page 04 MARKS Total marks — 35 Attempt ALL questions 1. Given tan y x x 7 2 , find dy dx. 2. Express    x x x x     2 2 3 14 3 1 in partial fractions. 3. A system of equations is defined by x y z x y z x y z           3 1 3 2 4 11 4 2 15 Use Gaussian elimination to determine whether the system shows redundancy, inconsistency or has a unique solution. 4. Use integration by parts to find ln x x dx  4 , x 0. 5. Find the particular solution of the differential equation 2 2 2 4 5 10 11 23 d y dy y x x dx dx      given that 2, 14 when 0 dy y x dx   . 6. (a) Express 1 3 z i  in polar form. (b) Hence, or otherwise, show that z3 is real. 2 3 3 3 9 2 2