|Derived Concepts or Derived Formulae:|
The GRE, GMAT and SAT Quant sections require you to know the basic concepts and formulas of Maths. For example, in geometry you need to know the formulae of area of a triangle, area of an equilateral triangle etc. But more importantly the test has questions on derived concepts.
For example, consider this example: what is the maximum area of a triangle with two sides equal to 8 and 6? This is a concept which I would call a derived concept.
The basic formula for area of a triangle is ½ * base * height. However we do not know if 8 and 6 are the base and height of the above triangle. When we think deeper we realize that the question asks for maximum area. The area will be maximum when the two sides are perpendicular to each other, since the height will be maximum.
Thus we get the derived concept – the maximum area of a triangle with two sides is obtained when the two sides are perpendicular to each other and is given by ½*product of the two sides. There are many such derived concepts or formulae which you are tested on.
Another example is of successive percentage change. When a quantity changes by x % followed by y % then the overall percentage change is given by x+ y + xy/100. This is another very common derived formula on the test. Thus when you are preparing for the test you have to know the basic formula for sure, but more importantly you need to know and master the derived concepts and formulae.
It is a very good idea to collect all such derived concepts and put them all together on mind-maps. Such mind maps will help you understand and revise the formulae very quickly. You will find these mind maps at our centres.
Also it is a very good idea to understand how formulae are derived. For example we all would know how to calculate the LCM of 12 and 20. But it is more important to understand what an LCM is and how the formula is derived as they will test you on the understanding of the concepts and formulae rather than a direct application of any formula.
Hope these tips help. For more information or to see our mind maps please visit our centres.