height S=2(ab+ac+bc)V=abc.
5. prism S-h- height V=Sh
6. pyramid S-h- height V=Sh/3
7.S 1 and S2- upper and lower h- height v = h [s1+S2+(s1S2)1/2]/3.
8.S 1- upper bottom area, S2- lower bottom area, S0- medium h- high, V=h(S 1+S2+4S0)/6.
9. The base radius, h- height, C- base perimeter, S- base area, S- side, S- surface area of R-cylinder, C=2πrS, S- side =Ch, S- table =Ch+2S, V = S- base h=πr2h.
10, hollow cylinder r- outer circle radius, R- inner circle radius h- height v = π h (r 2-r 2)
1 1, r- bottom radius h- height v = π r 2h/3.
12, r- upper bottom radius, r- lower bottom radius, h- height V=πh(R2+Rr+r2)/3 13, ball R- radius d- diameter v = 4/3 π r 3 = π d 3/6.
14, ball gap h- ball gap height, r- ball radius, a- ball gap bottom radius V=πh(3a2+h2)/6=πh2(3r-h)/3.
15, table r 1 and r2- radius h- height V=πh[3(r 12+r22)+h2]/6.
16, ring r- ring radius d- ring diameter R- ring section radius D- ring section diameter V = 2π 2RR2 = π 2d2/4.
17, barrel d- barrel belly diameter D- barrel bottom diameter h- barrel height V=πh(2D2+d2)/ 12, (the bus is round with the center of the barrel) v = π h (2d2+DD+3d2/4)/1.