23 June Mathematics I

MATHEMATICS Dr. T.K. Jain. AFTERSCHOOOL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk www.afterschoool.tk

The perimeter / circumference of a circle, triangle, rectangle and square are equal, which has the highest area?  Let

us assume perimenter to be 44.  Circle has area of 154.  Square has area of 121  Rectangle will have area less than 121 – so no need to calculate  Side of equilateral triangle = 44/3 = 14.6  1.732/4 *(14.6*14.6) = 92 approx. www.afterschoool.tk

Reduce 357/609 to lowest terms?  Find

HCF of these 2 numbers.  Divide 609 by 357, remainder is 252, now divide 357 by 252, remainder is 105, now divide 252 by 105, we get 42 as remainder, now divide 105 by 42, we get 21 as the remainder and 21 completely divides 42 – it is HCF.  Divide 357 & 609 both by 21, we get 17/29 answer. www.afterschoool.tk

Find the odd one out: 25,36,49,81,121,169,225  36

is the answer – rest all are squares of odd numbers.

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There are 21 mango, 42 banana and 56 orange trees, they have to be put in such form that each row contains only one type of trees and no. of trees in a row are equal. How many rows will be there?  Find

HCF of 21, 42,56 = 7  Each type of tree will have 21/7, 42/7, 56/7 rows thus total : 3+6+8 = 17 rows. www.afterschoool.tk

Find (100000)^2(99999)^2?  This

is the example of X^2-Y^2 = (X+Y) (X-Y)  X + Y = 199999  X-Y = 1  199999*1 = 199999  Thus answer is 199999 answer.

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One side of a square is increased by 10%, what is change in its area?

 Let

us assume side of square to be 1. now the side becomes 1.1  1.1*1.1 = 1.21  Earlier area was 1*1 = 1  Change in area = .21 (or 21%).

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One side of a cube is increased by 10%, what is change in its volume?

 Let

us assume side of cube to be 1. now the side becomes 1.1  1.1*1.1*1.1 = 1.331  Earlier area was 1*1*1 = 1  Change in area = .331 (or 33%).

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One side of an equilateral triangle is increased by 10%, what is change in its area?  Let

us assume side of equilateral triangle to be 1. now the side becomes 1.1  1.1*1.1 = 1.21 *(1.732/4) =.5239  Earlier area was 1*1 = 1 * (1.732/4)=.433  Change in area = .21 (or 21%).  (.5239-.433 = .09) www.afterschoool.tk

What % of 7.2 KG is 18 grams? =

18 / 7200 *100 = .25 % answer

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Convert 8.333% Into a fraction.  8+

3/9  75/9  Divide it by 100  75/9 *1/100  = 1/12 answer

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I paid 5% tax on my income and deposited 20% income as savings in bank account. Now I have Rs. 19190 with me. What is my gross income?  To

get income after tax, we should add back the money deposited in bank first.  19190 *100/80 = 2397.5  To find gross income, we will add back the tax paid by us: 23987.5*100/95=25250 www.afterschoool.tk

p/q +q/p = 9, what is p^2/q^2 + q^2/p^2?  Let

us assume p/q = X  Let us assume q/p = Y  X+Y = 9; square it: X^2 + 2XY+Y^2 = 81  We know that Y is reverse of X and XY = 1  X^2 + 2+Y^2 = 81  Therefore, X^2+Y^2 = 81-2 = 79 answer. (remember – (x+y)^2 = X^2+Y^2 www.afterschoool.tk

In an examination, 85% students were successful. The number of students who failed was 300. How many students appeared in the examination.  15%

students failed in the examination.  Thus total number of students is :  =100/15 * 300 = 2000 students answers. www.afterschoool.tk

A % of B plus B% of A is equal to?  Let

us assume A = 100, and B = 200.  Thus 200 + 200 = 400, which is B% of B.  Let

us assume A = 100, and B = 50.  Thus 50+50 = 100, which is A% of A  Thus

the number is A / B % of A or B (whichever is higher). www.afterschoool.tk

200 is X % of 6000. what is X?  3.33

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What % of 2.5 is 7.5?  300%

answer

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What is the average of first 5 multiples of 123?  123*3

= 369 answer.

