The International Olympiad of Mathematics (iOM) is one of the most prestigious Olympiad exams for students from Class 1 to Class 12. Preparing with the most relevant and class-wise important questions can help students boost their performance and confidence. This guide offers class-wise iOM important questions, covering key topics from the syllabus along with tips to help students excel in the exam.
iOM Class Wise Important Questions for 2025-26
The “important questions” for iOM are inherently tied to the syllabus for each class. While the core mathematical concepts remain consistent, the depth and complexity of questions increase with higher grades. The “Scholar’s Zone” or “Achiever’s Section” typically contains higher-order thinking questions that carry more marks, making them particularly “important” for top ranks.
Let’s explore some key topics and illustrative important questions for different class groups for the iOM 2025-26 exam.
iOM Important Questions for Classes 1 & 2
For younger students, the iOM focuses on foundational mathematical concepts and basic logical reasoning.
Key Topics:
- Number Sense: Counting, number names, place value (ones, tens, hundreds), comparing numbers.
- Computation Operations: Addition, subtraction, basic multiplication, and division facts.
- Patterns: Identifying and extending simple number and figure patterns.
- Money, Time, Calendar: Basic understanding of currency, reading time, days of the week, months of the year.
- Length, Weight, Capacity: Non-standard and standard units of measurement.
- Geometrical Shapes: Identification of basic 2D and 3D shapes.
- Reasoning & Aptitude: Simple logical sequencing, analogies, odd one out, spatial understanding.
Illustrative Important Questions:
- Number Sense: What number comes after 89 and before 91?
- Computation: If you have 15 apples and give away 7, how many do you have left?
- Patterns: Complete the pattern: 2, 4, 6, 8, ___, 12.
- Time: If it is 3 o’clock now, what time will it be in 2 hours?
- Shapes: How many sides does a square have?
- Reasoning: Which of these is different: a table, a chair, a bed, a tree?
iOM Important Questions for Classes 3 & 4
As students progress, the complexity of operations and introduction to new concepts increase.
Key Topics:
- Number System: Larger numbers (up to thousands), Indian/International place value system, expanded form.
- Fractions: Introduction to fractions, identifying parts of a whole, comparing simple fractions.
- Geometry: Lines, line segments, rays, angles (right angle), types of triangles, perimeter of basic shapes.
- Measurement: Standard units for length, weight, capacity, conversion between units (e.g., cm to m, kg to g).
- Data Handling: Reading and interpreting pictographs and bar graphs.
- Money & Unitary Method: Solving problems involving money, simple unitary method.
- Reasoning & Aptitude: Series completion, coding-decoding, blood relations, direction sense, mirror images.
Illustrative Important Questions:
- Number System: What is the place value of 7 in 47,215?
- Fractions: Which fraction is greater: 1/2 or 1/4?
- Geometry: A square field has a side of 10 meters. What is its perimeter?
- Measurement: Convert 2 kilograms into grams.
- Data Handling: A bar graph shows the favorite colors of students. If blue is liked by 12 students and red by 8, how many more students like blue than red?
- Reasoning: If “CAT” is coded as “DCT,” how would “DOG” be coded?
iOM Important Questions for Classes 5 & 6
These classes introduce more abstract mathematical concepts and deeper problem-solving.
Key Topics:
- Number System & Operations: Integers, properties of operations, factors, multiples, prime and composite numbers, LCM and HCF.
- Fractions & Decimals: Operations with fractions and decimals, conversion between them.
- Ratio & Proportion: Understanding ratios, solving problems using proportion, unitary method applications.
- Percentage: Introduction to percentages, converting percentages to fractions/decimals and vice-versa, simple percentage calculations.
- Algebra: Introduction to variables, simple algebraic expressions and equations.
- Geometry & Mensuration: Types of angles, triangles (classification by sides and angles), quadrilaterals, circles (circumference, area of circle’s parts), area and perimeter of complex shapes, volume of basic 3D shapes (cuboid, cube).
- Data Handling: Mean, median, mode, bar graphs, pie charts.
- Reasoning & Aptitude: Advanced series, analogies, classification, logical Venn diagrams, puzzles.
Illustrative Important Questions:
- Number Operations: Find the LCM of 12, 18, and 24.
- Fractions & Decimals: Simplify: (3/4)+(1/2)−(1/8).
- Percentage: If 20% of a number is 50, what is the number?
- Algebra: If x+7=15, what is the value of x?
- Mensuration: The length of a rectangle is 12 cm and its width is 8 cm. What is its area?
- Reasoning: If A is the brother of B, C is the sister of A, and D is the father of C, how is D related to B?
iOM Important Questions for Classes 7 & 8
Students in these classes will encounter more complex algebraic concepts, deeper geometry, and initial exposure to concepts like exponents and powers.
Key Topics:
- Rational Numbers: Properties and operations on rational numbers.
- Exponents and Powers: Laws of exponents, scientific notation.
- Algebraic Expressions & Identities: Multiplication of algebraic expressions, factorization, basic identities (a+b)2, etc.).
- Linear Equations in One Variable: Solving various types of linear equations.
- Comparing Quantities: Profit and loss, simple and compound interest, discount, tax.
- Geometry & Mensuration: Properties of parallel lines and transversals, congruence and similarity of triangles, understanding quadrilaterals (properties), area and volume of cylinder, cone, cube, cuboid.
- Data Handling: Probability (basic concepts), histograms, pie charts, mean, median, mode.
- Reasoning & Aptitude: Cube and dice problems, counting figures, embedded figures, matrix-based reasoning.
Illustrative Important Questions:
- Exponents: Simplify: (23×25)/22.
- Algebra: Solve for x: 3(x−2)+5=14.
- Comparing Quantities: A shopkeeper bought an item for ₹500 and sold it for ₹600. Calculate the profit percentage.
- Geometry: If two parallel lines are intersected by a transversal, and one interior angle is 70∘, what is the measure of its corresponding angle?
- Mensuration: Calculate the volume of a cylinder with radius 7 cm and height 10 cm. (Use π=22/7)
- Probability: What is the probability of rolling an even number on a standard six-sided die?
iOM Important Questions for Classes 9 & 10
These are crucial years for Olympiad preparation, as the concepts form the foundation for higher mathematics. Questions will be more analytical and multi-conceptual.
Key Topics:
- Number System & Real Numbers: Irrational numbers, rationalization, laws of radicals, Euclid’s Division Lemma (for Class 10), Fundamental Theorem of Arithmetic.
- Polynomials: Zeros of polynomials, remainder theorem, factor theorem, algebraic identities, division algorithm for polynomials.
- Linear Equations in Two Variables: Solving methods (substitution, elimination, cross-multiplication), graphical representation.
- Quadratic Equations: Solving by factorization, completing the square, quadratic formula, nature of roots.
- Arithmetic Progressions (AP): nth term, sum of n terms.
- Geometry: Triangles (Basic Proportionality Theorem, Pythagoras Theorem, similar triangles), Circles (tangents, properties of chords, arcs, angles), Constructions.
- Coordinate Geometry: Distance formula, section formula, area of a triangle using coordinates.
- Trigonometry: Trigonometric ratios, identities, heights and distances (applications).
- Mensuration: Surface area and volume of combinations of solids (cone, cylinder, sphere, hemisphere, cuboid), frustum of a cone.
- Statistics & Probability: Mean, median, mode of grouped data, cumulative frequency graphs, probability of events.
- Reasoning & Aptitude: Data interpretation, logical deductions, syllogisms, non-verbal reasoning (figure series, analogy).
Illustrative Important Questions:
- Polynomials: Find the zeros of the quadratic polynomial x2−2x−8.
- Linear Equations: Solve for x and y: 2x+3y=11 and 2x−4y=−24.
- Quadratic Equations: Find the nature of the roots of the quadratic equation 2×2−4x+3=0.
- Geometry: Prove that tangents drawn from an external point to a circle are equal in length.
- Trigonometry: If sinθ=3/5, find the value of cosθ and tanθ.
- Probability: A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is a red ball?
iOM Important Questions for Classes 11 & 12
At this advanced level, iOM questions demand a strong grasp of higher-order mathematics, including advanced algebra, calculus, and advanced geometry.
Key Topics:
- Sets, Relations & Functions: Types of sets, operations on sets, Cartesian product, relations, functions, domain, range, types of functions.
- Trigonometric Functions: Inverse trigonometric functions, properties, graphs.
- Complex Numbers: Argand plane, polar form, De Moivre’s theorem.
- Quadratic Equations (Advanced): Roots of quadratic equations, theory of equations.
- Sequences & Series: Arithmetic, Geometric, Harmonic progressions, sums of special series.
- Permutations & Combinations: Counting principles, arrangements, selections.
- Binomial Theorem: General term, properties, applications.
