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

• Counting Techniques
• Pigeon Hole Principle
• Principle of Inclusion and Exclusion

Mathematical Reasoning