Unicus Global Mathematics Olympiad Class 10 Sample Paper (PDF)

Mathematics in Class 10 represents the culmination of secondary mathematical education and preparation for advanced studies. Our Free Math Olympiad Sample Question Paper covers comprehensive topics essential for board examinations and competitive success.

This maths olympiad sample paper encompass real numbers and their properties, polynomial equations and relationships, coordinate geometry applications, trigonometry fundamentals, statistics and probability analysis, and advanced problem-solving strategies.

Our Question paper with answers also provides strategic approaches that help students achieve mathematical excellence while building confidence for competitive examinations.

Download Unicus Math Olympiad Sample Paper PDF For Class 10

This expertly made paper featuring mathematical topics and strategic problem-solving techniques.Grab this free sample paper PDF to excel in competitive mathematics.

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How to Start Preparation with Class 10 Math Sample Paper?

Use this PDF in three simple steps for structured Olympiad preparation:

• Step 1: Download materials and create a structured preparation plan covering all topics
• Step 2: Practice advanced problems consistently to develop mathematical sophistication
• Step 3: Analyze solution methods thoroughly and build strategic problem-solving skills

Benefits of Unicus Math Olympiad Sample Paper for Class 10

This well-structured sample paper offer substantial benefits for students and some of them are:

• Develops advanced algebraic and polynomial manipulation skills: Through comprehensive practice sessions
• Strengthens trigonometric problem-solving and application abilities:Get detailed solution approaches
• Builds sophisticated coordinate geometry and analytical capabilities:Enhances mathematical reasoning
• Increase statistical analysis and probability reasoning skills: Prepares students for high-level competitive examination excellence

Start Preparation with UGMO Question Paper

Regular practice with this Unicus Math Practice Paper material significantly enhances Class 10 mathematical proficiency and competitive readiness. This resource provides comprehensive preparation for board examinations and Olympiad competitions. It also ensures strong foundations for advanced mathematical studies and competitive success.

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

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