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SYLLABUS:
1. PLAYING WITH NUMBERS
Writing and understanding two-digit and three-digit numbers in generalized form such as (100a + 10b + c) – Solving puzzles involving missing digits represented by symbols or letters – Creating mathematical puzzles and games – Understanding the logic behind divisibility tests of 2, 3, 4, 5, 6, 7, 8, 9 and 11 – General rules of divisibility – Applications of number patterns in problem-solving.
2. RATIONAL NUMBERS
Properties of rational numbers including closure, commutative, associative and distributive properties – Representation of rational numbers on the number line – Understanding that another rational number exists between any two rational numbers – Representation of rational numbers in decimal form – Conversion of recurring decimals into rational numbers – Operations on rational numbers – Word problems involving rational numbers.
3. SQUARES, CUBES, SQUARE ROOTS AND CUBE ROOTS
Square numbers and square roots – Finding square roots using factorization and division methods – Square roots of numbers and decimals – Pythagorean triplets and their applications – Cube numbers and cube roots – Estimation of square roots and cube roots – Practical applications.
4. EXPONENTS AND POWERS
Decimal numbers in exponential notation – Integers as exponents – Laws of exponents with integral powers – Scientific notation for large numbers – Applications of exponential forms in mathematics and science.
5. ALGEBRAIC EXPRESSIONS
Addition, subtraction and multiplication of algebraic expressions – Algebraic identities such as (a ± b)² and a² – b² – Geometric verification of identities – Factorization of algebraic expressions – Division of algebraic expressions – Applications in problem-solving.
6. SIMPLE EQUATIONS
Solving linear equations in one variable – Equations arising from real-life situations – Word problems involving multiplication and division – Applications of equations in practical contexts.
7. BUSINESS MATHEMATICS
Compound ratio – Percentages – Profit and loss – Discounts – Taxes – Simple and compound interest – Direct and inverse variation – Mixed variation problems – Time and work – Time and distance problems – Applications in business and daily life.
8. GEOMETRY
Construction of quadrilaterals using different sets of measurements – Representation of three-dimensional objects in two-dimensional form – Isometric sketches – Euler’s relation for polyhedra – Congruent and similar figures – Reflection symmetry and rotational symmetry – Tessellations – Dilations – Estimation of heights and distances.
9. MENSURATION
Area of triangles, trapeziums, quadrilaterals and polygons – Area of circles and sectors – Circular paths – Surface area of cubes and cuboids – Volume and capacity – Measurement of volume using standard units – Practical applications of mensuration.
10. DATA HANDLING
Revision of mean, median and mode – Deviation method for mean – Frequency distribution tables – Cumulative frequency tables – Histograms – Frequency polygons – Frequency curves – Ogives and interpretation of statistical data.
• Practicing problem sets and solutions regularly to build muscle memory.
• Focusing on understanding the underlying core concepts and formulas clearly rather than just memorizing them.
• Solving additional challenge exercises to test their boundaries.
• Maintaining a positive, growth-oriented attitude toward learning math.
