Mid-term examination paper of the second volume of sixth grade mathematics
1. Fill in the blanks: (20 points)
1、6:5= 18? () = ()% = () (decimal)
2. 25% of a number is 20, and 60% of this number is ().
3, in a proportion, two internal terms are reciprocal, then the product of two external terms is ().
4. If 3a=4b, then A: B = (): (), and a and b are the ratio of ().
5. The original price of a down jacket is 400 yuan, and now it is 65% off. The current price is () yuan cheaper than the original price.
6. The turnover of a hotel in March was 78,000 yuan, and the business tax was paid at 5% of the turnover, and the business tax should be paid in March () yuan.
7. Rotate a rectangular paper with a length of 4 cm and a width of 3 cm around one of its long sides. The volume of the cylinder is () cubic centimeters, and the volume of the cone with the same bottom and height is () cubic centimeters.
8. When the radius of the bottom surface of the cylinder is doubled, the side surface area will be expanded by () times and the volume will be expanded by () times.
9, the area of the circle is certain, the diameter and pi ().
10, the flour yield is certain, and the kilograms of wheat and flour are directly proportional.
1 1, in the formula =c, if c is certain, b and a are the ratio of (); If b is definite, then c and a are proportional to ().
12, the price of a commodity is lower than in the past 15%. Think of () as a unit? 1? The current price is ()% of the original price.
Second, judge right or wrong (right? Wrong number? x？ ***5 points)
1. Original price of a pencil case 18 yuan, 50% discount for 9 yuan. ()
2. put 3? 4= 1? 12 is rewritten as a ratio of 3: 4 = 1: 12 ().
3. If two related quantities are not directly proportional, they are inversely proportional. ()
4. The volume of the cone is equal to the volume of the cylinder. ()
5, a certain number of days, the daily coal consumption is inversely proportional to the total coal consumption.
Three. Select (put the correct serial number in brackets, *** 10)
1, the ratio of energy to: is ()
a、4:5 B、 10:8 C、:D、20:25
2. The current price of a commodity in 4 yuan is 1 yuan lower than the original price, which is () lower than the original price.
a、20% B、25% C、
3. Knead a cylindrical plasticine into a cone with the same bottom and raise it ()
A, expanded to three times the original B, reduced to the original C, unchanged.
4, the following two disproportionate amount is ()
A, the surface area and side length of the cube b, the speed is constant, the distance and time.
C, tile the floor of a room, the area of each brick and the number of tiles.
5. The diameter of the cylinder bottom is10cm, and the height is15cm. After longitudinal cutting along the diameter, the surface area is
A, increase 150c㎡ B, decrease 150c㎡ C and increase 300c㎡.
Fourth, calculation
1, write the number directly (10 points)
0.328? 10= 10.6? 100= 7.4? 10= 1-20%= + =
- = 220? = ? = ? 2? 18= ( + )? 36=
2, can simplify (12 points)
12.5? 3.2? 25 ( + + )? 12
? -( - ) ? 2 1+ ? 2 1
3. Resolution rate (8 points)
3.75:X=:
Five, solve the problem (35 points)
1. There is a barrel of oil, which is poured out 37.5% for the first time, 24.5% for the second time and 62kg for the second time. How many kilograms is this barrel of oil?
2. There is a cylindrical pool, and the inner wall and floor of the pool should be inlaid with tiles. The diameter of the bottom is 6m, and the depth of the pool is1.2m.. How many square meters is the tile area?
3. Conical sand pile with a bottom area of 12.56 square meters and a height of 1.2 meters. Use this pile of sand to pave a road with a thickness of 2 cm on a road with a width of 10 meter. How many meters can it be paved?
The house is paved with square bricks. It needs 96 square bricks with an area of 9 square decimeters. If you use a square brick with a side length of 4 mm, how many pieces do you need? (Use proportional solution)
Xiao Li plans to finish reading a 290-page book in a week and read 40 pages every day for the first two days. If he wants to finish reading as planned, how many pages will he read on average every day? (Use proportional solution)
6. There is a cuboid iron block, which is 8 cm long, 4 cm wide and 3 cm high. It is completely cast into a cylinder with a radius of 5 decimeters at the bottom and a height of several decimeters. (Keep one decimal place)
There are two bookshelves in our school library. The administrator took 15 books from the upper level and put them on the lower level. At this time, the number of lower-level books is 40% of the number of upper-level books, and 85 lower-level books are known. How many books are there on the upper floor?
Analysis of the Mid-term Examination Paper of the Sixth Grade Mathematics Volume II
I. Basic information 。
In this math exam, there are 69 students * * *, with an average score of 90.4. Eight students got full marks, accounting for 1 1% of the total number, 38 students got 99-90, accounting for 55% of the total number, and 60 students got * * *, with an excellent rate of 85% and a qualified rate of 6544.
