1. Five knowledge points of compulsory mathematics in senior one.
⑵ Set and simple logic: concept and operation of set, simple logic, necessary and sufficient conditions ⑵ Function: mapping and function, distinguishing function and definition domain, range and maximum, inverse function, three properties, function image, exponent and exponential function, logarithm and logarithmic function, function application.
⑶ Sequence: related concepts of sequence, arithmetic progression, geometric progression, summation of sequence, and application of sequence.
⑷ trigonometric function: related concepts, homonym relationship and inductive formula, sum, difference, multiplication, semi-formula, evaluation, simplification, proof, images and properties of trigonometric function, and application of trigonometric function.
5. Plane vector: related concepts and elementary operation, coordinate operation, scalar product and its application.
[6] Inequality: concept and nature, mean inequality, inequality proof, inequality solution, absolute inequality, inequality application.
2. High school mathematics requires five 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.
3. High school mathematics requires five knowledge points.
Probability properties and formulas
(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
4. Five knowledge points of compulsory mathematics in senior one.
Functional understanding of 1. sequence: ① sequence is a special function. Its particularity is mainly manifested in its definition domain and value domain. A sequence can be regarded as a positive integer set N* or its finite set {1, 2,3, ..., n}, where {1, 2,3, ..., n} cannot be omitted.
② Understanding sequence from the perspective of function is an important way of thinking. Generally speaking, there are three representations of functions, and series is no exception. There are usually three representations:
A. tabular method;
B. mirror image method;
C. analytical methods.
Among them, the analytical methods include giving the sequence with general formula and giving the sequence with recursive formula.
③ Functions do not necessarily have analytical formulas, and similarly, not all series have general formulas.
2. General term formula: The relationship between the nth term an of a series and the ordinal number n of this term can be expressed by a formula an=f(n), which is called the general term formula of this series (note: the general term formula is not).
Characteristics of general term formula of sequence;
(1) The general term formulas of some series can have different forms, that is, none.
(2) Some series have no general formula (for example, prime numbers are arranged in a row from small to large, 2, 3, 5, 7, 1 1, ...).
3. Recursive formula: If the relationship between the nth item of the series {an} and its previous item or items can be expressed by a formula, then this formula is called the recursive formula of this series.
Characteristics of recurrence formula of sequence;
(1) The recurrence formulas of some series can have different forms, that is, none.
(2) Some series have no recurrence formula.
Recursive formulas do not necessarily have a general formula.
Note: The items in the series must be numbers, which can be real numbers or complex numbers.
5. Five knowledge points of compulsory mathematics in senior one.
The range of a function depends on the definition range and the corresponding laws. No matter what method is used to find the function value domain, the definition domain should be considered first. The common methods to find the function range are: (1) direct method, also known as observation method. For the function with simple structure, the range of the function can be directly observed by applying the properties of inequality to the analytical expression of the function.
(2) Substitution method: A given complex variable function is transformed into another simple function re-evaluation domain by algebraic or trigonometric substitution. If the resolution function contains a radical, algebraic substitution is used when the radical is linear and trigonometric substitution is used when the radical is quadratic.
(3) Inverse function method: By using the relationship between the definition domain and the value domain of the function f(x) and its inverse function f- 1(x), the value domain of the original function can be obtained by solving the definition domain of the inverse function, and the function value domain with the shape of (a≠0) can be obtained by this method.
(4) Matching method: For the range problem of quadratic function or function related to quadratic function, the matching method can be considered.
(5) Evaluation range of inequality method: Using the basic inequality a+b≥[a, b∈(0, +∞)], we can find the range of some functions, but we should pay attention to the condition of "one positive, two definite, three phases, etc." Sometimes you need skills such as Fang.
(6) Discriminant method: y=f(x) is transformed into a quadratic equation about x, and the definition domain is evaluated by "△≥0". The characteristic of the question type is that the analytical formula contains roots or fractions.
(7) Finding the domain by using the monotonicity of the function: When the monotonicity of the function on its domain (or a subset of the domain) can be determined, the range of the function can be found by using the monotonicity method.
(8) Number-shape combination method to find the range of function: using the geometric meaning expressed by the function, with the help of geometric methods or images, to find the range of function, that is, finding the range of function through the combination of numbers and shapes.