Page 04 MARKS Total marks – 100 Attempt ALL questions 1. Write down the binomial expansion of 3 2 2 5y y ⎛ ⎞ − ⎜ ⎟ ⎝ ⎠ and simplify your answer. 2. Express ( )( ) 2 2 6 20 1 2 x x x x − + + − in partial fractions. 3. On a suitable domain, a function is defined by ( ) 2 1 2 1 xe f x x − = − . Find ( ) f x ′ , simplifying your answer. 4. The fifth term of an arithmetic sequence is -6 and the twelfth term is -34. (a) Determine the values of the first term and the common difference. (b) Obtain algebraically the value of n for which 144 n S = − . 5. (a) (i) Use Gaussian elimination on the system of equations below to give an expression for z in terms of λ. 2 3 4 2 3 11 3 2 8 x y z x y z x y λz + − = − − + = + + = (ii) For what value of λ is this system of equations inconsistent? (b) Determine the solution of this system when λ = −2·5. 6. Use the substitution 2 5 u x = to find the exact value of 1 10 4 1 25 0 x dx x − ⌠ ⎮⌡ . 4 4 3 2 3 4 1 1 6