7 July Mathematics

MATHEMATICS

Afterschoool – developing change makers CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME – OPEN FOR ALL FREE FOR ALL

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

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

X/30 = 2/45, WHAT IS X?  LET

US CROSS MULTIPLY IT.  45 X = 60  X = 60/45  X = 1.33 ANSWER.

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FORTH PART OF A NUMBER EXCEEDS THE SIXTH PART BY 6, WHAT ARE THE NUMBERS?  X/4

– X/6 = 6  (6X-4X) /24 = 6  2X = 6*24  X = 3*24  X =72

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PR ODU CT OF 2 NUMBE RS IS 3200 AND QUOTI EN T WH EN THE LAR GER NUMBE R IS DIVI DED B Y T HE S MALLE R IS 2. WH AT A RE NU MB ER S?  LET

US ASSUME THAT NUMBERS ARE X & Y.  XY = 3200; X/Y = 2  X = 2Y Put the value of X in first equation.  2y*y = 3200; 2y^2 = 3200. (divide both by 2). : y^2 = 1600. or Y = 40 X =2y= 80. www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Denominator of a fraction exceeds numerator by 2. if 5 is added to numerator, fraction increases by unity. What is fraction:?      

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Let us assume numerator = x Let us assume denominator = y Y-X = 2; x = Y-2 add 5 to numerator: (X + 5)/Y = x/y +1 (Y-2+5) /y = (Y-2) /Y +1 (Y +3) / Y = Y-2+Y / Y (multiply both sides by Y – denominator Y gets cancelled). Y+3 = 2Y -2; -Y = -5; Y = 5, X = 3 answer.

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A num ber cons ists of 2 digi ts. The di gi t in ten’ s place is 3 tim es the di gi t in unit ’s pl ace. If 54 is subtract ed f rom the number , the di gi ts are reversed. The number i s ?        

Options: 92,93,94,39 (solve by option). Let us assume that digit at unit place is X and digit at ten’s place is Y. Y = 3X. (10Y +X)-54 = (10x+Y) 10Y+X-54=10x+y 9Y-9X =54 or Y-X = 6 (putting Y = 3x) 3X-X =6 or 2x =6, X = 3. Y = 9 The number is 93 anwer.

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

2x+5y = 9 and 3x-y =5, what are x & y?  

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Let us equate X. Multiply first equation by 3 and second equation by 2 (as in the first equation it is 2x and second equation it is 3x). 6x +15y = 27 and 6x -2y = 10 (both X are equal now). 17Y = 17 or Y = 17/17 = 1 Putting the value of Y in first equation. 2X +5 = 9 or 2X = 4 or X = 2 answer. ,

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2 numbers are such that twice the greater number exceeds twice the smaller one by 18 and 1/3rd of the smaller and 1/5th of the greater number are together 21. what are the numbers?      

Let us assume that the numbers are X & Y. X is bigger that Y. 2x-2y = 18 (divide all by 2) or X – Y = 9 or X = Y+9 1/5 x + 1/3 y = 21 (put value of X as Y +9) 1/5 (y+9) + 1/3 Y = 21 3Y+27 +5Y = 21*15 8Y = 315 -27 ; 8Y = 288 or Y = 288/8 = 36 and Y = 27

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What are the roots in x^2 – 5x+6 =0       

X^2 – (sum of roots)X + product of roots = 0 Or X =[-b + - square root of (b^2-4ac) ] / 2a A = 1. B = -5 ; C = 6 so 4ac = 24 and b^2 = 25 [5 + square root of (25-24)] /2 (5+1) /2 = 3 or (5-1) / 2 =2 ROOTS ARE 3 & 2 ANSWERS.

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Sum of 2 numbers is 8 and sum of their squares is 34. what are the numbers?  Options:  7,10,  3,5  2,6  4,4  Solve

by options : answer is option of 3,

5 ans. www.afterschoool.tk

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ABO UT A FTERSCH OOO L 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.

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

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

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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.

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

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

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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

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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

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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

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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 www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS material 

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)

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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

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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.

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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.

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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

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

www.afterschoool.tk social entrepreneurship for better society

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS