Topics
Click on the links below to dive deep into the topics.
ALGEBRA
Course Description
Level: Beginner (Grade 6/7)
This course introduces the basic concept of Algebra. The first reaction of any student while getting introduced to Algebra is apprehension! Apprehension of using letters in Mathematics, apprehension of finding an ‘unknown’, apprehension towards what they assume, or have been told that this is a very complicated field of mathematics! This course is intended to remove this fear from you and help you get the true essence of Algebra and be able to actually enjoy it.
Prior knowledge required:
- Concept of positive and negative numbers
- Operations ( )with numbers.
Units:
- The Unknown
- Unit I – Algebraic Expressions: An introduction
- Unit II – Algebraic Expression : Variables, Constants and Coefficients
- Unit III – Algebraic Expressions: Like terms in multi variable expressions
- Unit IV – Algebraic Expression: Finding the value of an expression:
- Unit V – Algebraic Expression – Simplifying
Think: What is the role of notations in mathematics? Could mathematics be understood easily even if the notations were not universal?
Course Description
Level: Intermediate (Grade 7/8)
Now that you have mastered the basic concepts of Algebra, you can now move on to learn further topics. Algebra forms the base for most of the modern mathematics including computer programming and modelling. How is algebra used in real life? How did the ancient mathematicians solved algebraic problems without the mathematical notations we use now? In this section, you will be learning about algebraic equations and how to solve them. Knowledge of coordinate geometry is required for the later part of this section.
Prior knowledge required:
Knowledge of plotting points on a coordinate axes (for Unit II and further of this section).
Units:
- Unit I: Equations – The beginning
- Unit II: Linear Equations
- Unit III: Forming Linear Equations
- Unit IV: Solving Equations
- Unit V: Two Linear Equations
Think: Many mathematicians relate God or Nature to mathematical equations. Srinivasa Ramanujam had once said: “An equation means nothing to me unless it expresses a thought of God.” Is this theory applicable to modern tech-based life?
Course Description
Level: Intermediate (Grade 8/9)
By now you would have developed lots of interest in algebra and will be eager to learn more on this topic. In the last section, you learned about ‘equations’. What if the two sides of the equations are not equal but one is more than the other? Are there statements in the form of equations that are true for any values of the variables?
This section deals with algebraic identities and inequalities.
Prior knowledge required:
- Knowledge of solving linear equations
- Graphing linear equations
- Knowledge of quadratic equations and their graphs (for unit IV only).
Units:
- Unit I: Algebraic Identities
- Unit II: Linear Inequalities in one variable
- Unit III: Linear Inequalities in two variables
- Unit IV: Quadratic inequalities
- Unit V: Inequalities between two functions
Think: What is the major difference between equations and identities? Equality plays major role in solving inequalities – Does this apply to our life as well? Is it important to understand the commonalities between humans to solve the differences?
Course Description
Level: Intermediate (Grade 8/9)
You must have learnt about negative and positive numbers. This chapter deals about making negative numbers into positive numbers. This is a very simple concept but later applied in many higher level mathematics.
Prior knowledge required:
- Concept of positive and negative numbers
- Representing all real numbers on a number line
- Solving linear equations in one variable (for solving equations with modulus unit)
- Linear and quadratic inequalities (for absolute inequalities unit)
- Functions (for Absolute value function unit)
Units:
- Meaning of Absolute Value
- Absolute value and its applications
- Properties of Absolute Value
- Solving equations with modulus
- Absolute inequalities
- Absolute value function
Think: Why do we need to convert negative values into positive values? Can this be connected to psychological approach to life: ” it is necessary to convert all negative thoughts into positive thoughts in one’s life”?
Course Description
Level: Intermediate (Grade 7/8)
This topic deals with one of the many interesting concepts in mathematics which has been in use since the ancient history of mathematics. Babylonians, Greeks, Egyptians, Chinese and Indians were among the most common civilizations that included the concept of angles in their measurements. In this unit, you will learn the basic idea of angles – what they are and how they are measured – and about various types of angles and how to construct them using a protractor.
This chapter starts from the basic and therefore no prior knowledge required.
Units
- Definition and Notations
- Types of angles
- Measuring and Constructing angles
- Angles between two parallel lines
- Angles in a polygon
Think: What are the different areas in which angles play a major role? Is it just on aesthetic grounds or is there any scientific reason that nature has different types of angles for each of its components?
Binomial Theorem
Course Description
Level: High school (Grade 10/11)
In this section, you will learn about expanding an expression in the form (x+
Prior knowledge required:
- Simple knowledge on expanding two terms in brackets
- Polynomials – the notations, terminology such as terms, coefficients, powers, degrees etc. of a polynomial.
- Know the meaning of the words ‘ascending’ and ‘descending’
- Knowledge of Permutations and Combinations
Units:
- Understanding binomial expansions
- Pascal’s Triangle
- Connecting ‘Combinatorials’ with Pascal’s triangle
- Binomial Theorem
- Applying binomial theorem in problems
- Finding general term
Calculus
Course Description
Level: High school (Grade 11/12)
Change is the only thing that does not change!!
Everything in the world changes – be it living or non – living. Living things grow, move, reproduce etc., while non-living things also undergo certain changes like shapes, size or even characteristics depending on their nature. But, there is definitely a change in everything. The change could be physical, environmental or even genetic. Some things change with time while others change relative to some other factors around them. In every change, there is mathematics and this branch of mathematics that deals with change is called Calculus.
Calculus is an important part of mathematics which helps in identifying and analyzing any changing aspect. This later extends to much higher level of mathematics that deals with infinity, infinitesimals, rate of change, creating mathematical models, finding area of any 2 dimensional shape and volume of any 3 dimensional solid and many more.
In this section, we will learn about different parts of Calculus. Click on each subtopic to learn more about them:
Course Description
This course introduces the basic concept of Limits. Calculus is based on the idea of infinity and infinitesimal. Hence, understanding the behavior of a function at infinity or at 0 or any other given point is important before getting deeper into calculus. Limit of a function shows how a function behaves around a specific point.
Enjoy this chapter limitlessly!
- Functions
- Sequences and series
Units:
- Introduction
- DNE – Limit Does Not Exist
- Limits on Polynomial functions
- Limits on trigonometric functions
- Limits on exponential functions
- Limits on hybrid functions
- Limits on rational functions
Course Description
Level: Higher (Grade 11/12)
This course explains how to find the average rates of change in different cases. You will learn about what is meant by rate of change and what is the implication of the average rate of change between two instances of occurrence.
Change is the only constant in the world!
Prior knowledge required:
- Functions
- Limits
- Idea of gradient (slope) of line
Units:
- Introduction
- Rates of Change from Table
- Rates of Change in Kinematics
- Rates of Change in functions
Course Description
This unit describes the various aspects of Differential Calculus from finding the derivatives of simple functions using The First Principle method and L’Hopital’s rule. It goes further to find the derivatives of product, quotient and composite functions using product rule, quotient rule and chain rule respectively. It ends with finding the derivative of implicit functions. At the end of this unit you can see the collection of derivatives of all basic functions.
This section starts with an activity given in the previous section Rates of change. It will be necessary to complete this activity to understand this section better.
- Functions
- Limits
- Rates of change
Units
- Derivatives
- The First Principle Method
- L’Hopital’s Rule
- Rules of Derivatives
- Implicit differentiation
- List of derivatives
Course Description
Level: Intermediate (Grade 7/8)
Have you ever tried to order a print of your favorite photo? If so, you would have come across various options in the output size. What is common about the measurements of these sizes?
If you compare the sides of A-size papers (A1, A2 etc.) you will find that they are in same proportion.
In many aspects, we prefer to have different sizes of the same object but would like to maintain the same shape. All such objects are called ‘similar’ objects. Sometimes, we would want exactly the same size as well as the shape to be replicated. Such are ‘congruent’ objects. In this unit, you will learn the differences and commonalities of the two types of objects. You will also learn how these concepts are used in finding their areas and volumes.
Prior knowledge required:
- Ratio and proportions
- Knowledge of triangles and their geometrical construction
- Properties of geometrical shapes
- Transformation of geometrical shapes
- Area and Volume of different shapes
Units:
- Definition of Congruency and Similarity
- Comparing triangles
- Area and Volume of Similar figures
Think: Artists create several representations of nature in their works at different scales. What do they base the selection of the dimensions of such works? Is it common for all types of art?
Numbers
Course Description
Level: Beginner (Grade 6/7) Intermediate (7/8)
This course deals with all types of numbers and various operations on each of them. You will know why and how different numbers were formed. You will also learn all operations on all types of numbers – addition, subtraction, multiplication, division, rationalization, simplification etc. The types of numbers start from Natural numbers to Complex numbers. Part of this course up to Integers are for beginner level and the remaining type of numbers (Rational to Real) are applicable to intermediate levels.
Hope you get innumerable pleasure from this topic!
Units:
- FIRST EVER NUMBERS!
- Numerals
- Types of Numbers
- Operations on Numbers
Think: How important it is to have an appropriate notation for numbers? How did the present number system overcome the difficulties that its predecessors had? Do you think there will be any limitations to the present decimal system in future? Is it that we are so much used to this system that we cannot find any limitations yet?
Ratio and Proportions
Course Description
Level: Intermediate (Grade 7/8)
A cake recipe gives measurements to make a cake of 1kg weight, but you need only 500 gm cake. How will you calculate the exact measurements for each ingredient?
You want to frame a picture that you took on your last trip to the mountains. How much do you have to enlarge your original photo to fit the frame?
All such questions involve a concept called Ratios and Proportions. In this unit, you will learn about how ratios are used and what are the different types of proportionality with some real life examples. For more problems on this topic, click on the Practice Worksheet tab on the menu bar.
Prior knowledge required:
- Fractions
- Decimals
- Units and conversions
- Map drawing
Units:
- Ratios
- Simplifying ratios
- Dividing quantities using ratios
- Proportions
- Direct and Inverse proportion
- Ratios in map scales
Think: Ratios and proportions are seen everywhere in nature. Is this for aesthetic purposes only or are there any other reasons? Artists use ratios often, in a way to reproduce what is in nature. Is it necessary? Is it possible to reproduce nature without using proportionality? Does modern art include proportionality?
Trigonometry
Course Description
Level: High school (Grade 9/10)
This section deals with basic trigonometry, starting from what is the meaning of trigonometry all the way to finding angles and sides of a non-right angled triangle using trigonometry. This session also deals with a new measure of angles called radians.
Prior knowledge required:
- Properties of triangles
You might need to know how to use a scientific calculator after a few units in this section.
Units:
- The Basics
- Trigonometric identities
- Compound & Double angle formulas
- Measuring angles : Degrees and Radians
- Trigonometric ratios of some standard angles
- Using trigonometry on non-right angled triangles
Think: Trigonometry has played a major role in history of mathematics. Is trigonometry such a basic mathematical concept that people could not have had a civilization without it? Has this concept evolved to cater the need of the modern civilization?
Happy Learning!
Course Description
Level: High school (Grade 10/11)
This section is an extension of Part I where we deal with higher concepts of trigonometry. In Part I, we restricted ourselves with trigonometry in triangles, but in this section we will take it further to see how the trig ratios can be applied beyond triangles!! That is, we will try to find the values of Sine, Cosine etc. beyond 90 degrees!
Prior knowledge required:
- Trigonometry Part I
- Coordinate geometry
Units:
- Trigonometry beyond triangles:
- Angles in the four quadrants and their trig ratios
- Solving trigonometry equations
- Transformation of trig functions
- Inverse Trigonometric functions
Think: Many mathematicians relate God or Nature to mathematical equations. Srinivasa Ramanujam had once said: “An equation means nothing to me unless it expresses a thought of God.” Is this theory applicable to modern tech-based life?
Course Description
Level: High school (Grade 10/11)
This section is an extension of Part I & II where we deal with real life applications of trigonometry. It is well known that trigonometry has been part of human life from as early as ancient civilizations, especially in Asia and Europe. From the basics of right angled triangle to the sine graph, trigonometry has wide range of applications, in many fields from engineering to rocket science.
Prior Knowledge required:
- Trigonometry Part I
- Trigonometry Part II
- Ability to understand questions based on real-life situations and convert to mathematical form
- Ability to sketch diagrams related to the word problems
- Use of graphing display calculator or graphing software.
Units:
- Unit I – Simple applications
- Unit II – Bearings
- Unit III – Angles of Elevation and Depression
- Unit IV – 3D Trigonometry
- Unit V – Modeling using
- trigonometric functions