This document provides an overview of mathematics topics covered on the learning point website. It includes summaries of concepts in algebra, trigonometry, calculus, coordinate geometry, vectors, linear algebra and probability. Quizzes and solved problems are provided for each topic. The website also covers computer science, physics, chemistry and English grammar topics.

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Contents
1 Mathematics
2 Fourier Series and the Discrete
Fourier Transform
3 Mathematics & Computing - A
few programs in C
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ISC 2014 Percentage to Percentile
ICSE/ISC-2014 Schools-wise Results
Popular articles
Exposing CBSE/ICSE Marking
Scams(2013)
Exposing CBSE/ICSE: A follow-up
(2015)
CBSE Score manipulation over a
decade
Mathematics
Quizzes on Progressions
MCQ #1: Arithmetic Progression
MCQ #2: Geometric Progression
MCQ #3 : More on Geometric
Progressions.
MCQ #4 : Harmonic Progressions.
MCQ #5: More on Harmonic
Progression
MCQ #6: Mixed Progressions
Coordinate Geometry - Straight Lines
MCQ #1: Cartesian Planes, Straight
Line Basics
MCQ #2 on Straight Lines
MCQ #3 on Straight Lines
MCQ #4 on Straight Lines
Circles
1 MCQ #1 on Circles.
2 MCQ #2 on Circles.
3 MCQ #3 on Circles.
Conic Sections- Parabola, Hyperbola,
Ellipse
1 MCQ- The Basics of Conic Sections
2 MCQ on Parabola..
3 MCQ on Hyperbola
4 MCQ on Ellipses.
Probability
MCQ #1 on Basic Probability
MCQ #2: More Challenging Problems
on Probability
MCQ #3- Conditional Probability and
Bayes Theorem
Complex Numbers
MCQ #1
MCQ #2: More on Complex Numbers
Mathematics
Factors
Factorial
Fibonacci Numbers
Rhombus
Prime Numbers
Squares
Lucas Numbers
Padovan Numbers
Triangular Numbers
Pentagonal Numbers
Hexagonal Numbers
Stern Diatomic Numbers
Lazy Carter Numbers
Geometry: Congruent Triangles
Geometry: Similar Triangles
Geometry: Pythagorean Theorem, Pythagorean
Triplets and Applications
Mensuration for Squares
Mensuration for Rectangle
Mensuration for a Rhombus
Mensuration of a Cube
Mensuration of a Sphere
Mensuration of a Cone: Volume, Total Surface
Area and Frustums
Mensuration of a Cylinder: Volume, Total
Surface Area, Hollow Cylinders
Mensuration of a Rectangular Prism (Cuboid):
Volume, Total Surface Area, Hollow
Rectangular Prisms/Cuboids
Co-Ordinate Geometry: The Distance Formula.
Distance between Two Points
Co-Ordinate Geometry: The Midpoint Formula
Co-ordinate Geometry: Basic Reflection of
Points in X, Y Axis and the line y=x
Evaluating Expressions Part 1
Evaluating Expressions Part 2

