1 July Mathematics Proportion & Indices
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Mathematics Dr. T.K. Jain. AFTERSCHOOOL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschoool.tk www.afterschool.tk
Which number should be subtracted from 19:31 so that the new ratio is 1:4? Options: 5,15,1,none • • • •
Try from options: 19-15 = 4 31-15 = 16 These are in 1:4 ratio.
www.afterschoool.tk
Ratio of 2 numbers is 7:10. their difference is 105. What are the numbers? • Let us assume the numbers to be 7x & 10x. • By question: 10x-7x = 105 • 3x = 105 • X = 35. • The two numbers are : 7*35 = 245 • 10*35 = 350 answer. www.afterschoool.tk
Anand earns Rs. 80 in 7 hours. Pramila earns Rs. 90 in 12 hours. Ratio of their earnings / efficiency? • Let us take common hours for them. Let us take LCM of 7 & 12= 84 • Let us identify their earnings in 84 hours. • A =80*12= 960, P = 90*7 = 630 • Ratio is 96:63 = 32:21 ans.
www.afterschoool.tk
Two ratio are in ratio 2:3. if 4 is subtracted from them, the ratio becomes 3:5. What are the numbers? • Let us assume that the numbers are 2x & 3x. • Thus 2x-4 / 3x-4 = 3/5 • Solving this : 10x -20 = 9x-12 • X = 8; now multiply 8 to 2 &3 to get numbers. www.afterschoool.tk • Thus numbers are 16 and 24.
Compound ratio of 2:3, 9:4, 5:6 and 8:10 is ? • 2/3 * 9/4 * 5/6 * 8/10 = 1:1 answer.
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What is sub-duplicate ratio of 25:36? • Take square roots of 25 & 36. • Answer : 5:6 .
www.afterschoool.tk
What is sub-triplicate ratio of 8:27? • Take cubic roots of 8 & 27. • 2/3 answer.
www.afterschoool.tk
What will get from the following: 2^5 / 2^3 ? • (deduct 3 from 5). • 2^2 answer.
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2^10 * 2^12? • Add the powers. • 2^22 answer.
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Value of 8/27 ^1/3? • 1/3 means cubic root – take one of three similar factors. • For example: 8 = 2*2*2 , so its cubic root is 2. • 27 =3*3*3 so its cubic root is 3 . • Thus answer is 2/3. www.afterschoool.tk
What is value of 2(256)^-1/8? • In order to solve negative power, we will shift the number as denominator. • The answer is : 2/ 256^1/8 • We know that 256 = 2*2*2*2*2*2*2*2 • Thus 256^1/8 = 2 • Thus answer is 2/2 or 1 ans.
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2x=3y =6z what is value of 1/x +1/y+ 1/z? • Let us take LCM of 2,3, 6 = Lcm IS 6 • Let us assume that all these numbers are equal to LCM (6) • 2X = 6 ; X=3. 3Y =6, Y = 2; Z =1 • Now put the values in X, Y, Z. • 1/3 + ½ +1 =11/6 answer.
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Change log 5 31 into common log base. • Common log base is 10 answer, Natural log base is E. since this is a simple log, we shall take common lag base. • We can write is as: • Numerator is = log 10 31 • Denominator = log 10 5
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Find log of 1728 to the base 2*3^1/2 • • • • • •
Let us find factors of 1728 first. 2*2*2*2*2*2*3*3*3 = 1728 3 has two factors as 3^1/2 Because 3^1/2 * 3^1/2 = 3 Thus 1728 has 6 such factors. So answer is 6. • We can write it as Log 2*3^1/2 1728= 6 www.afterschoool.tk
Find log of 1000 to the base 10? • 10*10*10 = 1000 therefore 3 is the answer. • Thus we can write it as: • Log 10 1000 = 3 answer.
www.afterschoool.tk
What is log 2 64? • Let us take factorisation of 64: • 2*2*2*2*2*2 = 64 • Thus answer is 6. • log 2 64 = 6
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log 2 64 * Log 64 2 ? • Answers of all such questions is 1.
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log 2 64 + log 2 64 + log 2 64 +log 2 64 + log 2 64+ log 2 64+ log 2 64 ? • We can write it as : • log 2 64^7 • We can write it as 7* log 2 64 • log 2 64 = 6 • Thus answer is 7*6 = 42 answer.
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What is : log 2000000000000000 1 • Answer is Zero. • Zero as power gives only one answer = 1.(what ever may be the number).
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log 200000 200000 ? • Answer is 1. Power 1 only can give the same number.
www.afterschoool.tk
log 8 25 • Let us solve it as: = 2log 8 5 = 2 * log 2 5 / log 2 8 =2*( 2.32/3) =2*.77 =1.54 approx. answer.
www.afterschoool.tk
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
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
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
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
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
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
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
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
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.
www.afterschoool.tk
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
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
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
Which number should be subtracted from 19:31 so that the new ratio is 1:4? Options: 5,15,1,none • • • •
Try from options: 19-15 = 4 31-15 = 16 These are in 1:4 ratio.
www.afterschoool.tk
Ratio of 2 numbers is 7:10. their difference is 105. What are the numbers? • Let us assume the numbers to be 7x & 10x. • By question: 10x-7x = 105 • 3x = 105 • X = 35. • The two numbers are : 7*35 = 245 • 10*35 = 350 answer. www.afterschoool.tk
Anand earns Rs. 80 in 7 hours. Pramila earns Rs. 90 in 12 hours. Ratio of their earnings / efficiency? • Let us take common hours for them. Let us take LCM of 7 & 12= 84 • Let us identify their earnings in 84 hours. • A =80*12= 960, P = 90*7 = 630 • Ratio is 96:63 = 32:21 ans.
www.afterschoool.tk
Two ratio are in ratio 2:3. if 4 is subtracted from them, the ratio becomes 3:5. What are the numbers? • Let us assume that the numbers are 2x & 3x. • Thus 2x-4 / 3x-4 = 3/5 • Solving this : 10x -20 = 9x-12 • X = 8; now multiply 8 to 2 &3 to get numbers. www.afterschoool.tk • Thus numbers are 16 and 24.
Compound ratio of 2:3, 9:4, 5:6 and 8:10 is ? • 2/3 * 9/4 * 5/6 * 8/10 = 1:1 answer.
www.afterschoool.tk
What is sub-duplicate ratio of 25:36? • Take square roots of 25 & 36. • Answer : 5:6 .
www.afterschoool.tk
What is sub-triplicate ratio of 8:27? • Take cubic roots of 8 & 27. • 2/3 answer.
www.afterschoool.tk
What will get from the following: 2^5 / 2^3 ? • (deduct 3 from 5). • 2^2 answer.
www.afterschoool.tk
2^10 * 2^12? • Add the powers. • 2^22 answer.
www.afterschoool.tk
Value of 8/27 ^1/3? • 1/3 means cubic root – take one of three similar factors. • For example: 8 = 2*2*2 , so its cubic root is 2. • 27 =3*3*3 so its cubic root is 3 . • Thus answer is 2/3. www.afterschoool.tk
What is value of 2(256)^-1/8? • In order to solve negative power, we will shift the number as denominator. • The answer is : 2/ 256^1/8 • We know that 256 = 2*2*2*2*2*2*2*2 • Thus 256^1/8 = 2 • Thus answer is 2/2 or 1 ans.
www.afterschoool.tk
2x=3y =6z what is value of 1/x +1/y+ 1/z? • Let us take LCM of 2,3, 6 = Lcm IS 6 • Let us assume that all these numbers are equal to LCM (6) • 2X = 6 ; X=3. 3Y =6, Y = 2; Z =1 • Now put the values in X, Y, Z. • 1/3 + ½ +1 =11/6 answer.
www.afterschoool.tk
Change log 5 31 into common log base. • Common log base is 10 answer, Natural log base is E. since this is a simple log, we shall take common lag base. • We can write is as: • Numerator is = log 10 31 • Denominator = log 10 5
www.afterschoool.tk
Find log of 1728 to the base 2*3^1/2 • • • • • •
Let us find factors of 1728 first. 2*2*2*2*2*2*3*3*3 = 1728 3 has two factors as 3^1/2 Because 3^1/2 * 3^1/2 = 3 Thus 1728 has 6 such factors. So answer is 6. • We can write it as Log 2*3^1/2 1728= 6 www.afterschoool.tk
Find log of 1000 to the base 10? • 10*10*10 = 1000 therefore 3 is the answer. • Thus we can write it as: • Log 10 1000 = 3 answer.
www.afterschoool.tk
What is log 2 64? • Let us take factorisation of 64: • 2*2*2*2*2*2 = 64 • Thus answer is 6. • log 2 64 = 6
www.afterschoool.tk
log 2 64 * Log 64 2 ? • Answers of all such questions is 1.
www.afterschoool.tk
log 2 64 + log 2 64 + log 2 64 +log 2 64 + log 2 64+ log 2 64+ log 2 64 ? • We can write it as : • log 2 64^7 • We can write it as 7* log 2 64 • log 2 64 = 6 • Thus answer is 7*6 = 42 answer.
www.afterschoool.tk
What is : log 2000000000000000 1 • Answer is Zero. • Zero as power gives only one answer = 1.(what ever may be the number).
www.afterschoool.tk
log 200000 200000 ? • Answer is 1. Power 1 only can give the same number.
www.afterschoool.tk
log 8 25 • Let us solve it as: = 2log 8 5 = 2 * log 2 5 / log 2 8 =2*( 2.32/3) =2*.77 =1.54 approx. answer.
www.afterschoool.tk
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
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
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
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
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
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
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
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
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.
www.afterschoool.tk
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
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
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
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