Mathematical fast calculation method
A fast mathematical calculation method of 1
Elementary school mathematics is some simple mathematical knowledge methods, and children only need to master the knowledge points when learning. For the acceptance of new knowledge, children must listen carefully at school, take notes according to the teacher's ideas, and ask teachers or classmates in time even if they don't understand.
Mathematics achievement determines children's comprehensive ability in science, and then affects the achievements of science and engineering students and other subjects. Timely Olympic math training in primary school is more conducive to the improvement of children's scientific achievements in junior high school. Don't let our children enter junior high school because mathematics affects the overall ranking and then affects the results of the senior high school entrance examination! Mastering fast calculation skills is the key for children to learn fast calculation in the shortest time. Therefore, parents should be good at guiding their children to discover and use quick calculation skills, and try to verify these skills as much as possible, so that these skills can better serve their children.
Method 1: refers to the algorithm.
The number of digits is 1 multiplied by 9: what is the number of digits of the previous factor, so the hand index is bent backwards, and there are several fingers on the left of the bent finger, indicating the product of several percent. Reading 0 with a bent finger indicates that the decimal digit of the product is 0, and there are several fingers to the right of the bent finger indicating the single digit of the product. Formula: How many numbers to bend backwards? One hundred fingers to the left, ten fingers to the left and one finger to the right. For example: 34× 9 = 306;
Any number with a unit number greater than ten digits multiplied by 9: When any number with a unit number greater than ten digits multiplied by 9, it is still the unit number of the previous factor. Bend the first finger backwards, and the bent finger will not read. This is the dividing line between the ten digits and the single digits of the product. What is the decimal place of the prefix factor? If you count a few fingers from the left, it represents the hundredth digit of the product. If you subtract the hundredth digit from the left of the bent finger, how many fingers are left, which means the decimal digit of the product. If there are several fingers on the right side of the bent finger, it means the single digits of the product. Formula: How many times is the digit? The original ten digits are hundreds. Subtract one hundred numbers from the left, and the remaining fingers are ten numbers. Take the bent finger as the dividing line, and bend the finger to the right.
Method 2: carry addition of two digits plus two digits.
Formula: plus 9 minus 1, plus 8 minus 2, plus 7 minus 3, plus 6 minus 4, plus 5 minus 6, plus 3 minus 7, plus 2 minus 8, plus/kloc-0 minus 9. (Note: all additions and subtractions in oral decisions are numbers in the unit) Example: 26+38=64 Solution: Add 8 and you will subtract 2. Who will subtract 2? 26 minus 2 equals 6. Three out of 38 will get four points. (Note: How to round the last ten digits is 1, I enter 2, 2, 3, 4, and so on. Where are you taking it? It reaches the tenth place in the second two digits. If this is 3, I enter 4, and these two digits are 2+4=6. ) Here, 26+38=64 means that 6-2=4 is written with one digit, and 3 into 4 plus 2 means that 6 is written with ten digits. Another example is 42+29=7 1. Just add 9 and subtract 1.
For example, 2- 1= 1, written in the unit 1, is 2, I input 3,4+3 = 7, and write 7 in the tenth place to get 7 1. If two numbers don't add up to carry, you can write the number directly, for example, 25+34=59, write one digit and one digit on the number after the equal sign, 5+4=9, and write ten digits and ten digits on the tenth digit, which is 2+3=5, which is 59. No vertical calculation is required. This method has learned a hundred tricks, which is faster than a calculator.
4 Method 3: Multiplication speed algorithm
Add 1 to the front of the number, and add the product of the number to the end of the number. For example: 56×54 5+ 1=6, 6×5=30. Add the product of 4 and 6 at the end of 30 to get 3024, so 56×54=3024. Another example: 6 1×69 (6+ 1)×6=42, 1×9=9. When the product of the number in a unit is a single digit, it still occupies two digits, so a 0 should be added before 9. So 6 1×69=4209. Exercise: 98× 92 75× 75 29× 21;
A fast calculation method of multiplying two digits by ten digits and the sum of single digits is not 10. Add a number in the unit of another number, multiply it by an integer consisting of numbers in the tenth place, and add the product of two numbers in the second place. For example: 53× 54 = (53+4 )× 50+3× 4 = 57× 50+12 = 2850+12 = 2862 Exercise: 85×84 67×68 3 1×38.
Mathematical analysis method
1 mathematical analysis method
Mathematical analysis is a compulsory course for graduate students majoring in mathematics and applied mathematics. Because this specialized course is rich in content and difficult, how to review this course in a limited time and make full preparations to get good grades?