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Quadratic Equations
MCQ Quadratic Equations
Quadratic In-equations
MCQ Quadratic In-equations
Computer Science
Quizzes on Basic Object Oriented
Programming with C++
1 MCQ #1: C++ and OOPS
2 MCQ #2: Inheritance in C++
Quizzes on C Programming- Arrays,
Strings and Pointers
1 C Programming MCQ #1: Strings- 1
2 C Programming MCQ #2: Strings (2)
3 C Programming MCQ #3: Strings (3)
4 C Programming MCQ #4: Arrays(1)
5 C Programming MCQ #5: Arrays (2)
6 C Programming MCQ #6: Arrays (3)
7 C Programming MCQ #7: Pointers
(1)
8 C Programming MCQ #8: Pointers
(2)
Quizzes on Java Programming
1 Java MCQ #1- Classes, Inheritances
and Interfaces
2 Java MCQ #2- Collections
3 Java MCQ #3- Threading
Quizzes on Data Structures,
Algorithms and Complexity
1 MCQ #1: The Basics of Sorting
Algorithms- Quadratic Sorts
2 MCQ #2: Efficient Sorting
Algorithms- Quick sort, Merge Sort,
Heap Sort
3 MCQ #3- The Radix Sort
4 MCQ #4: Divide and Conquer
5 MCQ #5- Dynamic Programming
6 MCQ #6- Complexity of Algorithms
7 MCQ #7- Application of Master's
Theorem
8 MCQ #8: Binary Search Trees
9 MCQ #9: B-Trees
10 MCQ #9: AVL-Trees
11 MCQ #10: Representing Graphs as
Data Structures
12 MCQ #11: Spanning Trees
Set Theory 1: Examples of Cardinal Number,
Union and Intersection of Sets
Set Theory 2: Difference and Symmetric
Difference of Two Sets
Set Theory 3: Cartesian Product of Two Sets
Triangles: The Triangular Inequality
Mensuration of a Circle: Area and
Circumference
Polygons
Factorizing Quadratic Expressions By Splitting
the Middle Terms
Regular Pentagons: Area, Perimeter, Interior
and Exterior Angles, Inradius,Circumradius
Regular Hexagons: Area, Perimeter, Interior and
Exterior Angles, Inradius,Circumradius
Regular Heptagons: Area, Perimeter, Interior
and Exterior Angles, Inradius,Circumradius
Regular Octagons: Area, Perimeter, Interior and
Exterior Angles, Inradius,Circumradius
Regular Nonagons: Area, Perimeter, Interior and
Exterior Angles, Inradius Circumradius
Regular Decagons: Area, Perimeter, interior and
Exterior Angles, inradius, Circumradius
Regular Hendecagons: Area, Perimeter, Interior
and Exterior Angles Inradius Circumradius
Regular Dodecagons: Area, Perimeter, Interior
and Exterior Angles, Inradius, Circumradius
Regular Tridecagons: Area, Perimeter, interior
and Exterior Angles inradius Circumradius
Regular Tetradecagons: Area, Perimeter, Interior
and Exterior Angles, Inradius, Circumradius
Regular Pentadecagons: Area Perimeter interior
and Exterior Angles Inradius circumradius
Regular Hexadecagons: Area Perimeter interior
and Exterior Angles Inradius circumradius
Regular Heptadecagons: Area Perimeter interior
and Exterior angles Inradius circumradius
Regular Octadecagons: Area Perimeter interior
and Exterior angles Inradius Circumradius
Regular Nondecagons: Area Perimeter interior-
and-exterior-angles-inradius Circumradius
Regular Isocagons: Area Perimeter interior and
exterior angles inradius circumradius

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13 MCQ #12: Algorithms - Graphs:
Spanning Trees - Kruskal and Prim
Algorithms
14 MCQ #13: Algorithms - Graphs:
Depth and Breadth First Search
Basic English Grammar
English Online: Articles (Quiz #1)
English Online: Articles (Quiz #2)
English Online: Articles (Quiz #3)
English Grammar- The Tenses: Quiz
#1
English Grammar- The Tenses: Quiz
#2
English Grammar- The Tenses: Quiz
#3
English Grammar- The Tenses: Quiz
#4
English Grammar- The Tenses: Quiz
#5
English Grammar: The Parts of
Speech (Quiz #1)
English Grammar: The Parts of
Speech (Quiz #2)
English Grammar: The Parts of
Speech (Quiz #3)
English Grammar: The Parts of
Speech (Quiz #4)
English Grammar: The Parts of
Speech (Quiz #5)
English Grammar: The Parts of
Speech (Quiz #6)
English Grammar: The Parts of
Speech (Quiz #7)
English Grammar: The Parts of
Speech (Quiz #8)
English Grammar: The Parts of
Speech (Quiz #9)
English Grammar: The Parts of
Speech (Quiz #10)
Examination Results 2016
Algebra
Introduction to
Complex Numbers
The Principle of
Mathematical
Induction
Quadratic
Equations
Quadratic
Inequalities
Series and
Progressions
Permutations and
Combinations
The Binomial
Theorem
Euclidean And Analytical Geometry
Geometry
The Equation of
Straight Line
The Circle
A Quick
Introduction to
Conic Sections:
Parabola,
Hyperbola, Ellipse
Parabola
Hyperbola
Ellipse

