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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