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Volumes of 2 spheres are in ratio of 1:8, what is the ratio of their radius?

 1:2

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Volumes of 2 cubes are in ratio of 1:8, what is the ratio of their sides?

 1:2

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Ratio of age of father & son is 4:1 and product of their age is 196.what will be ratio of their age 5 years hence?  4x*1x

= 196  4x^2=196  X^2= 49  X= 7, the ages are: 28 & 7  After 5 years, their ages will be : 33 & 12.  Thus the ratio will be 33:12 answer. www.afterschoool.tk

4X=7B=2Y=3Z, wha are the ratio of XBYZ?  4,7,2,3

- is it the answer

 Wrong.  Easiest

way is : ¼, 1/7, ½ & 1/3, now take ratio (LCM of 4,7,2,3 and multiply LCM to these numbers and get the ratio).  LCM is 84, multiply these numbers to 84.  21:12:42:28 answer. www.afterschoool.tk

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Why such a programme? 

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 

To promote people to take up entrepreneurship and help develop the society To enable people to take up franchising and other such options to start a business / social development project To enable people to take up social development as their mission To enable people to promote spirituality and positive thinking in the world www.afterschoool.tk

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our past beneficiaries, entrepreneurs and social entrepreneurs are supporting us.  You can also support us – not necessarily by money – but by being promotor of our concept and our ideas. www.afterschoool.tk

About AFTERSCHOOOL PGPSE – the best programme for developing great entrepreneurs       

Most flexible, adaptive but rigorous programme Available in distance learning mode Case study focused- latest cases Industry oriented practical curriculum Designed to make you entrepreneurs – not just an employee Option to take up part time job – so earn while you learn The only absolutely free course on internet www.afterschoool.tk

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Spiritualising business and society Rural development and transformation HRD and Education, Social Development NGO and voluntary work Investment analysis,microfinance and inclusion Retail sector, BPO, KPO Accounting & Information system (with CA / CS /CMA) Hospital management and Health care Hospitality sector and culture and heritage Other sectors of high growth, high technology and social relevance www.afterschoool.tk

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    

The only programme of its kind (in the whole world) No publicity and low profile course For those who want to achieve success in life – not just a degree Indepth knowledge and expertise Professional approac: World class approach Strong intellectual and business capabilities Flexible – you may stay for a month and continue the rest of the education by distance mode. / you may attend weekend classes Scholarships for those from poor economic background Latest and constantly changing curriculum – keeping pace with the time Placement for those who are interested Admissions open throughout the year Latest and most advanced technologies, books and study material www.afterschoool.tk

Components 

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Pedagogy curriculum and approach based on IIM Ahmedabad and ISB Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad) Meditation, spiritualisation, and self development Essential softwares for business Business plan, Research projects Participation in conferences / seminars Workshops on leadership, team building etc. Written submissions of research projects/articles / papers Interview of entrepreneurs, writing biographies of entrepreneurs Editing of journals / newsletters Consultancy / research projects Assignments, communication skill workshops Participation in conferences and seminars Group discussions, mock interviews, self development diaryng Mind Power Training & writing workshop (by Dr. T.K.Jain)

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Pedagogy          

Case analysis, Articles from Harvard Business Review Quiz, seminars, workshops, games, Visits to entrepreneurs and industrial visits Presentations, Latest audio-visuals Group discussions and group projects Periodic self assessment Mentoring and counselling Study exchange programme (with institutions out of India) Rural development / Social welfare projects www.afterschoool.tk

Branches  AFTERSCHOOOL

will shortly open its branches in important cities in India including Delhi, Kota, Mumbai, Gurgaon and other important cities. Afterschooolians will be responsible for managing and developing these branches – and for promoting social entrepreneurs.

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Case Studies  We

want to write case studies on social entrepreneurs, first generation entrepreneurs, ethical entrepreneurs. Please help us in this process. Help us to be in touch with entrepreneurs, so that we may develop entrepreneurs.

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Share to learn more Interact to develop yourself Fear is your worst enemy Make mistakes to learn Study & discuss in a group Criticism is the healthy route to mutual support and help Ask fundamental questions : why, when, how & where? Embrace change – and compete with yourself only www.afterschoool.tk

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