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Additional Mathematics Formula that are within the syllabus and which need to be learnt. The remainder theorem Given the polynomial f(x), then remainder when f(x) is divided by (x – a) is f(a). The factor theorem If the remainder when f(x) is divided by (x – a) is 0, then (x – a) is a factor of f(x) and x = a is a root of the equation f(x) = 0 Solution of quadratic equations By formula and completing the square For the quadratic equation ax 2 bx c 0 x b b 2 4ac 2a Binomial expansion This is on the formula sheet available in the examination in the form shown in the box: When n is a positive integer n n -1 n n -2 n n-r (a b )n an a b a b 2 ... a b r ... b n 1 2 r where n! n n r Cr r!(n r )! n n Also be aware that nCr nCn r r nr Coordinate Geometry Straight line Know the forms of the straight line, including y mx c y y1 m( x x1 ) y y1 x x1 y2 y1 x2 x1 Condition for parallel lines: m1 m2 Condition for perpendicular lines: m1 m2 1 Distance between two points ( x1 , y1 ), ( x2 , y2 ) x1 x2 y1 y2 2 2 x x y y Midpoint of two points ( x1 , y1 ), ( x2 , y2 ) 1 2 , 1 2 2 2 © MEI Additional Mathematics Formulae Updated Feb 2009 Page 1 The Circle x a y b 2 2 r 2 has centre (a, b) and radius r. Trigonometry In a right-angled triangle: opposite adjacent opposite , cos , tan hypotenuse hypotenuse adjacent Identities: sin tan = cos 2 sin cos 2 1 sin Sin rule: a b c SinA SinB SinC Cos rule: b2 c2 a 2 2bc 2 Note that a b 2 c 2 2bc cos A is on the formula sheet available in the examination. cos A Calculus y ax n dy nax n 1 dx Stationary points occur when dy 0 dx b Area under curve between x a and x b is y dx a Kinematics Constant acceleration formulae 1 s ut at 2 2 u v t s 2 v u at v 2 u 2 2as © MEI Additional Mathematics Formulae Updated Feb 2009 Page 2