Tutorials

In work life and personal life often we need to learn the basics on a subject. Base concepts on any subject form the foundation, but it is not easy to build it. Our focus here is on base concepts that can be used as a launch pad for further learning and subject specific problem solving.

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Basic maths: Basic concepts on maths. Other subjects will be added in due course.

Basic and Rich Geometry Concepts Part 7, Laws of sines and cosines

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What if we need to relate the sides of a triangle with the angles? Except Pythagoras theorem there is little help in the area of establishing a relationship between the sides and the angles of a triangle. The laws of sines and the laws of cosines meet this important gap...

Basic and rich Trigonometry concepts part 2, proof of compound angle functions

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Trigonometry first established relationships between the angle and side measurements of a right angled triangle by defining trigonometric functions and thus extended the reach of mathematics wonderfully. Like any other branch of mathematics, from the basic trigonometric function definitions more advanced function relations are built stage by stage. Here we will deal with compound angle trigonometric function relations in more details...

Basic and Rich Geometry Concepts Part 5, Proof of Median relations

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Medians form one of the most important set of components in a triangle closely tied to the triangle independent of any other geometric shape. In this discussion we will explain what are medians and their relations with the sides of the triangle along with the proofs...

Basic and Rich Geometry Concepts part 4, Proof of arc angle subtending concept

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To explain the Arc angle subtending concept exhaustively and comprehensively, we will use four different configurations and the corresponding mechanisms along with solving a specially selected problem. To be exhaustive, we needed to follow a systematic method...

Basic concepts on problems on speed time distance, train running and boats in rivers

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Traveling at same speed we would need twice the time we took last time, if we have to cover twice the distance we traveled last time. This follows from our common sense. The relationship between speed, time and distance is one of the most basic physical laws that affects our real life experiences extensively. Trains run from station to station at various speeds; boats ply in the river but their actual speeds are reduced by the river stream speed if the boat moves upstream...the applications of the relationship between speed time and distance form an important part of Arithmetic...

How to solve Arithmetic problems on Work-Time, Work-Wage and Pipes-Cisterns

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Different persons or types of persons complete the same work in different number of days as their work capacities are different. For example, a boy may complete a work in 6 days while a man may complete the same work in 3 days. In work-wage problems these work rates become important as the working agents receive wages in ratio of their work capacities. Finally, in pipes and cisterns problems similar working agents come into action in the form of pipes but they receive no wages...

Arithmetic problems on mixing liquids and based on ages

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When two materials are mixed together in a certain ratio homogeneously, a mixture is formed. Various operations on such a mixture give rise to the topic of Mixture. Usually liquids that can be mixed are used in mixtures. Examples are, Water and milk, Water and fruit juice. Alloys are also formed by mixing metals through specific processes. Grains of same cereal of different price can be mixed giving rise to a grain mixture of another price...

Ratio and proportion

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A ratio defines how many times is one quantity with respect to another of same type. It is expressed as a minimized fraction and its numerator is called antecedent and denominator consequent. In practice these terms are not very important...

Basic and rich Trigonometry concepts and its applications

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Trigonometry first established relationships between the angle and side measurements of a right angled triangle by defining trigonometric functions and thus extended the reach of mathematics wonderfully. At first look we may not find much application of trigonometry in real world, but one must consider, the modern civilization is based on the sinusoidal frequencies that are nothing but trigonometric functions...

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