The key to solve the problem: the clock problem belongs to the catching-up problem in the trip problem. The clock face is divided into 12 squares by "hour" and 60 squares by "minute". Hourly walk 1 with 5 squares, minute walk 12 with 60 squares. The rotation speed of the hour hand is the minute hand, and the speed difference between the two hands is the speed of the minute hand, which can be tracked every hour.
1, between 2 o'clock and 3 o'clock, when does the minute hand and the hour hand coincide?
Analysis: At two o'clock, the minute hand points to 12, the hour hand points to 2, and the minute hand is behind the hour hand 5×2= 10 (small grid). The minute hand can catch up with 1-= (square) every minute. To make the two stitches coincide, the minute hand must catch up with 10 square, so the time required should be (10÷) minutes.
Solution: (5× 2) ÷ (1-) =10 ÷ =10 (minutes)
A: At two o'clock, 10, the two stitches coincide.
The wall clock is 5 minutes slow every hour. At noon standard time 12, set the clock to standard time. It's 5: 30 pm standard time. How long will it take for the wall clock to go to 5: 30 pm?
Analysis: 1, this clock is 5 minutes slow every hour, that is, when the standard clock runs for 60 minutes, this wall clock can only run for 60-5 = 55 minutes, that is, the speed is = 1/4 of the standard clock speed.
2. Because the standard clock moves from noon 12 to 5: 30 pm, the wall clock * * * is 5× (17-12) = 27 (minutes), that is, the difference is 27 minutes to 5: 30.
This wall clock goes at 5: 30, and it goes for 27 minutes according to the standard time. Because its speed is the standard clock speed, the actual time to complete these 27 minutes should be 27 minutes.
Solution: 5×( 17— 12) =27 (minutes) 27÷30 (minutes).
A: It will take another 30 minutes for the wall clock to go to 5: 30.
Junior high school mathematics olympiad 3 olympiad, mathematics, junior high school, freshman, relationship
If you answer this question in one sentence, it is: "You don't have to learn all of them, but you need to learn the part that involves the finale of the senior high school entrance examination (the big question of the last 30 points); In addition, students with spare capacity can learn. "
Junior high school mathematics is divided into two parts as a whole: the guidance of the first grade; The deepening of the second and third grades.
Judging from the difficulty, generally speaking, the difficulty is reduced for children who have studied Olympic mathematics in primary school; Although there is a question of about 30 points in the senior high school entrance examination (for students, it is equivalent to the difficulty of Olympic mathematics), the overall senior high school entrance examination has not reached the difficulty of pure Olympic mathematics.
However, judging from the teaching and examination of mathematics experimental classes in key middle schools in the past two years, the difficulty is generally higher than that of senior high school entrance examination, especially the additional questions specially prepared for children in experimental classes after various examinations.
Take the monthly exam, mid-term exam and final exam of key schools as an example, the original questions in the Hope Cup or provincial and municipal competitions often appear. There is a question in the final exam of junior one, which appeared in the exercises of a competition class in a school and in the usual exam. In fact, this is a test of the Hope Cup 14 session.
Why is this happening? Doesn't the school know that most of the questions in the senior high school entrance examination are not that difficult?
There are several main reasons:
1。 Although the Hope Cup itself is a competitive exam, it limits the knowledge of the exam to the outline of the senior high school entrance examination, especially the preliminary exam; Many children have not received special competition training, but their basic skills are very solid, and they can get very high grades at a try;
2。 The students in the school mathematics experimental class are generally excellent. On the one hand, there is no distinction when passing the in-class test, on the other hand, it is not conducive to the selection and training of good students in high schools (every year, middle schools in good schools will sign contracts with a group of children in advance). Simple competition questions not only meet the test sites of the senior high school entrance examination, but also distinguish levels and cultivate thinking. It is natural to be liked by the school.
3。 There is no doubt that junior high school olympiad is more difficult than primary school. The competition questions in junior high school are closely related to school teaching in terms of knowledge points. National league exam outline:
1) real number
2) Algebraic expression
3) Identity and identity deformation
4) Equations and inequalities
5) Function
6) Logical reasoning problem
7) Geometry
We found that except for the sixth logical reasoning question, it was all in the textbook, but the difficulty and problem-solving skills were strengthened. In addition, according to incomplete statistics, more than 80% of the topics in the national junior high school mathematics league are related to the content in the class.
