17 June Maths
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MATHS Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk
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FIND THE SUM OF FIRST 20 TERMS OF THE SERIES – 5,11,17,23 .. ? • • • • • • •
This is Arithmetic Progression. A = 5, D = 6 N = 20 Formulae for sum = N/2 (2a + (n-1)*d) 20/2 (2*5 + (20 – 1)*6) =10 (10 + 19*6) =10(124) 1240 ans. www.afterschoool.tk
What is the 1st term of the Geometric Series, whose 4th and 9th terms are 1/3 & 81 respectively? • In a geometric series, the series is like this: a, ar, ar^(n-1) .. So on. • 4th item in the series is 1/3 • Thus (1) ar^3 = 1/3 and (2)ar ^8 = 81 • Divide (2) by (1) and we get r^5 = 81/1/3; or R^5 = 81*3 thus r = 3 • We know that r^3 = 27. ;; ar^3 = 1/3 • A = 1/3*1/27 thus A = 1/81 ans. www.afterschoool.tk
In an AP, we a sum of X terms. The sum is 190. the 2nd term is 5 and 4th term is 13. What is X? • In Arithmetic Progression, we have fixed difference = D. the series is like a, a+d, a+2d, a+3d ….. So on. • We have a+d = 5; a+3d =13 (solving these 2 equations, we get = 2d = 8) • D = 4, A = 1. • N/2 (2*1 + (n-1)4) = 190 • 2N + 4n^2 -4n = 380 • 4n^2 -2n -380 =0 • 2n^2 –n -190 = 0 • 2n^2 -20n +19n -190 =0 • 2n(n-10) +19(n-10) = 0; n = 10 or -19/2 • Thus N = 10 thus X = 10 ans.
www.afterschoool.tk
8X+3, 6X-3, and 2X+6 are in Arithmetic progression. What can be the value of X?
• In Arithmetic progression, the difference is always same. • Thus (6x-3) – (8X+3) = (2x+6) – (6X3) • -2X -6 = -4X +9 • 2X = 15; X = 7.5 ans.
www.afterschoool.tk
Nthb term of an AP is 2n-8. What is the sum of 20 terms of this series? • In every AP, We require A, D, and N to find the values. • 1st term is 2*1 – 8 = -6 • 2nd term of the series is 4-8 = -4 • 3rd term of the series = 6-8 = -2 and so on. • Sum of 20 term is : • 20/2 (2*-6 + (20-1) 2) • =10 (-12 +19*2) • =10 * 26 • =260 answer
www.afterschoool.tk
What is log
4
4
?
• 1 answer
www.afterschoool.tk
What is log
8
128
?
8 ^x = 128 (2^3)^X = 2^7 (taking 2 as common) 3X = 7 X = 7/3 128 Thus What is log = 7/3 answer . • 8 • • • •
www.afterschoool.tk
What is log
3*2^1/2
5832
?
• Let us take factors of 5832 • =2*2*2*3*3*3*3*3*3 • Thus we can see that there are six 3 and six 2^1/2 thus answer is 6.
www.afterschoool.tk
What is log
-1/3
81
?
• We know that -1/3 ^4 = 1/81. • The power in negative reverses the number, thus we can change power into -4 and we get reverse of 1/81 = 81. • Thus -4 is answer.
www.afterschoool.tk
What is log
10
.1
?
• We know that 10 ^-2 gives us 1/100, which is .01, so we have to take -1 as the answer • = -1 answer.
www.afterschoool.tk
What is log
10
.001
?
• We know that 10^3 = 1000 and 10^-3 is 1/1000 = .001 • = -3 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
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 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 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
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
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
www.afterschoool.tk
FIND THE SUM OF FIRST 20 TERMS OF THE SERIES – 5,11,17,23 .. ? • • • • • • •
This is Arithmetic Progression. A = 5, D = 6 N = 20 Formulae for sum = N/2 (2a + (n-1)*d) 20/2 (2*5 + (20 – 1)*6) =10 (10 + 19*6) =10(124) 1240 ans. www.afterschoool.tk
What is the 1st term of the Geometric Series, whose 4th and 9th terms are 1/3 & 81 respectively? • In a geometric series, the series is like this: a, ar, ar^(n-1) .. So on. • 4th item in the series is 1/3 • Thus (1) ar^3 = 1/3 and (2)ar ^8 = 81 • Divide (2) by (1) and we get r^5 = 81/1/3; or R^5 = 81*3 thus r = 3 • We know that r^3 = 27. ;; ar^3 = 1/3 • A = 1/3*1/27 thus A = 1/81 ans. www.afterschoool.tk
In an AP, we a sum of X terms. The sum is 190. the 2nd term is 5 and 4th term is 13. What is X? • In Arithmetic Progression, we have fixed difference = D. the series is like a, a+d, a+2d, a+3d ….. So on. • We have a+d = 5; a+3d =13 (solving these 2 equations, we get = 2d = 8) • D = 4, A = 1. • N/2 (2*1 + (n-1)4) = 190 • 2N + 4n^2 -4n = 380 • 4n^2 -2n -380 =0 • 2n^2 –n -190 = 0 • 2n^2 -20n +19n -190 =0 • 2n(n-10) +19(n-10) = 0; n = 10 or -19/2 • Thus N = 10 thus X = 10 ans.
www.afterschoool.tk
8X+3, 6X-3, and 2X+6 are in Arithmetic progression. What can be the value of X?
• In Arithmetic progression, the difference is always same. • Thus (6x-3) – (8X+3) = (2x+6) – (6X3) • -2X -6 = -4X +9 • 2X = 15; X = 7.5 ans.
www.afterschoool.tk
Nthb term of an AP is 2n-8. What is the sum of 20 terms of this series? • In every AP, We require A, D, and N to find the values. • 1st term is 2*1 – 8 = -6 • 2nd term of the series is 4-8 = -4 • 3rd term of the series = 6-8 = -2 and so on. • Sum of 20 term is : • 20/2 (2*-6 + (20-1) 2) • =10 (-12 +19*2) • =10 * 26 • =260 answer
www.afterschoool.tk
What is log
4
4
?
• 1 answer
www.afterschoool.tk
What is log
8
128
?
8 ^x = 128 (2^3)^X = 2^7 (taking 2 as common) 3X = 7 X = 7/3 128 Thus What is log = 7/3 answer . • 8 • • • •
www.afterschoool.tk
What is log
3*2^1/2
5832
?
• Let us take factors of 5832 • =2*2*2*3*3*3*3*3*3 • Thus we can see that there are six 3 and six 2^1/2 thus answer is 6.
www.afterschoool.tk
What is log
-1/3
81
?
• We know that -1/3 ^4 = 1/81. • The power in negative reverses the number, thus we can change power into -4 and we get reverse of 1/81 = 81. • Thus -4 is answer.
www.afterschoool.tk
What is log
10
.1
?
• We know that 10 ^-2 gives us 1/100, which is .01, so we have to take -1 as the answer • = -1 answer.
www.afterschoool.tk
What is log
10
.001
?
• We know that 10^3 = 1000 and 10^-3 is 1/1000 = .001 • = -3 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
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 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 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
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
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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