Second, the characteristics of the test paper:
1, choose realistic and vivid materials.
Adapting some materials closely related to real life into innovative test questions, causing students to find and solve practical problems. Let students realize the application of mathematics in life.
2. Create a platform for independent choice.
In order to choose new background materials and change the style of the topic structure appropriately, the test questions provide students with more opportunities for independent inquiry. For example, the eighth question.
3. Pay attention to the content of mathematical thinking.
Some questions let students observe, analyze, summarize and discover the mathematical laws contained in them, which not only apply what they have learned, but also cultivate students' application consciousness.
Third, the examination paper analysis
1, main achievements.
Judging from the volume, the following achievements are worthy of recognition:
(1) Students have a solid grasp of basic concepts and can use them well on the basis of understanding.
For example, the captain of the school basketball team just finished a group of pitching exercises, threw 38 balls and missed 12 balls. The formula for calculating the hit rate is
The correct answer rate of students to this question is 100%. The reason why the correct rate of this question is 100% is that when teaching similar teaching contents, the teaching plan design of math group teachers can make the teaching contents relate to students' lives, which is actually to create some learning scenarios for students and let them fully participate in the formation of math knowledge. For example, when calculating the percentage of teaching, the teacher creates a situation of pitching competition, so that students can choose the champion team while watching the game, and then ask the students to explain the reasons. Due to the full participation of all the students, the reasons have been fully answered. Should the champion team be produced? How many goals did you score? What is the total spacing? Then, the calculation results are converted into percentages. It can be seen that through the creation of students' favorite activities, students have mastered the new knowledge points of this lesson at once and laid a good foundation for teachers to successfully teach new lessons. Another example is: when teaching the problem of "percentage in shopping", the teacher first asks students to use weekends to observe and visit shopping malls, supermarkets and merchants to promote goods, and then communicate in class. This teaching design first allows students to understand the key points and difficulties of teaching through practical activities, and also disperses the key points and difficulties of teaching. There are many similar teaching cases. It can also be seen from here that students can easily understand the teaching content of life design, so they can better master it.
Another example: the seventh question is to find the area of the shadow part. The error rate of this question is only 2%.
This problem is to find the area of trapezoid. Students can calculate the upper bottom, lower bottom and height of the trapezoid by using the known conditional radius, so as to correctly calculate the area of the trapezoid. From this problem, it can be reflected that students have better ability to use basic concepts and solve problems.
(2) Students are proficient in computing skills.
In the test paper, the loss rate of students when calculating the unknown X by simple method and offline calculation is low, and the loss rate of a lesson in solving the unknown X is only 5. 1%, which fully shows that teachers attach great importance to the training and cultivation of students' computing skills in their usual teaching work and master the basic skills of students' computing more truly and in place. In math teaching on weekdays, every math teacher can do basic calculation, oral calculation and skillful calculation training in the first 5 minutes of the new class, and then the school regularly holds oral calculation competitions. The competition method is to complete 60 basic calculations in 5 minutes, and the score of 100 is rated as the champion of oral calculation. It is precisely because of this kind of training that students' computing ability has played a very good role in this exam. Another example: the second small question calculated by a simple method, 20? + + 10? The problem of 13 cannot be simply calculated by the multiplication distribution rate, so 10? 13 For the transformation, this problem is more difficult than the problem directly calculated by multiplication and division. Only two people made mistakes in this exam, which fully shows that teachers make full use of variant exercises to deepen their understanding and application of multiplication and division, so students can make better use of multiplication and division.
(3) Students can better grasp the basic quantitative relations in application problems.
Judging from the graduation thesis, most students can better understand the relationship between the number of application questions, basically grasp the structural characteristics of application questions, and have certain ability to answer application questions. This graduation thesis also illustrates this point. We know that the correspondence between the quantity and the rate of fractional percentage application problems is a difficult point for students to master, but from the examination paper, most students can master it well. The first, second and third application questions are slightly complicated fractional percentage application questions, and students have a good quantitative relationship and a low failure rate.
2. Main problems.
While seeing the achievements, we also found some problems.
First, use knowledge flexibly to solve practical problems. This kind of questions have a high rate of losing points.
Example 1 Fill in the blanks (10) Cut a square piece of paper with an area of 50 square centimeters into four identical triangular pieces of paper, and then make a rectangle with them. The length of this rectangle is centimeters.
This topic mainly examines students' comprehensive application ability of knowledge and spatial phenomena. However, the error rate of this question reached 77%, and there were two wrong answers, one was 12.5 and the other was 25. There are two reasons for analyzing the above two wrong answers (1). In the process of invigilation, I found that some students cut the square paper into four identical triangles and put them together to form a rectangle. But students can't find the relationship between rectangle and triangle, from which we can see that students' comprehensive application ability of knowledge is weak. (2) Students who don't start work use the method of drawing to analyze on the draft paper, but the total area is reduced due to the lack of spatial imagination. 4= area of each small triangle. Take the area of each triangle as the length of a rectangle. It can be seen that students' ability to combine numbers and shapes is weak.
