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Lower Primary - Class P1 & P2
Upper Primary - Class P3, P4 & P5
Level 1 - Class 6, 7 & 8
Ratio and Proportional Relationships
> Key Concept: Ratio and Proportion
> Example: Finding Ratio (Based on Ages)
> Example: Application of Ratio and Proportion
> Example:Percentage and its Application
> Example:Find Percentage Decrease
> Example:Calculate Amount and Compound Interest
> Example:Comparing Simple & Compound Interest
> Example:Solve Distance-Speed Problem using Direct Proportion
> Example:Solve using Inverse Proportion
> Example: Compare Population Density
> Example: Calculate Principal Amount
Geometry
> Example:Identify Point, Ray, Line Segment.
> Example: Identify Triangle Using Angle Sum Property
> Example: Find Angles in Triangle
> Example: Finding Angle Measure
> Example: Perimeter and its Application
> Example: Find Area of Land
> Example: On Concept of Area
> Example: Construct Perpendicular Bisector of Chords
> Example: Bisect an Angle
> Example:Find Angle Measure in Quadrilateral
> Example: Find Number of Sides of Polygon Given an Exterior Angle
> Example: Find Missing Angles in Parallelogram
> Example:Construct Quadrilateral given 2 Adjacent Sides
> Example:Construct Quadrilateral given 3 Sides & 2 Angles
> Example: Complementary and Supplementary Angles
> Example: Finding Angle Measure when Parallel Lines are Cut
   by a Transversal
> Example: Finding Interior Angle in Triangle
> Example: Finding Missing Angles in Triangle
> Example: Sum of Four Sides of a Quadrilateral is Less than Twice
   the Sum of its Diagonals?
> Example: Application of Pythagoras Theorem
> Example: Application of Pythagoras Theorem
> Theorem: Bisector of Vertical Angle of an Isosceles Triangle Bisects
   the Base
> Example:Based on Congruence of Triangles
> Example: Construct Isosceles Right Triangle
> Example: Finding Area and Height of a Triangle
> Example: Based on Circumference of Circle
> Example: Find Area of Crossroads of Two Rectangular Paths
> Example: Find Number of Revolutions made by Wheel
> Example: Identify Cross Sections
> Example: Identify Nets of Solids
Statistics and Probability
> Example: Draw Time Graph
> Example: Draw Bar Graph
> Example: Calculate Mean, Median and Mode
> Example: Draw Double Bar Graph
> Example: Finding Probability
> Example:List Outcomes of an Event
> Example:Interpret Histogram.
> Example:Find Probability of an Event
The Number System
> Example: Distance Covered in Time
> Example: Distributive Law of Multiplication
> Key Concept: Prime Numbers and Composite Numbers
> Example: Writing Consecutive Numbers
> Example: Finding Missing Number in a Factor Tree
> Example: Finding Highest Common Factor
> Key Concept: Introduction to Integers
> Example: Simplify Using Distributive Law
> Example: Comparing Unlike Fractions
> Example: Sum and Difference of Fraction
> Example: Add and Subtract Decimals
> Example: Convert Fraction into Decimal
> Example: Convert Decimals into Fractions
> Example: Based on Property of Division by Integers
> Example: Counting Number of Steps
> Example: Comparing Perimeters of Plane Figures
> Key Concept:Division of Decimals
> Example: Comparing Decimals
> Example: Finding Rational Numbers Between Fractions
> Example:Find Value of Expression
> Example:Find Multiplicative Inverse
> Example:Finding Square Root
> Example:Find Square Root using Long Division
> Example:Find Smallest Number to Obtain a Perfect Cube
> Example:Finding Cube Root
> Example:Find Value of an Expression using Laws of Exponent
> Example:Simplify an Expression using Laws of Exponent
> Example:Find Missing Digits in Adding Two Numbers using Reasoning.
> Example:Find Missing Digit using Divisibility Test
> Example: Comparing Fractions
> Example:Based on Multiplication and Division of Rational Numbers.
