Mathematics knowledge points and formula arrangement in senior two 1
1, vector addition
The addition of vectors satisfies parallelogram rule and triangle rule.
AB+BC=AC .
a+b=(x+x '，y+y ').
a+0=0+a=a .
Algorithm of vector addition;
Exchange law: a+b = b+a;
Law of association: (a+b)+c=a+(b+c).
2. Vector subtraction
If A and B are mutually opposite vectors, then the reciprocal of a=-b, b=-a and a+b=0.0 is 0.
AB-AC=CB。 That is, "* * * the starting point is the same, and the direction is reduced"
A=(x, y)b=(x', y') Then a-b=(x-x', y-y').
4. Multiply the number by the vector
The product of real number λ and vector A is a vector, which is denoted as λ a, λ a ∣ = ∣ λ ∣ ∣ A ∣.
When λ >; 0, λa and a are in the same direction;
When λ
When λ=0, λa=0, and the direction is arbitrary.
When a=0, there is λa=0 for any real number λ.
Note: By definition, if λa=0, then λ=0 or A = 0.
Real number λ is called the coefficient of vector A, and the geometric meaning of multiplier vector λa is to extend or compress the directed line segment representing vector A. ..
When ∣ λ ∣ > 1, indicating that the directed line segment of vector a is in the original direction (λ >; 0) or the opposite direction (λ
When ∣ λ ∣ < 1, the directed line segment of vector A is in the original direction (λ >; 0) or the opposite direction (λ
The multiplication of numbers and vectors satisfies the following algorithm.
Law of association: (λ a) b = λ (a b) = (a λ b).
The distribution law of vector logarithm (first distribution law): (λ+μ)a=λa+μa 。
The distribution law of number pair vector (second distribution law): λ(a+b)=λa+λb 。
The elimination method of number multiplication vector: ① If the real number λ≠0 and λa=λb, then A = B. ② If a≠0 and λa=μa, then λ = μ.
3. Quantity product of vectors
Definition: the included angle between two nonzero vectors is < a, b > and < a, b > ∈ [0, π].
Definition: the product of two vectors (inner product, dot product) is a quantity, denoted as a B. If A and B are not * * * lines, a b = | a || b | cos < a, b >；; If a, b***, then a b =+-∣ a ∣ ∣ b ∣.
The coordinates of the product of vectors are expressed as: a b = x x'+y y'.
Arithmetic ratio of the product of vectors
A b = b a (exchange rate);
(a+b) c = a c+b c (distribution rate);
Properties of scalar product of vectors
A a = the square of a |.
a⊥b〈=〉a b=0 .
|a b|≤|a| |b| .
Senior two mathematics knowledge points and formula arrangement II
1. The universal formula makes tan (a/2) = Tsina = 2t/(1+t2) COSA = (1-t2)/(1+t2) Tana = 2t/(65433).
2. The auxiliary angle formula asint+bcost = (A2+B2) (1/2) sin (t+r) cosr = a/[(A2+B2) (1/2)] SINR = b/.
3. The triple angle formula SIN (3a) = 3sina-4 (sina) 3cos (3a) = 4 (COSA) 3-3cotan (3a) = [3tana-(tana) 3]/[1-3 (tana2)]. -sin(a-b)]/2cosa _ cosb =[cos(a+b)+cos(a-b)]/2 Sina _ sinb =-[cos(a+b)-cos(a-b)]/2 Sina+sinb = 2 sin[(a+b)/2]Sina-sinb = 2 sin[(a-b)/2]cos[(a+b)/2]cosa+cosb = 2cos[(a+b)/2]cos[(a-b)/2]cosa-cosa
Senior two mathematics knowledge points and formula arrangement 3
1. Knowledge points of counting principle
① multiplication principle: n = n 1 N2 n3...nm (step by step) ② addition principle: n = n 1+N2+n3+...+nm (classification).
2. Arrangement (orderly) and combination (disorderly)
anm = n(n- 1)(n-2)(n-3)-(n-m+ 1)= n！ /(n-m)！ Ann=n！
Cnm=n！ /(n-m)！ m！
Cnm = Cnn-mCnm+Cnm+ 1 = Cn+ 1m+ 1k？ k！ =(k+ 1)！ -k！
3. The principle of solving the mixed problem of permutation and combination: choose the back row first, and divide it into the back row first.
The main method to solve the problem of permutation and combination: priority method: focusing on elements, meeting the requirements of special elements first, and then considering other elements. Consider the position first, that is, meet the requirements of special positions before considering other positions.
Binding method (group element method, which treats some elements that must be together as a whole)
Interpolation method (solving interphase problem), indirect method and impurity removal method.
When solving the application problem of permutation and combination, we should pay attention to:
(1) Convert or attribute specific problems to permutation or combination problems;
(2) Determine whether to apply the principle of classified counting or step-by-step counting through analysis;
(3) Analyze the topic conditions to avoid repetition and omission in "selection";
(4) List formulas to calculate and answer.
Commonly used mathematical ideas are:
(1) classification discussion ideas; ② Changing ideas; ③ Symmetrical thinking.
4. Binomial theorem knowledge points:
①(a+b)n = cn 0ax+cn 1an- 1b 1+Cn2an-2 B2+Cn3an-3 B3+…+Cnran-RBR+-…+Cnn- 1abn- 1+Cnn bn
Specifically: (1+x) n =1+cn1x+cn2x2+…+cnrxr+…+cnxn.
② main properties and conclusions: symmetry CNM = CNN-m.
Binomial coefficient is in the middle. (Note whether n is odd or even, and the answer is middle or middle. )
Sum of all binomial coefficients: cn0+cn1+cn2+cn3+cn4+…+CNR+…+CNN = 2n.
The sum of binomial coefficients of odd terms = even terms but the sum of coefficients.
cn0+Cn2+Cn4+Cn6+Cn8+…= cn 1+Cn3+Cn5+Cn7+Cn9+…= 2n- 1
③ The general term is r+1:tr+1= cnran-rbr function: it deals with problems related to specified term, specific term, constant term and rational term.
5. Application of binomial theorem: Solve the problem of approximate calculation and divisibility, and prove the inequality related to exponent by binomial expansion theorem and scaling method.
6. Pay attention to the difference between binomial coefficient and binomial coefficient (letter term coefficient, specified term coefficient, etc.). , refers to the coefficient of the operation result), pay attention to the application of assignment method when finding the sum of some coefficients.
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