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 Know how to derive terms in the expansions of (1 + x)n and (a + b)n where n is a positive integer. n n! The coefficients may be expressed in the form nCr r r !(n r )! n n 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 The Circle x a y b 2 © MEI 2 r 2 has centre (a, b) and radius r. Additional Mathematics Formula sheet. Draft 1 Page 1 Trigonometry In a right-angled triangle: opposite adjacent opposite , cos , tan hypotenuse hypotenuse adjacent Identities: sin sin cos 2 sin cos 2 1 tan = Sin rule: a b c SinA SinB SinC Cos rule: a 2 b 2 c 2 2bc cos A cos A b2 c2 a 2 2bc 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 Formula sheet. Draft 1 Page 2

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# Additional Mathematics