Analysis of the answers to the final exam of senior two mathematics.
1. Multiple choice questions (5 points for each question, * * 60 points, only one of the options given in each question below meets the meaning of the question. Please fill in the serial number of the correct answer on the answer sheet)
1. The following events: ① Toss coins twice in a row, both facing up; (2) opposite charges attract each other; (3) At standard atmospheric pressure, water freezes at 100℃, which is a random event, including C.
A.②; b .③； c .①； ②、③
2. ""is ""
A. Sufficient and unnecessary conditions B. Necessary and insufficient conditions
C. Sufficient and necessary conditions D. Conditions that are neither sufficient nor necessary
The smallest number in the following figures is d.
a . 85(9)b . 2 10(6)c . 1000(4)d . 1 1 1 1 1 1(2)
4. The variance of data a 1, a2, a3, …, an is A, then the variance of data 2a 1, 2a2, 2a3, …, 2an is D.
A.a 2B。 AC.2A D.4A
5. Take any point P on the line segment AB with the length of 10cm and make a square with the line segment AP as the edge. The probability that the area of this square is between 25cm2 and 49cm2 is b.
University of California, Los Angeles.
6. There are 900 high school students in a school, including 300 in Grade One, 200 in Grade Two and 400 in Grade Three. Now a sample with a capacity of 45 is stratified sampling, so the number of students in Grade One, Grade Two and Grade Three is D respectively.
A. 15，5，25B. 15， 15C. 10，5，30D
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7. When running the program on the right, the execution times of statements in the WHILE loop body are B ..
A.5 B.4 C.3D.9
8. If the proposition P is known, it is a..
A.B
C.D.9 Let the circle C be tangent to the straight line y=0, then the locus of the center of the circle C is a.
A. parabola b hyperbola c ellipse d circle
10. Let the asymptote equation of hyperbola be, then the value of is (c).
A.4B.3C.2D. 1
1 1. It is known that f is the focus of parabola, a and b are two points on parabola, and the distance from the midpoint of line segment AB to the Y axis is (b).
A. 1C.D
12. Someone fired five shots and hit three. The probability that two of the three shots hit an even number is (a).
University of California, Los Angeles.
Volume 2 (non-multiple choice questions ***90 points)
2. Fill in the blanks (there are 4 small questions in this big question, with 5 points for each small question and 20 points for * * *).
13. Calculate the value of polynomial f(x)=5+4+3+2+x+ 1 when x=5 by Qin algorithm.
14. The life tracking survey of electronic components is as follows.
Life (h)100 ~ 200200 ~ 300300 ~ 400400 ~ 500500 ~ 600
Number 2030804030
The proportion of components with expected service life within 100 ~ 400 h is 0.65.
15. If the proposition ""is false, the range of real numbers is.
16. Take three balls randomly from the bag containing five red balls and five white balls. There are events: ① "Take out two red balls and 1 white balls" and "Take out 1 red balls and two white balls"; ② "Take out 2 red balls and 1 white ball" and "Take out 3 red balls"; ③ "Take out three red balls" and "Take out at least 1 white ball from three balls"; ④ "Take out three red balls" and "Take out three white balls". Among them, there are three opposing events.
Three. Answer questions (***6 questions, 17, 10, the rest 12, ***70).
17. Verification: The necessary and sufficient conditions for δ ABC to be an equilateral triangle are a2+b2+c2=ab+ac+bc, (A, B and C are three sides of δ ABC. )
Proof: Sufficiency: If ABC is an equilateral triangle, then a=b=c holds, and right =3a2= left.
Necessity: If a2+b2+c2=ab+ac+bc, multiply both sides by 2.
2a2+2b2+2c2=2ab+2bc+2ca。
(a-b)2+(b-c)2+(c-a)2=0
So a=b=c holds, that is, the triangle is an equilateral triangle 18. (The full score of this small question is 12)
A maze has three passages, and everyone who enters the maze must pass through an intelligent door. When you first arrive at this door, the system will randomly open a channel for you (that is, if possible). If it is channel 1, it will take 1 hour to get out of the maze. If it is channel 2 and channel 3, it takes 2 hours and 3 hours to return to the smart door respectively. When you reach the smart door again, the system will randomly open a channel you have never been to until you get out of the maze.
(1) Find the probability of getting out of the maze in l hours;
(2) Find the probability that it will take more than 3 hours to get out of the maze.
Solution: (1) Let a mean that it took 1 hour to get out of the maze.
(2) Let B represent an event that takes more than 3 hours to get out of the maze, then.
19. Two cyclists A and B have done six tests under the same conditions, and their speed (m/s) data are shown in the following table.
A 27383037353 1
Second, 33298842336
(1) Draw the stem leaf diagram. What information can you get from the stem leaf diagram?
(2) Calculate the average, median and standard deviation of the speed (m/s) data of cyclists A and B respectively, and judge who is more suitable to participate in the race.
Solution: (1) Draw the stem and leaf diagram, and the middle number is the ten digits of the data?