> Example: Simplify Using Laws of Exponents
> Example:Solve for x in Equation using Laws of Exponents
Expressions and Equations
> Example: Forming Algebraic Expression
> Example: Form an Equation
> Example: Solve Linear Equation in One Variable
> Example: Form and Solve Linear Equation
> Example: Finding 3 Consecutive Integers by Forming an Equation
   in One Variable
> Example: Find Two Digit Number by Forming an Equation in
   Two Variables
> Example: Solve Linear Equation Involving Fractions
> Example:Adding Algebraic Expressions
> Example:Subtracting Algebraic Expressions
> Example:Simplify Polynomial Expression
> Example:Simplify using Algebraic Identity (a+b)²
> Example: Factorize by Splitting Middle Term
> Example :Factorize Expression and Simplify as Directed
> Example:Correct the Mathematical Statement
> Example:Graph Data and Identify if it is Linear or Not
> Example: Evaluating Expression for Unknown Variable
Level 2 - Class 9 & 10
Number and Quantity
> Key Concept:Real Numbers, Irrational Numbers and Decimal
   Expansion of Numbers.
> Example:Finding Rational Numbers
> Example:Represent Irrational Number on Number Line
> Example:Rationalize the Denominator
> Example:Finding Highest Common Factor(HCF) using Euclid's
   Division Lemma
> Example:Express the Number as Product of Prime Factors
> Example:Prove the Number is Irrational
Algebra
> Example:Based on Remainder Theorem
> Example:Factorize the Quadratic
> Example:Factorize a Polynomial
> Example:Solve using Algebraic Identity
> Example:Frame Linear Equation
> Key Concept: Linear Equations and Their Solution.
> Example:Forming a Quadratic
> Example:Dividing Polynomials
> Example:Find Zeros of Polynomial
> Example:Solve System of Equations(Cross multiplication)
> Solving System of Equations(Substitution Method)
> Solving System of Equations(Elimination Method)
> Example:Solving System of Equations Reducible to Linear Equation
> Example:Solving Quadratic by Factorization
> Example:Solve Distance -Speed Problem by Forming Quadratic
   Equation
> Example:Solving Quadratic Equation (Completing Square)
> Example:Nature of Roots
> Example:Form & Solve Quadratic Equation
> Example:Finding nth Term from End
> Example: Finding Common Difference for given Arithmetic
   Progression
> Example:Finding Sum of first n Multiples
Functions
> Example:Simplify Trigonometric Expression
> Example:Finding Unknowns using Trigonometric Ratios
> Example :Find Angle using Trigonometric Ratios of Complementary
   Angles
> Example:Prove Trigonometric Identity
> Example:Prove Trigonometric Identity Involving Acute Angles
> Example:Find Height given Angle of Elevation
> Example:Find Distance given Angle of Depression
Geometry
> Example:Locating Points on Plane
> Example:Find Angle Measure from given Figure
> Example:Find Angle Measure (Based on Parallel lines)
> Example:Find Angle Measure using Properties of Parallel Lines
> Example:Find Angle Measure using Triangle Properties
> Example:Based on Congruence rules.
> Example:Find Missing Angle in Quadrilateral
> Midpoint Theorem Application
> Application of Theorem (Triangle and Parallelogram on Same Base )
> Application of Area of Parallelogram
> Example:Finding Center of Circle by Construction
> Example:Based on Cyclic Quadrilateral.
> Example: Find Angle Measure using Circle Theorems
> Example:Construct Equilateral Triangle
> Example:Heron's Formula
> Example: Finding Altitude of Trapezium
> Example:Finding Lateral & Total surface Area of Cube & Cuboids
> Example:Find Height of Cylinder
> Example: Compare Surface Areas of Spheres
> Example: Find Volume of Cuboid
> Example:Find Volume of Sphere(word problem)
> Example:Prove Similarity of Quadrilaterals
> Example:Prove Triangles are Similar
> Proving Result using Pythagoras Theorem
> Example:Find Point using Distance Formula
> Co-ordinate Geometry :Section Formula
> Example:Find Triangle Area for given Coordinates of Vertices
> Application of Pythagoras:Shaded Region
> Example:Find Area of sector of Circle
> Example:Find Curved Surface Area of Frustum of a Cone
> Example:Find Volume of Cuboid from Two Cubes
> Example:Find Height of Cylinder from given Sphere
Statistics and Probability
> Example:Find Mean, Median ,Mode
> Example: Find Correct Mean
> Example:Find Probability of Event
> Key Concept:Six Sigma Quality
> Key Concept:Identify Parameters and Make Inferences for Population
> Example:Margin of Error
> Example:Test a Production Lot by Sampling.
