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Unicus Non-Routine Mathematics Olympiad Class 10 Sample Papers


Classic Section:


  • 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
  • Arithmetic Progressions
    • Arithmetic Progression Derivation of the nth term
    • Sum of the first ‘n’ terms of A.P. and their application


  • 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
  • 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
  • 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

Geometry & Mensuration 

  • Quadrilaterals
    • Quadrilateral and terms related to it
    • Angle sum property of a quadrilateral
    • Type of quadrilaterals and their properties
    • Conditions for a quadrilateral to be a parallelogram
    • Midpoint & Converse related questions
  • Lines and Angles
    • Angles and its type
    • Linear pair of angles, adjacent angles
    • Angles made by a transversal with two lines
  • Surface Areas and Volumes
    • Cubes
    • Cuboids
    • Spheres
    • Hemispheres
    • Right circular cylinders/cones
    • Frustum of a cone

Co-ordinate Geometry

  • Cartesian co-ordinate axes
  • Cartesian co-ordinate of a point
  • Sign convention, plotting of points
  • Distance between two points, Area of triangle
  • Distance formula
  • Section formula
  • Area of a triangle 

Triangles and Circles

  • 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
  • Circles
    • Tangents to a circle and length of tangents
    • Properties of Tangent to Circle
  • 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


  • 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

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

Scholar Section:

Higher Order Thinking Questions - Syllabus as per Classic Section

Sample Papers of Unicus Non-Routine Mathematics Olympiad for Class 10:

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Answers to Sample Questions from CREST Olympiads:

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