Course: Maths - Khan Academy, Educomp & Vimbue

Section outline

Select section General

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General

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Select section 1. Sets

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1. Sets
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  Introduction
  
  Select activity What are Sets?
  
  What are Sets? Lesson
  
  Students must
  
  Mark as done
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  Sets and their Representations
  
  Select activity Roster and Set-builder Form
  
  Roster and Set-builder Form Lesson
  
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  Solved Examples - Exercise 1( a )
  
  Select activity Example 1: Set builder to Roster form
  
  
  
  Example 1: Set builder to Roster form Lesson
  
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  Example 2: Roster to Set builder form Lesson
  
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  Example 3 Lesson
  
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  Example 4 Lesson
  
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  Example 5 Lesson
  
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  Example 6 Lesson
  
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  Example 7 Lesson
  
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  Empty, Finite and Infinite Sets
  
  Select activity Empty, Finite, and Infinite Sets
  
  Empty, Finite, and Infinite Sets Lesson
  
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  Solved Examples - Exercise 1( b )
  
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  Example 1 Lesson
  
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  Example 2 Lesson
  
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  Example 3 Lesson
  
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  Example 4 Lesson
  
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  Example 5 Lesson
  
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  Example 6 Lesson
  
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  Equal Sets
  
  Select activity Equal Sets
  
  Equal Sets Lesson
  
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  Subsets
  
  Select activity Subsets of Sets of Real Numbers
  
  
  
  Subsets of Sets of Real Numbers Lesson
  
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  Select activity Intervals as Subsets of R
  
  
  
  Intervals as Subsets of R Lesson
  
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  Select activity Conceptual Problems on Subsets of Sets
  
  
  
  Conceptual Problems on Subsets of Sets Lesson
  
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  Solved Examples - Exercise 1( c )
  
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  Example 1 Lesson
  
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  Example 2 Lesson
  
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  Example 3 Lesson
  
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  Example 4 Lesson
  
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  Example 5 Lesson
  
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  Example 6 Lesson
  
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  Example 7 Lesson
  
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  Example 8 Lesson
  
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  Venn Diagrams
  
  Select activity Part 1
  
  Part 1 Lesson
  
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  Operations on Sets
  
  Select activity Properties of Union of Sets
  
  
  
  Properties of Union of Sets Lesson
  
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  Select activity Properties of Intersection of Sets
  
  
  
  Properties of Intersection of Sets Lesson
  
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  Select activity Applying Properties of Intersection and Union of Sets
  
  
  
  Applying Properties of Intersection and Union of Sets Lesson
  
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  Select activity Example: Practical Problem on Union & Intersection of Sets
  
  
  
  Example: Practical Problem on Union & Intersection of Sets Lesson
  
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  Complement of a Set
  
  Select activity Demorgan's Law and other Properties of Complement Sets
  
  
  
  Demorgan's Law and other Properties of Complement Sets Lesson
  
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  Select activity Example 1: Verify Demorgan's Law
  
  
  
  Example 1: Verify Demorgan's Law Lesson
  
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  Example 2 Lesson
  
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  Example 3 Lesson
  
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  Example 4 Lesson
  
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Select section 2. Relations and Functions

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2. Relations and Functions
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  Introduction
  
  Select activity What are Ordered Pairs?
  
  What are Ordered Pairs? Lesson
  
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  Cartesian Products of Sets
  
  Select activity Cartesian Product of Sets
  
  
  
  Cartesian Product of Sets Lesson
  
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  Select activity Ordered Triplets
  
  
  
  Ordered Triplets Lesson
  
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  Select activity Example: Cartesian Product (AxB given)
  
  
  
  Example: Cartesian Product (AxB given) Lesson
  
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  Select activity Example: Cartesian Product (Set operations)
  
  
  
  Example: Cartesian Product (Set operations) Lesson
  
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  Select activity Example: Cartesian Product (Application based)
  
  
  
  Example: Cartesian Product (Application based) Lesson
  
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  Solved Examples: Exercise 2(a)
  
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  Example 1 Lesson
  
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  Example 2 Lesson
  
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  Example 3 Lesson
  
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  Example 4 Lesson
  
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  Example 5 Lesson
  
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  Example 6 Lesson
  
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  Relations
  
  Select activity What are Relations?
  
  
  
  What are Relations? Lesson
  
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  Select activity Finding Domain and Range
  
  
  
  Finding Domain and Range Lesson
  
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  Select activity Example - Finding the Relation
  
  
  
  Example - Finding the Relation Lesson
  
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  Select activity Total Number of Possible Relations
  
  
  
  Total Number of Possible Relations Lesson
  
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  Solved Examples: Exercise 2(b)
  
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  Example 1 Lesson
  
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  Example 2 Lesson
  
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  Example 3 Lesson
  
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  Example 4 Lesson
  
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  Example 5 Lesson
  
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  Example 6 Lesson
  
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  Example 7 Lesson
  
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  Example 8 Lesson
  
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  Select activity Example 9
  
  
  
  Example 9 Lesson
  
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  Functions
  
  Select activity Identity and Constant Functions
  
  
  
  Identity and Constant Functions Lesson
  
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  Select activity Polynomial Function
  
  
  
  Polynomial Function Lesson
  
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  Select activity Rational Functions
  
  
  
  Rational Functions Lesson
  
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  Select activity Modulus Function
  
  
  
  Modulus Function Lesson
  
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  Select activity Signum Function
  
  
  
  Signum Function Lesson
  
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  Select activity Greatest Integer Function
  
  
  
  Greatest Integer Function Lesson
  
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  Select activity Finding Domain and Range using Graph
  
  
  
  Finding Domain and Range using Graph Lesson
  
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  Select activity Algebra of Real Functions
  
  
  
  Algebra of Real Functions Lesson
  
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  Select activity Example: Finding Domain & Range
  
  
  
  Example: Finding Domain & Range Lesson
  
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Select section 3. Trigonometric Functions

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3. Trigonometric Functions
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  Trigonometric Functions
  
  Select activity Part 1
  
  
  
  Part 1 Lesson
  
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  Select activity Sign of Trigonometric Functions
  
  
  
  Sign of Trigonometric Functions Lesson
  
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  Part 2 Lesson
  
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  Select activity The Trigonometric Functions & Right Triangle Trigonometric Ratios
  
  
  
  The Trigonometric Functions & Right Triangle Trigonometric Ratios Lesson
  
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  Select activity Trigonometric Ratios for Common Angles
  
  
  
  Trigonometric Ratios for Common Angles Lesson
  
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  Select activity Graph of cos(x) and sec(x)
  
  
  
  Graph of cos(x) and sec(x) Lesson
  
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  Select activity Worked Example - Using the Unit Circle
  
  
  
  Worked Example - Using the Unit Circle Lesson
  
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  Select activity Strategy for finding Half Angle Ratios
  
  
  
  Strategy for finding Half Angle Ratios Lesson
  
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  Select activity Example: Half Angle Ratios
  
  
  
  Example: Half Angle Ratios Lesson
  
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  Select activity Trigonometric Challenge Problem: Cosine of Angle-Sum
  
  
  
  Trigonometric Challenge Problem: Cosine of Angle-Sum Lesson
  
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  Select activity Finding Ratios for 4x and 6x of Angles
  
  
  
  Finding Ratios for 4x and 6x of Angles Lesson
  
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  Select activity Value of Expressions by Angle addition Property
  
  
  
  Value of Expressions by Angle addition Property Lesson
  
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  Select activity Adding Subtracting from Multiples of pi/2
  
  
  
  Adding Subtracting from Multiples of pi/2 Lesson
  
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  Select activity Example: Angle Addition Property
  
  
  
  Example: Angle Addition Property Lesson
  
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  Solved Examples: Exercise 3(a)
  
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  Example 1 Lesson
  
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  Example 2 Lesson
  
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  Example 4 Lesson
  
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  Solved Examples: Exercise 3(b)
  
  Select activity Example I -1
  
  
  
  Example I -1 Lesson
  
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  Example I -2 Lesson
  
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  Example I -3 Lesson
  
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  Example I -4 Lesson
  
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  Example I -5 Lesson
  
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  Example II -1 Lesson
  
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  Example II -2 Lesson
  
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  Example II -3 Lesson
  
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  Example II -4 Lesson
  
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  Example II -5 Lesson
  
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  Solved Examples
  
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  Example 1 Lesson
  
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  Example 2 Lesson
  
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Select section 4. Complex Numbers and Quadratic Equations

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4. Complex Numbers and Quadratic Equations
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  Algebra of Complex Numbers
  
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  Part 1 Lesson
  
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  Part 2 Lesson
  
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  Select activity Square Root of Complex Number - General Formula
  
  
  
  Square Root of Complex Number - General Formula Lesson
  
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  Select activity Square Root of a Complex Number - Example
  
  
  
  Square Root of a Complex Number - Example Lesson
  
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  Select activity Identities Involving Two Complex Numbers
  
  
  
  Identities Involving Two Complex Numbers Lesson
  
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  The Modulus and the Conjugate of a Complex Number
  
  Select activity The Modulus and the Conjugate of a Complex Number / Argand Plane and Polar Representation
  
  
  
  The Modulus and the Conjugate of a Complex Number / Argand Plane and Polar Representation Lesson
  
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  Select activity Properties of Modulus and Conjugates
  
  
  
  Properties of Modulus and Conjugates Lesson
  
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  Select activity Finding Modulus of Complex Expressions
  
  
  
  Finding Modulus of Complex Expressions Lesson
  
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  Select activity Modulus and Conjugates Challenge Problem
  
  
  
  Modulus and Conjugates Challenge Problem Lesson
  
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  Select activity Solving Exponential Equations Involving Powers of i
  
  
  
  Solving Exponential Equations Involving Powers of i Lesson
  
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Select section 5. Linear Inequalities

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5. Linear Inequalities
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  Inequalities
  
  Select activity Inequalities (Basics)
  
  Inequalities (Basics) Lesson
  
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  Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation
  
  Select activity Algebraic Solutions
  
  
  
  Algebraic Solutions Lesson
  
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  Select activity Rules for Solving Inequalities
  
  
  
  Rules for Solving Inequalities Lesson
  
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  Select activity Testing Solutions to Inequalities
  
  
  
  Testing Solutions to Inequalities Lesson
  
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  Select activity Plotting an Inequality Example
  
  
  
  Plotting an Inequality Example Lesson
  
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  Solved Examples: Exercise 5(a)
  
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  Example 1 Lesson
  
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  Example 2 Lesson
  
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  Example 3 Lesson
  
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  Example 4 Lesson
  
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  Example 5 Lesson
  
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  Example 6 Lesson
  
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  Example 7 Lesson
  
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  Example 8 Lesson
  
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  Example 9 Lesson
  
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  Example 10 Lesson
  
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  Example 11 Lesson
  
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  Example 12 Lesson
  
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  Example 13 Lesson
  
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  Example 14 Lesson
  
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  Example 15 Lesson
  
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  Example 16 Lesson
  
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  Example 17 Lesson
  
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  Example 18 Lesson
  
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  Solved Examples: Exercise 5(b)
  
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  Example 1 Lesson
  
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Select section 6. Permutations and Combinations

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6. Permutations and Combinations
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  Fundamental Principle of Counting
  
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  Fundamental Principle of Counting I Lesson
  
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  Select activity Fundamental Principle of Counting II
  
  Fundamental Principle of Counting II Lesson
  
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  Solved Examples
  
  Select activity Example 1: Using AND and OR
  
  
  
  Example 1: Using AND and OR Lesson
  
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  Select activity Example 2: Using AND and OR (Constraints)
  
  
  
  Example 2: Using AND and OR (Constraints) Lesson
  
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  Select activity Example 3: Using AND and OR (with Constraints)
  
  
  
  Example 3: Using AND and OR (with Constraints) Lesson
  
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  Select activity Example 4: Curious Case of 0
  
