Basic concepts on a subject form the foundation. Basics are for building the foundational concepts in concise but comprehensive manner.
In work life and personal life often we need to learn the basics on a subject quickly. Usually it is not easy to acquire the basic concepts on any subject reliably in a short time from a concise material.
Basic concepts on any subject form the foundation, but generally we have found it is not easy to build it in a short time. Our focus here is on base concepts in a concise form that can be learned quickly and be used as a launch pad for further learning and subject specific problem solving.
Often we added a rich concept layer derived from the base concepts that helps to solve more complex problems with great ease. For us, it is a two layer concept model: Base concepts and Rich concepts derived from base concepts. Objective is efficient problem solving.
Basic maths: Basic concepts on maths. The content is primarily targeted for competitive test requirements.
Reasoning and logic analysis: Tutorials, problems and puzzles on competitive test reasoning and logic analysis.
Centroid divides triangle area into 3 equal parts formed by the longer median segments at centroid and 6 equal parts by all six median segments at centroid.
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...
Relation between median and sides of triangle: Sum of two sides is larger than the median from common vertex and three times sum of squares of length of sides equals four times the squares of medians of a triangle.
Arcs and subtended angles: Any arc in a circle will subtend an angle at the centre twice the angle it subtends at any point on its complementary arc.
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...
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...
Basic concept foundation on ratios is needed for quick solution of problems on mixing liquids and ages, the two major application areas of ratios concept.
Ratio proportion concepts play a very important role in solving questions on mixture and alligation, percentage, ages, numbers systems and so on.
Trigonometry concepts: Trigonometry functions, function values, identities, compound angle, multiple angle functions, laws of sine and applications.
Circle basic concepts: Chords, arcs, tangents, cyclic quadrilateral, angle subtended by a chord and secant of a circle with examples and exercise.
