Questions and answers on the monthly exam of mathematics in senior one.
First, multiple-choice questions (this question * * * has 12 small questions, each with 5 points, * * * 60; Only one item meets the requirements of the topic) 1, known set a? { y |； a 、{ 1，2}B 、{y|y？ 1 or 2}C, {(x,; x？ 0 or y? 1? x？ 1? ; y？ 2}D 、{y|y？ 1}2. let f? x3x？ ; ? 3. If the function f(x)? ( 1x； 4),? 1? x？
Daqing No.1 Middle School and Senior One took the second monthly exam last semester, 20 15-20 16 school year.
Math test 20 15.438+05438+0.26
A, multiple-choice questions (this question * * * 12 small questions, each question 5 points, ***60 points. Of the four options given in each small question,
Only one item meets the requirements of the topic) 1, known set a? {y|y？ x2？ 1，x？ R}，B？ {y|y？ x？ 1，x？ R}, then a? b？ ()。
a 、{ 1，2}B 、{y|y？ 1 or 2}C, {(x, y)|
x？ 0 or y? 1? x？ 1?
y？ 2}D 、{y|y？ 1}2. let f? x3x？ 3x？ 8. Use dichotomy to find equation 3x? 3x？ 8? 0 is in x 1 2? Get f in the process of inner approximate solution? 10，f？ 1.50，f？ 1.250, then the root of the equation falls in the interval () A. (1, 1.25) B. (1.25,1.5) C. (1.
3. If the function f(x)? ( 1x
4),? 1? x？ 0,
Then f(log43)= ()
4x，0？ x？ 1，a。
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6. Function f(x)? log 1(x2？ Ax) is a decreasing function in the interval (1, 2), so the value range of real number A is ().
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2B.a？ 2C.a？ 1D.0？ Answer? 1
7. Here are four numbers: e0.23, ln? ，(a2？ 3)
0(a？ The conclusion of the size of r) is correct (). A
、log0.23？ e？ (a2？ 3)0? Where is it? B
、e？ log0.23？ (a2？ 3)0? Where is it?
C
、e？ (a2？ 3)0? logD，
log0.23？ Where is it? 0.23? (a2？ 3)0? e？ Where is it?
8. If the point (1, 2) is located in the function f(x) at the same time? The values of a and b are () respectively.
a、a3、b？ 6B、a3、b6C、a？ 3、b6D、a？ 3，b？ 69. Set loga2? logb2？ 0, and then ()
A.0？ Answer? b？ 1B.0？ b？ Answer? 1C.a？ b？ 1D.b？ Answer? 1 10. How to find g(t) when the even function f(x) in the interval is known? f(2t
) range.
22. (Full score of this question 12) What is the known function y? The domain of f(x) is R. For any x, y? R, both
f(x？ y)？ f(x)？ F(y), what about any x? All zeros have f(x)? 0，f(3)3
(1) try to prove: function y? F(x) is a monotone function on r; (2) Judge Y? The parity of f(x) and prove it; (3) Solve the inequality f(x? 3)? f(4x)？ 2;
(4) Try to find the function y? F(x) is there? m，n？
(mn？ 0 and m, n? The range on the z axis).
Daqing No.1 Middle School and Senior One took the second monthly exam last semester, 20 15-20 16 school year.
Reference answers to math test questions
First, multiple-choice questions (5 points × 12=60 points)
DBBBBCAABACA II。 Fill in the blanks (5 points× 4 = 20 points) 1
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3 16.①③④
2
Third, answer questions.
17. Solution (1) Let the arc length be L and the bow area be S, then
α=60 =ππ= 10π
3R= 10, l=3 103, ... 2 points.
S = S-S 1 10π× 10- 1
2π bow fan△ = 2× 32×10× sin3
=
503π-32=50π? 3-3? 2
(square centimeter) ... 5 points (2) ∴ s1=1.
Fan =22C-2R)R=2-2R2+RC)
=-?
R-C422？ CC 16 Therefore, when R=4l=2R and α=2rad, this sector
Area, its value is
C2 16
..... 10 point
18. solution: from what is known, we get b = {2 2,3} and C={2,? 4}.
