Unicus Global Mathematics Olympiad Class 10 Sample Paper

Syllabus:

1. Content Domain: Number System

Real Numbers

1. Rational numbers, irrational numbers, and their properties
2. HCF, LCM, and their properties
3. Units digit
4. Surds: Types of surds, laws of surds, order of a surd, comparison of monomial surds, addition and subtraction of surds, multiplication and division of surds
5. Relationship between HCF and LCM

Logarithms

1. Natural logarithms, common logarithms
2. Properties of logarithms and problems based on them

2. Content Domain: Algebra

Polynomials

1. Division of polynomials
2. Degree of a polynomial
3. Factorisation of polynomials
4. Relationship between zeroes and coefficients of a polynomial
5. Remainder and factor theorem

Pair of Linear Equations in Two Variables

1. Standard form of linear equations in two variables
2. Different methods to solve equations: graphical method and algebraic method

Linear Inequations

1. Solving linear inequations in one variable
2. Word problems based on forming and solving linear inequations

Quadratic Equations

1. Discriminant of a quadratic equation
2. Finding the roots by factorisation and quadratic formula
3. Word problems based on the formation and solving of quadratic equations

Arithmetic Progressions

1. Sequence and series
2. Arithmetic Progression: nth term of AP, sum of n terms
3. Arithmetic mean
4. Word problems on AP

Geometric Progressions

1. Geometric Progression: nth term of GP, sum of n terms
2. Word problems on GP

3. Content Domain: Geometry

Triangles

1. Criteria for similarity of triangles
2. Areas of similar triangles
3. Basic proportionality theorem

Circles

1. Chord and its properties, theorems based on chords
2. Cyclic quadrilateral
3. Secant
4. Tangents and related theorems
5. Alternate segment and its angles

4. Content Domain: Coordinate Geometry

Coordinate Geometry

1. Area of a triangle
2. Distance formula
3. Section formula
4. Points of trisection
5. Centroid
6. Straight lines: inclination of a line, slope or gradient of a line, intercepts of a straight line, equation of a line in general form, different forms of equations: slope form, point-slope form, two-point form, intercept form, equation of a line parallel or perpendicular to the given line

5. Content Domain: Trigonometry

Introduction to Trigonometry

1. Trigonometric ratios
2. Trigonometric ratios of some specific angles (0, 30, 45, 60, etc.)
3. Trigonometric identities
4. Signs of trigonometric ratios
5. Trigonometric tables
6. Trigonometric formulas

Some Applications of Trigonometry

1. Angle of elevation, depression, and problems based on them

6. Content Domain: Mensuration

Areas Related to Circles

1. Area of circle, sector, and segment
2. Circumference of circle, sector, length of an arc

Surface Areas and Volumes

1. CSA (curved surface area)/LSA and TSA (total surface area) of cube, cuboid, right circular cylinder, pyramid, prism, sphere, hemisphere, and frustum
2. Volume of solids: cube, cuboid, right circular cylinder, pyramid, prism, sphere, hemisphere
3. Area and volume of combination figures

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
4. Empirical relationship among mean, median, and mode

Probability

1. Basic terminologies of probability
2. Theoretical vs experimental probability
3. Problems based on finding probability