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Basic maths

Basic concepts on maths, mostly up to class 10. This is the most important math knowledge used in almost all competitive exams.

How to solve the hardest geometry question 16b in New South Wales HSC Math extension 2 exam 2018 confidently

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The problem we'll take up this time was reported in The Sydney Morning Heraldas the hardest one in the Math Extension 2 exam paper in NSW HSW 2018 test in Australia. It was the question 16b on Geometry involving a large number of pairs of similar triangles.

Students not used to identify the key missing element from a host of elements spread all around and think strategically and systematically would find it difficult...

How to solve the hardest geometry question 16c in New South Wales HSC Math extension 2 exam 2019 confidently

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The challenging problem solved systematically now was reported in The Sydney Morning Herald as the hardest one in the recent Math Extension 2 exam paper in NSW HSW 2019 test in Australia.

The geometry problem and its solution hold rich learning potential...

Algebraic proof of Least value of sum of reciprocals for any number of positive variables

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The result of the least value of sum of reciprocals, used in Algebra represents an important principle of value sharing.

For two positive real variables $a$ and $b$ for example, if $a+b=1$, the least value of sum of reciprocals of $a$ and $b$ will occur when the value of the sum 1 is shared equally between the two variables. This remarkable equal value sharing principle hold true for any number of variables as well as for any positive sum of the variables...

How to solve Clock problems

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In an analog clock the minutes hand moves faster than the hour hand and crosses it 22 times in a day, both going round and round over the clock face. In a typical clock problem, we are asked to find the angle between the two clock hands at a specific time...

How to find perfect and approximate square root of integers or decimals

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For most needs of finding square root, if we remember by heart squares and cubes of a few common integers, using quick factorization we can figure out the square roots or cube roots of numbers be it integer or decimal. But occasionally, in a few specific types of arithmetic problems, there is no other option than to actually evaluate the square root of a number following a method specifically tailored for the purpose...

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