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Introduction: In the annual entrance examinations for elementary school, mathematics scores hold significant importance. To further differentiate scores during the school selection process, in addition to mastering basic mathematical knowledge, the expansion of mathematical content has also become a key assessment area. The expansion of mathematical thinking, commonly referred to as Olympiad mathematics.
All Olympiad mathematics knowledge can be categorized into seven major modules, and various types of questions stem from these seven modules. So, what are the modules of Olympiad mathematics? What important knowledge does each module contain? Let’s see how much you have mastered these modules. The seven modules of Olympiad mathematics include: calculation, number theory, geometry, motion, application problems, counting, and miscellaneous problems. Are you familiar with these seven modules?
Module 1: Calculation Module
1. Mental calculation and clever calculation
2. Mixed operations of fractions and decimals, and complex fraction operations
3. Converting repeating decimals to fractions and mixed operations
4. Arithmetic and geometric sequences
5. Comprehensive calculation formulas
6. Techniques for fraction calculations such as splitting terms, changing variables, and general term induction
7. Comparison and estimation
8. Defining new operations
9. Solving equations
Module 2: Number Theory Module
1. Prime and composite numbers
2. Factors and multiples
3. Divisibility characteristics and properties
4. Place value principle
5. Properties of remainders
6. Congruence problems
7. Chinese Remainder Theorem (successive satisfaction method)
8. Perfect squares
9. Odd-even analysis
10. Indeterminate equations
11. Base problems
12. Extremum problems
Module 3: Geometry Module
(1) Linear geometry
1. Length and angles
2. Lattice points and cutting and complementing
3. Area transformations of triangles and half-models
4. Pythagorean theorem and chord diagrams
5. Five major models
(2) Curvilinear geometry
1. Circumference and area of circles and sectors
2. Area problems of shapes swept by rotation
(3) Solid geometry
1. Surface area and volume of solid figures
2. Problems of solid figures formed by rotating plane figures
3. Plane unfolding diagrams
4. Liquid immersion problems
Module 4: Motion Module
1. Simple meeting and chasing problems
2. Circular track problems
3. Flowing and sailing problems
4. Train crossing bridge problems
5. Elevator problems
6. Departure interval problems
7. Pickup and drop-off problems
8. Clock problems
9. Multiple people meeting and chasing problems
10. Multiple meeting and chasing problems
11. Solving motion problems using equations and proportions
Module 5: Application Problems Module
1. Setting up equations to solve application problems
2. Application problems involving fractions and percentages
3. Proportional application problems
4. Engineering problems
5. Concentration problems
6. Economic problems
7. Cattle grazing problems
Module 6: Counting Module
1. Enumeration methods: classification enumeration, marking method, tree diagram method
2. Classification enumeration: overall method, correspondence method, exclusion method
3. Addition and multiplication principles
4. Permutations and combinations
5. Inclusion-exclusion principle
6. Pigeonhole principle
7. Induction and recursion
8. Geometric counting
9. Number theory counting
Module 7: Miscellaneous Problems
1. Starting from simple cases
2. Correspondence and transformation thinking
3. Thinking from the opposite and from special cases
4. Coloring and covering
5. Games and strategies
6. Sports competition problems
7. Logical reasoning problems
8. Number puzzles
9. Sudoku
Although we have introduced Olympiad mathematics here, it does not mean that the entrance examination for elementary school only tests Olympiad knowledge. With the adjustments in policies over the past two years, simply seeking difficulty will not guarantee good results in the entrance examination. While expanding mathematical knowledge, do not forget to solidify the basics!
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