Of course, it is by no means suggested that all children should study Olympiad like primary school, but we should grasp the degree of difficulty in mathematics learning. It is difficult to deal with the final exam questions in the future completely according to the textbook training questions, which is not conducive to the college entrance examination six years later; Without textbooks, simple Olympic mathematics learning does not conform to the learning reality of most junior middle school students. Among them, the test of Hope Cup is a better benchmark. Being able to skillfully solve the first question of the Hope Cup is already a very good level of difficulty.
Cultivate excellent students, not make up the difference. He was admitted to a key middle school by studying mathematics. Here, students exchange learning methods and learning materials with each other in key middle schools to understand the gap between themselves and their competitors.
Junior Middle School Mathematical Olympiad 4 I. Guiding ideology
Olympiad Mathematics is an important part of mathematics, the expansion of students' learning mathematics and the development of students' basic skills. Expanding thinking ability has an extremely important influence on students' basic computing ability; In order to further improve students' divergent thinking ability and calculation speed, cultivate students' observation, memory and thinking ability, and thus cultivate students' competitive consciousness and ability. According to the actual situation of our school, the junior high school science group specially held the whole school Olympic Games. The relevant matters are hereby notified as follows:
Second, the purpose of the activity:
Only in this way can we stimulate students' enthusiasm for learning mathematics, develop students' expanding thinking and improve their thinking ability. At the same time, math teachers should realize more clearly that it is a long-term work to cultivate students' divergent thinking ability and flexible thinking habits, which must be carried out persistently.
Third, the examination paper proposition arrangement
Teacher: Wei Zengyuyu
Fourth, the way of activity:
1. Participants: Choose six students from each class to participate.
2. Activity mode: paper test paper, and other calculation tools are not allowed.
3. Location: Multimedia Classroom.
4. Activity time: 20 1* year 165438+1October16 (Monday) at noon 16: 00- 17: 00.
5. invigilator: Jiang Gu Jiaqiong
6. Mark: Duan Jiang Yifeng Zhiyong
Verb (abbreviation for verb) Competition rules and requirements:
1. Students listen to the unified signal and announce "start" and "end".
2. Students should answer questions within the specified time and stop answering questions when the end signal rings.
Junior high school mathematics olympiad article 5 1, there are two unevenly distributed incense, and the burning time is one hour. What method can you use to determine the time of 15 minutes?
2. A manager has three daughters, and their ages add up to 13, which is equal to the manager's own age. A subordinate knows the manager's age, but still can't determine the age of the manager's three daughters. At this time, the manager said that only one daughter's hair was black, and then the subordinates knew the age of the manager's three daughters. What are the ages of the three daughters? Why?
3. Three people went to a hotel and stayed in three rooms. The price of each room is $65,438+00, so they pay the boss $30. The next day, the boss thought that $25 was only enough for three rooms, so he asked my brother to return $5 to three guests. Unexpectedly, my brother was insatiable, and only returned 1 USD each, and secretly took it away by himself. But at the beginning, the three of them paid 30 dollars, so 1 dollar?
4. There are two blind people. They all bought two pairs of black socks and two pairs of white socks. Eight pairs of socks are made of the same cloth, the same size, and each pair of socks is connected with trademark paper. Two blind people accidentally mixed up eight pairs of socks. How can each of them get back two pairs of black socks and two pairs of white socks?
5. The latest classic math puzzle for primary school students: A train runs from Los Angeles to new york at a speed of15km/h, and another train runs from new york to Los Angeles at a speed of 20km/h.. If a bird starts from two trains at a speed of 30 kilometers per hour, starts from Los Angeles, meets another train and returns, and flies back and forth in turn until the two trains meet, how long does the bird fly?
6. You have two cans, 50 red marbles and 50 blue marbles. Choose a jar at random and put a marble in the jar at random. How can you give red marbles the best chance? What is the exact probability of getting the red ball in your plan?
7. You have four jars full of pills, and each pill has a certain weight. The contaminated pill is the uncontaminated weight+1. Weighing only once, how to judge which can of medicine is contaminated?
8. You have a bucket of jelly, including yellow, green and red. Close your eyes and grab two jellies of the same color. How many can you catch to make sure you have two jellies of the same color?
9. For a batch of lights numbered 1 ~ 100, all the switches are turned up (turned on), and the following operations are done: always turn the switches in the opposite direction once in multiples of 1; A multiple of 2 toggles the switch in the opposite direction again; A multiple of 3 turns the switch in the opposite direction again ... Q: Finally, the number of lights in the off state.
10. Imagine you are in front of the mirror. Excuse me, why can the image in the mirror be upside down, but not upside down?