2 Mathematical analysis methods
First, think about whether you are interested in mathematics. Whether you are a math major or not, interest is the best teacher. In addition, to have confidence in yourself, the essence of mathematics is abstract, but it is also the wisdom of human beings. Mathematics is very noble.
First, learn mathematical analysis. I recommend reading the book on mathematical analysis written by Zhuo Ritchie. You can buy one and have a look. If you want to relax, you can first read Calculus Course, the book by Fechkin Goelz. There are many topics in the book and the proof is rigorous. Don't rush to look at the back, there are many connections between the back and the front.
You can learn mathematical analysis while watching algebra. It is not difficult to read Zhang Heduan's Advanced Algebra first. On rotman of Higher Modern Algebra from the Perspective of Abstract Algebra. There is also an introduction to algebra, Kostelikin of Russia, which can be used as a reference. The back of this book may be a bit difficult, involving a lot of content.
The most important thing is persistence and thinking. You can't read the front of a book for a while and the back of a book for a while. Take a rest when you need it. The title in the book is very good. Can the master write well? Be sure to think hard and do some questions. It is suggested to study for one and a half years, and then with these foundations, you can start by going up one flight of stairs in the kingdom of mathematics.
3 Mathematical analysis methods
Three bad habits in the process of knowledge mastery: ignoring understanding and memory: thinking that everything will be fine as long as you remember formulas and theorems, while ignoring the understanding of the process of knowledge deduction, it is not only difficult to extract applied knowledge, but also lose the absorption of ideas and methods involved in the process of knowledge deduction. For example, this is the fundamental reason why the trigonometric formula "often remembers and often forgets, but can't remember repeatedly", and then there is no sense of solving problems with trigonometric transformation.
Emphasis on conclusion over process: the characteristic of mathematical proposition is the causal relationship between conditions and conclusions. Ignoring the mastery of conditions will often lead to wrong results, even correct results and wrong processes. If you can't see when and how to discuss it in your study. One of the reasons is that the preconditions of mathematical knowledge are vague (such as monotonicity of logarithmic function, properties of inequality, summation formula of proportional series, maximum theorem, etc.). )
Ignore reviewing in time and strengthen understanding: Everyone knows the simple truth of "reviewing the past and learning the new", but few people persistently apply it in the learning process. Because under the careful guidance of the teacher, the content of each class seems to be "understood", so I can't bear to spend eight to ten minutes reviewing the old knowledge of the day. I don't know that "understanding" in class is the result of the joint efforts of teachers and students. If you want to "know" yourself, you must have a process of "internalization", which must extend from classroom to extracurricular. Remember, there must be a process of "understanding" from "understanding" to "meeting", and no one can forbid it.
Ignore the standardization of problem-solving process and only pursue the answer: the process of mathematical problem-solving is a process of transformation, and of course it is inseparable from standardized and rigorous reasoning and judgment. In solving problems, jumping too much, scribbling letters and drawing by hand, it is difficult to produce correct answers with such an attitude towards slightly difficult problems. We say that the standardization of problem-solving process is not only the standardization of writing, but also the standardization of "thinking method". Students should learn to constantly standardize their own thinking process and strive to solve problems perfectly.
Four kinds of bad mentality in the process of solving problems
Lack of accumulation of typical topics and methods that have been learned: some students have done a lot of exercises, but the effect is little and the effect is not good. The reason is that they are forced to finish the task passively, lacking the necessary summary and accumulation. On the basis of accumulation, we can strengthen the "theme" and "sense of theme", gradually form a "module", and constantly draw intellectual nutrition from it, thus realizing the mathematical thinking method hidden in the model. This is the process from quantitative accumulation to qualitative change, and only "accumulation-digestion-absorption" can "sublimate".
4 Mathematical analysis methods
Organize the knowledge points of each chapter: first read the contents of each chapter and section in the book, and then mark out what you don't understand, the key points emphasized by the teacher in class and what you think is important according to your actual situation, and organize them into notes.
Sorting out the textbook exercises: After sorting out the knowledge points, you have to go back to the questions, the after-class questions of each class and the final review questions of each chapter, and spend time doing them one by one (this also depends on the difficulty of the school you are admitted to and the requirements for yourself). Similarly, mark the ones that are not easy to make mistakes and organize them into notes.
Finishing the real questions of the postgraduate entrance examination: finishing the knowledge points and textbook questions is to be admitted to the graduate students of this institution, so the third part is to sort out the real questions of the chapter of the school you want to take, which is very important, because everything is to prepare for the final examination paper.
After reviewing all the chapters systematically, put all the notes together and then check whether there are any missing parts. If you don't understand, you can ask your teacher or classmates. You have to take out two textbooks and keep reading.
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