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www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
BUSINESS MATHEMATICS
AFTERSCHOOOL – DEVELOPING CHANGE MAKERS
CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME –
World’ Most Comprehensive programme in social entrepreneurship & spiritual entrepreneurship
OPEN FOR ALL FREE FOR ALL
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
BUSINESS MATHEMATICS
Dr. T.K. Jain.
AFTERSCHOOOL
Centre for social entrepreneurship
Bikaner
M: 9414430763
www.afterschool.tk
www.afterschoool.tk
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
IN A G.P., THE PRODUCT OF THE FIRST THREE TERMS IS 27/8, WHAT IS THE MIDDLE TERM?
Let us assume that the three terms are : A/r, A, Ar Multiply these, r will get cancelled, we
get A^3 A^3 =27/8 A = 3/2 answer.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
What is the sum of 8 terms in the series .1, .11, .111. . .? Let us multiply all these by 9 We get 1/9[ .9,.99, .999 . . . ] We can write it as: 1/9[(1-1/10), (1-1/100), (1-1/1000) . . . ] We can write the sum as: 1/9 [ 1*8 – (1/10 +1/100, 1/1000…) Sum of GP = A(1- R^n) / 1-R^n 1/9[ 8 – {1/10(1-.1^8)/1-.1}] 1/9 [8 - .1111] =1/9 * 7.88889 =.8765 answer.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
The sum of the first 2 terms of GP is 5/3 and sum to infinity of the series is 3. the ratio is ?
First term = A, second term = AR Sum to infinity = A / (1-r) A+AR = 5/3 or A(1+R) = 5/3 A = 5/[3*(1+r)] A/(1-R) = 3; put the value of A. 5/3(1+r) / (1-R) =3 5/(3+3R) = 3-3R; multiply by (3+3r) to both
sides. 5= 9 -9r^2 R^2 = 4/9 or R = 2/3 or -2/3 answer.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
N. Raju gets a salary of Rs. 1 Lakh per month now with annual increments of Rs. 1000 p.a.. How much money will he get in 20 years? Apply rules of AP. His salary in last month will be: 1lakh +(20-1)1000 =119000. Sum = n/2(first +last) 12 * (20/2(1lakh+119000) =12* 10* 219000 = 26280000 ans.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
If P,Q,R are in AP and X,Y,Z are in GP, what will we get for X^(q-r)* Y^(r-P)*z ^ (p-q)?
Let us assume that P,Q,R are 1,2,3 Let us assume that X,Y,Z are 1,2,4 1^(-1) * 2^(2)*4^(-1) =1*4* ¼ =1 answer. (you may try with any such
number, the answer will always be 1).
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
What is the sum of all numbers between 200 and 300?
This is AP. Formulae : n/2 (first term +last term) =99/2(201+299) =99/2* 500 =99*250 =24750 answer.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
Find GP when 4th term is 8 and 8th term is 128/625?
AR^3 = 8 (formulae = AR ^(n-1)) AR^7 = 128/625 Let us divide second by first. We get R^4 = 128 / (625*8) R^4 = 16/625 R = 2/5 ; AR^3 = 8 or A*8/125 = 8 A =125, IInd term = 125*2/5 = 50, IIIrd =
50*2/5 = 20 . So on. GP is 125,50, 20, 8,16/5 . . . Answer.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
How many terms should we add from series 1,2,4,8. . . So that we have 8191?
Sum of GP = A(R^n-1) / (r-1) =1(2^n – 1) / (2-1)= 8191 =2^n-1 = 8191 2^n =8192 N=13 answer.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
What is the sum of all rational numbers between 500 and 1000,which are divisible by 13?
The first number divisible by 13 in this series is 507 (13*39) and the last number divisible by 13 is 988 (13*76)
Sum = n/2 (first term+last term) N = Number of terms (76 – 39 +1)=38 =38/2(507+988) =19 * 1495 =28405
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
ABOUT AFTERSCHOOOL Afterschoool conducts three year integrated PGPSE (after
class 12th along with IAS / CA / CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
Why such a programme?
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 AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
Who are our supporters?
Afterschoolians, 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 AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
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 AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
Workshops from AFTERSCHOOOL IIF, Delhi CIPS, Jaipur ICSI Hyderabad Branch Gyan Vihar, Jaipur Apex Institute of Management, Jaipur Aravali Institute of Management, Jodhpur Xavier Institute of Management,
Bhubaneshwar Pacific Institute, Udaipur Engineering College, Hyderabad
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
Flexible Specialisations: 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 AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
Salient features: 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 AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
Components 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)
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
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 AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
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.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
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.
www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
Basic values at afterschoool 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 AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS
www.afterschoool.tk social entrepreneurship for better society