Basic concepts on maths, mostly up to class 10. This is the most important math knowledge used in almost all competitive exams.
To solve hard math, instead of thinking conventionally and mechanically, use your problem solving skills, inventive thinking and basic math concepts.
Simple interest for a year is the percentage rate of interest applied on the initial amount invested and it is fixed year to year. On the other hand, Compound interest is the percentage rate of interest applied on the amount available at the beginning of the year, and not at the beginning of the investment period...
Law of sines and cosines relate side with sine and cosine of an angle opposite the side in triangle. By sine law, ratios of side to sine of angle are equal.
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.
