# NATA MATH

SOLVED PROBLEMS EXPLAINING CONCEPTS

This page is designed for students appearing for the NATA written test architecture entrance exams in India. Here, the various concepts are explained and then illustrated through solved examples.

## ARITHMETICO-GEOMETRIC SERIES

What is an Arithmetic- Geometric series? How do you calculate its sum of n terms or sum to infinity?

Watch this video/presentation to find out.

Here, we learn what is an arithmetic -geometric series. We learn how to identify its nth term and learn techniques to calculate the sum of n terms or sum to infinity.We also use the three summation formulae for sum upto n terms.

This is useful for Grade 11 maths students and students preparing for the NATA eligibility test for architecture.

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## INTRODUCTION TO DIFFERENTIATION VIDEO

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This video explains the basic problems in differentiation from a beginner's point of view. Here, we discuss the basic formulae on exponents, trigonometry and the product and quotient rule. Problems are explained completely with the relevant formulae.

This is useful for Grade 11 maths students and also students preparing for the NATA eligibility test for Mathematics.

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## INTRODUCTION TO FUNCTIONS

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What are sets, relations and functions?

This presentation starts with the Cartesian product of 2 sets and how a relation is defined from it. It also goes on to show how this leads to a function . We cover the different types of functions and problems based on them. Types of functions explained are one-one, onto, many to one and into functions.We discuss 3 important functions, namely, the modulus function, signup function and the greatest integer function.

This is useful for grade 11 maths students and students preparing for the NATA eligibility test in architecture. For more videos, consider subscribing to my channel or visit my page

## FUNCTIONS-INVERTIBILITY VIDEO

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What are one-one and onto functions?

Learn about all this by watching this presentation. Here, we discuss what are functions, injective, surjective and bijective functions. We also learn how to calculate the inverse of a function if it exists.

This video is useful for grade 11 maths students and students preparing for the NATA eligibility test for architecture.

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## STRATEGY FOR LIMITS

How do you calculate the limit of functions ? Watch this video to find out!

Here, we start with the very basic concept of limits, a few formulae. We explain techniques of solving problems on limits. We then move to more complicated problems involving rationalisation and trigonometric limits.

This video is useful for grade 11 maths students learning Calculus and also students preparing for the NATA eligibility test for architecture.

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## LOGARITHMS: PROPERTIES

Do you know that logarithms are used extensively in Calculus, be it limits, derivatives or Integration? How then do you apply properties of logarithms while solving problems in Calculus?

Learn this by watching this video. Here, we discuss the basic properties of logarithms such as the product rule, quotient rule, exponent rule. We also learn how to apply the change of base formula and a few formulae on exponential limits.

This video is useful for grade 12 maths students and students preparing for the NATA eligibility test for architecture.

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## ANGLE BETWEEN 2 PLANES IN 3 D

How do you calculate angle between 2 planes in 3 D?

Watch this video to find out. Here, we learn how to calculate angle between 2 planes. We learn how to check if 2 planes are parallel or perpendicular. We also learn how to find the angle between a line and a plane. The intersection of 2 planes is also touched upon.

This is a part of grade 12 mathematics. It is also useful for the NATA ELIGIBILITY test for architecture.

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## EQUATION OF PLANES IN 3 D

This presentation deals with how to calculate the equation of a plane passing through 2 points and parallel to a line.

It also illustrates how to calculate equation of a plane passing through a point and parallel to 2 lines.

We learn how to check for coplanarity and how to find the equation of a plane passing through 2 lines.

Equation of a plane passing through the intersection of 2 planes is also explained.

This is useful for grade 12 maths students and students appearing for the NATA eligibility test for architecture.

## SHORTEST DISTANCE BETWEEN 2 LINES

How do you calculate the distance between 2 lines in 3 dimensional geometry?

Watch this presentation to find out how to calculate the shortest distance between 2 parallel and non parallel lines. We also learn about skew lines and how to test if 2 lines are skew.

This is a useful topic for students of grade 12 maths and students preparing for the NATA eligibility test in architecture

## Probability -(part 2)

About Body

## NATA STATISTICS -(PART 1)

This video is designed to help students preparing for the NATA math exam. It is also useful for grade 12 math students.

