SOF International Mathematics Olympiad – Class 8

The SOF International Mathematics Olympiad Class 8 syllabus 2026–27 tests mathematical reasoning, logical ability, real-life mathematical application and higher-order problem solving.

For Class 8, the Level 1 paper contains 50 multiple-choice questions for 60 marks and has a duration of 60 minutes. It is divided into four sections: Logical Reasoning, Mathematical Reasoning, Everyday Mathematics and the Achievers Section.

SOF IMO Class 8 Exam Pattern 2026–27

This is the official pattern for students in Classes 5 to 10.

SOF IMO Class 8 Level 1 Syllabus

The Class 8 Level 1 syllabus is divided into four sections.

Section 1: Logical Reasoning

The official syllabus defines this section as Verbal and Non-Verbal Reasoning.

Logical Reasoning does not simply test school Mathematics. It measures whether students can identify patterns, relationships, transformations and logical rules.

Typical areas can include:

• Analogy
• Classification
• Number series
• Alphabet series
• Mixed series
• Coding-decoding
• Ranking and order
• Direction sense
• Blood relations
• Logical sequences
• Mathematical operations
• Figure series
• Figure analogy
• Figure classification
• Figure matrix
• Mirror images
• Water images
• Embedded figures
• Pattern completion
• Paper folding
• Paper cutting
• Visual transformations

Verbal Reasoning

Verbal reasoning questions use words, letters, numbers or statements.

Students may be asked to identify:

• A relationship between two pairs
• A missing term in a series
• A coding rule
• Correct sequence
• Family relationships
• Directions
• Ranking positions

The key skill is recognising the rule quickly.

Non-Verbal Reasoning

Non-verbal reasoning uses figures, diagrams and visual patterns.

Questions may involve:

• Rotation
• Reflection
• Shape transformation
• Missing figures
• Figure sequences
• Embedded objects
• Analogy between figures
• Odd-one-out figures

Section 2: Mathematical Reasoning

Mathematical Reasoning is the largest dedicated section of Level 1. It contains 20 questions for 20 marks.

The official Class 8 syllabus includes the following topics:

A Square and A Cube

Students should understand the properties and patterns associated with square and cube numbers.

Preparation can include:

• Perfect squares
• Perfect cubes
• Square roots
• Cube roots
• Patterns in squares
• Patterns in cubes
• Prime-factorisation methods
• Relationships between consecutive squares
• Units digits of squares and cubes
• Applications involving squares and cubes

Olympiad questions may ask students to identify a pattern or deduce whether a number can be a perfect square or perfect cube without performing a long calculation.

Exponents and Powers

Important concepts include:

• Base and exponent
• Positive powers
• Negative powers
• Laws of exponents
• Multiplication of powers
• Division of powers
• Power of a power
• Standard form
• Comparing large and small numbers

Students should be able to simplify expressions involving several exponent rules in one problem.

Questions may also test whether a student understands the meaning of an exponent rather than merely remembering formulas.

A Story of Numbers

This area deals broadly with number properties and relationships.

Useful concepts can include:

• Natural numbers
• Whole numbers
• Integers
• Rational numbers
• Number representation
• Factors
• Multiples
• Divisibility
• Prime numbers
• Composite numbers
• Properties of operations
• Patterns involving numbers

Olympiad questions may use unusual number arrangements and ask students to discover the underlying property.

Quadrilaterals

Students should understand different types of quadrilaterals and their properties.

Important areas include:

• Quadrilateral
• Parallelogram
• Rectangle
• Square
• Rhombus
• Trapezium
• Kite
• Interior angles
• Exterior angles
• Diagonals
• Parallel sides
• Properties of special quadrilaterals

Number Play

Number Play focuses on numerical patterns and reasoning.

Preparation can include:

• Digit-based problems
• Number patterns
• Divisibility rules
• Factors and multiples
• Special numerical relationships
• Missing numbers
• Number puzzles
• Operations on digits

Questions may require students to discover a hidden relationship rather than apply a directly stated formula.

We Distribute, Yet Things Multiply

This topic develops understanding of algebraic multiplication and distributive relationships.

Important ideas can include:

• Distributive property
• Algebraic expressions
• Expansion
• Multiplication of expressions
• Common factors
• Algebraic identities
• Factorisation concepts

Students should understand how expressions change when brackets are expanded or factors are extracted.

Proportional Reasoning

Proportional reasoning is one of the most practically useful areas of Class 8 Mathematics.

Students should prepare:

• Ratios
• Proportions
• Unitary method
• Direct proportion
• Inverse proportion
• Percentages
• Rate
• Scale
• Comparisons
• Real-life proportion problems

Olympiad questions can combine several steps. For example, a problem may involve price, quantity and percentage change rather than directly ask for a simple ratio.

Fractions in Disguise

This area develops the relationship between fractions and other numerical representations.

Important concepts include:

• Fractions
• Decimals
• Percentages
• Ratios
• Equivalent fractions
• Comparison of fractions
• Conversion among forms
• Operations on fractions
• Rational-number applications

The Baudhayana–Pythagoras Theorem

This topic concerns the relationship between the sides of a right-angled triangle.

Students should understand:

• Right-angled triangles
• Hypotenuse
• Pythagorean relationship
• Finding a missing side
• Recognising Pythagorean triples
• Applications in geometry
• Distance-related problems

Questions may combine the theorem with:

• Area
• Perimeter
• Diagonals
• Squares
• Rectangles

The theorem may therefore appear as part of a larger problem rather than as a direct formula exercise.

Exploring Some Geometric Themes

This broad geometry area can involve:

• Lines
• Angles
• Triangles
• Polygons
• Parallel lines
• Symmetry
• Geometric constructions
• Relationships between shapes
• Angle properties
• Visual geometry

Data Handling

Students should be comfortable collecting, interpreting and comparing data.

Important areas can include:

• Tables
• Bar graphs
• Double bar graphs
• Line graphs
• Pie charts
• Mean
• Median
• Mode
• Basic probability
• Data comparison
• Data interpretation

Questions may provide a chart and ask for:

• Difference
• Percentage
• Ratio
• Average
• Trend
• Maximum or minimum
• Combined information

Algebra Play

Algebra Play develops reasoning with variables and expressions.

Important areas include:

• Variables
• Constants
• Terms
• Coefficients
• Algebraic expressions
• Simplification
• Substitution
• Linear equations
• Patterns
• Identities
• Relationships between expressions

Olympiad questions may present algebra through patterns, geometry or word problems rather than direct symbolic equations.

Area

Students should understand area relationships for common plane figures.

Preparation can include:

• Square
• Rectangle
• Triangle
• Parallelogram
• Trapezium
• Composite figures
• Shaded regions
• Area comparison
• Perimeter-area relationships

Section 3: Everyday Mathematics

SOF states that the syllabus for Everyday Mathematics is the same as Section 2 Mathematical Reasoning.

There are 10 questions for 10 marks.

The distinction lies in application. Everyday Mathematics presents mathematical ideas through real-world situations.

Examples can involve:

• Shopping
• Discounts
• Bills
• Measurements
• Travel
• Speed
• Distance
• Time
• Rates
• Area
• Construction
• Data
• Money
• Ratio
• Percentage

A student must first understand the situation and then identify the correct mathematical operation.

Section 4: Achievers Section

The Achievers Section contains Higher Order Thinking Skills questions.

The syllabus is the same as Mathematical Reasoning, but the questions are more demanding.

They may require students to:

• Combine multiple concepts
• Solve multi-step problems
• Identify hidden mathematical conditions
• Analyse diagrams
• Work backwards from an answer
• Compare several strategies
• Recognise non-obvious patterns
• Apply familiar concepts in unfamiliar situations

Why the Achievers Section Matters

The official Level 1 pattern also places the Achievers Section at the highest priority, followed by Mathematical Reasoning, Everyday Mathematics and Logical Reasoning.

This priority can become important when students obtain equal total scores.

Is the Achievers Section a Separate Syllabus?

Students therefore do not need separate chapters. They need deeper application practice from the existing mathematical topics.

Class 7 Syllabus in SOF IMO Class 8

Level 1 follows the SOF rule:

What Class 7 Topics Should Be Revised?

The exact previous-class component follows the relevant Class 7 syllabus rather than a separate Class 8 topic list.

Important mathematical foundations can include areas such as:

• Integers
• Fractions
• Decimals
• Rational Numbers
• Simple Equations
• Ratio and Proportion
• Percentage
• Profit and Loss
• Simple Interest
• Algebraic Expressions
• Lines and Angles
• Triangles
• Congruence
• Mensuration
• Data Handling
• Symmetry
• Visualising Solid Shapes

Students should give particular attention to Class 7 concepts that directly support the Class 8 topics.

SOF IMO Class 8 Level 2 Syllabus

Students qualifying Level 1 can appear for Level 2.

SOF IMO Class 8 Level 2 Pattern

For Classes 5 to 10, including Class 8:

The Level 2 paper therefore contains 50 questions for 60 marks.

Level 1 vs Level 2

Level 2 therefore shifts fully toward current-class Mathematics and higher-order mathematical application.

Does Level 2 Have Logical Reasoning?

The paper contains 45 Mathematics questions and 5 Achievers questions.

Students qualifying for Level 2 should therefore shift preparation toward deeper Class 8 Mathematics.

SOF IMO Class 8 Exam Duration

Students have 60 minutes to solve 50 questions.

However, an equal-time strategy is rarely ideal.

Straightforward reasoning or calculation questions may take less than 30 seconds, while Achievers problems can require several minutes.

Is There Negative Marking?

Students should nevertheless avoid careless errors because even one incorrect Achievers response can represent a three-mark opportunity loss.

Are Image-Based Questions Important?

These include:

• Non-Verbal Reasoning
• Quadrilaterals
• Pythagoras Theorem
• Geometry
• Area
• Data Handling

Students may encounter:

• Geometric diagrams
• Shaded figures
• Visual patterns
• Graphs
• Tables
• Figure sequences
• Shape transformations

Visual-question practice is therefore an important part of preparation.

Are All Questions Calculation-Based?

A problem may require a student to:

• Identify a pattern
• Eliminate impossible choices
• Visualise a shape
• Compare ratios
• Recognise an algebraic property
• Infer a missing value
• Interpret a graph

Fast arithmetic helps, but conceptual reasoning is equally important.

Does SOF IMO Follow Only NCERT?

Its current IMO information states that the competition is available to students in Classes 1–12 through participating schools, while its syllabus defines the examination scope independently.

Students should therefore use the official SOF syllabus as the examination reference rather than assuming every question will follow the order or wording of one specific textbook.

SOF IMO Class 8 Exam Dates

For 2026–27, schools can choose one of the following Level 1 dates:

Separate question papers are used for different dates.