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Probability
Probability: Introduction, examples, MC
Conditional, Compound Probability; Ra
Baye's Theorem
Probability: Part 1 - Some Definitions w
Set- Continuous and Discrete Random
Inequality
Probability: Part 2 - Distributions- Disc
with examples-
Bernouilli/Binomial/Geometric/Uniform
etc.
Probability - Part 3 - Joint Probability,
Distributions, Functions of Random Var
of Random Vectors - with examples, pr
Linear Algebra
Introduction to Matrices - Part
I Introduction to Matrices.
Theory, definitions. What a
Matrix is, order of a matrix,
equality of matrices, different
kind of matrices: row matrix,
column matrix, square matrix,
diagonal, identity and
triangular matrices. Definitions
of Trace, Minor, Cofactors,
Adjoint, Inverse, Transpose of a
matrix. Addition, subtraction,
scalar multiplication,
multiplication of matrices.
Defining special types of
Introduction to Matrices - Part
II Problems and solved
examples based on the sub-
topics mentioned above. Some
of the problems in this part
demonstrate finding the rank,
inverse or characteristic
equations of matrices.
Representing real life problems
in matrix form.

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matrices like Symmetric, Skew
Symmetric, Idempotent,
Involuntary, Nil-potent,
Singular, Non-Singular, Unitary
matrices.
Basic concepts in Linear
Algebra and Vector spaces
Theory and definitions. Closure,
commutative, associative,
distributive laws. Defining
Vector space, subspaces, linear
dependence, dimension and
bias. A few introductory
problems proving certain sets to
be vector spaces.
Introductory problems related
to Vector Spaces - Problems
demonstrating the concepts
introduced in the previous
tutorial. Checking or proving
something to be a sub-space,
demonstrating that something
is not a sub-space of something
else, verifying linear
independence; problems
relating to dimension and basis;
inverting matrices and echelon
matrices.
Definitions of Rank, Eigen
Values, Eigen Vectors, Cayley
Hamilton Theorem
Eigenvalues, eigenvectors,
Cayley Hamilton Theorem
More Problems related to
Simultaneous Equations;
problems related to eigenvalues
and eigenvectors
Demonstrating the Crammer
rule, using eigenvalue methods
to solve vector space problems,
verifying Cayley Hamilton
Theorem, advanced problems
related to systems of equations.
Solving a system of differential
equations .

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Vectors
Vectors 1a ( Theory and
Definitions: Introduction to
Vectors; Vector, Scalar and
Triple Products)
Introducing a vector, position
vectors, direction cosines,
different types of vectors,
addition and subtraction of
vectors. Vector and Scalar
products. Scalar Triple product
and Vector triple product and
their properties. Components
and projections of vectors.
Vectors 1b ( Solved Problem
Sets: Introduction to Vectors;
Vector, Scalar and Triple
Products )
Solved examples and problem
sets based on the above
concepts.
Vectors 3a ( Theory and
Definitions: Vector Differential
and Integral Calculus ) Vector
Differential Calculus . Derivative,
curves, tangential vectors,
vector functions, gradient,
directional derivative,
divergence and curl of a vector
function; important formulas
related to div, curl and grad.
Vector Integral Calculus. Line
integral, independence of path,
Green's theorem, divergence
theorem of Gauss, green's
formulas, Stoke's theorems.
Vectors 3b ( Solved Problem
Sets: Vector Differential and
Integral Calculus ) - Solved
examples and problem sets
based on the above concepts.

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0
Trigonometry
Trigonometry 1a ( Introduction to Trigonometry -
Definitions, Formulas ) Introducing trigonometric
ratios, plots of trigonometric functions, compound
angle formulas. Domains and ranges of
trigonometric functions, monotonicity of
trigonometric functions quadrant wise. Formulas
for double and triple angle ratios.
Trigonometry 1b ( T
based on Trigonome
the concepts introdu
Trigonometry 3a ( Introducing Inverse
Trigonometric Ratios)
Inverse trigonometric ratios - their domains, ranges
and plots.
Trigonometry 3b ( T
related to inverse tr
related to inverse tr
Single Variable Calculus

