Age (12-14)

Age (12-14) syllabus for MATH

Main Topics

• Work with integers, factors, multiples, primes, powers, and roots.
• Apply fractions, decimals, percentages, and ratio/proportion to real-life problems.
• Use algebraic expressions, equations, and simple inequalities.
• Explore sequences and identify mathematical rules.
• Solve problems involving angles, triangles, quadrilaterals, circles, area, and volume.
• Apply unit conversion, speed, distance, time, and rates.
• Interpret and analyze tables, graphs, averages, and data.
• Explore probability and basic counting principles.
• Use coordinates and basic transformations to solve problems.
• Solve challenging multi-step and Olympiad-style mathematical problems.

Detailed Syllabus

1. Number Systems

• Positive and negative integers.
• Number lines and ordering integers.
• Factors, multiples, primes, and prime factorization.
• HCF and LCM.
• Powers and squares.
• Square roots and simple estimation.
• Order of operations with integers.

2. Fractions, Decimals & Percentages

• Operations with fractions.
• Mixed numbers and improper fractions.
• Decimal operations.
• Converting between fractions, decimals, and percentages.
• Percentage increase and decrease.
• Discounts, profit, and simple real-life applications.
• Estimation and checking reasonableness of answers.

3. Ratio, Proportion & Rates

• Simplifying ratios.
• Equivalent ratios.
• Direct proportion.
• Unit rates.
• Scale and map problems.
• Speed, distance, and time.
• Real-life problems involving rates and proportional reasoning.

4. Algebra

• Understand variables and constants.
• Simplify algebraic expressions.
• Expand simple brackets.
• Substitute values into expressions.
• Solve one- and two-step linear equations.
• Solve simple inequalities.
• Translate word problems into mathematical expressions or equations.

5. Sequences & Patterns

• Arithmetic sequences.
• Identify and describe sequence rules.
• Find missing terms.
• Generate sequences from a given rule.
• Explore patterns using tables.
• Solve visual and number-based sequence problems.

6. Geometry & Measurement

• Properties of triangles and quadrilaterals.
• Angle relationships.
• Angles on a straight line and around a point.
• Parallel-line angle problems.
• Properties of circles.
• Perimeter and area.
• Area of composite shapes.
• Surface area and volume of basic 3D shapes.

7. Coordinates & Transformations

• Plot points on coordinate grids.
• Read and interpret coordinates.
• Calculate simple horizontal and vertical distances.
• Reflections.
• Rotations.
• Translations.
• Identify symmetry and transformations of shapes.

8. Data Handling & Statistics

• Read and interpret tables and graphs.
• Bar charts, line graphs, and pie charts.
• Calculate mean, median, mode, and range.
• Compare data sets.
• Identify trends and unusual values.
• Draw conclusions from data.
• Solve data-based reasoning problems.

9. Probability & Counting

• Understand probability from 0 to 1.
• Express probability as fractions, decimals, or percentages.
• Calculate simple theoretical probability.
• Use sample spaces.
• Simple two-step probability problems.
• Basic counting and arrangement challenges.
• Compare expected and actual outcomes.

10. Mathematical Problem Solving

• Multi-step mathematical problems.
• Identify useful and unnecessary information.
• Select an efficient solution strategy.
• Work backwards to find an unknown.
• Estimate and verify answers.
• Find patterns and shortcuts.
• Solve problems with multiple possible approaches.
• Explain and justify the solution.

11. Olympiad Challenge Problems

• Number puzzles.
• Logic-based mathematics.
• Pattern and sequence challenges.
• Geometry puzzles.
• Probability challenges.
• “Find the missing value” problems.
• Optimization and minimum/maximum challenges.
• Problems requiring creative mathematical thinking.

Important Note for Participants

The topics and subtopics provided are the main areas of the syllabus. They are not limited to only the examples mentioned.