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# Unicus Global Mathematics Olympiad Class 9 Sample Papers

## Syllabus:

### Classic Section

 Content Domain Main Topics Sub Topics Number system Real Numbers Rational numbers and their properties Identities of rational numbers Real numbers Surds HCF and LCM Algebra Polynomials Polynomials in 1 variable Zeroes of a polynomial Factor and remainder theorem Factorisation of polynomial Algebraic Identities Division of polynomial by polynomial Linear Equations in Two Variables Formation and standard form of linear equation in 2 variables Solving two Simultaneous linear equations Coordinate Geometry Coordinate Geometry Cartesian coordinate system Distance formula, section formula, area of triangle and mid- point formula Collinearity of points Geometry Euclid's Geometry Axioms and postulates Lines and Angles Angles formed by transversal -alternative interior angles, corresponding angles, etc. Problems based on theorems of lines and angles Triangles Congruence of triangles Problems based on theorems of triangles (mid-point theorem, converse of mid-point theorem) Properties of triangle Quadrilaterals Angle sum property of a quadrilateral Theorems based on quadrilateral Circles Theorems related to circles Cyclic quadrilateral Trigonometry Trigonometry Trigonometric Ratios: sine, cosine, tangent of an angle and their reciprocals Trigonometric ratios of standard angles - 0, 30, 45, 60, 90 degrees Evaluation of an expression involving these ratios Simple 2-D problems involving one right-angled triangle Concept of trigonometric ratios of complementary angles and their direct application Mensuration Heron’s Formula Problems based on the area of the triangle using heron's formula Surface Areas and Volumes Area of the ring, area of sector Surface area and Volume of solid shapes- cube, cuboid, right circular cylinder, pyramid, prism, sphere, hemisphere Statistics Statistics Types of data - primary data, secondary data Statistical graphs- bar graph, histogram, frequency polygon, frequency curve Measures of central tendencies for grouped and ungrouped data- mean, median, mode Probability Problems based on the formula of probability, theoretical probability

### Scholar Section

Higher Order Thinking Questions - Syllabus as per Classic Section

Sample Papers of Unicus Global Mathematics Olympiad for Class 9: