First, multiple-choice questions (12 questions, 5 points for each question, ***60 points)
Second, fill in the blanks (4 questions, 5 points for each question, ***20 points)
The knowledge points in the small questions are miscellaneous, but according to the college entrance examination situation over the years, the knowledge points are generally covered (the order may be adjusted according to the difficulty of the questions):
1. Investigate four operations of complex numbers, usually the division of complex numbers;
Example: Complex number-1+3i/ 1+i=
A 2+I B 2-I C 1+2i D 1- 2i
2. Investigate set operations, that is, intersection, union and complement of sets;
Example: given the set a = {1.3, radical m}, b = {1, m}, a and b = a, then m=
A 0 or root 3 B 0 or 3 C 1 or root 3 D 1 or 3.
It also includes conic 1-2 channels: such as calculating eccentricity, etc.
Function part 1-2 channel: such as finding the function range, maximum value and extreme value, finding the value range of a parameter, finding the number of zeros of the function and the number of intersections of two functions, etc.
Sequence part 1 orbit;
Plane vector1;
Trigonometric function 1-2 channel;
Binomial Theorem 1: Usually find the coefficients of each term in binomial expansion;
Arrangement and combination 1 lane;
Solid geometry 1-2.
Third, the answer (6 questions, ***70 points) general questions and exam knowledge points are relatively fixed.
Question 17: usually examine trigonometric functions or solve triangles;
Example: The opposite sides of the internal angles A, B and C of △ABC are A, B and C respectively. Given COS (A-C)+COSB = 1, a=2c, find c.
Question 18: We usually examine solid geometry, including proving the relationship between straight lines on different planes, proving the relationship between straight lines and planes, finding dihedral angles, finding the volume of a vertebral body in a graph, etc.
19 question: probability statistics and distribution table and expected peacetime inspection;
For example, the rules of table tennis match stipulate that in a game, before the scores of the two sides are even 10, after one side serves twice in a row, the other side serves twice in a row and rotates in turn. For each serve, the winner gets 1 point, and the loser gets 0 point. In the matching of A and B, the probability that the server gets 1 minute every time is 0.6, and the results of each service are independent of each other. In the match between A and B, A serves first.
(i) Find the probability that the ratio of A to B at the beginning of the fourth serve is 1 2;
(2) X represents B's score at the beginning of the fourth serve, and find the expected value of X..
Question 20: We usually investigate the function part, including finding the monotone interval of the function, the extreme value of the function, the range of parameter values and so on.
Example: let the function f(x)=ax+cosx, x∈[0, π].
(i) Discuss the monotonicity of f(x);
(Ⅱ) Let f(x)≤ 1+sinx, and find the value range of A. ..
2 1 Question: Conic curve: The first question usually finds the curve equation or eccentricity; The second problem is the intersection of a straight line and a conic curve (the amount of calculation is very large, so it is recommended to only formulate and give up the calculation)
Question 22: The part of sequence: including finding general formula or proving that a sequence is an arithmetic or geometric series, finding the sum of the first n terms, proving an inequality, etc.
Example:
The function f(x)=x2-2x-3, and the sequence {xn} is defined as follows: x 1=2, and xn+ 1 is the abscissa of the intersection of a straight line PQn passing through two points p (4,5) and Qn(xn, f(xn)) and the x axis.
(1) Proof: 2 < xnxn+1< 3;
(Ⅱ) Find the general term formula of sequence {xn}.