8 July Mathematics Ii

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

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

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

Simple test of the situation when both the roots are equal?  B^2

= 4ac

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

When will we have two real, rational and unequal roots?  B^2

– 4ac is a perfect square

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

When do we have imaginary roots?  B^2

– 4ac is a negative number

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

When do we have two irrational roots?  B^2

– 4AC is positive but not a perfect square.

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Which are irrational numbers ?  Where

is the value is not available in definite measurement.  Example: 2^1/2, 3^1/3, pi etc.

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Of the two numbers, 1/5th of the greater is equal to 1/3rd of the smaller and their sum is 16. what are the numbers?  Options:  6,

10  9,7  12,4  11,5  (first option gives you right answer) – solve by observation only. www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Wages of 8 men and 6 boys amount to Rs. 33. if 4 men earn Rs. 4.5 more than 5 boys, determine the wages of each man and boy?  Options:

1.5, 3, b. 3 &1.5 c. 2.5 &2 d.

2&2.5  Try from option b. – you get the answer.  Alternatively, let us assume wages of man = x, and that of boys = y.  4x-5y = 4.5; 8x +6y = 33 (multiply the first equation by 2 and divide it from II).  16Y = 24 ; Y = 1.5 and X = 3 ans. www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

The sum of the digits in a 3 digit number is 12. if the digits are reversed the number is increased by 495. reversing only ten’s and unit digits increases the number by 36. What is the number?  Option:

327, 372, 237, 273  Let us try with first and III options.  72-27 = 45 and 73-37 = 36. thus 237 is the right answer. www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Demand and supply equations for a certain commodity are 4a +7b =17 & b =a/3 +7/4. where A is quantity and B is market price. Equilibrium price and quantity will be ? 

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Taking LCM of 3 &4, we get: b = 4a+21 / 12 or 12B -4A = 21. subtracting it from 1st equation : 4a and 4a gets cancelled. Let us add 7b +12 B = 19 B. let us add 17 +21 = 38. we get: 19B = 38 or B = 2 Putting this value in first equation : 4A +14 = 17 A = ¾. Answer.

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

The age of a person is twice the sum of the ages of his 2 sons. 5 years ago his age was thrice the sum of their ages. What will be the age of person after 5 years?    

Let us assume age of person is X and sum of 2 sons age is Y. X = 2Y. Or X-2Y =0 X-5 = 3 (Y-10) (because 2 sons = 2*5 =10) = X -3Y = -25 (subtract 1st equation) Y = 25 and X =50. Thus age of the person will be 55 after 5 years. Ans.

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

A number consisting of 2 digits is 4 times the sum of its digits and if 27 be added to it, the digits are reversed. The numbers are ?  Options:

63, 35, 36, 60  Solve by observation – 36 is the answer.

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

What is the value of 4+ 1/ 4+ / 4+ …. To infinity ?  Let

us assume that the number is X.  4 + 1/x  X is infinite series, the value of which will be close to 4.2.  Thus 4 + ¼.2 = 4.2 approx. answer.

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

There are equal roots of the equation 2x^2 +8x – m^3 = 0. what is m?  B^2

= 4ac (condition for equal roots). B = 8 A = 2  C = - m^3  64 = - 4*2*m^3  M^3 = - 8  M = - 2 answer. www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

If 2^(2x+3) -3^2*2^x +1 = 0, what is X?       

Options: a. 0,1, b. 1,2 c, 0,3 d 0, -3. Let us try from option: let us assume =2 2^7 -9*2^2 +1 =0; 128 -9*4 +1 = 0 ( in correct). Let us try with 1. ; 2^5 -9*2 +1 = 0 (in correct). Let us try with Zero; 2^3 – 9*1 +1 (true). Let us try with 3:; 2^9 – 9*8 +1 (in correct) Thus option D is correct answer.

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

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