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
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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