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 n^{th } 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
Quadratic Equations
Standard form of a quadratic equation ax^{2} + 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
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 10:
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