The exam is just around the corner. Are the candidates ready for the exam? It is very important to review before the exam. The following are the practical knowledge points I have prepared for you, hoping to help you review efficiently. Here, I wish the candidates a smooth exam.
First, mathematical knowledge points: the phalanx problem
1, concept and classification
Students line up, soldiers line up, horizontal line is called a row, vertical line is called a column. If the number of rows and columns is equal, they are arranged in a square. This figure is called a square, also called a square.
Square matrix includes solid square matrix and hollow square matrix. If a square matrix is full of objects, it is called a real square matrix; If there is no object in the middle of a square, it is called a hollow square. And each layer of a solid square can be regarded as a hollow square separately, so the law of hollow square also applies to it.
2. Basic laws
(1) The number of people (or things) on each side of a phalanx is the same regardless of the level, and the number of people on each side decreases by 2 for each inward level.
There are eight people missing. (arithmetic progression related knowledge can be applied to solving problems)
(2) Total number of people on each floor = [number of people (or things) on each side-1]×4
Number of people (or things) on each side = total number of people on each floor ÷4+ 1.
(3) Strong phalanges
Total number of people (or things) = number of people (or things) per side × number of people (or things) per side.
(4) Hollow phalanges
Total number of people (or things) = (outermost number of people (or things) on each side-number of layers) × number of layers× 4
Total number of people (or things) = (outermost number (or things)+innermost number (or things) * number of layers /2
The outermost layer on each side = the total number of people (or things) ÷4÷ layers+layers.
Second, mathematics knowledge points: chickens and rabbits in the same cage
1, the origin of the problem of chickens and rabbits in the same cage
This question is one of the famous and interesting questions in ancient China. About 1500 years ago, this interesting question was recorded in Sun Tzu's calculation. The book says: "Today, chickens and rabbits are in the same cage, with 35 heads above and 94 feet below. What are the geometric figures of chickens and rabbits? " These four sentences mean: there are several chickens and rabbits in a cage, counting from the top, there are 35 heads; It's 94 feet from the bottom. How many chickens and rabbits are there in each cage?
Can you answer this question? Do you want to know how to answer this question in Sunzi Suanjing?
2. The idea of solving problems with chickens and rabbits in the same cage.
(1) foot cutting method
The solution is as follows: if the feet of each chicken and rabbit are cut off in half, then each chicken becomes a "chicken with one leg" and each rabbit becomes a "rabbit with two legs". In this way, the total number of feet of chickens and rabbits has changed from 94 to 47; If there is a rabbit in the cage, the total number of feet is more than the total number of heads 1. So the difference between the total number of feet 47 and the total number of heads 35 is the number of rabbits, that is, 47-35= 12 (only). Obviously, the number of chickens is 35- 12=23 (only)
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