Example 2 (12) first tapered copper blank with a volume of 7 cubic decimeters was cut from the upper third, and the rest was put into a cylindrical box with a minimum volume of cubic decimeters.
This problem mainly investigates the volume relationship between cylinder and cone. Judging from students' error analysis, most students can't comprehensively use the volume relationship between cylinder and cone, and most students don't understand the meaning of the problem. What is the relationship between the remaining volume and the volume of the cylindrical box? Therefore, from a large number of students' wrong answers, it can be concluded that students' ability to imagine the body in space is not enough, and their ability to comprehensively use knowledge needs to be cultivated and improved.
Example 3 (4) of the eighth question is canned almond dew produced by Chengde Lulu Group. If these six cans are put into a rectangular plastic bag, what are the length, width and height respectively? This question mainly examines whether students can apply mathematical knowledge to solve practical problems in life, and the answer is not unique. Individual students did not find the relationship between the height and diameter of a cylinder and the length, width and height of a cuboid. Therefore, more people ask the wrong questions.
Second, good math study habits have not been fully developed.
1. Slightly complicated data and words will have a certain impact on some students with weak ability or bad habits. Pay attention to one thing and lose sight of another when calculating, and don't understand the clue when facing a lot of information.
2. You can't patiently interpret, comprehensively observe and choose the original materials, situations and information provided in the question to help solve the problem.
3. There are some common low-level mistakes in the paper, such as simple calculation errors, misreading data, missing decimal points and missing problems. It can be seen that the non-intellectual factors that usually affect the learning effect, such as homework habits, reading habits, verification habits, etc., can not be controlled just by trying to take the exam, but need the consistent attention of math teachers, step by step and persistent training.
Faced with the above problems, I conducted targeted teaching research on the problems in the test paper with a number of math teachers, and deeply reflected on our usual teaching behavior improvement measures as follows:
(1) Continue to strengthen the training of basic computing skills.
? Class standards? Mentioned in? Should pay attention to oral calculation, strengthen estimation and encourage algorithm diversification? . ? Class standards? Also mentioned? Should complicated operations be avoided? But the basic training should be persisted and the calculation should reach a certain speed. To cultivate students' computing ability, we must lay a good foundation for oral calculation, and students should also have certain oral calculation ability to lay a good foundation for future study. In short, we should adhere to regular and planned training.
(2) Pay attention to thinking training, no? Exam? Training.
Thinking training, like oral arithmetic training, should be carried out regularly and in a planned way. Because the current textbook topics are relatively simple and not difficult, students can't do flexible topics. Teachers should fully tap the living resources according to the teaching content, change the teaching concept, and make full use of the teaching resources to make the mathematics content live and the life content mathematical. Students who take this kind of math class will find it lively and interesting. Doing so can help students (at least some students) train their thinking flexibility.
(3) Pay attention to the results of learning and pay more attention to the learning process.
Like what? What is the relationship between the volume of a cylinder and a cone? It is important for students to know that the volume of a cone with equal base and equal height is cylindrical. But it is more important for students to experience the process of discovering this law. The loss rate of 12 in the fill-in-the-blank test paper is the highest, which is 77%; Worth our deep thought! If students want to really understand it, they must go through the process of discovering this law.
(4) Pay more attention to the learning of mathematical knowledge and the application of mathematical knowledge.
? Class standards? It's mentioned in many places? Cultivate students' awareness of applying mathematics and their ability to solve problems by comprehensively applying what they have learned? . Professor Zhou said: The problem is the heart of mathematics. The essence of children's learning mathematics is the process of finding problems, exploring problems, refining mathematical models and solving problems by using existing knowledge and experience. In other words, learning mathematics means applying mathematics, which is precisely the weak link of our students. It is not difficult for students to master mathematical knowledge, but it is difficult to use what they have learned flexibly to solve practical problems. For example, (4) of the eighth question shows the canned almond dew produced by Chengde Lulu Group. If these six cans are put into a rectangular plastic bag, what are the length, width and height respectively? This kind of problem is ignored by us in daily teaching. Our practical activities are not enough, and the cultivation of practical ability needs to be strengthened.
(5) Pay attention to the development of every student, and pay more attention to the development of students with learning difficulties.
These students can be said to be? Learning difficulties? Yes Because of them? Learning difficulties? There are many reasons, but whatever the reason, since they are studying in our class, we should do our best to pay more attention to them, pay attention to the guidance of their learning methods, and cultivate their study habits, so that they can develop on the original basis.