## HOMC Index (Junior Level)

1. Mental Ability:

Problems on Ages, Number, Ranking and time sequence Test, Mathematical Operations, Problems solving by substitution.

Introduction, Solving Quadratic equation by Factorization Method, The zero product rule, The Square root method, The completing the square method, Solving quadratic equation by quadratic formula, Equations reducible to quadratic equations, Nature of the roots, Relation between roots and coefficient of a quadratic equation, Framing the quadratic equation using its roots.

3. Sequences and Series:

Sequences, series, nth term, progressions, Arithmetic Progression (A.P.), Arithmetic Mean (A.M.), Sum of first n terms.

4.Geometry& Mensuration:

Introduction, Triangles, Perimeter of Triangles, Angles of the triangles, Interior and Exterior angles of the triangle, Classification of Triangles, Concurrent lines in a triangle, Median, Altitude, Perpendicular Bisector, Angle Bisector, Centroid, Orthocentre, Circumcentre, Incentre, Excentre, Similarity and Congruency of Triangles, Properties of Triangle.

Introduction to Quadrilaterals, Trapezium, Median of Trapezium, Altitude of Trapezium, Isosceles Trapezium, Kite, Parallelogram, Rectangle, Rhombus, Square, (Properties of Trapezium, Parallelogram, Rectangle, Rhombus and Square).

Area of Triangle, Quadrilateral, Parallelogram, Introduction to Circles, Circumference of the Circle, Area of Circle, Sector of Circle, Length of Arc.

5.Number Theory:

Even and Odd Numbers, Prime and Composite Numbers, Square and Square roots, Cubes and Cube roots, Prime Factorization method for HCF, LCM by Prime Factorization and Common Division, Relation between HCF and LCM of two numbers, HCF and LCM of Fractions.

Factorial of a given positive integer N, How to find the number of zeroes at the end of N!?

Unit Digit, Cyclicity, Congruence, Properties of Congruence.

6.Permutations and Combinations:

Factorial Notation, Exponent of prime P in n!, Fundamental Principle of Counting (Addition and Multiplication Law).

## HOMC Index (Senior Level)

Introduction, Solving Quadratic equation by Factorization Method, The zero product rule, The Square root method, The completing the square method, Solving quadratic equation by quadratic formula, Equations reducible to quadratic equations, Nature of the roots, Relation between roots and coefficient of a quadratic equation, Framing the quadratic equation using its roots.

2. Sequences and Series:

Sequences, series, nthterm, progressions, Arithmetic Progression (A.P.), Arithmetic Mean (A.M.), Sum of first n terms of AP, Geometric Progression (G.P.), Geometric Mean (G.M.), Sum of first n terms of GP, Sum of Infinite terms of GP, Insertion of n GM between two numbers a and b.

3. Geometry:

Classification of Triangles, Concurrent lines in a triangle, Median, Altitude, Perpendicular Bisector, Angle Bisector, Centroid, Orthocentre, Circumcentre, Incentre, Excentre, Similarity and Congruency of Triangles, Properties of Triangle.

4. Number Theory:

Divisibility, Prime Factorization, Factorial of a given positive integer N, How to find the number of zeroes at the end of N!?Unit Digit, Cyclicity,Congruence, Properties of Congruence, Euler’s Totient Function, Theorem of Fermat and Wilson.

5.Permutations and Combinations:

Factorial Notation, Exponent of prime P in n!, Symbol for Permutations and Combinations, Fundamental Principle of Counting (Addition and Multiplication Law), Definition of Permutation and Combination, Practical problems involving Permutation and combination, Pascal’s Rule, Rank of given Word, Permutation of the things not all different.