1.
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.
(7) Equation of straight line and circle: equation of straight line, positional relationship between two straight lines, linear programming, circle, and positional relationship between straight line and circle.
(8) Conic curve equation: the positional relationship between ellipse, hyperbola, parabola, straight line and conic curve, the trajectory problem and the application of conic curve.
(9) Lines, planes and simple geometry: space lines, lines and planes, planes and planes, prisms, pyramids, spheres and space vectors.
⑽ permutation, combination and probability: permutation, combination, binomial theorem and its application.
⑾ Probability statistics: probability, distribution table, expectation, variance, sampling and normal distribution.
⑿ derivative: the concept, derivation and application of derivative.
[13] Complex number: the concept and operation of complex number.
2. The second semester of senior high school mathematics knowledge arrangement
1. Sine, cosine and tangent formulas of sum and difference of two angles: Emphasis: Through exploration and discussion, eleven formulas of trigonometric function of sum and difference of two angles are derived, and their internal relations are understood.
Difficulties: exploration and proof of cosine formula of two-angle difference.
2. Simple trigonometric identity transformation:
Key points: master the contents, ideas and methods of trigonometric transformation, and experience the characteristics of trigonometric transformation.
Difficulties: Flexible application of the formula.
Several explanations of trigonometric function;
1. We only need to know the arc length formula, which can be simply applied, and it doesn't need to be deepened when applied.
2. Prove trigonometric identity and evaluation calculation with the basic relationship of trigonometric function with the same angle, and be skilled in supporting roles and calculation of sin and cos.
3. The problem of finding the angle of trigonometric function is known, and it can meet the requirements of teaching materials without expansion.
4. Grasp the function y=Asin(wx+j) image, monotone interval, symmetry axis, symmetry point, special point and maximum value.
5. Sum-difference integral, sum-difference integral and half-angle formula are only practiced and do not need to be memorized.
6. Sine, cosine and tangent formulas of sum and difference of two angles.
3. The second semester of senior high school mathematics knowledge arrangement
Probability property and formula (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 cause.
Bayesian formula: p (aj | b) = p (aj) p (b | aj)/∑ p (ai) p (b | ai). It is made of fruit;
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 n times of hard test (three conditions: n times
4. Math knowledge arrangement in the second semester of senior high school
Application of derivative 1. Study the maximum value of function with derivative.
Make sure that the function is differentiable in its definition domain (usually open interval), find out the zero point of the derivative function in the definition domain, and study the monotonicity of the function around zero point. If the left side increases and the right side decreases, the function will reach the maximum at this zero point. If the left side decreases and the right side increases, the function at the zero point takes the minimum value. After learning how to study the maximum value of a function with derivatives, you can do a comprehensive problem about derivatives and functions to test your learning effect.
2. Common function optimization problems in life.
1) cost and minimum cost.
2) the problem of profit and income
3) The biggest problem of area and volume.
5. Finishing the knowledge points of mathematics in the second semester of Senior Two.
Given that the function has zero (the equation has roots), the common methods to find the parameter value are 1 and direct method:
The inequality of parameters is constructed directly according to the conditions of the topic, and then the parameter range is determined by solving the inequality.
2. Separation parameter method:
Firstly, the parameters are separated and transformed into the problem of finding a function domain to solve.
3. Number-shape combination method;
Firstly, the analytic formula is deformed, and the image of the function is drawn in the same plane rectangular coordinate system, and then the solution is combined with the number shape.
6. Finishing the knowledge points of mathematics in the second semester of Senior Two.
The value of determinant algorithm 1 and triangular determinant is equal to the product of diagonal elements. When calculating, it usually takes many operations to convert determinant into upper triangle or lower triangle.
2. Swap two rows (columns) in the determinant, and the determinant changes sign.
3. The common factor of a row (column) in the determinant can be placed outside the determinant.
4. Multiply one row of the determinant by a and add it to another row. Determinants are invariant and are often used to eliminate certain elements.
5. If the two rows (columns) in the determinant are exactly the same, the determinant is 0; It can be inferred that if two rows (columns) are proportional, the determinant is 0.
6. Expansion of determinant: the value of determinant is equal to the sum of the products of each element of a row (column) and its algebraic cofactor; However, if the elements of another row (column) are added to the algebraic cofactor product of that row (column), the sum is 0.
7. When solving the related problems of algebraic cofactor, the determinant can be replaced by value.
8. Cramer's rule: use the coefficient determinant of linear equations to solve equations.
9. Homogeneous linear equations: When all the constant terms on the right side of a linear equation group are 0, the equation group is called homogeneous linear equations, otherwise it is nonhomogeneous linear equations. Homogeneous linear equations must have zero solutions, but not necessarily non-zero solutions. When D=0, there is a nonzero solution; When d! When =0, the equation has no zero solution.