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# Unicus Non-Routine Mathematics Olympiad Class 8 Sample Papers

## Syllabus:

Classic Section:

Arithmetic

• Playing with Numbers
• Various types of numbers (Natural numbers, Whole numbers)
• Addition, Subtraction, Multiplication and Division of integers
• Properties of numbers (Associative, Commutative, Distributive, Multiplicative and Additive identity)
• Rational Numbers
• Rational number and its examples
• Natural number, Whole number and integer
• Properties of rational numbers (Using identities)
• Representation of rational number on the number line
• Linear Equation in One Variable
• Equation, linear equations
• Linear equation in one variable
• Solution of a linear equation
• Laws of equality
• Problems based on linear equations
• Linear graph
• Cartesian system
• Squares and Square Root, Cube and Cube Root
• Square and square root
• Square, perfect square and square root
• Properties of squares
• Estimating the squares of numbers
• Determining the square and square roots of positive numbers
• Cube and cube root
• Cube, perfect cube and cube roots
• Estimating the cubes of numbers
• Determining the cube and cube roots of positive numbers
• Estimating the cubes of numbers

Lines and angles

• Lines
• Definition of line
• Parallel and perpendicular lines
• Transversal
• Angles
• Supplementary and complementary angles
• Linear pair of angles
• Various types of angles (Adjacent, Vertically opposite and Alternate angles)
Geometry and Mensuration
• Polygons
• Classification of polygons
• Angle sum property
• Interior and exterior angles of a regular polygon
• Area and Perimeter
• Definition of area and perimeter
• Area and perimeter of rectangle
• Area and perimeter of square
• Area of four walls of room
• Area and perimeter of triangle
• Area and perimeter of parallelogram
• Area and circumference of circle
• Area of sector and segment
• Length of arc
• Volume
• Volume of cube, cuboid and cylinder
• Total surface area of cube, cuboid and cylinder
• Lateral surface area of cube, cuboid and cylinder
• Diagonal of cube and cuboid

The triangle and its properties & Congruence of triangles

• Properties of Triangles
• Definition of triangle
• Various types of triangles (on the basis of their sides and angles both)
• Angle sum property of a triangle
• Exterior and interior opposite angles
• Triangle inequality
• Pythagoras theorem
• Converse of Pythagoras theorem
• Pythagorean triplets
• Congruence of triangles
• Congruent figures
• Congruence triangles
• Types of congruence conditions (SAS, SSS, ASA and RHS congruence condition)

Ratio and proportions

• Ratio and proportion
• Terms of a ratio
• Ratio in simplest form
• Comparison of ratios
• Continued proportion
• Problems on property- product of extremes = product of means
• Direct and Inverse Proportions
• Unitary method
• Direct proportion
• Inverse proportion

Commercial Mathematics

• Problems on percentage
• Simple interest and compound interest
• Profit and loss
• Problems on Partnership

Exponents and Powers

• Exponential equation
• Standard form of numbers
• Laws of exponents (Integers and rational numbers)
• Positive and negative integral exponent of a rational number

Algebraic Expressions and Identities

• Algebraic expression
• Definition of algebraic expression
• Like and unlike terms
• Polynomial
• Degree of a polynomial
• Types of polynomials
• Multiplication of polynomials
• Important identities- (a + b)2 = a2 + 2ab + b2
• (a – b)2 = a2 - 2ab + b2
• (a + b) (a – b) = a2 – b2
• Special Products and Factorizations

Statistics & Data Handling

• Data
• Definition of data, raw data, array, tabulation, observation, frequency, range, frequency distribution
• Tally marks
• Grouped data
• Mean, median and mode
• Graphical representation
• Histogram
• Line graph
• Bar graph
• Double bar graph
• Pie chart

Scholar Section:

Higher Order Thinking Questions - Syllabus as per Classic Section

Sample Papers of Unicus Non-Routine Mathematics Olympiad for Class 8: