The second volume of the first day of junior high school is the key knowledge point of mathematics.
1, monomial: The product of numbers and letters is called monomial.
2. Polynomial: The sum of several monomials is called polynomial.
3. Algebraic expressions: monomials and polynomials are collectively referred to as algebraic expressions.
4. The number of monomials: The sum of the indices of all the letters in the monomials is called the number of monomials.
5. Degree of Polynomial: The degree of the term with the highest degree in the polynomial is the degree of the polynomial.
6. Complementary angle: The sum of two angles is 90 degrees, and these two angles are called complementary angles.
7. Complementary angle: The sum of two angles is 180 degrees, and these two angles are called complementary angles.
8. Relative vertex angles: two corners have a common vertex, and two sides of one corner are opposite to the extension lines of two sides of the other corner. These two angles are antipodal angles.
9. Equiangular angle: inches? Three-line octagon? The angles in the same position are congruent angles.
10, Internal angle: in? Three-line octagon? The angle sandwiched between two straight lines and staggered is the inner angle.
1 1, same internal angle: in? Three-line octagon? The included angle between the two straight lines and the third straight line on the same side is the inner angle on the same side.
12, significant number: an approximation, starting with the first number on the left that is not 0 and ending with the exact 1, all numbers are significant numbers.
13, probability: the probability of an event is the probability of this event.
14, triangle: A figure composed of three line segments that are not on the same line is called a triangle.
15, Angle bisector of triangle: In a triangle, the angle bisector of an inner angle intersects its opposite side, and the line segment between the intersection of the vertex and this angle is called the angle bisector of triangle.
16, triangle midline: the line segment connecting the vertex and the midpoint of the opposite side of the triangle is called the midline of the triangle.
17. Height line of triangle: Draw a vertical line from one vertex of triangle to the line where its opposite side is located, and the line segment between vertex and vertical foot is called height line of triangle.
18, congruent graphics: two graphics that can overlap are called congruent graphics.
19, variable: the number of changes is called variable.
20. Independent variable: If there is an active change in the amount of change, it is called an independent variable.
2 1, dependent variable: the quantity that changes passively with the change of independent variables is called dependent variable.
22. Axisymmetric figure: If a figure is folded along a straight line and the parts on both sides of the straight line can overlap each other, then this figure is called an axisymmetric figure.
23. Symmetry axis: A straight line folded in half in an axisymmetric figure is called symmetry axis.
The second volume of the first day of junior high school focuses on mathematics.
1. Grade 7 students in a middle school go out for social practice. If there are 45 people in each car, then 15 students don't have a car. If there are 60 people in each car, then one car can be vacated. Q * * * How many cars and students are there?
2. Fujian Xinxin Electronics Co., Ltd. applied for two kinds of loans, A and B, with an amount of 680,000 yuan and an annual interest of 84,200 yuan. The annual interest rate of loan A is 12%, and that of loan B is 13%. How much are these two loans?
3. A clothing factory wants to produce a batch of certain kinds of students' clothes. It is known that a 3-meter-long cloth can be used to make two coats or three pairs of trousers, and one coat and one pair of trousers are a set. It is planned to use this 600-meter-long fabric to produce coats and trousers. How much cloth does it take to produce them? * * * How many sets can you produce?
4. A shopping mall sells an electrical appliance at a fixed price, and each one can make a profit in 48 yuan. Selling six electrical appliances at a 10% discount on the fixed price is equal to the profit of selling nine electrical appliances in 30 yuan. What is the purchase price and fixed price of each electrical appliance?
5. A square table consists of 1 desktop and 4 legs. If 1m3 wood can be used as 50 desktops or 300 legs of a square table, how many cubic meters of wood can be used as desktops and legs to make a square table with the existing 10m3 wood? How many square tables can you make?
6. At 8: 00 am, Party A and Party B walk to each other from A and B at the same time, with a distance of 36km at 10 in the morning, and continue to move forward, with a distance of 36km at 12. As we all know, Party A walks 2 kilometers more than Party B every hour, so we can find the distance between A and B. 。
7. A middle school organizes students to have a spring outing. It was originally planned to rent a number of 45-seat buses, but 15 people had no seats. If you rent the same number of 60 buses, there will be one more bus, and the rest of the buses are just full. It is understood that the daily rent of 45 buses is 220 yuan, and the daily rent of 60 buses is 300 yuan.
(1) How many students are there in the spring outing? How many 45-seat buses were originally planned to rent?
(2) If you rent a similar car and want everyone to have a seat, how to rent a car is more cost-effective?
8. Class A and Class B of Guangming Middle School donated money for Project Hope. The total donations of the two classes are the same, both higher than 300 yuan and lower than 400 yuan. It is known that one person from Class A donated to 6 yuan, and the rest donated to 9 yuan. One person in Class B donated 13 yuan, and the rest donated to 8 yuan. What is the total number of students in Class A and Class B?
9. Xiaoyue Automobile Sales Company went to an automobile factory to buy two kinds of cars, A and B. With 3 million yuan, it can buy 10a car and 15 B car, and with 3 million yuan, it can also buy 8 A car and 18 B car.
(1) How much are the A and B cars?
(2) If the car sales company can get 8,000 yuan for selling 1a cars and 5,000 yuan for selling 1b cars, and the car sales company is prepared to buy 30 cars A and B for no more than 4 million yuan, and the total profit after all these two cars are sold is not less than 204,000 yuan, how many car purchase schemes are there? In these car purchase schemes, how many million yuan did the car sales company earn after selling all these cars?
10. The owner of Shuangrong Clothing Store went to the factory to buy two kinds of clothes, A and B. If he bought 9 pieces of A clothes and 10 pieces of B clothes, he would have to 18 10 yuan. If you buy 12 pieces of A-type clothes and 8 pieces of B-type clothes, you need 1880 yuan.
(1) How much is each piece of clothing A and B?
(2) If you sell 1 piece of type A clothing, you can make a profit 18 yuan, and if you sell 1 piece of type B clothing, you can make a profit in 30 yuan. According to the market demand, the clothing store owner decided that the number of type A clothing should be 4 more than that of type B clothing, and the maximum number of type A clothing can be 28. When all the clothes are sold out, the total profit can be no less than 699 yuan. How to purchase goods?
1 1. In the maintenance project of Wuhan Jianghan First Bridge, it is planned that two engineering teams, A and B, will jointly complete a project. From the data of the two engineering teams, we can know that if the two engineering teams work together for 24 days, it will just be completed; If two teams work together 18 days, then team a works alone 10 days, which just ends. Excuse me:
(1) How many days does it take for Team A and Team B to complete the project alone?
(2) It is known that the daily construction cost of Team A is 6000 yuan, and that of Team B is 3500 yuan. If the total cost of this project does not exceed 220 thousand, how many days will Team B have to work at least?
12. An enterprise purchased Phyllostachys pubescens in Zhuhai, southern Sichuan for rough processing, and it can process 8 tons per ton, with a profit of 800 yuan. If Phyllostachys pubescens is finely processed, it can be processed 1 ton every day, and the profit per ton is 4000 yuan. Due to the limitation of conditions, only one kind of bamboo can be processed every day, and it is required to sell all the bamboo within one month (30 days). So, the factory director called the staff to a meeting. B said: 30 days to complete the processing, unprocessed bamboo directly sold; C said: how many days in 30 days can we sell it after rough machining? Who says the scheme adopted by the factory director is the most profitable?
Mathematics learning methods of junior high school grade one
First, pay attention to the convergence of learning content.
1. Senior one mathematics is developed and improved on the basis of primary school mathematics. The difficulty is moderate and the breadth is increased. The biggest difference between it and primary school mathematics is that the concept of junior one mathematics has obviously increased. Primary schools only need to understand some concepts, while the first-grade mathematics concepts need to be firmly grasped. A spirit of daring to be true, grasping the essence and seriously excavating the content, grasping and applying concepts on the basis of understanding runs through the middle school mathematics learning.
2. The calculation of primary school mathematics is relatively simple, while that of middle school mathematics is relatively complicated. Try to cultivate the habit of accurate and fast calculation. This requires a good understanding and proficiency in the previous concepts and definitions, followed by concentration and carefulness, and strict demands on yourself not to make careless mistakes, not to find objective reasons for low scores in exams, and to develop the habit of being cautious in everything.
3. On the basis of primary school study, cultivate your ability to overcome problems. Some students have studied olympiad in primary school, so they will encounter difficulties in middle school. It is necessary to carry forward the spirit of nailing, solve many problems for one problem, draw inferences from others and be brave in exploration.
Second, pay attention to the cultivation of learning methods.
1. First of all, you must learn. A good learning method is to do well in all aspects of learning: preview, listening, review, summary and examination. Preview before class so that you can listen to the class with questions. High-quality class attendance is the foundation and key of middle school mathematics learning. After-class review and summary is the sublimation of the learning process, and it is an important embodiment of your earnest completion of your homework. Don't neglect your homework every day, because the so-called details determine success or failure! Only by implementing the previous learning tasks and treating the exam with normality and confidence can we be in an invincible position in the exam.
2. Actively cultivate the habit of autonomous learning. There are many more courses in grade one than in primary school. As teachers, we should cultivate students' habit of studying independently. As students, we should actively adapt to the changes in study habits, find problems in time, solve problems, and don't put today's problems overnight! Otherwise, there will be endless troubles, so we should sum up a set of study plans that suit us, and regularly check and review its implementation.
3. Learn to learn from others' strengths and make up for your own shortcomings. There must be some students around you who study more easily and get good grades. Learn more from them. When you want to do specific work, prepare a "good problem book" and include some good problem-solving methods and wrong exercises at any time. In a few years, you will find that your study has made rapid progress and your problem-solving ideas have been effectively opened. More valuable things can be taken out for targeted review before the mid-term exam. For you, only "it" is the most targeted! Isn't that twice the result with half the effort
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