The document provides information about an afterschool mathematics program called "Mathematics Afterscho☺ol" run by the Centre for Social Entrepreneurship. It includes examples of mathematics word problems and their solutions. It also discusses plans to open branches in other cities, writing case studies on social entrepreneurs, and basic values of sharing, interacting, embracing change and self-improvement promoted by the program.

1. MATHEMATICS AFTERSCHO☺OL – DEVELOPING CHANGE MAKERS CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME – World’ Most Comprehensive programme in social entrepreneurship & spiritual entrepreneurship OPEN FOR ALL FREE FOR ALL

2. MATHEMATICS Dr. T.K. Jain. AFTERSCHO☺OL Centre for social entrepreneurship Bikaner M: 9414430763 [email_address] www.afterschool.tk www.afterschoool.tk

3. What will come next in the series? : 107,111,115,119 . . .? There is a fix gap of 4 between any two numbers, thus next number will be 123. This is called AP or Arithematic Progression.

4. What is the sum of infinite series starting with 512 and next terms are 256 and 128 . . ? We can calculate sum of Infinite GP by the following formulae: Formulae : A / (1-r) A = first term, R = Ratio of second term to first term. R = 256/512 = 1/2 =512/(1 – ½) =512/.5 = 1024 answer.

5. What will come in the series as next 5 items? : 512,256,128,64. . . . This is GP or Geometric Progression. Second term is half the first term. Thus in order to get next term, we have to multiply 64 by ½, and we will get the answer. Next 5 terms will be as under:: 32,16,8,4,2 answer.

6. What will be sum of first 10 terms of the series : 12,21,30,39 . . ? We can see that the series is AP. (arithematic progression). There is a gap of 9 between any two terms. Thus the formula for sum is as under: Sn = n/2 (2a+(n-1)d) A = first term = 12; d = gap or difference =9 and Sn= sum of the n numbers. N=10 =10/2(2*12 + (10-1)9) =5* (24+81) or 525 answer .

7. What is the sum of the first 10 terms of the series : 2, 8,32, . . ? Here we can see that this is GP (geometric progression). Here each term is four times the previous term. R = 8/2 = 4; A =first term =2, N=10 Formulae = A (R^n-1) / (r-1) =2(4^10 -1)/(4-1) =2*(1048576-1) /3 =699050 answer.

8. AM of two numbers is 25 and HM of these two numbers is 24, what is GM of these two numbers? AM= arithematic mean (simple average) GM = geometric mean HM = Harmonic mean Formulae = GM = Square root of (AM *HM). GM = Square root of (25*24) GM = square root of 600 = 24.49 ans.

9. Will 1042 come in the series: 12,16,20,24 . . . . NO as we can see that there is a gap of 4 in two terms. Test using following formulae: X = given number, A = first number, D = Difference or gap beween two terms. (X-A) must be completely divisible by D. (1042-12) gives us 1030, which is not divisible by 4 and therefore this number will not come in the series.

10. What will be the sum of first 10 terms of the series : 99,33,11,11/3 . . . ? This is GP (because the ratio between two terms is same. ). A = 99, R = 1/3 (solve it as 33/99). Formulae for sum = A (1-r^n)/(1-r) =99(1- 1/3^10)/(1-1/3) =148.47 answer.

11. 3 terms are in AP. Their sum is 48 and their product of first and last numbers is 240. what are the numbers Let us assume that the three numbers are as : (A-d),A, (A+d). A= first term, D = difference. Let us add these terms: (A-D) + A + (A+D) = 48; (D will get cancelled) 3A =48 or A = 16 (the middle term). (16-D) * (16+D) = 240. 256 – D^2 =240 or D^2 = 16 OR d = 4 Thus series is (16-4), 16, (16+4) or 12,16,20

12. What is the avarage speed of a car that takes average speed of 12 KM per hour while going and returns at the speed of 48 KM per hour? For any such question, always calculate harmonic mean or HM. The harmonic mean will be as under: ½(1/12 + 1/48) =1/2 (4+1 / 48) OR ½* 5/48 Or 5/96; reverse it : 96/5 = 19.2 answer.

13. Branches AFTERSCHO☺OL 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.

14. 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.

15. 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

16. www.afterschoool.tk social entrepreneurship for better society