  
  
  Example 4: Curious Case of 0 Lesson
  
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  Select activity Example 5: Using AND and OR for Letters
  
  
  
  Example 5: Using AND and OR for Letters Lesson
  
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  Select activity Example 6: Repeated Letters
  
  
  
  Example 6: Repeated Letters Lesson
  
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  Select activity Example 7: Multiple Repetitions
  
  
  
  Example 7: Multiple Repetitions Lesson
  
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  Select activity Example 8: Putting it All Together (Challenge)
  
  
  
  Example 8: Putting it All Together (Challenge) Lesson
  
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  Select activity Example 9: Bundling
  
  
  
  Example 9: Bundling Lesson
  
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  Select activity Example 10: Ranking
  
  
  
  Example 10: Ranking Lesson
  
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  Permutations
  
  Select activity Factorial
  
  
  
  Factorial Lesson
  
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  Select activity Permutations
  
  
  
  Permutations Lesson
  
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  Select activity Formulae for Permutation & Combination
  
  
  
  Formulae for Permutation & Combination Lesson
  
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  Combinations
  
  Select activity Combinations I
  
  
  
  Combinations I Lesson
  
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  Select activity Combinations II
  
  
  
  Combinations II Lesson
  
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  Select activity Example: Equations involving formulae of PnC
  
  
  
  Example: Equations involving formulae of PnC Lesson
  
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  Select activity Example: Finding Number of Combinations
  
  
  
  Example: Finding Number of Combinations Lesson
  
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  Example: Multiple Selections Lesson
  
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  Select activity Example: Number of Ways of Forming Groups
  
  
  
  Example: Number of Ways of Forming Groups Lesson
  
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  Select activity Example: Applications of PnC in Geometry
  
  
  
  Example: Applications of PnC in Geometry Lesson
  
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Select section 7. Binomial Theorem

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7. Binomial Theorem
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  Binomial Theorem for Positive Integral Indices
  
  Select activity Introduction
  
  
  
  Introduction Lesson
  
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  Select activity Pascal's Triangle
  
  
  
  Pascal's Triangle Lesson
  
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  Select activity Pascal's Triangle and Binomial Expansion
  
  
  
  Pascal's Triangle and Binomial Expansion Lesson
  
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  Select activity Some Special Cases of (a+b)^n
  
  
  
  Some Special Cases of (a+b)^n Lesson
  
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  Solved Examples - Exercise 7(a)
  
  Select activity Example 1: Approximations using Binomial Theorem
  
  
  
  Example 1: Approximations using Binomial Theorem Lesson
  
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  Solved Examples - Exercise 7(b)
  
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Select section 8. Sequences and Series

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8. Sequences and Series
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  Sequences
  
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  Solved Example: Exercise 8(a)
  
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  Geometric Progression (G.P)
  
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  Relationship Between A.M. and G.M.
  
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  Solved Example: Exercise 8(b)
  
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Select section 9. Straight Lines

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9. Straight Lines
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  Slope of a Line
  
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  Solved Examples: Exercise 9(a)
  
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  Various Forms of the Equation of a Line
  
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  Solved Examples: Exercise 9(b)
  
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  Distance of a Point From a Line
  
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  Solved Examples: Exercise 9(c)
  
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Select section 10. Conic Sections

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10. Conic Sections
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  Introduction
  
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  Sections of a Cone
  
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  Circle
  
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  Solved Examples: Exercise 10(a)
  
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  Parabola
  
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  Solved Examples: Exercise 10(b)
  
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  Ellipse
  
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  Solved Examples: Exercise 10( c )
  
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  Hyperbola
  
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  Solved Examples: Exercise 10(d)
  
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  Solved Examples: Exercise 10(e)
  
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Select section 11. Introduction to Three Dimensional Geometry

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11. Introduction to Three Dimensional Geometry
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  Introduction
  
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  Coordinate Axes and Coordinate Planes in Three Dimensional Space
  
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  Distance between Two Points
  
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  Solved Examples: Exercise 11(b)
  
