Computational class
Calculation is the basic knowledge of mathematics learning, and it is also the basis of learning olympiad well. Whether the answer can be worked out quickly and accurately is a basic point in mathematical competitions over the years. The calculation of senior three includes: quick calculation and skillful calculation, law of series, sum of series, sum of arithmetic progression, etc.
Application theme category
Since the third grade, many specialized knowledge of Olympic Mathematics is the key knowledge that must be tested in all competitions and exams in all grades. Students must lay a good foundation in the early stage of learning various application problems.
(1) sum and difference times;
By mean of line segment identification and other methods, various quantitative relation in these two kinds of problems are revealed,
Sum and multiple problem: decimal = sum ÷ (multiple+1).
Differential multiple problem: decimal = differential ÷ (multiple-1)
(2) Age:
Teach the main methods to solve the age problem: sum times and difference times; Marking method of drawing line segments.
(3) profit and loss problem:
Introduce the main forms of profit and loss problem.
(Double profit, double loss, one profit and one loss)
Total number of people allocated = total profit and loss ÷ the difference between the two allocations.
(4) Planting trees:
Quantitative relationship among total length, plant spacing and number of plants;
Total length = plant spacing × number of nodes,
Closed graph: number of trees = number of line segments.
Open graphics:
Two species: number of plants = number of segments+1.
Do not plant at both ends: number of plants = number of segments-1.
Plant one without planting the other: number of trees = number of segments.
(5) The problem of chickens and rabbits in the same cage:
This paper introduces the origin and main forms of the problem of chickens and rabbits in the same cage.
Reveal the quantitative relationship in the problem of chickens and rabbits in the same cage,
Hypothetical method
(6) Travel problems:
Encounter a problem, chase after a problem, etc.
Meet time = total distance ÷ speed sum,
Catch-up time = distance ÷ speed difference.
(7) cycle problem
(8) Reduction problem
(9) Standardization
(10) Skillful Solutions to Mathematics and Interesting Questions in Sports Competition
Geometric class
In the study of the third grade school, some simple graphics will involve finding the perimeter and area, so in the Olympics, the graphics problem involves finding the perimeter and rectangular area skillfully.
Number theory course
Now the third grade also begins to involve number theory, which is a relatively simple property divisible by 2, 3 and 5, odd and even numbers, remainder and period.
Logic class
Logical reasoning problem is a kind of problem that many students are good at.
other
Graphic rules, search rules, crossword puzzles, one stroke, multiple strokes, pigeon hole principle.