Level 3 - Class 11 & 12
Number and Quantity
> Example:Finding Argument and Modulus
> Example:Calculate Complex Roots
> Example: Polar Form of Complex number
> Key Concept:Order and Types of Matrices
> Example:Multiply the Matrices
> Example:Verify Property of Transpose
> Example:Finding Inverse of a Matrix (Elementary Transformation)
> Example:Evaluate using Properties of Determinants
> Application of Determinants:Find Area
> Example:Solve System of Equations using Matrix Method
Geometry
> Example:Find Angle Between Two Lines using Slope Concept
> Example:Find Length of Perpendicular
> Example:Find Angle Between Lines
> Example:Find Equation of Line
> Example:Finding Equation of Circle
> Example:Finding Equation of Parabola
> Example:Finding Equation of Ellipse
> Example:Equation of Hyperbola
> Key Concept: Co-ordinate Axes and Co-ordinate Planes
> Example:3D Geometry- Prove Points are Collinear
> Example: 3D Geometry - Find ratio using Section Formula
> Example:Solve to Find an Unknown Vector when Two Vectors
   are Equal
> Example:Finding Unit Vector
> Example:Finding Angle Between Two Vectors
> Example:Finding Projection of a Vector
> Example:Finding Value of Unknown for Perpendicular Vectors
> Example:Finding x for a Unit Vector
> Example:Find Direction Cosines
> Example:Find Equation of Plane
> Example:Finding Direction Cosines for given Direction Ratios
> Example:Finding Equation of a Line Parallel to Vector
> Example:Angle between Pair of Lines
> Example:Finding Shortest distance
> Example:Finding Coordinates of Foot of Perpendicular
> Example:Finding Intercepts Cut off by a Plane
> Example:Finding Distance of a Point from Plane
Statistics and Probability
> Example:Based on Permutation (Arrangement of Letters)
> Example:Based on Combination (Ways of Selecting a Card)
> Example:Finding Mean Deviation
> Example:Finding Standard Deviation
> Example:Finding Conditional Probability
> Example:Finding Probability of Independent events
> Example:Finding Probability using Multiplication Rule
> Example:Finding Probability using Bayes Theorem
> Example:Finding Probability Distribution
> Example:Finding Probability using Binomial Distribution
Algebra
> Example:Solving Inequality
> Application of Linear Inequation:Temperature Range
> Example:Finding Middle Term using Binomial Expansion
> Example:Find Power of Binomial
> Example:Finding Last Term of Arithmetic Progression(AP)
> Example:Finding Terms of Geometric Progression(GP)

Discrete Mathematics
> Example:Verify Demorgan's Law
> Example:Practical Problem on Union & Intersection of Sets
> Example:Write in Set Builder Form
> Example:Solving Minimization Linear Programming Problem(LPP)
   Graphically
> Key Concept: Introduction to Linear Programming
> Example:Solving Maximization Linear Programming Problem(LPP)
   Graphically
> Example:Form and Solve Linear Programming Problem(LPP)
Functions
> Example:Finding Domain & Range
> Example:Cartesian Product of Two Sets
> Example :Introduction to Trigonometry
> Example:Prove Trigonometric Identity
> Example:Solving Trigonometric Equation
> Example:Finding Limit
> Example:Find Limit if Exist
> Example:Find Derivative using First Principle
> Example:Finding Inverse of a Function
> Example:Prove Equivalence Relation
> Example:Find Domain and Range
> Example:Find Principle Value of Function
> Example:Evaluate Inverse Trigonometry function
> Example:Solve Inverse Trigonometric Function
> Example:Points of Discontinuity
> Example:Derivative using Chain rule
> Example:Implicit Function Derivative
> Example:Logarithmic Differentiation
> Example:Parametric Function Derivative
> Example:Verify Mean Value Theorem
> Application of Derivative:Find Rate of Change
> Application of Derivative:Increasing & Decreasing Function
> Application of Derivative: Verify Lines are Parallel
> Application of Derivative:Finding Maxima or Minima
> Example:Finding Integral
> Example:Evaluate Integral using Substitution
> Example:Evaluate integral of Trigonometric Function
> Example:Integration by Parts
> Example: Evaluate Definite integral
> Example:Solve Definite Integral using Properties
> Example:Solve Definite Integral using Properties
> Example:Finding Area Between Curve and Line
> Example:Finding Area Between Curves
> Example:Solve Differential Equation using Variable Separable
   method
> Example: Find Order and Degree of Differential Equation
> Example:Form Differential Equation
> Example:Solving Homogeneous Differential Equation
> Example:Solving Equation using Integrating Factor
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