Online Non-Routine Mathematics Olympiad Class Syllabus for Grade 5

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Syllabus

Number theory

Rational Numbers
- Rational number and its examples
- Natural number, Whole number and integer
- Properties of rational numbers (Using identities)
- Representation of rational number on the number line

Real Numbers
- Natural numbers, Integers
- Euclid's Division Lemma and Factor Tree
- Fundamental Theorem of Arithmetic
- Rational numbers as recurring/terminating decimals
- Irrational numbers
- Laws of exponents with integral powers

Diophantine Equations

Factors and Multiples
- Divisibility tests for 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11
- HCF and LCM by Prime factorization and by Division method
- HCF and LCM of more than two numbers
- Results of Prime and Elementary results of Prime

Geometry & Mensuration

Triangles
- Triangle, Congruent triangles, Interior and Exterior of a triangle
- Various types of triangles (On the basis of length and angles)
- Angle sum property of a triangle

Quadrilaterals
- Introduction of Quadrilateral (Adjacent and opposite sides, Adjacent and opposite angles)
- Convex and Concave Quadrilaterals
- Interior and Exterior of a Quadrilateral
- Angle sum property of a Quadrilateral
- Various types of Quadrilaterals with their properties (Square, Rectangle, Parallelogram, Trapezium, Rhombus)

Circles
- Introduction of Circle (Radius, Diameter, Chord, Secant, Segments, Arc and Sector of a circle)
- Circumference of circle
- Semicircle
- Concentric circles

Line segment, Ray and Line
- Introduction of Plane, Point, Line Segment, Ray and Line
- Intersecting lines, Concurrent lines, Parallel lines and Perpendicular lines
- Distinction between A line segment, A ray and A line

Polygons
- Classification of polygons
- Angle sum property
- Types of quadrilaterals
- Properties of quadrilaterals
- Interior and exterior angles of a regular polygon

Area and Perimeter
- Definition of area and perimeter
- Area and perimeter of rectangle
- Area and perimeter of square
- Area of four walls of room
- Area and perimeter of triangle
- Area and perimeter of parallelogram
- Area and circumference of circle
- Area of sector and segment
- Length of arc

Volume
- Volume of cube, cuboid and cylinder
- Total surface area of cube, cuboid and cylinder
- Lateral surface area of cube, cuboid and cylinder
- Diagonal of cube and cuboid

Algebra

Algebraic Expression
- Definition of literals
- Operation on literals and numbers (Addition, Subtraction, Multiplication and Division)
- Powers of a literal
- Variable and constant

Various types of algebraic expression
- Monomials, Binomials, Trinomials, Quadrinomials and Polynomials
- Factors and Coefficients
- Constant term
- Like and unlike terms
- Operations on algebraic expression (Addition and Subtraction)

Linear Equations
- Definition of equation and linear equation
- Problems on application of equations

Pair of Linear Equations in Two Variables
- Pair of linear equations in two variables and their graphical solution
- Conditions of different possibilities of solutions/inconsistency
- Solution of a pair of linear equations in two variables algebraically
  - Substitution method
  - Elimination method
  - Cross multiplication method

Complex Numbers
- Introduction to complex numbers
- Problems related to 'I' IOTA

Quadratic Equations
- Standard form of a quadratic equation ax²+ bx + c = 0, (a ≠ 0)
- Solution of the quadratic equations (only real roots)
  - Factorization method
  - Completing the square method
  - Quadratic formula method
- Relationship between discriminant and nature of roots

Probability

Probability
- Probability of occurrence defined by P(E) – Outcomes for samples spaces involving coins, cards and dice
Graph Theory
- Problems on Graphs and graphs related questions

Combinatorics