Online Math Olympiad Class Syllabus for Grade 10

Olympiads are the stepping stones to achieve better results in the competitive world that lies ahead in the life of the child. Math Olympiad examinations help students to improve their mathematical skills along with their analytical and problem solving abilities.

Hence, Olympiad Success Live has designed the course for Math Olympiad for class 10 in such a way that the foundation of the child is built up. For this, we have done great efforts in finding the tutor for class 10 Math Olympiad with relevant background and experience.

If you are interested in purchasing this course, then please Enrol Now. You will be redirected to the batch detail page, wherein you can see all the details like batch start and demo dates, fess and the registration link related to Math Olympiad for class 10 course.

Syllabus

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

Polynomials

  • Coefficients of a polynomial, terms of a polynomial and zero polynomial
  • Degree of a polynomial
  • Zeros of a polynomial
  • Division algorithm for polynomials with real coefficients

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

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

Arithmetic Progressions

  • Arithmetic Progression Derivation of the 9thterm
  • Sum of the first ‘n’ terms of A.P. and their application.

Triangles

  • Similar figures , similar polygons
  • Basic proportionality theory or Thales theorem
  • Criterion for similarity of triangles
  • AAA similarity Criterion.
    • Corollary(AA similarity)
    • SSS Similarity Criterion.
    • SAS Similarity Criterion.
  • Area of similar triangles
  • Pythagoras theorem and converse of pythagoras theorem

Coordinate geometry

  • Concepts of coordinate geometry, graphs of linear equations
  • Distance formula
  • Section formula
  • Area of a triangle

Introduction to Trigonometry

  • Trigonometric ratios of an acute angle of a right-angled triangle
  • Values of the trigonometric ratios at specified angles
  • Trigonometric Identities
  • Trigonometric ratios of complementary angles

Application of trigonometry

  • Problems on heights and distances
  • Angles of elevation / depression should be only 30o, 45oand 60o

Circles

  • Tangents to a circle and length of Tangents
  • Properties of Tangent to Circle
    • Theorem 1, 2: The tangent at any point of a circle is perpendicular to the radius through the point of contact and its converse.
    • Theorem 3: The lengths of tangents drawn from an external point to circle are equal

Constructions

  • Division of a line segment in a given ratio (internally)
  • Tangent to a circle from a point outside it
  • Construction of a triangle similar to a given triangle

Areas Related to Circles

  • Understanding terms- Sector, segment, Major arc, Minor arc
  • Problems based on areas and perimeter / circumference of Plane figures involving
    • Circle, semi- circle, quadrant, ring, sector, segment, triangles, simple quadrilaterals

Surface Areas and Volumes

  • Cubes
  • Cuboids
  • Spheres
  • Hemispheres
  • Right circular cylinders/cones
  • Frustum of a cone

Statistics and Probability

  • Statistics
    • Mean, median and mode of grouped data
    • Cumulative frequency graph
  • Probability
    • Probability of occurrence defined by P(E) – Outcomes for samples spaces involving coins, cards and dice
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