As can be seen from this stem leaf diagram, the scores of A and B are evenly distributed, but B is better. The median of B is 35, and that of A is 33. Therefore, B's performance is relatively stable, and the overall score is better than A's.
(2)=33,=33; =3.96,=3.56; The median of A is 33, and the median of B is 35.
20. Assume that the service life x and maintenance cost y (ten thousand yuan) of a certain equipment are as follows:
Service life x23456
Maintenance cost 2.23.85.56.57.0
If you know from the data that there is a linear correlation between y and x, try to find:
(3) Linear regression equation;
(4) When the estimated service life is 10 years, what is the maintenance cost?
Y = 1.23x+0.08 123800。
2 1. It is known that the left and right focal points of ellipse C are (,0) and (,0) respectively, and the eccentricity is that the straight line y=t intersects ellipse C at two different points M, N, and the diameter of line segment MN is used as a circle P with the center of the circle P. 。
(1) equation for finding ellipse c
(2) If the circle P is tangent to the X axis, find the coordinate solution of the center P: (i) Because, and therefore.
So the equation of ellipse c is
(2) From the meaning of the problem.
allow
So the radius of circle p is
The coordinate of point p is (0,).
22. (The full score of this short question is 12)
It is known that a straight line with a slope of 1 intersects a hyperbola at two points, where the point is.
(i) the obtained eccentricity;
(2) Let the right vertex be and the right focus be, and prove that the passing circle is tangent to the axis.
(a) from the topic, the equation is:
Substitute into the equation of c, simplify, and get,
Settings,
Then ①
Because it is the midpoint of BD, so
Namely ②
So, so the eccentricity of c.
(2) From ① ②, the equation of c is:
Therefore, it is recommended to set,
.
Say it again,
Therefore,
Solve, or (give up),
Therefore,
If you connect a horse, you can know it, so it is the axis. Therefore, a circle with M as the center and MA as the radius passes through points A, B and D and is tangent to the axis at point A, so the circle passing through points A, B and D is tangent to the axis.
A small way to learn mathematics
If you have a good interest in learning, try to cultivate your interest in mathematics. Over time, you will find that math is not that difficult. Try to read more cartoons and books about mathematics, which can cultivate your interest in mathematics.
Review before class, read the original words in the book as much as possible, draw them with marks if you don't understand, listen carefully in class, understand if you don't understand, or raise your hand and ask the teacher, who will explain them to you.
Pay attention to the understanding of concepts, don't memorize what you can understand, understand what you can understand, and give examples of what you can't. For example, because positive numbers are greater than 0 and negative numbers are less than 0, positive numbers are greater than negative numbers. Derive it step by step, of course, the foundation still needs to be memorized, and everything else can be understood.
Strong spatial imagination, learning geometry requires strong spatial imagination, and the ways to cultivate spatial imagination are: 1. Good at drawing, draw more, 2. Cultivate your observation imagination with teaching AIDS, 3. Learning first, practicing first, and drawing first are helpful to cultivate imagination. 4. Do more experiments by yourself to make abstract objects three-dimensional.
Find a person who is super good at learning and ranks in the top 3 in the class as an "enemy", try to regard him as your enemy, think about why you can't surpass him and why you can't study as well as him, try to anger yourself and try to surpass him. Sometimes success requires the help of the enemy.
Face the facts correctly. If you fail the exam, don't lose heart. Think more about why you made a mistake in that place and get 100 points. After that, write the wrong questions in the wrong book, and write the methods and answers to the wrong questions on it, which will help improve your grades in the next exam. In the words of celebrities: how can you succeed without failure? Edison said: failure is the mother of success. Think about these words more when you fail in the exam and encourage yourself.
Listen carefully in class and review carefully after class. Follow the teacher's train of thought in class, you can look at whatever the teacher says, ask if you don't understand after class, raise your hand actively in class, develop the good habit of listening to lectures, go to the toilet and come back during recess, think about what the teacher says on the table, and put movies in your head to improve efficiency.
Do more questions and form good habits. If you want to learn math well, it is inevitable to do more problems. When you solve a problem, don't rush to do the next one. Try other methods and see if you can solve this problem. If not, you should actively ask the teacher, who will explain it to you. You just need to remember the methods and routines. Practice has proved that at the critical moment, your problem-solving habit is no different from your usual practice. If you are careless and careless when solving problems, it is often exposed in the big exam, so it is very important to develop good problem-solving habits at ordinary times.
What are the tips for learning mathematics?
When learning mathematics, we must know what the way of thinking is. Only by mastering the thinking mode can we know how to think when we see a math problem. Once we have an idea, it will be easier to do any problem. The most important thing in mathematics is to have ideas when doing problems. If you don't even have an idea, you can't do this math problem. The importance of thinking in mathematics goes without saying by Bian Xiao, and students all know it in their lives.
In fact, some ideas of science are similar, so as long as you master a learning idea, no matter which subject you study, it will be much easier. In mathematics, although some problems are the same, some students are still not good at doing them even if they have done the same problems. In this case, it is basically difficult to improve our grades.