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# Unicus Non-Routine Mathematics Olympiad Class 9 Sample Papers

## Syllabus:

Classic Section:

Arithmetic

• 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

Algebra

• 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
• 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
• Relationship between discriminant and nature of roots

Geometry & Mensuration

• 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

Trigonometry

• 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 9: