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Unicus Non-Routine Mathematics Olympiad Class 7 Sample Papers


Classic Section:


  • 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
    • Types of quadrilaterals
    • Properties of quadrilaterals
    • 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 7:

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Answers to Sample Questions from CREST Olympiads: