1 July Mathematics Basics
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Mathematics Basics Dr. T.K. Jain. AFTERSCHOOOL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschoool.tk www.afterschool.tk
What is the result of 2 -3 *5/ 2 of 2(1/5)? • • • • • •
Use BODMAS. 2 – 3 * 5 / 2 OF .4 2 – 3 * 5 / .8 2-3 *6.25 2-18.75 =-16.75 ANSWER.
www.afterschoool.tk
WHAT IS AREA OF A TRIANGLE? • • • • • • • •
THERE ARE 3 FORMULAES: RIGHT ANGLE : ½ BASE * HEIGHT EQUILATERAL TRIANGLE: 1.732/ 4 *SIDE ^2 OR .433 * SIDE ^2 HERO’S FORMULAE: SQUARE ROOT OF (S(S-A)(S-B)(S-C)) WHERE A, B, C, ARE THREE SIDES OF A TRINAGLE. • S = (A+B+C)/2 www.afterschoool.tk
What is the area of a square? • • • • •
All sides are equal. There are angles of 90 degree each. Area: side * side Diagonal = side *1.4142 Area = ½ * diagonal * diagonal.
www.afterschoool.tk
Area of rhombus? • All sides are equal. • Angles are not of 90 degrees. • Area = ½ * diagonal * diagonal.
www.afterschoool.tk
Area of parallelogram? • Parallel sides are equal. Angle is not 90 degree. • Area = height • Height * base
www.afterschoool.tk
Area of trapezium? • Area: • ½ (sum of parallel sides) • * (distance between them)
www.afterschoool.tk
Height
Circle: • • • • •
Circumference (perimeter or boundary) = 2pi *radius Pi = 22/7 = 3.142857 Area : Pi * radius *radius
www.afterschoool.tk
Rectangle • Angles are of 90 degree each • Parallel sides are equal Area = length * width Diagonal ^2 = length^2 + width^2
www.afterschoool.tk
Cuboid? • • • • • • •
There are 3 dimensions: length, height, width 6 face 8 vertices 12 edges Volume = length * width * height Diagonal = square root of (l^2 + w^2 + h^2) Surface area = 2 (lb + lh+ bh)
www.afterschoool.tk
Cube? • Similar to cuboid. • Length, Width & Height (all three) are equal. • Diagonal = side *1.732 • Surface area: 6 * side *side
www.afterschoool.tk
Cylinder? • Volume: pi * radius * radius * height • Curved surface area: 2* pi * radius * height • Total surface area = • Curved suface area + (2 pi *radius *radius)
www.afterschoool.tk
Cone: • Volume : 1/3 * pi * radius * radius * height • Curved Surface area : pi * radius * slant height • Slant height = square root of ( height ^2 + radius ^2) • Total surface area: • Curved surface area +( pi*radius * radius) www.afterschoool.tk
sphere: • Volume: 4/3 * pi * radius * radius * radius • Surface area = 4 * pi * radius * radius
www.afterschoool.tk
Hemisphere • Volume = 2/3 * pi * radius * radius * radius • Curved surface area : 2 pi* radius * radius • Total surface area; • Curved surface area + pi*radius * radius • Or • 3 pi * radius * radius. www.afterschoool.tk
Acute angle? • If an angle is less than 90 degree, it is called acute angle.
www.afterschoool.tk
Obtuse angle? • If an angle is more than 90 degrees, it is called obtuse angle.
www.afterschoool.tk
Reflex angle? • If angle is more than 180 degree, it is reflex angle.
www.afterschoool.tk
Right angle? • 90 degree
www.afterschoool.tk
Straight angle? • 180 deg.
www.afterschoool.tk
Complement angles? • When we add 2 angles and we get 90 degrees, these two angles are called complement angles.
www.afterschoool.tk
Supplement angles? • When we add 2 angles and we get 180 degrees, it is called supplement angles. • Or • Linear pair
www.afterschoool.tk
Orthocentre? • Points of intersection of altitudes (in a triangle) is called orthocentres • Altitude = height
www.afterschoool.tk
Circumcentre • Point of intersection of perpendicular bisectors of sides ( in a triangle) is called circumcentre. • Perpendicular = forming 90 degree.
www.afterschoool.tk
Incentre? • Point of intersection angular bisectors ( in a triangle) is called incentre
www.afterschoool.tk
Centroid • Point of intersection of medians ( in a triangle) is called centroid
www.afterschoool.tk
Exterior angle? • Sum of interior angle + exterior angle = 180 degree. • Exterior angle = 180 – interior angle. • Exterior angle = 360 / no. of sides. • Sum of all exterior angles = 360 degrees. (apply to all polygons).
www.afterschoool.tk
Interior angles? • Sum of all interior angles: • ( 2n – 4) * 90 degrees. • N = number of sides.
www.afterschoool.tk
Number of diagonals? • [N ( N -1) / 2] - n
www.afterschoool.tk
Regular polygon? • Where all sides are equal and all angles are equal.
www.afterschoool.tk
Convex v/s concave polygon? • A polygon, whose one angle is more than 180 degree is concave polygon. • A polygon, whose no angle is more than 180 degree is convex polygon.
www.afterschoool.tk
Slope ? • (y2 – y1) / (x2-x1)
www.afterschoool.tk
Distance of two points? • Distance = • Square root of ( (x2-x1)^2 + (y2-y1)^2)
www.afterschoool.tk
Prism • Area : • Area of base * height
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
What is the result of 2 -3 *5/ 2 of 2(1/5)? • • • • • •
Use BODMAS. 2 – 3 * 5 / 2 OF .4 2 – 3 * 5 / .8 2-3 *6.25 2-18.75 =-16.75 ANSWER.
www.afterschoool.tk
WHAT IS AREA OF A TRIANGLE? • • • • • • • •
THERE ARE 3 FORMULAES: RIGHT ANGLE : ½ BASE * HEIGHT EQUILATERAL TRIANGLE: 1.732/ 4 *SIDE ^2 OR .433 * SIDE ^2 HERO’S FORMULAE: SQUARE ROOT OF (S(S-A)(S-B)(S-C)) WHERE A, B, C, ARE THREE SIDES OF A TRINAGLE. • S = (A+B+C)/2 www.afterschoool.tk
What is the area of a square? • • • • •
All sides are equal. There are angles of 90 degree each. Area: side * side Diagonal = side *1.4142 Area = ½ * diagonal * diagonal.
www.afterschoool.tk
Area of rhombus? • All sides are equal. • Angles are not of 90 degrees. • Area = ½ * diagonal * diagonal.
www.afterschoool.tk
Area of parallelogram? • Parallel sides are equal. Angle is not 90 degree. • Area = height • Height * base
www.afterschoool.tk
Area of trapezium? • Area: • ½ (sum of parallel sides) • * (distance between them)
www.afterschoool.tk
Height
Circle: • • • • •
Circumference (perimeter or boundary) = 2pi *radius Pi = 22/7 = 3.142857 Area : Pi * radius *radius
www.afterschoool.tk
Rectangle • Angles are of 90 degree each • Parallel sides are equal Area = length * width Diagonal ^2 = length^2 + width^2
www.afterschoool.tk
Cuboid? • • • • • • •
There are 3 dimensions: length, height, width 6 face 8 vertices 12 edges Volume = length * width * height Diagonal = square root of (l^2 + w^2 + h^2) Surface area = 2 (lb + lh+ bh)
www.afterschoool.tk
Cube? • Similar to cuboid. • Length, Width & Height (all three) are equal. • Diagonal = side *1.732 • Surface area: 6 * side *side
www.afterschoool.tk
Cylinder? • Volume: pi * radius * radius * height • Curved surface area: 2* pi * radius * height • Total surface area = • Curved suface area + (2 pi *radius *radius)
www.afterschoool.tk
Cone: • Volume : 1/3 * pi * radius * radius * height • Curved Surface area : pi * radius * slant height • Slant height = square root of ( height ^2 + radius ^2) • Total surface area: • Curved surface area +( pi*radius * radius) www.afterschoool.tk
sphere: • Volume: 4/3 * pi * radius * radius * radius • Surface area = 4 * pi * radius * radius
www.afterschoool.tk
Hemisphere • Volume = 2/3 * pi * radius * radius * radius • Curved surface area : 2 pi* radius * radius • Total surface area; • Curved surface area + pi*radius * radius • Or • 3 pi * radius * radius. www.afterschoool.tk
Acute angle? • If an angle is less than 90 degree, it is called acute angle.
www.afterschoool.tk
Obtuse angle? • If an angle is more than 90 degrees, it is called obtuse angle.
www.afterschoool.tk
Reflex angle? • If angle is more than 180 degree, it is reflex angle.
www.afterschoool.tk
Right angle? • 90 degree
www.afterschoool.tk
Straight angle? • 180 deg.
www.afterschoool.tk
Complement angles? • When we add 2 angles and we get 90 degrees, these two angles are called complement angles.
www.afterschoool.tk
Supplement angles? • When we add 2 angles and we get 180 degrees, it is called supplement angles. • Or • Linear pair
www.afterschoool.tk
Orthocentre? • Points of intersection of altitudes (in a triangle) is called orthocentres • Altitude = height
www.afterschoool.tk
Circumcentre • Point of intersection of perpendicular bisectors of sides ( in a triangle) is called circumcentre. • Perpendicular = forming 90 degree.
www.afterschoool.tk
Incentre? • Point of intersection angular bisectors ( in a triangle) is called incentre
www.afterschoool.tk
Centroid • Point of intersection of medians ( in a triangle) is called centroid
www.afterschoool.tk
Exterior angle? • Sum of interior angle + exterior angle = 180 degree. • Exterior angle = 180 – interior angle. • Exterior angle = 360 / no. of sides. • Sum of all exterior angles = 360 degrees. (apply to all polygons).
www.afterschoool.tk
Interior angles? • Sum of all interior angles: • ( 2n – 4) * 90 degrees. • N = number of sides.
www.afterschoool.tk
Number of diagonals? • [N ( N -1) / 2] - n
www.afterschoool.tk
Regular polygon? • Where all sides are equal and all angles are equal.
www.afterschoool.tk
Convex v/s concave polygon? • A polygon, whose one angle is more than 180 degree is concave polygon. • A polygon, whose no angle is more than 180 degree is convex polygon.
www.afterschoool.tk
Slope ? • (y2 – y1) / (x2-x1)
www.afterschoool.tk
Distance of two points? • Distance = • Square root of ( (x2-x1)^2 + (y2-y1)^2)
www.afterschoool.tk
Prism • Area : • Area of base * height
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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