00 - Formula Sheet

St Joseph’s Institution Secondary Four Mathematics TOPIC − A Mathematics Formulae Sheet

1. ALGEBRA Quadratic Equation For the equation ax 2 + bx + c = 0 , x=

− b ± b 2 − 4ac 2a

Binomial expansion n n n (a + b) n = a n +  a n −1b +  a n − 2 b 2 +  +  a n − r b r +  + b n , 1  2 r n n! n(n − 1) ( n − r + 1) = where n is a positive integer and   = r!  r  r!(n − r )!

2. TRIGONOMETRY Identities sin 2 A + cos 2 A = 1 sec 2 A = 1 + tan 2 A cosec2A = 1+ cot 2 A sin( A ± B ) = sin A cos B ± cos A sin B cos( A ± B) = cos A cos B sin A sin B tan A ± tan B tan( A ± B ) = 1 tan A tan B sin 2 A = 2 sin A cos A 2 cos 2 A = cos A − sin 2 B = 2 cos 2 A − 1 = 1 − 2 sin 2 A 2 tan A tan 2 A = 1 − tan 2 A 1 1 sin A + sin B = 2 sin ( A + B ) cos ( A − B ) 2 2 1 1 sin A − sin B = 2 cos ( A + B ) sin ( A − B ) 2 2 1 1 cos A + cos B = 2 cos ( A + B ) cos ( A − B) 2 2 1 1 cos A − cos B = −2 sin ( A + B) sin ( A − B ) 2 2 Formulae for ∆ABC a b c = = sin A sin B sin C a 2 = b 2 + c 2 − 2bc cos A 1 ∆ = bc sin A 2 © Jason Ingham 2009

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