Introduction: A summary of the common knowledge points of Olympic Mathematics in primary schools compiled by the fresh graduates training network. Thank you for reading.

First, the law of periodic cycles and numerical tables

Periodicity: In the process of movement change, some features appear regularly and periodically.

Period: We call the time elapsed between two consecutive appearances as a period.

Key problem: determine the cycle.

Leap year: there are 366 days in a year;

(1) year is divisible by 4; ② If the year is divisible by 100, the year must be divisible by 400;

Average year: There are 365 days in a year.

① The year cannot be divisible by 4; ② If the year is divisible by 100, but not by 400;

9. Average

Basic formula: ① average = total amount? Total shares

Total = average? Total shares

Total number of copies = total quantity? average number

② Average value = benchmark number+sum of differences between each number and benchmark number? Total shares

Basic algorithm:

① Find out the total quantity and total number of copies, and calculate with the basic formula ①.

② Benchmark number method: according to the relationship between given numbers, determine a benchmark number; Generally, the number or intermediate number close to all numbers is selected as the reference number; Taking the reference number as the standard, find the difference between all given numbers and the reference number; Then find the sum of all differences; Then find the average of these differences; Finally, the sum of this difference and the average value of the reference number is the average value, and the specific relationship is shown in the basic formula ②.

Second, the principle of filing.

Drawer principle 1: If (n+ 1) objects are put in n drawers, there must be at least 2 objects in one drawer.

Example: put four objects in three drawers, that is, decompose four into the sum of three integers, then there are the following four situations:

①4=4+0+0 ②4=3+ 1+0 ③4=2+2+0 ④4=2+ 1+ 1

Observing the arrangement of the above four items, we will find a common feature: there are always two or more items in a drawer, which means there must be at least two items in a drawer.

Pigeonhole principle II: If you put n objects in m drawers, where n >；; M, then there must be at least:

①k=[n/m ]+ 1 object: when n is not divisible by m.

②k=n/m objects: when n is divisible by m.

Understanding knowledge points: [x] refers to the largest integer that does not exceed X.

Example [4.351] = 4; [0.32 1]=0; [2.9999]=2;

Key issues: constructing objects and drawers. That is, find the quantities representing objects and drawers, and then calculate them according to pigeonhole principle.

Third, define a new operation.

Basic concept: define a new operation symbol, which contains a variety of basic (mixed) operations.

Basic idea: strictly follow the newly defined operation rules, substitute the known numbers into the operation of addition, subtraction, multiplication and division, and then operate according to the basic operation process and rules.

Key problem: correctly understand the meaning of defined operation symbols.

Note: ① The new operation may not conform to the operation procedures, so special attention should be paid to the operation sequence.

② Each newly defined operation symbol can only be used in this problem.

Fourth, summation of series.

Arithmetic progression: In a column, the difference between any two adjacent numbers is certain. This number of columns is called arithmetic progression.

Basic concepts: the first item: the first number of arithmetic progression, which is generally expressed by a 1;

Number of terms: the number of all arithmetic progression, generally represented by n;

Tolerance: the difference between any two adjacent numbers in a series, generally expressed by d;

General term: a formula representing each number in a series, which is generally represented by an;

Sum of series: the sum of all numbers in this series, usually represented by Sn.

Basic idea: arithmetic progression involves five quantities: a 1, an, d, n and sn, and the general formula involves four quantities. If we know three of them, we can find the fourth; There are four quantities involved in the summation formula. If we know three of them, we can find the fourth one.

Basic formula: general formula: an = a1+(n-1) d;

General project = first project+(project number 1 1)? Tolerance;

Sequence and formula: sn, = (a 1+ an)? n？ 2;

Sum of series = (first item+last item)? Number of projects? 2;

Term number formula: n= (an+ a 1)? d+ 1；

Number of items = (last item-first item)? Tolerance+1;

Tolerance formula: d =(an-a 1)? (n- 1)；

Tolerance = (last item-first item)? (project number-1);

Key problems: determine the known quantity and unknown quantity, and determine the formula used;

Five, binary and its application

Decimal system: represented by a decimal number from 0 to 9, every 10 decimal1; Numbers with different digits have different meanings, with the tenth digit of 2 representing 20 and the hundredth digit of 2 representing 200. So 234=200+30+4=2? 102+3? 10+4。

= Ann? 10n- 1+An- 1？ 10n-2+An-2？ 10n-3+An-3？ 10n-4+ An -4? 10n-5+An-6？ 10n-7++A3？ 102+A2？ 10 1+A 1？ 100

Note: n0 =1; N 1=N (where n is an arbitrary natural number)

Binary: represented by two numbers: 0 ~ 1, in which1is entered for every two digits; Numbers on different numbers have different meanings.

(2)= An？ 2n- 1+An- 1？ 2n-2+An-2？ 2n-3+An-3？ 2n-4+ An -4? 2n-5+An-6？ 2n-7

++A3？ 22+A2？ 2 1+A 1？ 20

Note: An is 0 or 1.

Decimal to binary:

(1) According to the characteristics of binary all binary 1, divide this number by 2 continuously until the quotient is 0, and then write the remainder from bottom to top.

(2) First, find that the n power of 2 is not greater than this number, then find their difference, and then find that the n power of 2 is not greater than this difference. According to this method, it has been found that the difference is 0 and can be written according to the characteristics of binary expansion.

Six, the principle of addition, subtraction, multiplication and division and geometric counting

Addition principle: If there are n methods to complete a task, the first method has m 1 different methods, the second method has m2 different methods, and the nth method has mn different methods, then there are * * * m1+m2 ...+Mn+Mn different methods to complete this task.

Key problem: determine the classification method of work.

Basic characteristics: each method can complete the task.

Multiplication principle: If a task needs to be divided into n steps, there are m 1 methods to do the first 1 step. No matter which method is used in step 1, there are always m2 methods in step 2. N- 1 step No matter which method is used, there are always mn methods in step n, so there are m 1 methods to complete this task. The second money supply? Different methods.

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