- Matrices & Determinants: Types of matrices, operations, inverse, solving systems of linear equations.
- Calculus (Differential & Integral): Limits, continuity, differentiability, applications of derivatives (tangents, normals, maxima, minima), indefinite and definite integrals, applications of integrals (area under curves).
- Coordinate Geometry (Advanced): Straight lines, circles, conic sections (parabola, ellipse, hyperbola).
- Vectors & 3D Geometry: Vector algebra, dot product, cross product, lines and planes in 3D.
- Probability: Conditional probability, Bayes’ theorem, random variables, probability distributions (Binomial, Poisson, Normal).
- Reasoning & Aptitude: Critical thinking, analytical reasoning, data sufficiency, abstract reasoning.
Illustrative Important Questions:
- Functions: Find the domain and range of the function f(x)=9−x2.
- Trigonometry: Prove that tan(45∘+A)=(1+tanA)/(1−tanA).
- Calculus (Differentiation): Find dy/dx if y=sin(x2).
- Calculus (Integration): Evaluate ∫(x+sinx)dx.
- Probability: Two cards are drawn without replacement from a well-shuffled deck of 52 cards. What is the probability that both cards are kings?
- Matrices: If A=(21 34), find A−1.
Strategies to Master iOM Important Questions for 2025-26
Identifying important questions is just the first step. Effective preparation requires a strategic approach:
- Understand the Syllabus Thoroughly: Begin by downloading the official iOM 2025-26 syllabus for your specific class from the SilverZone Foundation or EduHeal Foundation website. This is your blueprint.
- Master NCERT/School Textbooks: The iOM syllabus is largely aligned with the school curriculum. A strong foundation from NCERT or your respective board textbooks is non-negotiable. Ensure you understand every concept and practice all examples and exercises.
- Solve Previous Year Papers (PYPs): This is perhaps the most crucial step. PYPs give you an authentic feel of the exam pattern, question types, and difficulty level. Look for SilverZone iOM previous year papers with solutions.
- Focus on Recurring Themes: Notice which topics appear repeatedly in PYPs. These are your “important questions” in disguise.
- Analyze Difficulty: Identify the questions that you find challenging and dedicate more time to them.
- Practice Sample Papers and Mock Tests: After covering the syllabus and PYPs, attempt iOM sample papers and mock tests under timed conditions. This simulates the actual exam environment and helps in time management.
- Prioritize the “Scholar’s Zone” / “Achiever’s Section”: These sections carry higher marks per question. Devote extra attention to advanced concepts and problem-solving techniques for these questions.
- Focus on Conceptual Understanding, Not Rote Learning: Mathematics is about understanding concepts and applying them. Memorizing formulas without understanding their derivation or application will not suffice for iOM.
- Develop Strong Logical Reasoning Skills: The reasoning and aptitude section is a significant component. Practice various types of logical puzzles, series, analogies, and coding-decoding questions.
- Create a Study Schedule: Plan your study time effectively, allocating sufficient time to each topic and section.
- Make Short Notes/Formula Sheets: Condense important formulas, theorems, and key concepts into concise notes for quick revision.
- Review and Revise Regularly: Consistent revision of previously studied topics and solved problems is vital to retain information and solidify understanding.
- Seek Clarification: Don’t hesitate to ask teachers, mentors, or peers for help if you encounter difficulties with any concept or problem. Online forums and educational platforms can also be valuable resources.
Recommended Resources for iOM 2025-26 Preparation
To maximize your chances of success in the iOM 2025-26 exam, consider utilizing a combination of resources:
- Official iOM Syllabus and Sample Papers: Always the first and most reliable source.
- NCERT Textbooks: The fundamental building blocks of your mathematical knowledge.
- Olympiad-specific Preparation Books: Publishers like MTG, S. Chand, and Disha Publication offer dedicated Olympiad workbooks and guides. Ensure you choose books specifically for the iOM (SilverZone/EduHeal) and your class.
- Previous Year Question Papers with Solutions: Essential for understanding exam patterns and types of questions.
- Online Platforms: Reputable educational websites and apps that offer practice questions, mock tests, and video lessons for Olympiad preparation.
- School Teachers/Coaching Institutes: Guidance from experienced educators can be invaluable.
Conclusion
The International Olympiad of Mathematics 2025-26 presents a fantastic opportunity for students to showcase their mathematical prowess. By focusing on the important questions and topics relevant to your class, adopting a structured preparation strategy, and consistently practicing, you can significantly enhance your performance. Remember, success in Olympiads is a culmination of dedication, smart work, and a genuine love for learning. Embark on your iOM journey with enthusiasm, and let the numbers work in your favor.
iOM Important Questions for 2025-26 Exam FAQs
- “I’m starting my iOM preparation now. What are the most important topics I should focus on first to get a good head start?”
Answer: To get a strong start, focus on the core mathematical concepts that form the foundation of your current and previous grades’ syllabus. For younger students (Classes 1-5), this typically includes Number Sense and Operations (addition, subtraction, multiplication, division), basic Geometry (shapes, measurement), Time & Calendar, and Money. As you move to higher classes (Classes 6-12), Algebra, Geometry (including mensuration), Number Systems, Fractions & Decimals, Ratio & Proportion, and Data Handling become increasingly important. Always refer to your specific class syllabus as provided by Silverzone, but these are generally high-weightage areas. Don’t forget the Reasoning and Aptitude section and the Scholar’s Zone, as these often carry higher marks and can be key differentiators.
- “I’ve heard about the ‘Scholar’s Zone’ section in iOM. What exactly is it, and how do I prepare for it?”
Answer: The “Scholar’s Zone” in iOM is designed to test higher-order thinking skills and problem-solving abilities. It typically contains more challenging questions that require deeper conceptual understanding and analytical reasoning, often carrying higher marks per question. To prepare for it, you need to go beyond rote memorization.
- Focus on conceptual clarity: Ensure you truly understand why a mathematical concept works, not just how to apply a formula.
- Practice advanced problems: Work through challenging problems from previous years’ iOM papers, other Olympiads, and competitive math books.
- Develop logical reasoning: The Scholar’s Zone often integrates logical reasoning with mathematical problems. Practice puzzles, series completion, coding-decoding, and other aptitude-based questions.
- Time management: These questions can be time-consuming, so practice solving them efficiently under timed conditions.
- “Are there any significant changes in the iOM syllabus or exam pattern for the 2025-26 exam that I should be aware of?”
Answer: While Silverzone usually maintains a consistent structure, it’s always crucial to check the official iOM 2025-26 syllabus and exam pattern released by the Silverzone Foundation. These are generally aligned with CBSE/ICSE and State Board curricula.
- Syllabus: The core mathematical topics generally remain consistent. However, there might be minor adjustments in the emphasis on certain sub-topics or the inclusion/exclusion of very specific concepts.
- Exam Pattern: The number of questions, total marks, and duration can vary by class (e.g., Classes 1-2 have 25 questions, Classes 3-5 have 30, etc.). It’s important to confirm these details for your specific class.
- No Negative Marking: Historically, iOM has no negative marking, which is a significant advantage, but it’s good to reconfirm this for the upcoming exam.
- Stay updated: Keep an eye on the official Silverzone website or reliable educational portals for any announcements regarding syllabus changes or pattern updates.
- “I get stuck on complex problems and often run out of time during mock tests. How can I improve my speed and accuracy for iOM?”
Answer: This is a very common challenge! Improving speed and accuracy requires consistent practice and strategic approaches:
- Master fundamentals: A strong grasp of basic concepts is crucial. If you struggle with a topic, revisit its fundamentals before moving to complex problems.
- Regular practice: Solve a variety of problems daily. The more you practice, the more familiar you’ll become with different question types and problem-solving techniques.
- Time management during practice: Use a timer even for individual practice sessions. This helps you get a feel for how long you spend on each question.
- Analyze mistakes: Don’t just check if your answer is right or wrong. Understand why you made a mistake. Was it a conceptual error, a calculation mistake, or a time management issue?
- Learn shortcuts and mental math: For competitive exams, knowing quick methods and improving your mental calculation skills can save valuable time.
- Solve sample papers and previous year papers: This is the best way to familiarize yourself with the actual exam format, question types, and time constraints. Aim to solve these papers under exam-like conditions.
- “My child is in a lower primary class (e.g., Class 2 or 3). How can I make iOM preparation fun and engaging for them, rather than a chore?”
Answer: Making learning enjoyable is key for younger children:
- Use games and puzzles: Incorporate math-related games, board games, and puzzles that reinforce concepts like counting, addition, subtraction, shapes, and patterns.
- Relate math to everyday life: Point out mathematical concepts in daily activities – counting groceries, measuring ingredients while baking, telling time, identifying shapes around the house.
- Interactive learning apps/websites: Many educational apps and websites offer gamified learning experiences for math.