(1) ∵ A = b ∴ 2,3 is x2? Axe? a2？ 19? Two of 0.
∴2? 3? a
The solution is a=5.
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19 ...6 points (2) from A∩B≦? ，A∩C=？ , get 3 ∈ a.
∴9? 3a？ a2？ 19? 0, a=5 or a= 2...8 points
When a=5, a = {2 2,3}, A∩C=? Contradictions When a=? 2 when A={3,? 5}, in line with the meaning of the question.
∴a=？ 2 ...12 point
19. The solution (1) depends on that the intersection of parabola f(x)=x2+2mx+2m+ 1 and the x axis is in the interval (-
m & lt- 1? f？ 0? = 2m+ 1 & lt； 0,
2 1, 0) and (1, 2), what? f？ - 1? = 2 & gt0,
f？ 1? = 4m+2 & lt； 0,
f？ 2? = 6m+5 & gt； 0
m∈R，m & lt- 1
2? m & gt-56
That is -5- 1? five
16
..... 6 points
(2) The intersections of parabola and X axis all fall within the interval (0, 1). What are the inequalities? f？ 0? = 2m+ 1 & gt； 0,
m & gt- 12? f？ 1? = 4m+2 & gt； 0,
δ= 4 m2
-4? 2m+ 1？ ≥0,? m & gt-2,
0 & lt-m & lt； 1
1m≥ 1+2 or m≤ 1-2,
- 1
That is-1, so the range of m is 1?
2
..... 12 point
20. Solution: (1)? The function f(x) is odd function. f(？ x)？ f(x)？ 0, that is:
(2a？ 1 13x 1
3? x？ 1)? (2a？ 3x？ 1)? 0, with: 4a? 3? x？ 3x？ 1? 3x？ 3x
1
0, namely: 4a? 3x？ 1
3x
1
0,? 4a？ 1? 0，a？ 14; ..... 6 points ② Take x 1, x2? R and x 1? X2, then f(x 1)? f(x2)？ (2a？
13x 1？ 1)? (2a？ 1
3x2
1
)
1 13x 1？ 3x2x？ x2？ X 1。 Add functions on r, and x 1? x2，？ x 1？ y？ 33? 13? 1(3? 1)(3x2？ 1)
_x
3x 1？ 3x2, namely: 3 1? 32? 0. Another 3? 0,? f(x 1)？ f(x2)？ 0,? 3x 1？ 1? 0，3x2？ 1? 0,
f(x2？ x 1)？ 0, that is, f(x2)? f(x 1)
Is ∴f(x) a monotone decreasing function? 0, with f(0)? 0………………4
Namely: f(x 1)? F(x2), so F(x) is increasing function ... 12 on R.
Make yx, have f (? x)？ f(x)？ f(0)？ 0
(2)∫g(t)？ f(2t)？ (2t)2？ 2? 2t？ 2? (2t？ 1)2? 1 ...8 points.
When will you t again? Hours, 2t
, ... 9 points.
∴(2t
1)? ，(2t？ 1)2
∴g(t)？ When, when you find g(t)? f(2t
) There is a range. .................... 12 point
22. solution: (1) take x 1, x2? R, do x 1? x2
f(x2)？ f(x 1)？ f(x2？ x 1？ x 1)？ f(x 1)？ f(x2？ x 1)？ f(x 1)？ F(x point
1)? f(x…… 12？ x 1)
x 1？ x2，？ x2？ x 1？ 0, x again? 0，f(x)？ 0
f(？ x)f(x)……5？ F(x) is an odd function ... f (x? y)？ f(x)？ f(y)？ f(x？ 3)? f(4x)？ f(5x？ 3)
Then f (? 2)f(2)2f( 1)？ 2.................7 ∴ The original inequality is: f(5x? 3)? f(？ 2)5x？ 32
∴ What is the solution set of inequality? _ 1?
