Category: Blog

I. Strategic Planning: A Four-Phase Practice Order and Objectives

Starting your practice with the most recent papers is inefficient. It is recommended to break your past paper preparation into four progressive stages, each with a clear goal.

Phase	Timing	Core Objective	Materials & Order	Specific Actions & Key Points
Phase 1: Familiarization & Exposure	Early preparation (3-4 months before the exam)	Get to know the question types, difficulty distribution, and style of the exam. Build intuition and reduce unfamiliarity.	Choose 3-5 older papers (e.g., from 5-8 years ago). Order: from oldest to newest or any order. Do not time yourself.	1. Open-book practice: You may refer to materials. The only goal is to understand each problem. 2. Classify and tag: Categorize problems by the four main modules (Number Theory, Geometry, Combinatorics & Logic, Algebra) to get a feel for their weight and style. 3. Record first impressions: Note down "Which question types felt easiest/most difficult?"
Phase 2: Modular Breakthrough	Mid-preparation (1-3 months before the exam)	Tackle weak areas, solidify core knowledge points, and develop a systematic problem-solving approach for each module.	Use past papers from the last 5-8 years, but break them down by topic instead of doing them as full sets.	1. Thematic drills: Gather all "Number Theory" or "Geometry" problems from past years and practice them together. 2. Summarize patterns: Identify common solution methods, standard thought processes, and traps for each type of problem. 3. Make connections: Explicitly link problems to core knowledge (e.g., prime factorization, Pythagorean theorem, enumeration).
Phase 3: Full Simulation & Speed Building	Sprint phase (1 month before the exam)	Simulate the real exam environment, optimize time management, and improve speed and first-time accuracy.	Use the 3-5 most recent papers. Order: Full simulation strictly timed to 60 minutes.	1. Strict conditions: Use an answer sheet and a timer to mimic exam conditions. 2. Test strategies: Practice the "easy first, steady then fast" approach. 3. Score and review: Mark your answers strictly against the solutions, but try to review your thought process before looking at explanations.
Phase 4: Maintaining Momentum & Building Confidence	1 week before the exam	Maintain your problem-solving feel, fill any final gaps, and adjust your mindset.	Redo mistakes + selectively redo 1-2 medium-difficulty past papers.	1. Redo mistakes: Work through your mistake notebook from scratch to ensure true mastery. 2. Keep the rhythm: Complete one timed practice, but don't focus on difficult problems. The goal is to keep your mind active and your sense of timing sharp. 3. Mental preparation: Review your progress, acknowledge your achievements, and approach the exam with a calm, confident mindset.

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II. In-Depth Review: Turning Every Mistake into a Stepping Stone

Practicing without reviewing is ineffective. A thorough review is far more important than doing new problems. Follow this process for each practice test:

The 3-Step In-Depth Review Method

Data Diagnosis: After completing a simulation, fill out a "Single Simulation Diagnostic Analysis Table".

Causal Analysis: For incorrect answers and time-consuming questions, identify the cause and record it in a "Mistake Attribution & Action Log".

Regular Review: Review the "Mistake Attribution & Action Log" once a week.

Sample Single Simulation Diagnostic Analysis Table

Simulated Test: 2024 JMC Past Paper

Score Analysis by Module	Time Allocation Analysis	Score Loss Cause Statistics
Core Issues Summary from this Simulation:

Template: Mistake Attribution & Action Log

Question No.	Review Focus Points
Example: 14

Key Principles for Effective Review:

Be specific in attribution: Don't just write "careless". Specify whether it was "forgetting to change signs when transposing terms" or "incorrect unit conversion".

Make actions actionable: "Review geometry formulas" is less effective than "Write out the area and perimeter formulas for triangles, quadrilaterals, and circles three times each".

Track your status: Update the "Mastery Status" column regularly. Problems that are fully mastered can be removed from your notebook.

III. Precision Score-Boosting: From "Knowing How to Solve" to "Fast and Accurate"

With a solid knowledge base, your exam strategy becomes the key to maximizing your score.

