page 07 MARKS 13. Points scored in the long jump element of the decathlon can be calculated using a solution of the differential equation ( ) 220 1.4 dP m P dm   , m > 220 where m is the distance jumped in centimetres and P the points scored. Given that a jump of 807 centimetres scores 1079 points, find an expression for P in terms of m. 14. A complex number is defined by w = a + ib, where a and b are positive real numbers. Given w2 = 8 + 6i, determine the values of a and b. 15. A function ( ) f x has the following properties: • ( ) ( )4 1 1 1 x f x x     • the first term in the Maclaurin expansion of ( ) f x is 1. (a) Find the Maclaurin expansion of ( ) f x up to and including the term in x2. (b) Use the substitution ( )2 1 u x   to find ( )4 1 1 1 x dx x     . (c) Determine an expression for ( ) f x . [END OF QUESTION PAPER] 6 4 3 3 2 page 08 [BLANK PAGE] DO NOT WRITE ON THIS PAGE