0，n？ 0
f(x？ y)？ f(x)？ f(y)，？ f(3)？ 3f( 1)3？ F( 1) 1 and f(n)? f(n？ 1)? f( 1)
f(n？ 2)? 2f( 1)
...
nf( 1)
Ordinary ................ 10 point
From (2) it can be known that it is odd function? f(m)f(？ m)m…… 1 1
From (1), where is f(x)? m，n？ Decreasing upward,
The range of f(x) is n,? m？ .................. 12 point
Some suggestions on learning mathematics well.
1. Interested in learning mathematics. Interest is the best teacher. Do anything, as long as you are interested, you will take the initiative to do it, and you will try your best to do it well. But the key to cultivate students' interest in mathematics is to master the basic knowledge and skills of mathematics first. Some students always want to do difficult problems, and when they see others taking math classes, they also want to go. If these students can't even master the basic knowledge in class, they can only make it up in class, which will not help them, but will make them lose confidence in learning mathematics. I suggest that students can read some famous stories about mathematics and interesting mathematics to enhance their self-confidence in learning.
2. Have a correct learning attitude. First of all, it must be clear that learning is for yourself, not for teachers and parents. Therefore, we should concentrate, think positively and speak boldly in class. Secondly, after returning home, you should finish your homework carefully, review what you learned that day in time, and then preview what you will learn tomorrow. In this way, you will learn more easily and understand more deeply.
3. Have the spirit of "perseverance". If you want to improve your academic performance, you should do it step by step. Don't expect to learn everything overnight. Even if the progress is slow, as long as you persist, math learning will be successful! We should also have the spirit of "not ashamed to ask questions" and not be afraid of losing face. In fact, no matter how difficult the knowledge is, as long as you learn and understand it, that is the greatest face!
4. Pay attention to learning skills and methods. Some formulas and laws should not be memorized by rote, but should be understood by analysis and applied flexibly. Special attention should be paid to the study of new knowledge and the analysis of exercises in class. We shouldn't be distracted and mind our own business. Attention must be highly focused and think positively. When you don't understand the topic, you should make a good record in time, discuss it with your classmates after class, and do a good job of filling the vacancy.
5. Have a good habit of observing and reading. As long as we pay attention to mathematics and carefully observe and think, we will find that there is mathematics everywhere in our lives. In addition, students can learn mathematics from many aspects and channels. For example, learn mathematics from newspapers and magazines such as TV, Internet, Math Newspaper for Primary School Students, Math PHS, etc., and constantly expand their knowledge.
6. Have your own opinions. At present, most students encounter some difficult or unclear problems and give up easily without thinking, and some simply listen to the opinions of teachers, parents and books. Even teachers, elders, books and other authorities are not without some mistakes. We should attach importance to authoritative opinions, but it does not mean that we agree without thinking.
7. Learn to generalize and accumulate. Summarize the law of solving problems in time, especially accumulate some classic and special problems. In this way, we can study easily and improve the efficiency and quality of learning.
8. Pay attention to the study of other subjects. Because there is a close relationship between disciplines, it can promote the study of mathematics. For example, learning Chinese well is very helpful to understand the purpose of math problems, and so on.
How to learn math skills well
1, the habit of "listening" seriously.
In order to synchronize teaching and learning, teachers require students to concentrate their thoughts in class, listen attentively to the teacher's lectures, listen carefully to the students' speeches, grasp the key points, difficulties and doubts, think while listening, and encourage middle and advanced students to take notes while listening.
2. The habit of positive "thinking".
It is an important guarantee to improve the quality and efficiency of learning to actively think about the questions raised by teachers and classmates and keep yourself in teaching activities. Students' thinking and answering questions are generally required to be well-founded, organized and logical. With the growth of age, we should gradually infiltrate mathematical ideas such as association, hypothesis and transformation when thinking about problems, and constantly improve the quality and speed of thinking about problems.
3. The habit of "taking exams" seriously.
The ability to examine questions is the comprehensive embodiment of students' various abilities. Teachers should ask students to read the content of the textbook carefully, learn to master the words and correctly understand the content, carefully scrutinize and ponder the key contents such as tips, marginal notes, formulas, rules, charts and so on, and accurately grasp the connotation and extension of each knowledge point. It is suggested that teachers often carry out special training of "the difference between one word and ten thousand words" to continuously enhance the profoundness and criticism of students' thinking.