Dimension	Specific Strategy & Action Guide	Practical Examples
Time Allocation Strategy	The "3322" Time Allocation Method: - Questions 1-15 (Basic): Aim for 15-20 minutes. Target near 100% accuracy. These are the foundation for a medal. - Questions 16-20 (Intermediate): Aim for 15-20 minutes. These are solvable with a solid grasp of fundamentals. - Questions 21-25 (Challenging): Reserve 15-20 minutes. Be willing to attempt and make educated guesses. - Last 5 minutes: Use to check your answer sheet and re-examine marked questions.	Quickly browse the first 5 questions to build confidence. Stick to the time allocation per section. If stuck on a question for more than 2 minutes, mark it and move on.
Question-Ordering Strategy	"Easy first, two passes": 1. First pass: Go through questions in order. If you hit a wall (no idea after 1.5 minutes), mark it and skip it. 2. Second pass: After completing all questions, return to the marked ones. Your mindset will be more relaxed, and you might have gained insights from later problems.	Use a pencil to mark questions with symbols like "?" for unsure, "○" for no idea. Prioritize the "?" questions during the second pass.
Multiple-Choice Techniques	Make full use of the "no penalty for wrong answers" rule: - Substitution: Plug answer choices back into the problem, especially effective for number theory and equation problems. - Extreme/Special Values: Test with simple special values that meet the conditions (like 0, 1, prime numbers) to eliminate incorrect options. - Diagram: For geometry problems, draw an accurate diagram on scratch paper to aid analysis. - Dimensional Analysis: Use units and magnitude to rule out obviously unreasonable options.	For complex calculations, look at the numerical characteristics of the options first; sometimes you can directly eliminate options with large differences. For geometry problems without a drawn-to-scale diagram, draw a standard figure yourself to aid thinking.
Mindset & Checking Strategy	"Secure the basics, win the intermediates, challenge the hard ones": - Prioritize the accuracy of the first 15 questions. - When checking, review the calculations for the first 15 questions first. - For difficult problems, if time allows, try a different perspective or use the characteristics of multiple-choice questions to make an educated guess (e.g., after eliminating clearly wrong options, choose from the remaining).	Before handing in your paper, double-check that the question numbers and answers on your answer sheet correspond correctly to avoid filling in the wrong row.

I. Number Theory Module: The Wisdom and Patterns of Numbers

Number theory is the most heavily weighted and distinctive module in the JMC, accounting for approximately 25%-30%. It does not require complex formulas, but greatly tests sharp insight into the properties of integers and the ability to discover patterns.

Assessment Area	Core Knowledge & High-Frequency Topics	Typical Question Examples (based on past papers)	Common Errors & Difficulties	Preparation Strategies
Number Properties & Operations	Prime & composite numbers, factors & multiples, GCD & LCM, parity analysis.	Determine whether a multi-digit number meets a specific condition (e.g., the sum of squares of its digits is prime).	Omitting 1 or the number itself during prime factorization; repeating or missing combinations when counting factors.	Memorize the table of prime numbers within 100; master short division for quick prime factorization; systematically practice finding the number and sum of factors.
Congruences & Modular Arithmetic	Using modular arithmetic (especially mod 7, mod 9, mod 10) to solve problems involving date cycles, last digits, and divisibility.	Using modulo 7 to deduce the distribution of weekdays for a given month.	Confusing the properties of modular arithmetic, performing addition/subtraction/multiplication/division incorrectly; not understanding the essence of the congruence concept.	Understand the core concept of "remainder", transforming periodic problems (like weekdays, repeating decimals) into modular arithmetic models. Master quick divisibility rules like "sum of digits for divisibility by 3 or 9" and "last digits for divisibility by 4 or 8".
Number Puzzles & Digit Analysis	Involves number puzzles, magic squares, digit manipulation (e.g., reversal, rearrangement), and basic base conversion.	Decipher encrypted equations where digits are replaced by symbols; perform operations in a specific base.	Confusing place values during base conversion; incomplete enumeration or broken logical chains when solving number puzzles.	Strengthen logical reasoning, learn to start analysis from special positions like the units digit or the highest digit; master conversion between decimal and other bases.
Comprehension & Application	Applying number theory knowledge to real-life scenarios, such as distribution problems and pattern-filling.	Problems involving resource allocation, constructing integers that meet specific conditions, etc.	Inability to abstract word descriptions into number theory models; ignoring hidden constraints in the problem (e.g., integers, positive integers).	Practice translating real-world problems into mathematical language (equations, inequalities, congruences), paying attention to the range of solutions.

II. Geometry Module: Intuition in Shapes and Space

The geometry module accounts for about 20%-25%, testing the ability to perceive, measure, and transform shapes from plane to space, emphasizing the combination of numbers and shapes.

Assessment Area	Core Knowledge & High-Frequency Topics	Typical Question Examples (based on past papers)	Common Errors & Difficulties	Preparation Strategies
Plane Geometry	Properties of basic shapes (triangles, quadrilaterals, circles), perimeter and area calculations, Pythagorean theorem, symmetry, angle calculations.	Calculating the perimeter or area of composite shapes; solving problems using symmetry.	Incorrect memorization or application of area formulas; inability to effectively divide or fill in complex shapes; ignoring unit conversions.	Master the perimeter and area formulas of common shapes; for irregular shapes, focus on training the concepts of "cut-and-paste method" and "equal area transformation". Memorize common Pythagorean triples (e.g., 3-4-5, 5-12-13).
3D Geometry & Spatial Imagination	Identifying net diagrams of basic 3D shapes like cubes and cuboids, restoring 2D projections, calculating surface area and volume.	Deducing vertex positions by folding a cube net; determining whether a given 2D shape can be folded into a cube.	Insufficient spatial imagination, inability to mentally transform between 3D and 2D; confusing the 11 standard nets of a cube.	Must master the 11 standard nets of a cube and be able to quickly determine if a given shape is a valid net. Practice hands-on manipulation to develop spatial sense.
Coordinate Geometry & Transformations	Locating points on a coordinate plane, calculating distances, determining symmetry, simple transformations (translation, rotation, reflection).	Finding the number of shortest paths on a grid; determining the position of a shape after transformation.	Coordinate calculation errors; inaccurate grasp of positional relationships after transformations (especially rotation).	Understand the coordinate rules for transformations; algebraize geometric problems and use coordinates for precise calculation.
Measurement & Conservation	Applying conservation of area and volume, equal-area transformations.	Problems where area remains unchanged after shape is divided and reassembled.	Confused by complex shapes, failing to find the conserved quantity.	Focus on the core principle of "total quantity unchanged"; regardless of how shapes are cut or moved, the total area or volume remains constant.

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III. Combinatorics & Logic Module: Gymnastics of the Mind

This module (often combined with logical reasoning and data processing, accounting for about 20%-30%) is the embodiment of JMC's interest and differentiation, focusing on systematic thinking and rigorous reasoning.

Assessment Area	Core Knowledge & High-Frequency Topics	Typical Question Examples (based on past papers)	Common Errors & Difficulties	Preparation Strategies
Counting Principles	Enumerative method, addition and multiplication principles, simple permutations and combinations (without complex formulas), basics of the inclusion-exclusion principle.	Calculating the total number of different movement paths for pieces on a chessboard; determining how many numbers or arrangements satisfy specific conditions.	Repeating or omitting cases during enumeration; unclear steps in multi-step counting; confusing "ordered" permutations with "unordered" combinations.	Train the ability to enumerate systematically without omission. For complex counting, first clarify whether to "add by classification" or "multiply by steps", using tree diagrams or lists when necessary.
Logical Reasoning	Determining truth values of statements (e.g., "three truths, one false" problems), conditional reasoning, Sudoku-like puzzles, strategy game analysis.	"Three truths, one false" scenario reasoning, needing to find the answer through contradiction elimination.	Confusion when faced with multiple conditions; inability to effectively use assumptions and proof by contradiction.	Learn to organize conditional relationships using tables and hypothesis methods. Expose yourself to classic logic puzzles to develop reverse and critical thinking.
Paths & Graph Theory Basics	Shortest path problems, Eulerian path problems, simple network analysis.	Finding the number of shortest paths from one point to another on a grid.	Not considering constraints (e.g., only moving right or up) when counting paths; unfamiliar with basic graph theory concepts like odd and even vertices.	Master the recurrence or combination formulas for counting shortest paths on a grid. Understand the "odd vertex" theorem for Eulerian path problems.
Intro to Probability & Statistics	Simple classical probability calculations, reading and analyzing data charts (bar charts, line graphs, pie charts).	Inferring information or comparing data based on composite charts (e.g., bar chart plus line graph).	Incorrectly calculating total or favorable outcomes in probability; inaccurate information extraction or interpretation from charts.	Clarify the meaning of numerator and denominator in probability formulas. Strengthen chart reading skills, paying attention to titles, axis units, legends, etc.

IV. Algebra Module: Abstraction and Expression of Patterns

The algebra module accounts for about 15%-20%, focusing on abstracting real-world problems or numerical patterns into algebraic expressions or equations and solving them.

一九Given conditions, find the value of a complex algebraic expression.

Assessment Area	Core Knowledge & High-Frequency Topics	Typical Question Examples (based on past papers)	Common Errors & Difficulties	Preparation Strategies
Equations & Solving	Linear equations in one variable, simple systems of equations, ratio problems, fraction and percentage operations.	Solving "chicken and rabbit in the same cage" problems using equations; solving models involving tiered fees.	Setting incorrect variables leading to complex equations; calculation errors during solving; misunderstanding ratio relationships.	Strengthen basic computational skills. Learn to assign variables based on key quantities in problems and find equality relationships. Master conversions between ratios, fractions, and percentages.
Sequences & Patterns	Discovering patterns in number sequences (arithmetic, geometric, Fibonacci sequences, etc.), exploring patterns in shapes, basic recursive thinking.	Finding missing terms based on given sequence patterns; identifying changing patterns in shape sequences.	Incorrectly identifying patterns, especially for non-simple arithmetic/geometric sequences; inability to accurately express discovered patterns algebraically.	Observe and experiment frequently to develop sensitivity to numerical and visual changes. Master formulas for common sequences and practice expressing general terms with letters.
Variable Relationships & Modeling	Expressing quantitative relationships with algebraic expressions, building simple function models (e.g., linear relationships).	Building algebraic models based on real-life scenarios (e.g., shopping discounts, travel problems) and solving them.	Inability to accurately translate word descriptions into mathematical language; ignoring the practical meaning and range of variables.	Strengthen practice with applied problems, focusing on the ability to "translate" keywords like "more", "less", "times", "ratio" into algebraic symbols.
Algebraic Manipulation & Evaluation	Simplifying algebraic expressions, evaluating expressions (substitution method), simple inequalities.	Sign errors during manipulation; not noticing the form of known conditions when using substitution.	Reinforce the rules for addition, subtraction, multiplication, and division of polynomials. Master the overall substitution approach to avoid unnecessary expansion.

V. Comprehensive Preparation Strategies and Trend Insights

Trend in Questions: In recent years, JMC questions have featured longer problem statements, the incorporation of cross-disciplinary elements (e.g., simple physics, economic models), and an emphasis on verifying answers using multiple methods. This places higher demands on students' information extraction skills, comprehensive application abilities, and rigorous thinking.

Core Preparation Advice:

Past Papers are King: Studying past papers from the last 5-10 years is the most direct and effective way to familiarize yourself with the topics, difficulty, and question style.

Create a Mistakes Log: Categorize your mistakes according to the four modules above, deeply analyze the reasons (unclear concepts, incorrect approach, carelessness), and review regularly.

Timed Mock Tests: Conduct full-length mock tests strictly within 60 minutes to practice time management. It is recommended to complete the first 15 basic questions within 15-20 minutes to ensure high accuracy, leaving ample time to tackle the last 10 questions.

Expand Your Thinking: Regularly engage with fun activities like Sudoku, logic puzzles, and visual reasoning to improve mental flexibility and resilience.

Exam Strategy: Keep in mind that there is no penalty for wrong answers in the JMC. For difficult problems with no clear approach, don't guess blindly. However, for problems where you have some ideas or can eliminate some options, dare to make reasonable attempts. The foundation of winning an award is to be steady and ensure you get all the points from questions you can solve.

Through systematic review and targeted training on these four core modules, you will not only effectively prepare for the JMC but also solidify the foundations of mathematical thinking, paving the way for more advanced mathematical challenges in the future.