Unicus Global Mathematics Olympiad Class 9 Sample Paper

Syllabus:

1. Content Domain: Number System

Real Numbers

1. Rational numbers and their properties
2. Identities of rational numbers
3. Real numbers
4. Surds
5. HCF and LCM

2. Content Domain: Algebra

Polynomials

1. Polynomials in one variable
2. Zeroes of a polynomial
3. Factor and remainder theorem
4. Factorisation of polynomial
5. Algebraic identities
6. Division of polynomial by polynomial

Linear Equations in Two Variables

1. Formation and standard form of linear equation in two variables
2. Solving two simultaneous linear equations

3. Content Domain: Coordinate Geometry

Coordinate Geometry

1. Cartesian coordinate system
2. Distance formula, section formula, area of triangle, and midpoint formula
3. Collinearity of points

4. Content Domain: Geometry

Euclid's Geometry

1. Axioms and postulates

Lines and Angles

1. Angles formed by transversal: alternate interior angles, corresponding angles, etc.
2. Problems based on theorems of lines and angles

Triangles

1. Congruence of triangles
2. Problems based on theorems of triangles (mid-point theorem, converse of mid-point theorem)
3. Properties of triangles

Quadrilaterals

1. Angle sum property of a quadrilateral
2. Theorems based on quadrilateral

Circles

1. Theorems related to circles
2. Cyclic quadrilateral

5. Content Domain: Trigonometry

Trigonometry

1. Trigonometric Ratios: sine, cosine, tangent of an angle and their reciprocals
2. Trigonometric ratios of standard angles: 0, 30, 45, 60, 90 degrees
3. Evaluation of an expression involving these ratios
4. Simple 2-D problems involving one right-angled triangle
5. Concept of trigonometric ratios of complementary angles and their direct application

6. Content Domain: Mensuration

Heron’s Formula

1. Problems based on the area of the triangle using Heron's formula

Surface Areas and Volumes

1. Area of the ring, area of sector
2. Surface area and volume of solid shapes: cube, cuboid, right circular cylinder, pyramid, prism, sphere, hemisphere

7. Content Domain: Statistics

Statistics

1. Types of data: primary data, secondary data
2. Statistical graphs: bar graph, histogram, frequency polygon, frequency curve
3. Measures of central tendencies for grouped and ungrouped data: mean, median, mode

Probability

1. Problems based on the formula of probability, theoretical probability