Xiaoshengchu Mathematics Knowledge Test Site Induction One
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] means an integer not exceeding 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.
Xiaoshengchu Mathematics Knowledge Test Site Induction II
Average problem
There are some basic formulas and algorithms that need to be mastered in the Olympic Games average at the beginning of Xiaoshengchu, as follows:
Basic formula: ① Average value = total quantity ÷ total number of copies.
Total quantity = average x total number of copies
Total number of copies = total quantity/average value
② Average value = benchmark number+sum of differences between each number and benchmark number ÷ total number of copies.
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.
Induction of mathematics knowledge test sites in junior high school
economic problem
Profit percentage = (selling price-cost) ÷ cost×100%;
Selling price = cost ×( 1+ profit percentage);
Cost = selling price ÷( 1+ profit percentage);
The pricing of goods is determined according to the expected profit;
Pricing = cost ×( 1+ expected profit percentage);
Principal: savings amount;
Interest rate: the ratio of interest to principal;
Interest = principal × interest rate × number of periods;
Price including tax = price excluding tax ×( 1+ VAT rate);
Summary of mathematics knowledge test sites in junior high school
The chicken and the rabbit are in the same cage.
Basic concepts: the problem of chicken and rabbit in the same cage, also known as replacement problem and hypothesis problem, is the wrong part of replacement hypothesis;
Basic idea:
(1) hypothesis, that is, assume that some phenomenon exists (like a and b or b and a):
(2) Assuming that there are differences different from the subject conditions, find out what the differences are;
(3) The difference caused by everything is fixed, so as to find out the reasons for this difference;
(4) According to these two differences, make appropriate adjustments to eliminate the differences.
Basic formula:
① Assume that all chickens are rabbits: the number of chickens = (number of rabbit feet × number of total heads-number of total feet) ÷ (number of rabbit feet-number of chicken feet)
② Suppose all rabbits are chickens: the number of rabbits = (total number of feet-chicken feet × total number of heads) ÷ (rabbit feet-chicken feet)
Key problem: find out the difference between total quantity and unit quantity.
Summary of five test sites of mathematics knowledge in Xiaoshengchu
Unit of calculation for the number and classification of prepayment rate
1, length measurement unit and rate:
Kilometers (kilometers), meters, decimeters, centimeters and millimeters.
1 km = 1 km 1 km = 1000 m
1 m = 10 decimeter 1 decimeter = 10 cm
1 cm = 10/0mm
2. Unit of measurement and rate of area:
Square kilometers, hectares, square meters, square decimeters, square centimeters
1 km2 = 100 hectare
1 km2 = 1000000 m2
1 ha = 1 10,000 m2
1 m2 = 100 square decimeter
1 square decimeter = 100 square centimeter
3. Volume measurement unit and rate:
Cubic meters, decimeters, centimeters, liters and milliliters.
1 m3 = 1000 cubic decimeter
1 cubic decimeter = 1000 cubic centimeter
1 cubic decimeter = 1 liter 1 cubic centimeter = 1 ml.
4, quality unit and grade:
Ton, kilogram, kilogram, gram
1 ton = 1000 kg
1 kg = 1 kg
1 kg =1000g
5. Time unit and rate:
Century, year, month, day, hour, minute and second.
1 century = 100 1 year =65438+ February.
1 day =24 hours 1 hour =60 minutes
1 min =60 seconds
(The months of 3 1 day are 1, 3, 5, 7, 8, 10, 65438+February, and the months of 30 days are April, June and September,165438+/kloc-0.
Table of common calculation formulas
1, rectangular area
= length × width, and the calculation formula is S=ab.
2. Square area
= side length × side length, and the calculation formula is S=a×a=a2.
3, rectangular perimeter
= (length+width) ×2, and the calculation formula is C=(a+b)×2.
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