Here, we discuss the topics

mean, standard deviation, frequency distribution, probability -addition theorem, multiplication theorem, conditional probability

## DISTANCE OF A POINT FROM A PLANE IN 3 D GEOMETRY

Welcome Paragraph Title

How do you calculate distance of a point from a plane?

Watch this presentation to find out. Here, we learn how to calculate the perpendicular distance from a point to a plane. We also learn how to find the distance between 2 parallel planes. How to calculate the equation of a plane mid parallel to 2 planes.

This channel is useful for students of grades 11 and 12 studying Mathematics and also students preparing for the NATA eligibility test for architecture.

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## ANGLE BETWEEN 2 LINES

Welcome Paragraph Title

How do you calculate angle between 2 lines in 3 dimensional geometry?

Learn this and much more in this presentation/video. Here, we learn how to calculate angle between 2 lines, equation of a line passing through 2 points and perpendicular to a line and how to find the foot of a perpendicular from a point to a line.

These are useful for grade 12 mathematics students and students appearing for the NATA eligibility test in architecture which has maths as a section

## EQUATION OF A PLANE IN CARTESIAN AND VECTOR FORM

How do you calculate equation of a plane in Cartesian and Vector form?

In this presentation/video, we learn how to calculate equation of a plane given the distance from the origin and a unit vector normal to the plane. We learn how to calculate the Cartesian and Vector form of a plane and convert one form to the other. We learn how to calculate equation of a plane passing through a point and perpendicular to a line whose direction ratios are given. We also learn how to find the point where a line meets a plane.

This is useful for grade 12 math students and students preparing for the NATA eligibility test in architecture.

## APPROXIMATIONS VIDEO

What are approximations?

Here, we use the concept of differential to find the approximate value of a function. We can find the values easily with a calculator as well! If y = f(x), we learn the differential of y, and learn the formulae used to calculate the approximate values of y. This video is application oriented. It focuses on solving problems based on the formula. We also learn about absolute error, approximate error and %error. As a teacher, I have found students getting confused about approximate error and actual value of the function.i have explained the difference in the video. So, watch this video to understand approximations.

This video is useful for Class 12 Maths students , ISC MATHS, CBSE MATHS and other boards.It is also useful for the NATA (maths) aptitude test for architecture

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For further help, you can enrol for my masterclass on Applications of Derivatives which involves derivative as a rate measure, approximations, tangent and normal, increasing and decreasing functions, maxima and minima problems.Students tend to find this topic difficult.

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## DERIVATIVE AS A RATE MEASURE

Welcome to the story of Application of Derivatives.

Here, we learn about derivative as a rate measure and how to calculate the rate of change of the variables in each problem. We touch upon problems in Geometry like a cone and sphere. We deal with real life situations such as flying a kite or moving away from a pillar.

In this series, we also explain topics such as equation of tangent and normal to a curve, maxima , minima problems, increasing and decreasing functions . Watch out for the next video on approximations.

This channel has videos for grade 11, 12, engineering maths, Gre quant and the NATA maths section.

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For further help, you can join my online classes for grade 12 maths.

## Trigonometric functions of sums and differences

In this video we learn how to calculate trigonometric sums and differences of angles We also learn how to convert trigonometric products into sums or differences. The video is application oriented , it is helpful to understand problems based on these formulae.

This is useful for class 11 maths students studying the ICSE, CBSE and other syllabi. This is also useful for the NATA maths section.

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## PROPERTIES OF DETERMINANTS

This video helps us to understand how to solve determinants and simplify them using properties. Board questions have been solved and illustrated. This is useful for class 12 maths students of the ISC and CBSE boards.

This channel has videos for grades 12 and 11 and for the NATA eligibility test for maths. Consider subscribing to this channel.

## SYSTEM OF EQUATIONS

How do you solve a system of 3 equations in 3 unknowns? How do you find the inverse of a matrix?

Learn this and much more by watching this video. Here, we learn how to calculate the inverse of a 2 by 2 and 3 by 3 matrix. We learn about adjoint of a matrix and how it is used to solve a system of equation. We consider the cases of a unique solution, infinitely many solutions or inconsistency of the equations.

This video is useful for grade 12 maths students and students preparing for the NATA eligibility test in architecture.