Analysis of an important knowledge point of mathematics elective course in senior two 1
1, the definition of a circle
The set of points whose distance from a point on a plane is equal to a fixed length is called a circle, with the fixed point as the center and the fixed length as the radius of the circle.
2. Equation of circle
(x-a)^2+(y-b)^2=r^2
(1) standard equation with (a, b) as the center and radius r;
(2) Method of solving cyclic equation:
Generally, the undetermined coefficient method is adopted: first set, then seek. Determining a circle requires three independent conditions. If the standard equation of a circle is used,
Demand a, b, r; If you use general equations, you need to find d, e, f;
In addition, we should pay more attention to the geometric properties of the circle: for example, the vertical line of a chord must pass through the origin, so as to determine the position of the center of the circle.
3. The positional relationship between a straight line and a circle
The positional relationship between a straight line and a circle includes three situations: separation, tangency and intersection:
(1) Set a straight line and a circle, and the distance from the center of the circle to L is, then there is; ;
(2) Tangent to a point outside the circle: ①k does not exist, so verify the existence of ②k, establish an oblique equation, and solve k with the distance from the center of the circle to the straight line = radius, and get two solutions of the equation.
(3) The tangent equation of a point passing through a circle: circle (x-a)2+(y-b)2=r2, and a point on the circle is (x0, y0), then the tangent equation passing through that point is (x0-a) (x-a)+(y0-b) (y-b) =
Exercise questions:
2. If the circle (x-a)2+(y-b)2=r2 passes through the origin, then ()
a2-b2=0B.a2+b2=r2
C.a2+b2+r2=0D.a=0，b=0
Analytical choice B. Because the circle passes through the origin, (0,0) satisfies the equation.
That is, (0-a)2+(0-b)2=r2,
So a2+b2=r2.
Analysis of an important knowledge point in mathematics elective course in senior two.
I. Random events
Master it (3, 4, 5)
Three operations of (1) event: union (sum), intersection (product) and difference; Note that the difference A-B can be expressed as the product of the reciprocal of A and B.
(2) Four operating laws: exchange law, correlation law, distribution law and democritus law.
(3) Five relationships of events: inclusion, equality, mutual exclusion (mutual incompatibility), opposition and mutual independence.
Second, the definition of probability
(1) Statistical definition: the frequency is stable near a number, which is called the probability of an event; (2) Classical definition: it is required that there are only a limited number of basic events in the sample space, and the possibility of each basic event is equal, then the ratio of the number of basic events contained in event A to the number of basic events contained in the sample space is called the classical probability of events;
(3) Geometric probability: there are infinite elements in the sample space, and the probability of each element is equal, so the sample space can be regarded as a geometric figure, and event A can be regarded as a subset of this figure, and its probability can be calculated by the ratio of the size of the subset figure to the size of the sample space figure;
(4) Axiomatic definition: any mapping from a subset set of sample space to [0, 1] that satisfies three axioms.
Third, the nature and formula of probability
(1) addition formula: P(A+B)=p(A)+P(B)-P(AB), especially if a and b are incompatible with each other, then p (a+b) = p (a)+p (b);
(2) Difference: P(A-B)=P(A)-P(AB), especially if B is included in A, then P (a-b) = P (a)-P (b);
(3) Multiplication formula: P(AB)=P(A)P(B|A) or P(AB)=P(A|B)P(B), especially if A and B are independent of each other, then P (AB) = P (A) P (B);
(4) Total probability formula: P(B)=∑P(Ai)P(B|Ai). This is the result of the cause,
Bayesian formula: p (aj | b) = p (aj) p (b | aj)/∑ p (ai) p (b | ai).
If event B can occur (cause) A 1, A2, ..., An in various situations, then the probability of B's occurrence is calculated by the full probability formula; If event B has occurred, you need the probability that it is caused by Aj, and then use Bayesian formula.
(5) binomial probability formula: pn (k) = c (n, k) p k (1-p) (n-k), k = 0, 1, 2, ..., n. When a problem can be regarded as an N-fold shell hard test (three conditions
Analysis of an important knowledge point in the third mathematics elective course in senior two.
Derivative is an important basic concept in calculus. When the independent variable x of the function y=f(x) generates an increment δ x at the point x0, if there is a limit a in the ratio of the increment δ y of the function output value to the increment δ x of the independent variable when δ x tends to 0, then A is the derivative at x0, which is denoted as f'(x0) or df(x0)/dx.
Derivative is the local property of function. The derivative of a function at a certain point describes the rate of change of the function near that point. If the independent variables and values of the function are real numbers, then the derivative of the function at a certain point is the tangent slope of the curve represented by the function at that point. The essence of derivative is the local linear approximation of function through the concept of limit. For example, in kinematics, the derivative of the displacement of an object with respect to time is the instantaneous velocity of the object.
Not all functions have derivatives, and a function does not necessarily have derivatives at all points. If the derivative of a function exists at a certain point, it is said to be derivative at this point, otherwise it is called non-derivative. However, the differentiable function must be continuous; Discontinuous functions must be non-differentiable.
For differentiable function f(x), x? F'(x) is also a function called the derivative function of f(x). The process of finding the derivative of a known function at a certain point or its derivative function is called derivative. Derivative is essentially a process of finding the limit, and the four algorithms of derivative also come from the four algorithms of limit. Conversely, the known derivative function can also reverse the original function, that is, indefinite integral. The basic theorem of calculus shows that finding the original function is equivalent to integral. Derivation and integration are a pair of reciprocal operations, both of which are the most basic concepts in calculus.
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