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Select section 12. Limits and Derivatives

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12. Limits and Derivatives
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  Intuitive Idea of Derivatives
  
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  Limits
  
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  Select activity Limit of x^n - a^n / (x - a)
  
  
  
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  Limit of Trigonometric Functions
  
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  Solved Examples: Exercise 12(a)
  
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  Derivatives
  
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  Solved Examples: Exercise 12(b)
  
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  Solved Examples: Exercise 12( c )
  
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13. Statistics
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  Statistics
  
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  Mean Deviation
  
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  Solved Examples: Exercise 13( a )
  
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  Variance and Standard Deviation
  
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  SD and Variance - Shortcut Method (Derivation) Lesson
  
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  SD and Variance - Another Formula (Derivation) Lesson
  
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  Select activity SD and Variance of a Scaled Data Set
  
  
  
  SD and Variance of a Scaled Data Set Lesson
  
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  SD and Variance - Finding the Missing Entries Lesson
  
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  SD and Variance of a Shifted Data Set Lesson
  
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  SD and Variance - Fixing Corrections Lesson
  
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  Solved Examples: Exercise 13( b )
  
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  Examples
  
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  SD and Variance of a Scaled Data Set Lesson
  
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  SD and Variance - Finding the Missing Entries Lesson
  
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  SD and Variance - Fixing Corrections Lesson
  
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Select section 14. Probability

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14. Probability
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  Event
  
  Select activity All about Events (Overview)
  
  
  
  All about Events (Overview) Lesson
  
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  Select activity Formal definition of Occurrence of an Event
  
  
  
  Formal definition of Occurrence of an Event Lesson
  
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  Impossible and Sure Events Lesson
  
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  Simple and Compound Events Lesson
  
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  Complementary Events Lesson
  
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  Mutually Exclusive Events Lesson
  
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  Exhaustive Events Lesson
  
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  Select activity Probability of Union of Three Events
  
  
  
  Probability of Union of Three Events Lesson
  
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  Axiomatic Approach to Probability
  
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  Axiomatic Approach to Probability Lesson
  
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  Select activity Probability of Equally Likely Outcomes
  
  
  
  Probability of Equally Likely Outcomes Lesson
  
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  Select activity Probability of the Event 'A or B'
  
  
  
  Probability of the Event 'A or B' Lesson
  
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  Select activity Probability of the Event 'not A'
  
  
  
  Probability of the Event 'not A' Lesson
  
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  Solved Examples
  
  Select activity Example 1: Probability (Visualisation)
  
  
  
  Example 1: Probability (Visualisation) Lesson
  
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  Select activity Example 2: Algebra of events
  
  
  
  Example 2: Algebra of events Lesson
  
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  Select activity Example 3: Probability (Formula Based)
  
  
  
  Example 3: Probability (Formula Based) Lesson
  
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  Select activity Example 4: Probability of Forming Numbers
  
  
  
  Example 4: Probability of Forming Numbers Lesson
  
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  Select activity Example 5: Probability of Getting a Sum on Dice Rolls
  
  
  
  Example 5: Probability of Getting a Sum on Dice Rolls Lesson
  
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  Select activity Example 6: Probability through Sorting a List
  
  
  
  Example 6: Probability through Sorting a List Lesson
  
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  Select activity Example 7: Probability of a given Arrangement
  
  
  
  Example 7: Probability of a given Arrangement Lesson
  
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  Select activity Example 8: Probability of a given Selection
  
  
  
  Example 8: Probability of a given Selection Lesson
  
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  Select activity Example 9: Probability of Winning a Relay Race
  
  
  
  Example 9: Probability of Winning a Relay Race Lesson
  
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  Select activity Example 10: Probability of a given Grouping
  
  
  
  Example 10: Probability of a given Grouping Lesson
  
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  Select activity Example 11: Probability of Winning a Lottery
  
  
  
  Example 11: Probability of Winning a Lottery Lesson
  
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  Select activity Example 12: Letters and Envelopes
  
  
  
  Example 12: Letters and Envelopes Lesson
  
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