1_mathematics_reading_book.pdf - MATHEMATICS BOOK FOR 10 2 ENTRANCES BOOKS FOR B.SC MATHEMATICS\/STATISTICS ENTRANCE EXAMS 1 Challenge Thrill of

1_mathematics_reading_book.pdf - MATHEMATICS BOOK FOR 10 2...

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MATHEMATICS BOOK FOR 10+2 ENTRANCES BOOKS FOR B.SC MATHEMATICS/STATISTICS ENTRANCE EXAMS: 1. Challenge & Thrill of Pre-College Mathematics 2. Mathematics Olympiad by Rajeev Manocha 3. An excursion in Mathematics by Modak 4. Mathematical Circles by Fomin 5. Play with Graphs by Arihant 6. Maths Wit Volume 1 & 2 by S.Chatterjee 7. Plane Trigonometry by SL Loney 8. Coordinate Geometry by SL Loney 9. Essential Calculus early transcendentals by James Stewart 10. Test of Mathematics at 10+2 level by East-West Press
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ALGEBRA 2 Arithmetic series General ( k th) term, u k = a + ( k – 1) d last ( n th) term, l = u n = a + ( n – l) d Sum to n terms, S n = n ( a + l ) = n [2 a + ( n – 1) d ] Geometric series General ( k th) term, u k = a r k –1 Sum to n terms, S n = = Sum to infinity S = , – 1 < r < 1 Binomial expansions When n is a positive integer ( a + b ) n = a n + ( ) a n –1 b + ( ) a n –2 b 2 + ... + ( ) a n–r b r + ... b n , n H11934 where ( ) = n C r = ( ) + ( ) = ( ) General case (1 + x ) n = 1 + nx + x 2 + ... + x r + ... , | x | < 1, n H11938 Logarithms and exponentials e x ln a = a x log a x = Numerical solution of equations Newton-Raphson iterative formula for solving f( x ) = 0, x n +1 = x n Complex Numbers { r (cos θ + j sin θ )} n = r n (cos n θ + j sin n θ ) e j θ = cos θ + j sin θ The roots of z n = 1 are given by z = exp( j) for k = 0, 1, 2, ..., n –1 Finite series n r =1 r 2 = n ( n + 1)(2 n + 1) n r =1 r 3 = n 2 ( n + 1) 2 1 4 1 6 2 π k –––– n f( x n ) –––– f'( x n ) log b x ––––– log b a n ( n – 1) ... ( n r + 1) ––––––––––––––––– 1.2 ... r n ( n – 1) ––––––– 2! n + 1 r + 1 n r + 1 n r n ! –––––––– r !( n r )! n r n r n 2 n 1 a ––––– 1 – r a ( r n – 1) –––––––– r – 1 a (1 – r n ) –––––––– 1 – r 1 2 1 2 Infinite series f( x ) = f(0) + x f'(0) + f"(0) + ... + f ( r ) (0) + ... f( x ) = f( a ) + ( x a )f'( a ) + f"( a ) + ... + + ... f( a + x ) = f( a ) + x f'( a ) + f"( a ) + ... + f ( r ) ( a ) + ... e x = exp( x ) = 1 + x + + ... + + ... , all x ln(1 + x ) = x + – ... + (–1) r +1 + ... , – 1 < x H11088 1 sin x = x + – ... + (–1) r + ... , all x cos x = 1 – + – ... + (–1) r + ... , all x arctan x = x + – ... + (–1) r + ... , – 1 H11088 x H11088 1 sinh x = x + + + ... + + ... , all x cosh x = 1 + + + ... + + ... , all x artanh x = x + + + ... + + ... , – 1 < x < 1 Hyperbolic functions cosh 2 x – sinh 2 x = 1, sinh2 x = 2sinh x cosh x , cosh2 x = cosh 2 x + sinh 2 x arsinh x = ln( x + ), arcosh x = ln( x + ), x H11091 1 artanh x = ln ( ) , | x | < 1 Matrices Anticlockwise rotation through angle θ , centre O: ( ) Reflection in the line y = x tan θ : ( ) cos 2 θ sin 2 θ sin 2 θ –cos 2 θ cos θ –sin θ sin θ cos θ 1 + x ––––– 1 – x 1 2 x 2 1 x 2 1 + x 2 r +1 –––––––– (2 r + 1) x 5 –– 5 x 3 –– 3 x 2 r –––– (2 r )! x 4 –– 4! x 2 –– 2! x 2 r +1 –––––––– (2 r + 1)! x 5 –– 5! x 3 –– 3! x 2 r +1 –––––– 2 r + 1 x 5 –– 5 x 3 –– 3 x 2 r –––– (2 r )! x 4 –– 4! x 2 –– 2! x 2 r +1 –––––––– (2 r + 1)! x 5 –– 5! x 3 –– 3! x r –– r x 3 –– 3 x 2 –– 2 x r –– r !
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