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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