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Quick and introductory
definitions related to Funtions,
Limits and Continuity - Defining
the domain and range of a
function, the meaning of
continuity, limits, left and right
hand limits, properties of limits
and the "lim" operator; some
common limits; defining the
L'Hospital rule, intermediate
and extreme value theorems.
Functions, Limits and Continuity - Solve
Set I - The Domain, Range, Plots and G
Functions; L'Hospital's Rule
demonstrating how to compute the dom
range of functions, drawing the graphs
the mod function, deciding
or not; calculating limits for some
examples, solving 0/0 forms, applying L
rule.
Introductory concepts and
definitions related to
Differentiation - Basic
formulas, Successive
Differentiation, Leibnitz,
Rolle and Lagrange
Theorems, Maxima ,
Minima, Convexity,
Concavity, etc - Theory
and definitions
introducing
differentiability, basic
differentiation formulas
of common algebraic and
trigonometric functions ,
successive differentiation,
Leibnitz Theorem, Rolle's
Differential Calculus - Solved Pr
I - Common Exponential, Log ,
trigonometric and polynomial fu
- Examples and solved problem
differentiation of common algeb
exponential, logarithmic, trigono
and polynomial functions and te
problems related to differentiab

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Theorem, Lagrange's
Mean Value Theorem,
Increasing and decreasing
functions, Maxima and
Minima; Concavity,
convexity and inflexion,
implicit differentiation.
Differential Calculus -
Solved Problems Set IV -
Points of Inflexion, Radius
of Curvature, Curve
Sketching -
Examples and solved
problems - Slope of
tangents to a curve,
points of inflexion,
convexity and concavity of
curves, radius of
curvature and asymptotes
of curves, sketching
curves
Differential Calculus - Solved Pr
V - Curve Sketching, Parametric
Curves - More examples of inve
and sketching curves, parametri
representation of curves
Integral Calculus - Solved
Problems Set II - More
integrals, functions
involving trigonometric
and inverse trigonometric
ratios - Examples and
Integral Calculus - Solved Probl
- Reduction Formulas, Using Par
FractionsI- Examples and solved
- Reduction formulas, reducing
integrand to partial fractions, m
definite integrals

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solved problems -
integration by
substitution, definite
integrals, integration
involving trigonometric
and inverse trigonometric
ratios.
Introduction to
Differential Equations and
Solved Problems - Set I -
Order and Degree, Linear
and Non-Linear
Differential Equations,
Homogeneous Equations,
Integrating Factor -
Theory and definitions.
What a differential
equation is; ordinary and
partial differential
equations; order and
degree of a differential
equation; linear and non
linear differential
equations; General,
particular and singular
solutions; Initial and
boundary value problems;
Linear independence and
dependence;
Homogeneous equations;
First order differential
equations; Characteristic
and auxiliary equations.
Introductory problems
demonstrating these
Differential Equations - Solved P
Set II - D operator, auxillary equ
General Solution - Examples
problems - Solving linear differe
equations, the D operator, auxili
equations. Finding the general s
+ PI )

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concepts. Introducing the
concept of Integrating
Factor (IF).
Multiple Variable Calculus
Calculus -
Multiple
Variables -
Part I-
Functions of
severable
variables;
limits and
continuity
Calculus -
Multiple
Variables -
Part 2-
Functions of
several
variables,
theorems
and co-
ordinates
Calculus -
Multiple
Variables -
Part 3-
Multiple
Integrals;
double and
triple
integrals
Applied Mathematics : An Introduction to Game
Theory
An Introduction to Game
Theory
Extensive Games
Applied Mathematics : An Introduction to
Operations Research

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Introduction to Operations
Research
A quick introduction to Operations
Research. Introducing Linear
Programming, standard and
canonical forms. Linear
Programming geometry, feasible
regions, feasible solutions,
simplex method. Some basic
problems.
Fourier Series and the Discrete Fourier
Transform
The Fourier Series
Discrete Fourier Transform
Mathematics & Computing - A few
programs in C
Basic Number Theory
C Program: Source code to solve the Josephus Pro
C Program: Using the Sieve of Eratosthenes to prin
C Program: Check for Armstrong Numbers
C Program: Source Code for computing the GCD(HF
Linear Algebra and Matrices
C Program: Computing the Upper Triangular Matri
C Program: Demonstrating Operations on Matrices
C Program: Solving Simultaneous Equations in Two
C Program: Source Code for Solving Quadratic Equa

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Popular Examples from Numerical Computing
C Program: Numerical Computing - The Gaussian El
C Program: Numerical Computing - Implementing th
C Program: Numerical Computing - the Bisection Me
C Program: Numerical Computing - The Gaussian El
C Program: Numerical Computing - the Jacobi Meth
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