1. Two knowledge points must be tested in the first volume of senior two mathematics.
Derivative is an important basic concept in calculus. When the independent variable x of the function =f(x) generates the increment δ x at the point x0, if there is a limit a of the ratio of the increment δ of the output value of the function to the increment δ x of the independent variable when δ x approaches 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 the derivative function f(x), xf'(x) is also a function, which is 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 are also among 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.
Let the function =f(x) be defined in the neighborhood of point x0. When the independent variable x has an increment Δ x at x0 and (x0+Δ x) is also in the neighborhood, the corresponding function gets the increment Δ = f (x0+Δ x)-f (x0); If the ratio of Δ to Δ x has a limit when Δ x→ 0, the function =f(x) can be derived at point x0, and this limit is called that the derivative of function =f(x) at point x0 is f'(x0), or │x=x0 or d/dx│x=x0.
2. Two knowledge points must be tested in the first volume of high school mathematics.
basic concept
Axiom 1: If two points on a straight line are in a plane, then all points on this straight line are in this plane.
Axiom 2: If two planes have a common point, then they have only one common straight line passing through this point.
Axiom 3: When three points that are not on a straight line intersect, there is one and only one plane.
Inference 1: Through a straight line and a point outside this straight line, there is one and only one plane.
Inference 2: Through two intersecting straight lines, there is one and only one plane.
Inference 3: Through two parallel straight lines, there is one and only one plane.
Axiom 4: Two lines parallel to the same line are parallel to each other.
Equiangular Theorem: If two sides of one angle are parallel and in the same direction as two sides of another angle, then the two angles are equal.
3. Two knowledge points must be tested in the first volume of senior two mathematics.
1. Definition of geometric probability: If the probability of each event is only proportional to the length (area or volume) of the event area, such a probability model is called geometric probability model, or geometric probability model for short. 2. Probability formula of geometric probability: P(A)= the length (area or volume) of the region that constitutes event A;
The length (area or volume) of the area formed by all test results.
3, the characteristics of geometric probability:
1) There are infinitely many possible results (basic events) in the test;
2) The possibility of each basic event is equal,
4. Comparison between geometric probability and classical probability: on the one hand, classical probability is limited, that is, the test results are countable; Geometric probability is that there are infinitely many results in the test, and it is related to length (or area, volume, etc.). ), that is, the test results are infinite. This is the difference between the two; On the other hand, the experimental results of classical probability and geometric probability have the same possibility, which is their * * * property.
4. Two knowledge points must be tested in the first volume of senior two mathematics.
1. Inequality relations and inequality knowledge points 1. Definition of inequality
In the objective world, the unequal relationship between quantity and quantity is universal. We use the mathematical symbol,, to connect two numbers or algebraic expressions to express the unequal relationship between them. Formulas containing these inequalities are called inequalities.
2. Compare the sizes of two real numbers
The sizes of two real numbers are defined by their operational properties, where a-baa-b=0a-ba0 and a/baa/b= 1a/ba.
3. The nature of inequality
(1) symmetry
(2) Transitivity: ab, ba
(3) additivity: aa+cb+c, ab, CA+C.
(4) multiplicity: ab, cacb0, c0bd.
(5) Multiplication formula: a0bn(nN, n
(6) Prescription: a0
(nN，n2)。
note:
A skill
Skills of deformation in difference method: deformation is the key in difference method, and factorization or formula is often carried out.
A method
Undetermined coefficient method: find the range of algebraic expression, use known algebraic expression to represent the target expression, then use the principle of polynomial equality to find the parameters, and finally use the properties of inequality to find the range of the target expression.
5. Two knowledge points must be tested in the first volume of senior two mathematics.
Arithmetic progression For a series {an}, if the difference between any two adjacent terms is a constant, then this series is arithmetic progression, and this determined value difference is called tolerance, which is recorded as d; The sum from the first term a 1 to the nth term an is represented as Sn.
Then, the general formula is, and its solution is very important, using the idea of "superposition principle":
Adding the above expressions of n- 1 will eliminate many related terms one by one, and finally an will remain on the left side of the equation, while a 1 and n- 1 d will remain on the right side, thus obtaining the above general term formula.
In addition, the specific derivation of the sum of the first n items in the series is relatively simple, and the above similar superposition method or iterative method can be adopted, which is not repeated here.
It is worth noting that after the sum of the first n terms Sn is divided by n, a new series with a 1 as the first term and d/2 as the tolerance can be obtained. Using this feature, many series of problems involving Sn can be easily solved.
geometric series
For a series {an}, if the quotient of any two adjacent terms (that is, their ratio) is a constant, then this series is geometric progression, and this constant quotient is called the common ratio q; From the first item a 1 to the n item an, the record is Tn.
Then, the general formula is (that is, a 1 times q to the power of (n- 1), which is derived from the idea of "continuous multiplication principle":
a2=a 1_q，
a3=a2_q，
a4=a3_q，
````````
an=an- 1_q，
Multiply the above-mentioned (n- 1) term, and after eliminating the corresponding term left and right, the left is an, and the right is the product of a 1 and (n- 1) Q, that is, the general term formula is obtained.
In addition, when q= 1, the sum of the first n terms of the sequence TN = a1_ n.
When q≠ 1, the sum of the first n terms of the sequence TN = a1_ (1-q (n))/(1-q).