4. The habit of "doing" independently.
Practice is an important part and natural continuation of teaching activities, the most basic and frequent independent learning practice of students, and the main way to reflect students' learning situation. Teachers should educate students not to blindly follow the viewpoint of eugenics in their understanding of knowledge, not to be influenced by others, and to easily change their own viewpoints; The use of knowledge does not copy other people's ready-made answers; After-school homework should be completed in good quality, quantity, time and neatly, and the best method should be achieved, and mistakes must be corrected.
5. Be good at asking questions.
As the saying goes, "curious children will become great people." Teachers should actively encourage students to question and ask difficult questions, ask teachers, classmates and parents with knowledge doubts, and strongly encourage students to design their own math problems and communicate with others boldly and actively. This can not only harmonize the relationship between teachers and students, enhance the friendship between students, but also gradually improve students' communication and expression skills.
6. The habit of being brave in "arguing".
Discussion and demonstration are the best thinking media, which can form multi-channel and extensive information exchange between teachers and students and between classmates. Let students express themselves in the debate, inspire each other, exchange gains, increase their talents, and finally unify their understanding of true knowledge.
7. Try to "break" the habit.
The innovation ability of a nation is an important embodiment of comprehensive national strength, so the new syllabus emphasizes the importance of cultivating students' innovative consciousness in mathematics teaching. Teachers should actively encourage students to think without the limitation of conventional ideas, be willing and good at discovering new problems, be able to interpret mathematical propositions from different angles, answer questions in different ways, and creatively operate or make learning tools and models.
8. The habit of "learning" early.
Judging from the cognitive law of primary school students, in order to achieve good academic performance, we must firmly grasp the four basic links of preview, listening to lectures, homework and review. Among them, previewing textbooks before class can help students understand the main points, key points and problems of new knowledge, so as to focus on solving them in class, master the initiative of listening to lectures, and make lectures targeted. With the increase of grade, the importance of preview becomes more prominent.
9. The habit of "checking" repeatedly.
Cultivating students' checking ability and habit is an important measure to improve the quality of mathematics learning, a necessary process to cultivate students' consciousness and sense of responsibility, and this is also a clear teaching requirement in the new syllabus. After the exercise, students should generally check and check from the following aspects: "Whether it conforms to the meaning of the question, whether the calculation is reasonable, flexible and correct, and whether the method of solving applied and geometric problems is scientific".
10, the habit of objective "evaluation".
It is a high-level learning for students to objectively evaluate the performance of themselves and others in learning activities. Only by objectively evaluating ourselves and others can we judge our own self-confidence and shortcomings, thus achieving the goal of facing ourselves squarely, constantly reflecting and pursuing progress, and gradually forming a dialectical materialist view of understanding.
1 1, the habit of "moving" frequently.
Mathematics knowledge is highly abstract, and primary school students' thinking is obviously concrete, so the new syllabus emphasizes that we should pay attention to learning and understanding mathematics from students' life experience and strengthen the cultivation of practical ability. In teaching, teachers should emphasize the use of students' hands and brains to stimulate thinking, solve difficult concepts through examples, find the correct solution to complex application problems through drawing, and ask for directions through cutting vague geometric knowledge or experiments.
12, the habit of intentional "gathering".
It is not terrible for students to make mistakes in learning activities. What is terrible is that they have made many mistakes on the same question. In order to avoid making the same mistakes frequently, a responsible teacher arranged an error consultation column in the classroom, and students with computing ability set up an error knowledge file to collect the wrong questions in their usual exercises or exams and repeatedly admonish themselves, which is worth promoting.
13, the habit of flexible "use".
The purpose of learning lies in application, which requires students to use what they have learned in class flexibly, which can not only consolidate and digest knowledge, but also help to transform knowledge into ability, and also achieve the purpose of cultivating students' interest in learning mathematics.